Nonrandom extinction and the evolution and conservation of continental mammal faunas


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Nonrandom extinction and the evolution and conservation of continental mammal faunas
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vi, 253 leaves : ill. ; 29 cm.
Cristoffer, Cris, 1956-
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Thesis (Ph. D.)--University of Florida, 1990.
Includes bibliographical references (leaves 232-252).
Statement of Responsibility:
by Cris Cristoffer.
General Note:
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University of Florida
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This project could not have been carried out without

the help of several people. Foremost, I thank John

Eisenberg for his patience and financial assistance. I

would also like to thank John Kaufmann, who found many

mistakes everyone else missed; John Robinson, who managed

to provide constructive criticism even when very busy;

Larry Harris, for his enthusiasm and because he encouraged

further research in productive areas; and Steve Humphrey,

whose firm grasp of the practical kept me from going too

far astray. Sydney Anderson provided most of the

information on geographic range sizes used in my analyses.

Last but not least, I thank Mildred Cristoffer, who

supported me without qualification.




ABSTRACT ........................ .... ............. ........ v


INTRODUCTION BY EXAMPLE ................... 1

Introduction...................... .... ....1
Materials and Methods...........................15
Results............ ..... .. ......................24

PROBABILITIES OF MAMMALS .....................41

Introduction.......................... ........41
Materials and Methods..............................48
Results .......... ........................... ... 61
Discussion................................... ....65

EXTINCTION ................................... 66

The Basic Model.................. ................71
Shotgun Blasts and Logistic Growth--
a Unification........... .................85


Introduction.......... .........................86
Materials and Methods................. ..........93
Results..................... ......... ...97


,Materials and Methods.........................123
Results......... .... ..........................134



Introduction .. .......... ................. ....157

Some Examples and an Assessment of the
Predictions ..........................................158
Conclusion ........ ... .........................182

VII CONCLUSION AND SYNTHESIS........................184



FOOD ABUNDANCE ......................... ...... 201

PERIOD, EURYTOPY AND DENSITY....................210



PERIOD AND HOME RANGE SIZE.....................228

MAMMALS................ ................... ........230

LITERATURE CITED .........................................232

BIOGRAPHICAL SKETCH...................................253

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy




May 1990

Chairman: Dr. John F. Eisenberg
Major Department: Wildlife and Range Sciences
(Forest Resources and Conservation)

I investigated extinction processes and their

applications to the the study and conservation of mammals. I

found evidence that nonrandom extinction explains part of

the pattern of associations among the variables; population

density, geographic range size and body size, for North

American mammals.

I then posited that if extinction can explain

associations among variables, then we ought to be able to

use associations among variables to make predictions about

extinction. Using data for North American (north of Mexico)

and Australian mammals, I developed a method to predict

which species not currently threatened with extinction are

most likely to become so in the near future.

I then sought ways to predict extinction over much

longer spans of time, by combining several of the features

of existing theories of extinction into a shotgun/logistic

model of adaptive radiation and nonrandom extinction. In

this model, adaptive radiation is a wasteful process that

produces many species, most of short duration. However, the

few species resulting from the subsequent species selection

are generally, more K-selected, poorer colonists and more

specialized in a number of respects; but they are less prone

to extinction except during periods of environmental

disturbance. I then assessed the validity of assumptions of

the shotgun model and tested predictions derived from it.

My general conclusion was that knowledge of patterns

of extinction were useful for 1) the study of relationships

among several variables; 2) prediction of species

endangerment; and 3) the study of evolutionary trends.

Extinction might thus be considered as a common currency for

the disciplines of conservation, ecology and evolution.

Paradigms developed by workers in each of these fields can

sometimes be modified to apply to the others as well,

resulting in a useful framework of study.



The concept of species selection has a venerable

history (Grant 1989). Although various authors have coined

their own terms (e.g., differential extinction and natural

selection at the level of species) to encompass only certain

aspects of the process, all probably agree on the basic

process involved. Nevertheless, in some ways, species

selection is a more difficult process to study than is

natural selection. Investigators of natural selection can

frequently identify the agents responsible for differential

reproductive success among individuals, but investigators of

species selection can rarely do so. In this dissertation I

posit new ways to uncover species selection that derive from

knowledge of extinction. This investigation will take the

form of a series of predictions, the explications of which

are found in the text of the dissertation. Although these

predictions will probably make little sense to the reader at

present, he or she may find it easier to keep track of them

by referring to Table 1-1. A prediction can be located in

Table 1-1. Predictions explicated in Chapters I, IV, V and

1.1 The RS / density correlation for size-restricted
mammals should be more positive than the correlation
for mammals of all sizes.

1.2 The correlation between RS and density for Australian
mammals will be intermediate in strength or direction
between those for North American birds and North
American mammals.

1.3 When body size is controlled, any association between
RS and density will no longer be significant.

1.4 When both direct and indirect influences of size are
controlled, the association will no longer be

1.5 Body size will be the most important independent
variable in a regression with density as dependent
variable, whereas density will be the most important
variable in a regression with RS as dependent
variable. Stratigraphic range and RS will have large variances
among the species within a genus.

4.1b Litter size and HBL will have smaller intrageneric
variances than stratigraphic range and RS.

4.1c Length of lactation will have a smaller intrageneric
variance than the above-mentioned variables.

4.2 Variation among monospecific genera is similar to that
among speciose genera when intrageneric variation is
controlled statistically.

4.3 Signs of association will tend to differ among
taxonomic levels, and the differences will be greater
with widely-disparate levels than among taxa that are
fewer levels apart.

5.1 Monospecific genera will have greater stratigraphic
ranges than species from speciose genera.

5.2 Monospecific genera have more unusual characteristics
than species from speciose genera.

Table 1-1--continued.

5.3 Variables for monospecific genera will differ from
species in speciose genera in the same direction that
K- strategist species differ from r- strategist

6.1 Species of mammals that are able to expand their
geographic ranges during a period of disturbance are
expected to be r- strategists relative to species
whose ranges remain stable or shrink during

6.2 Endemics should experience high extinction rates
during periods of great environmental change.

6.3 Colonist species should make few successful incursions
into old and climatically stable habitats.

6.4 With time, K- selection will transform colonists into
specialized endemics.

Predictions are explicated in the chapter denoted by their
number. For example, Prediction 6.1 is the first
prediction elaborated in Chapter six.


the text by referring to the chapter denoted by its number.

For example, Prediction 4.2 is the second prediction

described in Chapter IV.

In this first chapter I will investigate whether the

associations among certain variables are most readily

explained as being due to species selection. In the next

chapter I will shift emphasis from comparing variables to

comparing groups of species that differ in attributes, in

order to develop a specific application of extinction theory

to conservation. In subsequent chapters I will elaborate the

concept that the attributes of species can be used to

predict extinction, but I will extend the investigation into

the distant past.

As a first principle, I considered that since species

selection requires the extinction of species, it is almost

axiomatic that species selection will be most readily

detected when there have been many extinctions of species. A

corollary assumption is that no selective agent should be

invoked if the species becoming extinct were a random subset

of the biota. There is a large body of work supporting the

contention that there is a strong deterministic component to

the extinction process, and that the species most likely to

become extinct differ in attributes from those less likely

to perish. I therefore list only a few examples, including

Guilday (1984); Brown (1971, 1984); Brown and Maurer (1986);

Anstey (1978); Hansen (1980, 1982); Vrba (1980); Jablonski


and Lutz (1983); Ward and Signor (1983); Cassels (1984);

Guthrie (1984); Horton (1984); Kiltie (1984); McDonald

(1984); Murray (1984); Trotter and McCulloch (1984); Webb

(1984); Heaney (1986); Knoll (1986); Lawlor (1986); Morgan

and Woods (1986); Moulton and Pimm (1986); Patterson and

Atmar (1986); and Brown and Maurer (1987). Herein I consider

valid the assumption that the extinction of species with

certain attributes is implicated in species selection.

In the first chapter I posited that it is easier to

detect species selection among the associations of some

variables than among others. Using published information on

North American land mammals, I concentrated on three

variables. One of these was body size, manifested in this

study by head-and-body length (HBL). The other variables

investigated were density, expressed as number of

individuals per hectare; and geographic range size

(hereafter designated as RS), expressed in km2 X 102. I

chose these three variables because there were some hints

that species selection is especially appropriate in

explaining the pattern of associations among them. Several

other variables were also included in some analyses, but

they did not play an important part in this investigation.

Data from Australian mammals were also used to assess

associations among variables, although more detailed

investigations were considered impractical because of small

sample sizes.


I considered RS to be an especially interesting

variable for several reasons. RS varies far more among North

American mammals than many other variables, such as

gestation period (Appendix B). Furthermore, this variation

is nearly as great at lower taxonomic levels as at higher

levels. This is exemplified by such genera as Peromyscus,

Microtus, Reithrodontomys, and Spermophilus, and (in recent

history) by the genera Canis and Mustela. It seems likely

that diverse and interesting factors affect RS. Table 1-2

lists some of these variables. One of the most intriguing of

these is the second variable of special interest, body size.

Body size differs between taxonomic levels in sign of

association with RS. Furthermore, the range of body size

differs greatly between birds and mammals, two classes that

will be shown below to differ in another, perhaps related

aspect. That aspect involves the third variable of interest,

population density (hereafter simply referred to as

density). Although most studies have indicated a positive

association between density and RS (e.g., Bock and Ricklefs

1983; Brown 1984; Brown and Maurer 1987), theoretical

considerations led me to doubt the generality of this

assertion. Referring to Table 1-2, we can see that RS has

been suggested to correlate positively with both density and

body size. Since body size and density have the same sign of

association with a third variable, we might expect them to

correlate positively with each other.

Table 1-2. Sign of association of various variables with


Sign of
Ac c fi = 4-


Mean Litter Size
Maximum Litter Size

Area of Land Mass

Use of Marginal Habitats

Number of Sympatric
Body Size (w/in Genus)
Body Size (w/in Class)

Maximum Reproductive
Reproductive Effort
Age at First
Species Richness of
Genus or Family
Number of Subspecies/
Population Density

Colonizing Ability


Glazier (1980)
Glazier (1980)
Hesse et al. (1937);
Anderson (1977);
Rapoport (1982)
Hesse et al. (1937);
Flessa (1981);
Anderson & Koopman
(1981); Brown &
Maurer (1987)
Baker (1968)
Baker (1968);
Stanley (1979);
Glazier (1980)
Glazier (1980); Mace
& Eisenberg (1982)
Glazier (1980)
Glazier (1980)
VanValen (1972);
Anderson (1977);
Rapoport (1982)
Glazier (1980)

Glazier (1980)
Glazier (1980)

Rapoport (1982)

Rapoport (1982)

Bock & Ricklefs
(1983); Brown
Dwyer (1978);
Stanley (1979);
Glazier (1980)
Hesse et al. (1937);
Anderson (1977);
Glazier (1980)


Table 1-2--continued.


Sign of
"& a-f < s ji 1 hi^r

'r-selected' Traits


Diversity of Fauna
Dietary Breadth

Carlquist (1965);
MacArthur & Wilson
(1967); Diamond
(1974, 1975); Boucot
(1975); Glazier
Mace and Eisenberg

Rosenzweig (1975)
Hesse et al. (1937)

The qualitative designations "+" and "-" are used to
describe all associations because several of the cited
references did not quantify relationships among variables


W id


However, empirical studies on mammals have reported density

and body size to correlate negatively (e.g., Eisenberg

1981; Peters 1983; Robinson and Redford 1986). Thus RS is a

rather whimsical variable that defies understanding by

reference to bivariate associations alone.

One possible explanation for the anomalous signs of

association among density and RS is that the relation is

spurious, such that the association would disappear when a

third variable is controlled. I reasoned that body size was

the variable most likely to influence the correlation

between RS and density. My rationale for this comes largely

form Brown (1981) and Brown and Maurer (1987), although

they might not agree with my interpretation. My reasoning

is as follows.

Large species tend to reach lower densities than do

smaller species for reasons dictated by energetic

constraints. Since individuals of large species of

endotherms use absolutely more energy than do individuals

of small species of endotherms, a given unit of area

generally can support more individuals of small than of

large species of mammals. Density is simply the number of

individuals per unit area or volume; hence, when

individuals are large, there will be fewer individuals in

the same area and their density will be lower.

Furthermore, large species of the same RS as small

species should have smaller population sizes. Since


population size correlates inversely with probability of

extinction, large species with the same RS as small species

will have a greater probability of extinction than will

small species. Thus, in general, small species should be

able to survive with smaller RS than will large species.

Over long periods of evolutionary time, this should result

in a paucity of large species that have small RS; and

hence, an overall negative correlation between density and

RS. However, small species can survive in either small or

large RS; hence, the overall correlation between RS and

size, though positive, is rather weak.

If this body-size-dependent process is the only one

tending to produce a negative association between RS and

density, then controlling for body size should eliminate a

negative correlation. Furthermore, since the variation in

body mass of North American mammals is nearly two orders of

magnitude greater than that for birds, this process should

be more important for mammals than for birds. I

hypothesized that if the analysis for mammals were

restricted to a size range similar to that in a study of

the correlation between RS and density in birds, then the

correlation for the mammals would be more similar to that

for birds than would an overall analysis with mammals of

all sizes. Since the RS/density correlation for birds is

positive, then Prediction 1.1 was that the RS/density

correlation for size-restricted mammals should be more


positive than the correlation for mammals of all sizes. I

also suspected (Prediction 1.2) that since the range of

body sizes of Australian mammals is intermediate between

that of North American birds and North American mammals,

the associations between variables would be intermediate in

strength or direction.

To test Prediction 1.1 I undertook tests of

association for North American mammals as a whole and then

for mammals less than 160 mm head-and-body length (HBL).

Although this analysis will be discussed further below, for

the moment I will mention that it was consistent with my

hypothesis. The analysis was not, however, particularly

satisfying. One reason to doubt the generality of the

analysis on small mammals was that it used slightly fewer

species than an analysis using mammals of all sizes; hence,

the lack of significance could simply have been due to a

smaller sample size. Furthermore, if the test was

nonsignificant but nevertheless indicated a negative

association, the suspicion could always be entertained that

a larger or more accurate data set would yield a

significant result.

I therefore undertook more quantitative and objective

regression analyses that included all the North American

nonvolant species of mammals, but that statistically

controlled for HBL. One way to control for a variable that

can be interpreted visually is to separately regress the


two variables in question against the variable to be

controlled, then to plot the residuals of both regressions

against each other. This double residual plot can then be

inspected for trends. I was particularly interested in the

slope of these plotted residuals; a negative slope on a

plot of the residuals of the RS regression vs. the

residuals of the density regression would indicate that

density and RS are still negatively correlated even when

HBL is controlled. This subjective assessment can then be

followed by a regression that includes all three variables

simultaneously, to more objectively quantify the strength

and significance of relationships among variables when

others are controlled. Hence, Prediction 1.3 was that if

body size is controlled, the association between RS and

density would be nonsignificant.

However, body size is such a pervasive variable that

it could have indirect effects on density or RS by

affecting other variables that in turn influence density or

RS. Although one of the requirements for statistical

analyses is that the sample is random, living species are

themselves a nonrandom set of all species that have lived

or could possibly live. Since evolution is not the result

of natural selection on each character of an organism in

the absence of all other characters, it is inevitable that

characters will sometimes be so subtly linked as to elude

attempts at perfect statistical control. Complete


statistical control would require an assessment of all the

indirect effects of size that result from the association

of the variable in question with other variables that are

influenced by size. Thus there was always a possibility

that the effect of body size was still not completely

removed, despite my attempts to do so by statistically

controlling HBL. Hence, I included in the model three other

variables that were known to correlate significantly with

HBL, in the hope that controlling for their influence would

simultaneously eliminate most of the indirect influences of

body size. I reasoned that if the association was still

significantly negative after both the direct and indirect

influences of body size were removed from the model, then

some process other than size-dependent species selection

has been at work to produce a negative relation. Prediction

1.4 was thus that controlling for the combination of direct

and indirect influences of HBL would eliminate the

significant correlation between density and RS.

I was then ready to investigate the sequence of cause

and effect events. Heretofore in the regression analyses I

undertook, I had somewhat arbitrarily specified density as

the dependent variable. Although disentangling cause and

effect relationships among variables is difficult, the

primacy of body size as an ecological variable suggested

that it should be considered an independent variable in the

model. Of the variables RS and density, the latter seemed


to be the most directly influenced by the independent

variable, body size (HBL). By contrast, I posited RS to be

affected by body size only indirectly, through density. As

an example, consider species of small RS and at low

density, which have a relatively high probability of

extinction. If species of large body size have low density,

then they are likely to be extinction-prone in small RS.

Thus there could be an overall correlation between RS and

body size, simply because both of these variables are

correlated with the intermediate variable, density.

I reasoned that if this purported chain of causation

is correct, then the associations between variables should

be strongest among a pair of variables whose members are

directly linked, than among a pair whose members are only

linked via an intermediary variable. Regression of Y on X

is not in general the same as regression of X on Y (Sokal

and Rohlf 1973), especially when there is more than one

independent variable. Hence, when variables switch from

being considered dependent to independent (or vice versa),

there could be different results. Thus a regression with RS

as dependent variable and density and HBL as independent

variables, could yield different associations than one

specifying density as dependent variable and the other two

variables as independent variables. Prediction 1.5 was that

body size would be the most important independent variable

in a regression with density as dependent variable, whereas


density would be the most important variable explaining RS

in a regression with RS as dependent variable.

Materials and Methods

Initially I chose North American mammals for my

subjects because of my familiarity with the taxa and

because natural history information was available for many

species. I did not undertake analyses for North American

bats for several reasons, not the least of which was lack

of data for densities. Data for Australian mammals was used

in a more perfunctory manner.

Using data for North American mammals only, I created

models using log transformed data for the variables

gestation period (in days), home range size (in hectares),

and litter size, were also created to test the possibility

that they might eliminate the negative association between

RS and density.

The Variables

Head-and-body length (HBL) information was available

for all but one species. Gestation period (in days)

information was available for 130 species. Gestation

periods of species with delayed development were not

recorded or used in the analysis, not only because the

variance would increase greatly but also because the

occurrence of delayed development tends to follow

phylogenetic lines rather than the ecology or behavior of

the species. For example, mustelids of diverse habits have


delayed development, whereas the opossum Didelphis, like

all marsupials, has a short gestation period.

Density information was available for more than the 97

species shown in my data set. However, certain species with

extremely variable densities (e.g., the lemmings

Dicrostonvx and Lemmus) were excluded because their

calculated means are difficult to interpret biologically.

Since this study concentrated on the implications of

RS, only species were included for which RS information was

available. This was not an important limitation because RS

data were available for almost all North American species.

The baseline RS values for both North American and

Australian mammals were provided by Dr. Sydney Anderson of

the American Museum of Natural History in New York City.

However, Dr. Anderson's estimates are for RS within the

continent of North America, and I felt that the RS values

used in my analysis should refer to the total RS for the

species. Therefore I measured the extralimital RS of

species which also live in Eurasia or South America and

added them to the North American values. For species found

also in Eurasia I used maps from Corbet (1978) and Burton

(1979); for species found also in South America I used maps

made by Dr. Ralph Wetzel and provided for me by Dr. John

Eisenberg. To measure areas I drew the contours of these

maps by eye onto standardized photocopies of maps of

Eurasia and South America, then estimated the areas on my


maps with a compensating polar planimeter. Although the

margins for errors in these estimates of RS are high, the

ranks of RS are probably more nearly correct because of the

large variance of RS among species. All units are expressed

in units of km X 102.

Clearly the RS of a species could change because of

anthropogenic activities and thus automatically alter its

relation to other variables that remain more constant. In

practice, however, the range maps found in most texts

depict a primitive, unfragmented range, such as might be

attributed to natural forces of evolution. The range maps

from which my RS data were calculated depict these

unfragmented geographic ranges. Hence, they are suitable

for studies of evolution and species selection.

The Data Set

The primary data sets for mammals used in this and

subsequent chapters are presented in Appendices A-F.

Published sources of data for North American mammals

included, in addition to those mentioned previously,

Armstrong and Jones (1972); Baker and Schump (1978a,

1978b); Beckoff (1977); Bednarz (1977); Best (1986); Best

and Lackey (1985); Birkenholz (1972); Bleich (1977); Case

(1978); Carraway and Verts (1985); Carroll and Genoways

(1980); Chapman (1974, 1975a, 1975b); Chapman and

Feldhammer (1981); Chapman et al. (1982); Chapman and

Willner (1978; 1981); Clark et al. (1971, 1987); DeMaster


and Stirling (1981); Dolan and Carter (1977); Dowler and

Genoways (1978); Egoscue (1979); Ernest and Mares (1987);

Eshelman and Cameron (1987); Franzmann (1981); French

(1980); Fritzell and Haroldson (1982); Galbreath (1982);

Gardner (1982); Getz (1985); Godin (1977); Green and

Flinders (1980); Hallett (1978); Heaney (1984); Hillman and

Clark (1980); Hoffmann and Owen (1980); Hoffmeister (1986);

Howard and Marsh (1982); Ingles (1965); Jenkins and Busher

(1979); Jenkins and Eshelman (1984); Jones et al. (1983,

1985); Kaufmann (1982); Keller (1985); King (1983);

Kirkland (1981); Kirkland and Jannett (1982); Lent (1988);

Limm (1987); Linzey and Packard (1977); Long (1974); Ludwig

(1984); MacDonald and Jones (1987); Maser et al. (1981);

McCallister and Hoffmann (1988); McCarty (1975, 1978);

McGrew (1979); Meagher (1986); Mech (1974); Merritt (1981,

1987); Michener and Koeppl (1985); Murie and Michener

(1984); Nadeau (1985); Nash and Seaman (1977); O'Farrell

and Blaustein (1974a, 1974b); O'Gara (1978); Oaks et al.

(1987); Owen (1983, 1984); Paulson (1988); Peek (1982);

Pembleton and Williams (1978); Pizzimenti and Collier

(1975); Pizzimenti and Hoffmann (1973); Powell (1981);

Richart (1987); Rideout and Hoffmann (1985); Shackleton

(1985); Shellhammer (1982); Smolen and Keller (1987);

Snyder (1982); Streubel and Fitzgerald (1978a, 1978b);

Sullivan et al. (1986); Tamarin and Kunz (1974); Tim

(1985); Verts and Carraway (1987a, 1987b); Webster et al.


(1985); Whitaker (1972, 1974, 1980); Whitaker et al.

(1972); Williams (1982); Williams and Baker (1974); Wolf

(1982); Woods (1973); Young and Jones (1982); and Zegers

(1984). John Eisenberg also provided unpublished

information on heteromyids. The nomenclature is as in Hall

(1981), with some minor changes, shown below. These names

reflect changes suggested by taxonomists subsequent to the

publication of Hall (1981). For comparative purposes mice

of the genus Peromyscus were excluded from this analysis.

By excluding Peromyscus I assured that my data were

independent and comparable to Glazier (1980), who did a

somewhat similar analysis for that genus.

Name Used Herein Name in Hall (1981).

Sorex monticolus Sorex vagrans
Sorex pacificus Sorex vagrans
genus Tamias genus Eutamias
Marmota broweri Marmota caliqata

Variation in values was considerable for some species.

I used arithmetic means whenever possible; even when the

literature presented maximum and minimum values for a

variable, I used the midrange. When data for more than one

subspecies were provided I first calculated means for each

subspecies, then calculated the mean of those values. When

data for both sexes were provided, I found the means for

each sex and then the mean of those two values. There were

many missing values. These were simply ignored by the

computer analysis. Although specialists could probably have


provided information to fill in some of these blanks, the

time necessary to obtain the most complete data for every

species was prohibitive. Several variables in the

appendices had small sample sizes or were not useful for

other reasons. These will not be discussed further or will

be mentioned only briefly.

Most of the Australian data are from Strahan (1983),

with additional information from the following sources:

Aslin (1975a, 1975b); Aslin and Watts (1980); Barnett et

al. (1977); Begg et al. (1983); Braithwaite (1983);

Braithwaite et al. (1984); Breed (1979); Caughley (1986);

Christensen et al. (1984); Cockburn (1981); Fanning (1982);

Fleming and Frey (1984); Floyd (1980); Friend (1987); Gall

(1980); Jarman and Taylor (1983); Johnson (1987); Johnson

and Jarman (1987); Johnson (1980); Johnson (1979); Kaufmann

(1974); Kerle (1984); Merchant et al. (1984); Morton

(1978); Nelson and Goldstone (1986); Norton (1987); Poole

and Merchant (1987); Read (1987); Rose and McCartney

(1982a, 1982b); Russell (1986); Short et al. (1983); Smith

(1979); Southwell (1987); Suckling (1984); VanDyck (1979);

Wells (1978); Wilson (1986); Wilson et al. (1986); Woolley

(1984); Woolley and Valente (1986).

Statistical Procedures

Statistical procedures are described in Agresti and

Agresti (1979). Kendall's tau-b correlation, available in

the SAS statistical package (SAS Institute 1985) was the


measure of association used for exploratory tests of

associations. Nonparametric tests such as tau-b are far

superior to parametric tests for data that exhibit

nonnormal distibutions or heterogeneity of variance, such

as occurs in several of the variables in my data set. Tau-

b was especially appropriate for my investigation because

it does not require normally distributed variables and can

make use of either interval or ordinal variables. Although

very versatile, tau-b is sensitive to small sample sizes

(Agresti and Agresti 1979). Sample sizes for my analyses

were, however, adequate.

I did not undertake tests of association for North

American birds because this information is already

available in the published literature (Bock and Ricklefs

1983). To test my hypothesis about the RS/density anomaly

(Prediction 1.1), I ran the North American analysis again

but included only mammals in approximately the same size

range as the birds (HBL < 160 mm).

My second approach to correcting for body size was to

regress the log of each variable separately on the log of

HBL (log transformations were necessary because the raw

data for the variables were not linearly related). Then I

plotted the residuals of each regression against the other.

If size accounts for all the significant variation in

either variable, then a double residual plot should exhibit

a random scatter of points. Conversely, if the plotted


residuals tend to indicate either a positive or negative

slope, then RS and density will probably be found to be

significantly associated even when the effects of HBL are

removed. To test Prediction 1.2 I undertook a tau-b

correlation of the variables density and RS for Australian


To test Prediction 1.3 I included all three variables

in a single model. The first regression was of density on

RS and HBL. I undertook regressions with both log and rank

transformations, although the results of the two were very


To control for indirect effects of size on RS and

density (Prediction 1.4), I included in the model log

transformed data for the three variables home range size

(in hectares), gestation period (in days) and litter size.

Data were from Appendices A and B. Since these variables

also have significant correlations with HBL, their

inclusion in the model might be expected to reduce the

effects of HBL to nonsignificance. Ideally I would have

included all of these variables in a single model in the

hope that controlling for all of them together would all

but eliminate indirect effects of HBL on density and RS. In

reality, this required a larger data set with far fewer

missing values for observations than the set available to

me. Although the 258 observations in my data set were

sufficient for a regression model with three or four


variables, it is really too small for analyses that include

many variables. Furthermore, since the regression procedure

excludes observations with missing values, and since many

of my observations were missing one or more value, each

variable added to the model greatly reduced the sample

size. For example, a model with density as dependent

variable and HBL, RS and home range size as independent

variables, used a sample size of only 44. Therefore I

limited my models to a maximum of four variables.

Prediction 1.5 was tested using a forward selection,

stepwise procedure. This procedure begins with a model that

includes the independent variable that accounts for the

most variation in the model, providing that the association

was significant. Successively less important variables are

then added to the model until the added variable makes no

significant (P < 0.05) contribution. Stepwise regression

has frequently been misused to find subsets of a set of

independent variables that are individually important as

predictors of the independent variable. Stepwise regression

is, however, appropriate for use in analyses such as mine

to discern which variables make additional contributions to

the prediction of the dependent variable, given that one or

more independent variables are already in the model

(Chalmer 1987). In my study, one stepwise regression

specified density as the dependent variable; the second,




The tau-b correlation of density and RS for mammals as

a whole was significant and negative. By contrast, the

association for small mammals was weak and not

statistically significant. The correlation coefficient was

-0.148, and the P-value was 0.2114. The double residual

plot in Figure 1-1 does suggest a negative trend, although

there is considerable scatter. The correlation between RS

and density for Australian mammals was significant and

negative (coefficient = 0.163, P = 0.036).

A summary of all the regression analyses is in Table

1-3 and 1-4. The analyses revealed that HBL is responsible

for most of the variation in density, but that RS also made

a small but statistically significant contribution to the

model. When I repeated the analysis using rank

transformation of the data rather than a log

transformation, the results were almost identical.

Models using rank transformed data for the variables

gestation period, home range size and litter size, also

reduced but did not eliminate the negative association

between RS and density. Furthermore, in all but one case,

the forward stepwise regression including home range size as

an independent variable, the association was statistically

significant (E < 0.05).

Figure 1-1.

Double residual plot from linear regressions
of geographic range size and population
density against head-and-body length. Data
used in the analyses were natural-
logarithmically-transformed values for North
American mammals.

RS Residuals



U -- -- --
U mum

a a




-4 -2 6 2 4
-4 -2 0 2 4

Density Residuals


Table 1-3. Summary of linear regressions involving density
or RS. Both partial and model correlation coefficients are
listed for the final model for the stepwise regressions, but
information about the incomplete models is not shown.

Variahl P

Vairiahl a I s%

Partial Model
R2 R2

Log Density
Log Density
Log RS
Log Density
Log RS
Rank Density

Rank Density

Rank Density

Log RS
Log RS
Log Density
Rank Home
Range Size
Rank HBL
Rank RS
Rank RS
Rank HBL
Rank HBL
Rank RS
Rank Litter










0.028 0.493 0.0247

The second independent variable, Log HBL, made very little
contribution (P > 0.5) and was excluded from the final
model by the stepwise procedure.

P Value

............... Z-


Table 1-4. Linear regressions involving density or RS.

'T7. I 11 a

\Tav ai 1>1 a/Ia \



Log Density
Log Density
Log RS
Log Density
Log RS
Rank Density

Rank Density

Rank Density

Log RS
Log RS
Log Density
Rank Home
Range Size
Rank HBL
Rank RS
Rank RS
Rank HBL
Rank HBL
Rank RS
Rank Litter













As predicted, the stepwise regressions indicated that

HBL was better than RS as a predictor of density, and that

density was a better predictor of RS than was HBL. However

the nonsignificance of HBL in the latter model was rather



Consistent with my model, the correlation between

density and RS was most negative for North American mammals,

intermediate for Australian mammals, and most positive for

North American birds. Thus the negativity of the association

increases with range of body size, a result consistent with

the interplay of two forces. One of these forces is the

tendency for natural selection to couple abundance with

expansion into a larger RS. The second force is species

selection acting to eliminate species of large body size and

small RS. Birds have a small range of body size; hence,

exhibit a strong positive relation between RS and density.

North American mammals exhibit a much larger range of body

sizes and have undergone considerable species selection,

resulting in a negative correlation. Australian mammals are

intermediate between the former two taxa in range of body

size and exhibit an association that is less positive than

birds but more positive than mammals.

As hypothesized, the strong negative association

between RS and density is in part spurious. When HBL was

controlled, the association between these variables was


greatly weakened. Furthermore, although RS and density are

strongly associated in bivariate analyses, a regression with

density as dependent variable and two independent variables

indicated a minor importance for RS. Thus for mammals,

bivariate associations can be very misleading in elucidating

the evolutionary interactions among variables.

Although I could not be confident that I completely

controlled for all the indirect effects of size, I examined

enough variables to greatly reduce such effects. I therefore

present as an alternative an entirely different explanation

for the negative RS/density association that remains when

influence of HBL is removed.

Poor colonization ability as a cause of negative correlation

In accord with published information, I suggest that

for most animal classes, not only are RS and density

positively correlated, but that RS and colonizing ability

are positively correlated. I will concentrate on two

attributes of good colonists, namely fecundity and vagility.

The importance of fecundity to colonizing species is a

cornerstone of r- and K- selection theory. Fecundity is

probably also important to species colonizing mainland

habitats, as exemplified by a simple calculation.

Suppose that the geographic range of a hypothetical

species is contained within a circle of radius 10 km2. The

RS of this hypothetical species would then be approximately

314 kmt. If the species were to expand its geographic range


to encompass the area within a circle of radius 20 km, it

would then have an RS of approximately 1,250 km2. Thus in

doubling the diameter of its geographic range, a species

would quadruple its RS. Therefore, to maintain constant

density with a doubling of radius of geographic range, the

species would have to quadruple its population size. Clearly

this would require a high population growth rate if

colonization were to proceed rapidly. Thus selection for

high fecundity would be expected even among colonists

inhabiting continents. Of course r- and K-selection are

relative terms, and there are phylogenetic constraints on

fecundity; hence, not all colonists are more fecund than all

species from stable and saturated habitats. I suggest that

since birds and small mammals are similar in several

respects, including body size, endothermy, and those

features of morphology and physiology common to amniotes,

they are suitable groups for comparison.

Another generalization about colonists is that they are

highly vagile. It thus comes as no surprise that birds are

much more speciose on oceanic islands than are nonvolant

mammals, since the latter are less likely to reach the

islands. Furthermore, even within continents, bird species

are generally found at more sites than are mammals.

Let us now return to the hypothetical species of mammal

with the circular home range. Let us suppose that when still

confined to a circle of 10 km radius, that the area in the


outer circle yet to be colonized is a habitat mosaic.

Furthermore, suppose that only part of this mosaic is

suitable for inhabitation by the mammal species, the rest

being to some extent or another, a barrier. If the patches

of suitable habitat are large, colonization would be slow

and patchy or might cease altogether. Thus for species that

have low vagility, the extent of suitable habitat might be a

poor predictor of RS. Furthermore, since species with a

small RS have a higher overall extinction probability than

species with a large RS, species that are poor colonists

might be at greater risk of extinction.

Thus the evolution of a colonizing strategy should

favor both relatively high fecundity and high vagility.

However, nonvolant mammals are unable to acheive high

vagility, even if they possess the high fecundity

characteristic of a colonist syndrome. Small mammals of low

vagility could reach high local densities as a result of

fecundity or a lack of a dispersal sink to accommodate

population recruitment. The consequence of a combination of

high fecundity and low vagility would be species of low RS

and high density. Of course selection could sometimes

change this pattern. For example, restricted species of

Peromyscus tend to be less fecund than more widespread

species (Mace and Eisenberg 1982). Nevertheless, for

nonvolant mammals in general, limits to vagility could

preclude a positive correlation among RS, density and


fecundity. In support of this assertion, for North American

mammals, there is a nonsignificant and slightly negative

tau-b correlation (E = 0.72, correlation coefficient = -

0.017) between litter size and RS.

Low vagility also inhibits the rescue effect, whereby

immigration counteracts loss of individuals from small,

local populations. Comparative studies of birds and mammals

as regards both primary colonization and the rescue effect

include studies of nonequilibrium island biogeography and

faunal surveys of oceanic and habitat islands. A general

conclusion of such comparisons is that birds not only have

higher initial colonization rates than mammals, but also a

more pronounced rescue effect. The discrepancy in vagility

of birds and small mammals is probably even greater in

temperate climates, such as in the Nearctic, than in the

tropics. It is easy to imagine a small species of bird

colonizing a new habitat patch simply by slightly altering

its annual migration. There is some empirical support for a

generally greater dispersal ability in birds than in

mammals. Using data reported in Rapoport (1982), I

calculated a mean dispersal distance of 2.8 km/year for 14

species of mammals and 12.2 km/year for two species of

passerine birds.

Thus birds, but not nonvolant mammals, can have both

the fecundity and the vagility associated with a colonist

syndrome. Similarly, for birds, but perhaps not for mammals,


it may possible for a positive feedback to develop between

RS and density. Although for both birds and mammals, high

fecundity is likely to increase the number of propagules for

potential colonization, an increase in RS is much more

likely to result from this in birds than in mammals.

Furthermore, populations of small mammals trapped in

small patches of habitat and thus thwarted from colonization

would soon reach high population sizes, thus setting the

stage for K- selection. In fact, populations that are unable

to maintain a stable density in a small RS are likely to go

extinct; hence, there might even be a species selection

component to the negative association. If species in small

RS are under stronger selection pressure to maintain stabler

densities, then the RS/density association should be

stronger in small RS. Fig. 1-2 supports this prediction.

Fig. 1-2 is a scatter diagram of the residuals from an

RS/density regression, plotted against the RS values for

each density. Clearly RS and density are more tightly linked

in species of small than in species of large RS.

Furthermore, note that the data used in these analyses were

logarithmically transformed; hence, plots of residuals of

untransformed data show an even greater increase in scatter

with increase in RS.

The notion that RS and density are more strongly

correlated in species of small than in species of large RS

Figure 1-2.

Scatter diagram of density residuals from a
geographic range size/population density,
linear regression, plotted against geographic
range size values for each density. Data used
in the analysis were naturally-
logarithmically-transformed values for North
American mammals.

Density Residual

c~-"I'~---~~'~----~-`-`~" --U



.......... .

a. ... ,

U *
i ."



- U
U) U



* a


I I I 1 I

4 5 6 7 8 9 10 11 12 13 14

Log RS



is also consistent with the dichotomy between large and

small mammals proposed by Caughley and Krebs (1983). They

suggest that small species of mammals tend to have self-

regulating populations, whereas the populations of larger

species are extrinsically regulated. Since there is a

correlation between RS and body size, we might infer that

populations of species of small RS tend to be more

intrinsically regulated that species of large RS. If small

mammals were as vagile as large mammals, they might tend to

be more extrinsically regulated. Although relevant data are

sparse, I suggest that bats, which are among the most vagile

of mammals, may prove to have more extrinsic regulation than

small mammals in general. Not surprisingly, Nearctic bats

tend to have large RS. Mammals, perhaps more than any other

animals, seem to exhibit a tradeoff of traits characteristic

of a good colonist. Small nonvolant mammals often have the

high reproductive rate characteristic of good colonists, but

are poor dispersers. Bats are good dispersers but have low

reproductive rates. The endotherms that seem to be most

successful at combining high reproductive rates and high

vagility, are passerine birds, which also comprise the most

speciose and widespread order of endotherms.

Birds might be more able than nonvolant mammals to

circumvent the selection pressures within a restricted

geographic range. Not only can birds more readily emigrate

as densities become high, but the rescue effect will prevent


populations in small patches of habitat from going extinct

when population size is low. Furthermore, passerine birds in

particular also have high reproductive rates; hence, their

high species richness could be attributed at least in part

to their ability to colonize habitat patches.

The process I have just posited to occur for mammals

does not need to be strong to account for the slight

negative density/RS correlation that remains in mammals

after body size has been controlled. However, like the body-

size-dependent species selection, it is a process likely to

be more prevalent in mammals than in birds. In fact, mammals

(exclusive of bats) are probably one of the few classes of

animals that possess the dual combination of large range in

body size, and low vagility, that are conducive to a strong

negative RS/density correlation. Thus the apparently

anomalous negative correlation might be caused by two

fundamentally different but reinforcing processes. The more

important of these processes is species selection that

eliminates from the species pool those species that have

small RS and a large body size.

The less powerful process is a decoupling of vagility

from the general suite of characters associated with a

colonizing syndrome. This decoupling need not be considered

an adaptive trait but rather is simply a consequence of the

greater constraints on vagility in nonvolant than in volant

vertebrates. Alternatively, restriction to a small


geographic range could impose K- selection on these

populations, perhaps even leading to extinction of species

of small RS that are unable to maintain dense populations.

There is insufficient evidence to determine whether

decoupling alone is responsible for the negative

correlation, or whether subsequent natural and species

selection should also be invoked. In any case, vagility

should be considered when investigating the relationship

between abundance and distribution of mammals.

Species Selection and RS

I interpret the results of the stepwise regression to

be consistent with a model of species selection on RS. To

reiterate and elaborate, energetic dictate the negative

influence of HBL on density. Generally speaking, large

species of endotherms require more energy than do small

species. Hence, a given area will support fewer individuals,

and therefore a lower density, of large than of small

species. This effect of HBL on density is via natural

selection, and the resulting negative correlation between

density and HBL requires no species extinctions.

By contrast, the greater importance of density than of

HBL as a predictor of RS is more readily explained by

species selection. Neither density nor HBL should have a

direct influence on RS, their effects occurring via their

influence on population size. Species of large size should

exist at lower densities (see above). Hence, for a given RS,


large species should have smaller population sizes than

small species. Note, however, that density and RS interact

directly to determine population size, yet the relationship

of HBL to RS could be primarily indirec. The purported

sequence is as follows: HBL influences density, which

interacts with RS to determine population size. Remember

that in the species selection model of RS evolution, it is

the extinction of species of small population size that

results in a negative correlation between RS and density.

Since body size is related to RS only indirectly, the

correlation between HBL and RS is expected to be weaker than

that between HBL and density. Thus species selection not

only plays a role in the overall model of RS evolution, but

it also provides a better explanation than natural selection

of correlations among variables included in the model.

Finally, although it would have been preferable to

conduct decisive tests among rival hypotheses, other

hypotheses have not been proposed. I have seen no other

speculations about the anomaly of the mammalian RS/density

relationship; hence, I was forced to offer my own as

starting points. As is often the case when exploring a new

question, my conclusions were not definitive, but I hope I

have compensated by making them thought-provoking and


In the next chapter I will use RS and density to rank

extinction probabilities of North American mammals.




As noted by Thornback and Jenkins (1982), it would be

wrong to assume that all threatened mammals are included in

the official International Union for the Conservation of

Nature and Natural Resources (IUCN) list because there are

undoubtedly many taxa that are threatened but little known.

Periods of great disturbance and mass extinction, such as

the present, are expected to favor "r-selected" species over

their relatives and Myers (1985) has pointed out that these

species are in less danger of extinction. However, as I

noted in the previous chapter, reproductive rate and

colonizing ability have tended to become uncoupled in

mammals, thus perhaps somewhat weakening the negative

correlation between r-selected traits and extinction rate.

Furthermore, there are some species that by typical

mammalian standards would be considered r-strategists yet

are still in danger of extinction, so clearly

conservationists could make use of other methods to

ascertain probability of extinction. Hence, many criteria

have been suggested and used for various taxa and even

general rules-of-thumb have been proposed. Unfortunately,

although these methods are not necessarily mutually

exclusive they are nevertheless often difficult to use



comrehensively. For example, theory predicts that extinction

probability correlates positively with both trophic level

and body size. However, when one tries to apply these

generalizations to predicting extinction probabilities of,

for example, various species of the genus Microtus, the

species are not readily separable. Since all Microtus are

small herbivores, a prediction based on generalizations

relating trophic levels and food habits to extinction, would

be unlikely to indicate much difference among these species

in probability of endangerment. It is, however, unlikely

that all these species have identical or even very similar

probabilities of extinction.

One approach to more precisely predicting extinction

probability would be to attempt to take into account all the

important variables that influence probability of

extinction. Unfortunately the intensity of effort needed to

acquire the relevant information for each species would be

enormous, even if predictive models equal to the task were

available. Alternatively, one could concentrate on one or a

few especially predictive and readily quantifiable

variables, and then use these variables to numerically rank

all species by extinction probability. This method provides

a practical yardstick of extinction probability, even for

poorly-known species, by making use of existing endangerment

information on other species. Therefore in this chapter I


make more novel predictions about which species are likely

to become extinct soon.

I herein suggest that population size is one of the

most important criteria for assessing species endangerment.

In a review of historic extinctions, Diamond (1984) noted

that at every time scale examined, from a decade to

evolutionary times, there is an inverse relation between

extinction rates and population size, which is itself

proportional to area and population density. Thus although

small population size is not the only criterion for

assessing endangerment, it is perhaps the most important,

and is undoubtedly a factor considered by conservation

agencies in determining endangerment status. Furthermore,

population size can be estimated for many little-known

species and then used as a guideline for determining

allocation of further conservation effort. Since there may

be species not currently designated as endangered but that

have population sizes as small as those of species that are

currently designated as endangered by conservation agencies,

a ranking scheme could be used to troubleshoot for incipient

endangerment. To this end, I attempted to compare

population size estimates of endangered species with those

of other species that have small geographic range size (RS)

on the assumption that species with very small RS cannot

have a large population size. Although this assumption is

often wrong, the positive association between RS and


population size is greatly strengthened when body size,

trophic habits, and metabolic rate (i.e., endothermy vs.

ectothermy) are controlled.

Realistically, I do not expect agencies to change any

designations solely because of my estimates, but then this

was not my primary goal in creating the estimates: my

primary purpose was to pinpoint species of questionable

status for further investigation. It is not practical to

attempt an assessment of the conservation status of every

species of North American mammal, so where does one begin?

There are, for example, many species of mammals with a very

small RS--are all these species at risk? In a world of

finite resources, we should have a way to compile a short

list of potentially endangered species from a much longer

list of species with small RS, and then concentrate

conservation efforts on species from the short list. Species

that do not make the long list are probably at much less

risk than species on the list and require no immediate

action. By contrast, species on the short list should be

investigated at once to determine their true endangerment


Species made my short list by having estimated

population sizes within the same range as species currently

designated as "Endangered" or "Vulnerable" by the IUCN in

1982. The officially designated species were thus used as


benchmarks to assess the potential for other species to

become threatened.

Of course this presupposes that there are always

estimates of population size available, an invalid

supposition. Therefore I sought methods to estimate

population size. One such method is simply to make use of

the purported positive relation between population size and

RS. Generally speaking, species with larger RS have larger

population sizes; and hence, are less prone to extinction.

The problem with this generalization is that there is also

much variation in population size that could be attributed

to other variables, such as trophic habits, fragmentation of

habitat, eurytopy of the species, and body size of the

species. Unfortunately, using many other variables to make

predictions of population size is often impractical (but see

Humphrey 1985). Fortunately, there is one variable that

correlates with several other variables and which can

therefore act as a rough-and-ready substitute for them in an

assessment of population size: that variable is population

density. Indeed, since the population density of North

American mammals varies over several orders of magnitude

(Appendix C), any serious estimate of population size should

account for density. I suggest that an estimate of

population size that uses both RS and population density is

superior to one that uses either variable alone even if one

of the variables must be estimated indirectly. Furthermore,


although such factors as habitat fragmentation and genetic

variability also influence probability of extinction, these

factors are difficult to incorporate with RS and density

into a comprehensive, quantitative model. Thus I suggest

that the best way to assess proneness to extinction is to

first calculate population size, then to compare this

estimate with values for known threatened species, then to

modify this conclusion with other, sometimes qualitative

information. In other words the calculations I present can

be taken as starting points in the process of assessing

endangerment status.

Thus I did not intend for this work to supplant that of

specialists more familiar than I with the various taxa. My

primary purpose was to act as a troubleshooter for the

various specialist groups of the IUCN by screening lists of

species for those with the potential of becoming threatened

soon. The opinions of these specialists on my endangerment

designations will fall into three categories: they will

accept my designations, they will reject them or they will

feel unqualified to either agree or disagree. If the

specialists are confident enough to either agree or disagree

with my designations, I will concede to their greater

knowledge and consider the matter of the proper status of

the species to be closed. If, however, the specialists are

uncomfortable about either confirming or denying my


assertions that certain species are endangered then those

species should be investigated.

The IUCN apparently imposes no uniform techniques for

determining population size (Thornback and Jenkins 1982),

presumably for practical reasons. Most workers probably take

into account both density and RS when making their

assessments. However, probably few do so quantitatively by

multiplying density times RS. The IUCN does provide a

standard format, the Inventory Report Form, for reporting

information on endangerment status; unfortunately much of

the information they request is not available for most

species (Thornback and Jenkins 1982). Therefore I proposed a

method intended to be applicable to all nonvolant,

terrestrial species of North American mammals. Although my

method is likely to overestimate population size because it

assumes the reported density obtains throughout the range of

the species, it is often the only practical method.

Furthermore, the population sizes of benchmark endangered

species will also be overestimated by my method. Thus

relative population sizes could be approximately correct

even if absolute population sizes are in error.

Unfortunately even this crude technique often cannot be

applied because either RS or density are frequently

unavailable. For the particular biota I examined, Nearctic

and Australian mammals, at least RS information is available

for most species but density estimates were available for a


much smaller number. This is not necessarily a fatal

weakness, however, because density can be estimated

indirectly from other parameters by taking advantage of

interspecific relations between density and those


Materials and Methods

Unless stated otherwise, data for North American

mammals were from Appendices A-D, and for Australian mammals

from Appendices E and F. Sources of data for the appendices

were listed in Chapter I. Variables for North American

mammals included HBL, gestation length, litter size, a

ranking of purported food abundance, population size,

eurytopy, density, birth weight, length of lactation, growth

rate, RS, genic polymorphism, genic heterozygosity and home

range size. There were fewer variables in my data set for

Australian mammals because the information was not


The analyses I used are described in Agresti and

Agresti (1979), and computations were facilitated with

programs in the SAS statistical package (SAS Institute

1985). First I assessed association of each variable with

density using Kendall's tau-b, a nonparametric measure of

association. I then used linear regression to establish

quantitative relations for those associations that were

found to be significant (P < 0.05) by tau-b. Since density

estimates were not available for many species, I used linear


regression to predict densities based on information from

species for which density is known. The final step was to

compare the estimated population size against those

calculated by the same method for endangered species. I used

this method for Nearctic and Australian mammals. The two

continents were analyzed separately. There were several

reasons for not lumping the data for the two continents into

a single assessment; one of these was that maximum possible

values for Australian mammals cannot be as great as for the

Nearctic, simply because the Nearctic is much larger than

Australia. Another was that the interspecific patterns of

relationship among variables might differ quantitatively

between the two continents. Therefore the steps in my

procedure will now be discussed in turn.

Assessing Associations Among Variables

Assessing associations among variables was useful for

species of unknown density to screen variables of potential

use as quantitative predictors of density. The procedure

used for the screening, Kendall's tau-b correlation, does

not provide quantitative predictions of values for one

variable given a value for another variable. Nevertheless

tau-b was useful in providing quick summaries of the

strength and statistical significance of association of many

variables. To test for association using untransformed data

in correlation analyses from ANOVA or regression would have

been misleading because many variables are not normally


distributed. By contrast, the tau-b procedure uses ordinal

scale information, does not require normally distributed

data and will detect and measure any monotonic relationship.

Furthermore, tau-b, in contrast to Kendall's tau, can

utilize ties. Hence, tau-b seemed the ideal measure for my

purposes. Tau-b was also calculated for taxonomic levels

below that of class, and the significant (P < 0.05)

correlations resulting from these are shown in Table 2-1.

Tests were conducted at the levels of genus, family,

order and class, but only the significant correlations were

listed and it was these that I considered suitable for

further investigation. In fact, few of the regression

analyses I subsequently performed were statistically

significant unless the data were transformed, and the tau-b

correlations were employed to indicate which variables would

be most likely to have statistically significant linear

regressions if they were transformed.

Calculation of Density

Usually direct density information was not available

for a species of interest so I calculated density indirectly

by making use of interspecific correlations of density with

other variables. This method requires some explanation.

A rigorous scientist would probably consider it folly

to predict the density of one species based on information

from other species. Not only would the estimate probably be

in error but there is no way to know how large that error

Table 2-1. Significant (2 < 0.05) Kendall's tau-b
correlations of density with other variables for North
American and Australian mammals.



P value Correlation

North America
Gestation Period'
Gestation Periodc
Birth Weightd
Litter Size
Gestation Periodc
Gestation Periodc
Litter Size
Food Abundancee
Lactation PeriodC
Birth Weightd
Growth Rate'
Home Range Size9

Litter Size



a Subjective ranking of habitat breadth. Ranking of 1
indicates extreme stenotopy, ranking of 4 indicates
extreme eurytopy. Otherwise high values were reduced for
species if they were highly localized within habitats.

b Head-and-body length in mm.

c Days.

d Grams.

e Subjective ranking of food abundance. Ranking of 1
indicates species is mainly a browser or grazer, ranking
of 4 indicates species is primarily carnivorous upon

' Grams/day.

9 Hectares.






is. Therefore scientific studies incorporating densities of

several species have traditionally excluded species for

which density data are not available. For detecting general

interspecific patterns the deletion of a few points from a

data set made up of many species is of no great moment but

for someone working with endangered species the lack of

density information for each species of interest could be

crippling if densities are prerequisite to determining

endangerment status. For species of unknown but possibly

perilous status there is simply no time to wait for data

from the field that may never arrive. I argue that in such a

situation it is better to derive an indirect estimate than

to let a species become extinct because we were never really

sure it was threatened. Narrow confidence intervals and high

certainty are difficult enough to achieve for common

species, and for species in precarious survival status such

assurance may be unobtainable. Our understanding of even the

simplest natural systems is now barely within our grasp, yet

now anthropogenic disturbances of wild populations have

increased the complexity of natural systems to the point

that our science has very little predictive power in many

habitats. To expect conservationists to achieve the same

precision of prediction as conventional naturalists is


Another pragmatic reason for using indirect estimates

is that there is almost no risk involved. One possible


consequence of using my proposed method is that a species

might be transferred into the 'endangered' category. If in

fact the estimate is too low and the species is really not

threatened, then the true status of the species would soon

be discovered during rescue operations and further

expenditure would cease. The American alligator (Alligator

mississippiensis), for example, was once classified as

endangered but is now subject to limited, controlled

hunting. Conservationists would probably rather accept the

embarrassment of an overestimated population size than the

shame of having done too little, too late.

Another possible outcome of the indirect method is for

a species to retain the designation of being not endangered,

thus reaffirming the status conferred by conservation

agencies. The species is then no worse off than if the

estimate had not been undertaken.

The equations suggested for use in calculating density

and their predictive abilities are summarized in Table 2-2.

Printouts for the regression analyses from which the

equations were made provided a variety of information

including the significance level of the analysis, so I was

able to eliminate from further consideration any

nonsignificant (P > 0.05) relation from the list of

predictive equations. Unfortunately, the least squares

linear regression is only effective at detecting linear

associations. In practice, the relations between variables


using raw data were usually nonlinear and therefore

nonsignificant even when I used variables that were found to

be significantly associated by Kendall's tau-b. I therefore

used transformations, which can linearize relations that are

monotonic but superficially nonlinear. A variety of

transformations was examined by trial and error, including

exponentiation of the values for one or both variables. Some

of the variable transformations that could be used for North

American and Australian mammals are shown in Table 2-2 and

can be calculated easily with a small computer or pocket


Even after excluding the nonsignificant relations from

further consideration, there were often many possible

significant relations at the level of class that could be

used to predict density. The technique of multiple

regression would seem to be ideal for estimating density

from several other variables. Unfortunately, as pointed out

in Chapter I, this technique excludes observations that have

missing values for variables. Since data for more than two

or three variables was unavailable for most species, the

resulting multiple regression equation would rely on a very

small sample size and would not provide even approximately

reliable estimates.

Therefore I deemed it most appropriate to use only one

variable. However, for the reader more interested in making

accurate estimates of population size than in ranking

Table 2-2. Regression equations used to estimate density of
North American and Australian mammals.



North America: Mammalia
Log Density, HBL"- 0
Log Density, Log
Gestation Period 0
Log Density, Log
Litter Size 0
Log Density, Log
Lactation Period 0
Log Density, Log
Birth Weight 0
Log Density, Log
Growth Rate 0
Log Density, Log
Home Range Size 0

North America: Leporidae
Log Density, HBL 0
Log Density, Log
Gestation Period 0



.531 11.9818

.080 -2.2091

.351 11.1570









.718 62.3078 -16.6110

North America: Carnivora
Density", Birth
Density25, HBL-25
Log Density, Log
Litter Size 0
Log Density, Log

North America: Rodentia

Gestation Period

Australia: Mammalia
Log Density, Log
Litter Size
Density Log HBL

a Natural logarithm.



.039 -6.1365

0.463 10.4537
















V- ariab as R I on


extinction probability, I have also listed some associations

for several variables and at several taxonomic levels.

The choice of which variable to use for a predictor was

somewhat subjective. One might be inclined, as I was at

first, to invariably choose the variable exhibiting the

strongest association with density. There are, however,

reasons why this is sometimes inadvisable. First, the

strength of association for each variable varied

unpredictably with taxonomic level. Thus the variable

exhibiting the strongest association at one level did not

necessarily yield the strongest association at another.

Although I could have chosen for each species the regression

providing the highest coefficient of determination, the

estimates would not be comparable between species if

different equations were used for each species. I reasoned

that a single equation that could be used for all species

would be more useful in ranking extinction probability than

would equations useful for a taxonomic subset of the

species--even if the R2 for regressions using certain taxa

were higher than the one for the class as a whole. Thus to

solve the first problem I chose the taxonomic level of

class, since only associations at this level would be

applicable to the entire data set.

Secondly, data were often unavailable for many

variables for many species; hence, a strong interspecific

correlation between variables was useless when the


information for one of the variables was lacking for the

species of interest. Furthermore, subsequent analyses

revealed that estimates of density varied considerably

depending on which variable was used to estimate them. To

solve the second problem I had to concentrate on variables

for which information was available for the most species.

Those variables were RS and HBL. As explained below, RS was

not suitable as a predictor of density because RS is also

used in the equation RS times density equals population

size. HBL, however, was available for almost every species,

and was therefore the variable chosen to estimate density.

For general interest I have also listed other equations that

could be used to estimate density, but will not discuss them

further here. The equation used to calculate densities of

North American mammals was Log Density = -0.2699 HBL'5 +

5.01300. The equation used to estimate densities of

Australian mammals was Density"333 = -0.3906 Log HBL +

3.37802. For the interest of specialists, the details used

in calculating density and population size by using SAS are

elaborated in Appendix G.

Better-fitting first-order equations than any I listed

might exist, since it is possible mathematically to derive

an exact polynomial equation for the relationship between

the variables, based on the data included in the

calculations. Unfortunately such an equation would be very

complex and would be unrealistic unless new data fell


exactly along the curves calculated to link the existing

data points (Agresti and Agresti 1979). In other words, an

equation fitting the data points exactly would be indicative

of a completely deterministic association, which is

unrealistic. Furthermore, more complex models are not

parsimonious and are usually not preferred unless they are

supported by other information.

A major difference between the Nearctic and Australian

sets of analyses was that there were many more density

estimates available in the literature for the Nearctic than

for the Australian mammals; hence, the predictions for the

former are probably more accurate. Note also that bats

(Chiroptera) were excluded from both data sets; and hence,

my predictive equations are not appropriate for the

Chiroptera. The genus Peromyscus was also excluded from the

North American analyses for theoretical reasons, to assure

independence of another part of my study from one by another

author. Nevertheless the interested reader could use methods

similar to my own to calculate population sizes for species

in that genus.

Calculation of Population Size

Once densities were available they were multiplied by

RS to estimate total population size for a species. When

recent numerical estimates of RS were not available from the

literature I calculated RS from current distribution maps by

using a planimeter. Of the nonvolant, terrestrial species of


North American mammals considered to be endangered by the

IUCN and compiled by Thornback and Jenkins (1982), most are

technically only subspecies. Several of these are, however,

full-fledged species. It was these that I used as my

benchmark species, although the technique could probably be

modified to include subspecies. Note that the RS figures

that I used for this study were not the same as those I used

in other studies for the same species in other chapters. The

other chapters are concerned with evolutionary ecology and

assume RS to be an evolved characteristic; for such

investigations it is probably better to use values for RS

that more nearly reflect Precolumbian selection pressures.

By contrast, the current study is concerned with

anthropogenic extinction and does not assume that the RS of

species have had sufficient opportunity to reach a new

ecological equilibrium.

For the current study I was most interested in

establishing the maximum population sizes that are

associated with threat of extinction on the grounds that

species with population sizes as small or smaller than these

are also threatened. That is, to establish population size

guidelines for endangerment it is not the smallest RS

associated with threat that is of interest, but rather the

largest RS. Using RS values from populations so small that

the species is virtually extinct would greatly underestimate

the minimum RS necessary to curtail extinction, so I


endeavored to do just the opposite: that is, to use the

maximum RS associated with a high probability of extinction.

For both theoretical and practical reasons I was not able to

determine exact maximum RS sufficient to remove immediate

threat of extinction, but my estimates are as objective and

fair as was possible for me to make. Thus the values for RS

used as benchmarks were not necessarily the most recent

estimates for the species in question; my rationale for

sometimes using older RS values was that species sometimes

become endangered before they reach their current, very

small RS.

By now the reader may have guessed one of my reasons

for excluding RS from the correlation analyses: RS varies

over evolutionary time to a degree that is important to

conservationists. Furthermore, in the equation, (population

size = RS multiplied by density), the factors would not be

independent if the density estimates were calculated by the

method discussed above. This is because the method uses

other variables to calculate density; hence, if RS were used

to estimate density then the population size estimate would

really be calculated by multiplying RS times a correlate of

RS. Thus to avoid circularity, RS was not used to calculate

density estimates that were used in the estimation of

population size. The loss of RS as a predictor of density is

not, however, critical, because there are other variables

that are just as useful as predictors. Thus, by maintaining


RS as a variable completely independent of density it was

possible to calculate how changes in RS affect population


It should be emphasized that the estimation technique I

propose is only as good as the data used in the analyses,

but the actual model is iterative and subject to improvement

with new information, such as changes in RS. One process in

particular, habitat fragmentation, is likely to result in

many overestimates of population size (eg., Harris 1984)

unless a correction is employed that reflects the total loss

of RS resulting from fragmentation. Habitat specificity

should also be considered at the same time, if possible.


Estimated population sizes for the least abundant

species are shown in Tables 2-3 and 2-4. The values ranged

widely and the population sizes of threatened species

overlapped considerably with those of the other species. I

have excluded many species of very low population size from

the lists, especially the Australian list. The species

excluded are well-recognized in the literature as being

scarce so inclusion in my list would be redundant.

Furthermore, the purpose of my list was not to name every

species of low population size, but to highlight species

whose status is unknown and perhaps precarious, for further


Table 2-3. Estimated abundances
North American mammals.


Bison bison
Cervus elaphus
Cvnomvs parvidensa
Dipodomvs elatora
Eutamias ochrogenvs
Eutamias palmeri
Marmota olVmpus
Oreamnos americana
Ovibos moschatus
Ovis canadensis
Ovis dalli
Rangifer tarandus
Reithrodontomys raviventris8
Sorex alaskanus
Spermophilus mohavensis
Spermophilus washinatoni
Thomomys bursarius

for selected species of


a Classified as endangered or threatened by the IUCN.

Table 2-4. Estimated abundances
Australian mammals.

for selected species of

Antechinus Qodmani
Antechinus leo
Echvmipera rufescens
Hemibelideus lemuroides
Hvpsiprvmnodon moschatus
Macropus bernardus
Macropus irma
Macropus parma
Melomys cervinipes
Perameles gunni
Petrocale burbidgei
Potorous longipes
Pseudocheirus herbertensis
Pseudomvs pilligaensis




The Australian species presented an unexpected problem.

Many species of Australian mammals have estimated population

sizes below those I estimated for endangered species. Since

my purpose was to come up with a short list of species in

need of further study, I needed some way to pare this number

down. By consulting the literature I discovered that

several of the species on my list were apparently extinct.

Although a more assiduous study of the literature would have

excluded these species from initial consideration, their

very inclusion on my short list suggests that my method is

useful as a predictor of extinction probability. In any

case, the list presented is one from which extinct species,

as well as extant species whose conservation status is

already well-known, have been excluded.

Note that the lists can be lengthened simply by

inclusion of species with slightly higher estimated

population sizes. Those so inclined need only to use the

data from the Appendices and the equations presented herein

to estimate the population sizes of other species of North

American and Australian mammals. I somewhat arbitrarily

chose as a cutoff point for Nearctic mammals, the population

size of the most populous of the endangered species of North

American mammals. However, interested investigators could

use a value of their own choosing.



An estimated population size within range of known

endangered species is cause for alarm. The status of these

species warrant investigation. The estimated values for

population size should not, however, be taken as reliable.

One should especially avoid comparing population sizes of

Australian and Nearctic mammals, because the two sets of

estimates were calculated from different equations.

Furthermore, specialists could easily criticize the values

for certain species. For example, my equation estimates

population size of the river otter (Lutra canadensis) to be

over fifteen million, which is almost certainly an

overestimate. Thus there is no substitute for basic natural

history information, and my estimates should be considered

as rough guesses of greatest utility when relevant natural

history information is lacking. For many species, we have

little more to go on than measurements from museum

specimens, and a map of the geographic range. For these

species, my equations, imperfect though they may be, are a

first step in ranking extinction probability.




The previous chapter used natural history information

to predict extinctions. In this chapter I take a much larger

view of the extinction process in nature. In the three

subsequent chapters I will explicate this model and test

hypotheses derived from it.

Let us first consider the level at which selection

occurs. The rate of natural selection is probably highest at

the level of the individual and some authors have defined

natural selection to occur only only among individuals of a

population. Species, however, do not all survive and

produce new species at the same rates. When there is a

pattern to this differential survival then a type of

selection could be said to occur at the level of species.

This concept of species selection has been presented under

several different guises. Grant (1989) prefers the term

"speciational trends" and describes the venerable history of

the concept. One of the more popular discussions of species

selection is found in Stanley (1979), but perhaps the least

controversial description of the basic principles is Fowler

and MacMahon (1982). Briefly, if the species that survive

longest and/or speciate most rapidly exhibit characteristics


that differ from those that do not, then the overall

character of the biota will shift.

There is much discussion in the literature concerning

the ecosystem importance of extinction of species. For

example, the extinction of most species of large herbivorous

mammals during the Quaternary of North America not only

resulted in a statistical decrease in the body size of

herbivores, but also deleted their predators and scavengers

from the vertebrate roster and probably increased the

abundance of small herbivores (Webb 1969, 1984). The

extinctions in South America were even more profound. In the

Pleistocene there were as many genera of large (>44 kg)

mammals in South America as in any of the other continents,

including Africa (Martin 1984). During the Pleistocene,

however, extinction of megafauna was extensive in the

neotropics, so that today Africa has far more genera of

large mammals than South America. Since megafauna exert

different ecosystem effects than microfauna (e.g., Caughley

and Krebs 1983; Emmons and Gentry 1983; Kortlandt 1984;

Cristoffer 1987) it follows that these extinctions held some

ecosystem importance.

Pushed to its logical extreme every extinction or

speciation event will shift the overall character of the

biota to some extent because every species has some unique

characteristic, and obviously the extinction of species that

are hosts in obligate ecological relationships will result


in the subsequent extinction of their dependent species.

Normally, however, the loss or addition of a small number of

species is not expected to markedly affect the "gestalt" of

the community unless the species are unusually important

(i.e., if they are keystone species). However, the loss or

addition of many species over a short interval of time often

has profound effects, especially if the species lost are a

nonrandom subset of the total biota (e.g., Stanley 1979;

Fowler and McMahon 1982; Webb 1969, 1984). Furthermore,

extinctions over longer intervals could also produce trends,

although these may be more difficult to detect. I will

hereafter refer to the selective processes that occur above

the taxonomic level of species as "higher-level selection."

I also suggest herein that brief but massive pulses of

extinction, such as those engendered by humans, leave a

different signature on the evolutionary record than do

background levels of extinction.

Thus I assumed that selection could occur at any

taxonomic level. However, there are theoretical reasons for

believing that selection is more prevalent at some levels

than at others. Selection might occur at levels of

organization below that of individual (e.g., Dawkins 1976)

but if so is beyond the scope of this work. Restricting

myself to individuals or more inclusive entities, I

considered that a prerequisite for selection is discreteness

of the units selected. For example, if one accepts for a


definition of evolution one used by population geneticists,

"a change in allele frequencies among generations" (Endler

1986) then the removal of clones from a population of plants

or cells from a metazoan is not natural selection because

the genotypes of the individual units removed are continuous

with those that persist and thus allele frequencies remain

constant. Individual mammals are, however, discrete

entities; hence, selection may be common among them. Species

are also relatively discrete, albeit somewhat less so than

individuals when hybridization occurs. Taxonomic units above

the level of species are even more genetically discrete than

are species. There are, however, levels between that of

species and individual in which the units are often too

indistinct to meet the prerequisite for selection; among

these are kin groups, social groups, demes, populations and

subspecies. Therefore I will not discuss selection at these


If higher-level selection occurs it must be at a much

slower tempo than that of natural selection because there is

a greater turnover rate of individuals than of species.

Higher-level selection might thus be observed as a long-

term trend. During the span of the few months or years

available for a typical scientific investigation there are

too few extinctions and speciations for trends in extinction

and speciation to be detected, but the geological record

might reveal them. Rensch (1960); Webb (1983, 1984) Knoll et


al. (1984) and Vermeij (1987), among others, have described

many such trends, and Kurten (1971), in a capsule summary of

evolutionary trends among mammals in the Tertiary, even

remarks of a general increase in efficiency, beauty,

gracefulness and elegance. More prosaically, trends at lower

taxonomic levels are often implicit in discussions of

evolutionary polarity, and transitions from primitive to

derived can be interpreted as trends if they occur in

several sequential steps. Long-term trends are sometimes

better explained by higher-level selection in conjunction

with natural selection, rather than by natural selection

alone. Speciation and the extinction of species have been

proposed to sometimes work as a ratchet, permitting

directional changes of a magnitude not possible for natural

selection. A recent example of this concept is provided by

the equids, the evolutionary record of which is fairly well

known. Earlier interpretations of horse evolution depicted

an unbroken lineage of taxa with progressive

characteristics, such as increasing hypsodonty, size, and

relative limb length. As the record became more complete it

became apparent that this interpretation was an

oversimplification (McFadden 1985). Although general trends

did occur they were confounded by radiations which sometimes

obscured the overall directionality of the process. Someone

observing only extant equids would be unlikely to detect


overall trends because there would not have been enough time

for selective extinction and speciation to occur.

The characteristics of individuals within a species are

not, however, determined by higher-level selection; they are

determined by natural selection at lower levels, especially

that of the individual. When there is a loss of individuals

from a population, there is potential for invoking natural

selection; all that is required is that the individuals lost

differ significantly in value for heritable traits from

those individuals that persist; and that both are from

"equivalent" environments.

Similarly, for higher-level selection to be important

the species lost must have heritable traits that differ from

those of individuals that survive. In a given biota both

processes can and probably do occur, but usually only

natural selection occurs sufficiently rapidly for study by

mankind. The problem then becomes one of detecting the

effects of higher-level processes from the background level

of selection among individuals.

The Basic Model

Adaptive radiation has also been called explosive

radiation, a term that suggests species burst into being as

a riot of adaptive types. An elaboration of this concept is

herein suggested as a useful heuristic tool.

Imagine viewing a slow-motion film of a marksman firing

a shotgun at a target. When the shotgun pellets leave the


gun they are close together and all seem to be heading in

approximately the same direction. However, as the pellets

approach the target they will begin to diverge, and if one

could film these in extreme slow motion it would then become

apparent which pellets have the most divergent trajectories.

Eventually the pellets will travel as far as the target, but

if the target is small and distant only a few pellets will

strike it; the rest will miss because of their divergent

trajectories (Fig. 3-1).

Now, after shooting is finished it is quite easy to see

which pellets were on the correct trajectory to hit the

target because they will be imbedded in the target. Note,

however, that at the instant the shot was fired there was no

practical way to determine which pellet would strike the

target. The marksman must wait until the shooting is over in

order to determine his hits and misses, and even a

technician using sophisticated high-speed cameras would

have difficulty predicting which pellets would strike the

target when the pellets were only an inch from the barrel of

the gun.

Pursuing this analogy further, if explosive radiation

can be likened to the firing of a shotgun then we can also

consider the marksman to be the ancestral species and the

target to be long-term survival of species. In reality,

0 0

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gravity alters the trajectory and therefore the distance

pellets will reach, but for the purpose of this analogy let

us assume the gun is fired in the absence of gravity.

To continue with the analogy, note that if the target

is large and close to the marksman then all the pellets will

strike the target. Similarly if we observe an adaptive

radiation immediately after it occurs a high proportion of

species will be seen to survive. But if the target

(survival) is moved farther away fewer pellets (species)

will strike it (Fig. 3-2). The farther away the target, the

longer it will take the species to reach it and the more

important deviation from the optimum trajectory will become

in determining long-term survival. I will now digress for a

moment to discuss what "survivors" really are.

In reality all species are both survivors and failures

because all species survive for some length of time, yet all

will probably perish eventually. The comparison intended

herein is between those species that are relatively long-

lived and those that are shorter-lived. Thus the terms

"survivors" and "failures" are actually shorthand for

"species of large actual stratigraphic range" and "species

of small actual stratigraphic range".

Continuing with the shotgun analogy, it can be seen

that the easiest way to determine which species have the

optimum trajectory for survival is to wait until the shoot

0 -*

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is over and study the survivors imbedded in the target. The

radiation itself may be interesting but radiation at its

peak tells us nothing about large scale trends in evolution.

Only by studying the aftermaths of several firings can we

generalize whether the marksman tends to bias his aim in a

certain direction; similarly, by examining the aftermath of

several adaptive radiations we might detect a trend in


To elaborate, if the marksman's aim is a bit off, only

the pellets near one edge of the scatter will strike the

target. Thus the mean trajectory of the pellets as they

leave the gun could well differ from the trajectories that

belong to pellets that strike the target, in which case the

mean trajectory of the pellets as they leave the gun would

not be the optimum trajectory to strike the target.

Similarly the general trends apparent during an adaptive

radiation might not be the ones consistent with long-term

survival. Note also that the farther away the target is from

the marksman, the easier it is to tell if he is a bad shot,

and the longer we wait after an adaptive radiation the

easier it is to tell whether short-term trends differ from

long-term trends. The longer the time elapsed after

radiation the more species are likely to become extinct and

the more selective extinctions and speciations have



This principle can be illustrated at a higher taxonomic

level by an example from the Miocene epoch of North America,

as discussed by Webb (1983). At the beginning of the

adaptive radiation of savanna ungulates in the Miocene of

central North America, there were a moderate number of

genera of browsers but few or no grazers. Then, coincident

with climatic changes, the vegetation took on a more open

aspect as savanna woodland and grassland replaced closed-

canopy forest. As grassland interdigitated with forest a

variety of grazers and mixed feeders evolved, such that at

the peak of diversity in vegetative structure, a rich fauna

of browsers, grazers, and mixed feeders was present.

However, as the climatic trend toward coolness and aridity

continued, forest-dwelling mammals began to disappear

altogether on the Great Plains and browsers became extinct

at a faster rate than they evolved. Eventually the species

richness of grazers declined as well, with the ultimate

result of the climatic trends being the impoverished

ungulate fauna of the Great Plains of present day North

America. Note that a biologist living at the peak of species

richness would probably not be able to predict which

morphologies and food habits would persist the longest after

the radiation. With the advantage of hindsight made possible

by a good fossil record we can discern the loss of

evolutionary trajectories inconsistent with long-term

survival. Thus even though Webb (1983) did not address


intrageneric extinctions the process described therein is

consistent with my own model in at least one important

aspect: the taxa that survived were a very nonrandom

ecological subset of the original adaptive radiation.

Clearly in both my study and that of Webb, there were

selective agents at work weeding out species unsuited to

changing conditions. It would be inappropriate to attribute

the trend to natural selection alone, because few or none of

the identified changes in character state were intraspecific

(unless you consider the changes that occur at speciation to

be intraspecific). It was the community as a whole that

changed, by adding and deleting species with certain

character states. The point I have tried to make with this

example is that evolutionary changes are sometimes so subtle

and so slow that they can only be detected by observing

through a very wide window of time, and certainly are not

easily discerned in the midst of an adaptive radiation.

There are many other examples illustrating that the

survivors of adaptive radiations are usually specialized

subsets of the taxon. For example, the longest lasting forms

of ammonite molluscs shared a morphological structure that

is thought to have enabled them to live at great depths

(Ward and Signor 1983). Another example is that of Paleozoic

hydrozoans (marine invertebrates), in which the

morphologically complex genera had the greatest longevity,

at least during the intervals between mass extinctions


(Anstey 1978). There are many such sequences of radiation,

extinction, and reradiation of the survivors among South

American marsupials and other mammals (Simpson 1961; Pascual

et al. 1985), and perhaps in other faunas as well. As a

final example, among benthic molluscs and some other

invertebrates the mode of larval development appears to have

had an important influence on extinction rates. Locally-

extirpated populations of the species with more sedentary

larvae are often unable to recolonize after extirpation, but

more pelagic larvae can do so. The more sedentary species

are probably better competitors under stable conditions but

fare poorly during periods of great disturbance. Periods of

great environmental disturbance can be analogized to a mass

extinction event, albeit on a local scale (Hansen 1980;

Jablonski and Lutz 1983).

Thus, periods of great environmental change tend to

favor generalized species (Jablonski 1986), as predicted by

r- and K-selection theory. Someone observing a biota under

flux might conclude that long-term trends would favor the

generalized species to be seen prospering during a

perturbation. However, biotic succession exemplifies the

concept that a change in conditions could reinstate long-

term processes that favor other species than those that

prosper during disturbance. I suggest that the relative

importance of natural vs. species- and higher-level

selection changes with time elapsed since the most recent


adaptive radiation. Furthermore, there are long-term

evolutionary trends (e.g., Vermeij 1987); mosaic evolution

occurs, especially in vascular plants (Knoll et al. 1984);

and kin and sexual selection have enhanced the evolutionary

success of many organisms (e.g., eusocial species) in ways

that could not have been predicted by natural selection

theory until it was greatly modified, a problem of much

concern to Darwin. However, perhaps the most interesting

challenge to the traditional concept of evolution by natural

selection is the amount of control that some organisms seem

to have over their genetic destiny. This is exemplified most

completely by structurally dynamic genes, as summarized in

Campbell (1982). There are, for example, dynamic genes that

sense their environment and change structure in response to

detected conditions; automodulating genes that change their

future responsiveness to stimuli when stimulated; and

experiential genes that transmit specific modifications

induced in somatic phenotype to descendants. There are as

yet no examples identified of genes that acquire changes in

anticipation of their usefulness, although of course genetic

engineering enables humans to do so. All of these phenomena

attest to the notion that some understanding of natural

selection alone is far from being synonomous with a

comprehensive knowledge of organic evolution, a sentiment

recently reiterated by Endler and McLellan (1988).


Furthermore, although my investigation is primarily

concerned with certain aspects of macroevolution, this does

not require that we abandon all hope of finding general

principles of selection that apply to any taxonomic level.

For example, a possible parallel of higher-level selection

discernible among individual-level variables is that of the

logistic growth curve. A population in an exponential growth

phase is likely to be under different selection pressures

than when it is close to the carrying capacity of the

environment, and if one form of selection predominates long

enough, it is likely to result in a character shift in the

population as a whole.

Jumping to the level of species, we can see a similar

process at work. Pimm et al. (1988) have shown that the

attributes rendering species most sensitive to extinction

shift with population size; perhaps they also shift with

time. An adaptively-radiating clade corresponds to r

selection at the species level, whereas a very old

monospecific genus could be nearer the K end of the

spectrum. Just as K-strategy species tend to have greater

longevity than their close relatives that are r-strategists,

species that survive adaptive radiations could differ from

those that perish. Besides longevity, surviving species

might be predicted to have other characteristics of K-

strategists, including greater body size, longer gestation

and lactation periods, higher birth weights, larger home and

geographic range sizes, and lower densities. Dial and

Marzluff (1988) suggested that during periods of large

fluctuation of environmental conditions, species of small

body size are favored, whereas during periods of stability,

large sizes are favored. This is consistent with my own

model in which small size predominates during exponential

(radiating) phases, but large size is selected for at

equilibrium. Furthermore, Dial and Marzluff have also

studied life history traits of taxa that affect extinction

and speciation, but their work had not gone to press at the

time of this writing.

A logistic model for diversity of orders of marine

metazoans was elaborated and tested by Sepkoski (1978, 1979,

1981) and I suggest that the same is true for Cenozoic land

mammals. I have already suggested as a general principle

that species in the midst of adaptive radiation will tend to

differ in predictable ways from species that are not. Thus

in some small way I have wedded the process of exponential

adaptive radiation proposed by Sepkoski to evolutionary

trends, such as escalation, a process proposed and discussed

at great length by Vermeij (1987), Dial and Marzluff (1988)

and others. I now advance a more precarious prediction,

namely that evolutionary escalation is a major cause of the

collapse of an adaptative radiation. Thus I hypothesize that

the improvements associated with escalation will be

measurably more pronounced in species that persist the


longest during periods of adaptive radiation, or that

survive past the radiation altogether. I did not test this

hypothesis and only offer it as food for thought.

Shotgun Blasts and Logistic Growth--a Unification.

In summary, I suggest that adaptive radiation is

analogous both to the blast of a shotgun and to the logistic

curve. Species come into being as variations on a theme

occurring in a single genus. These variations are

constrained by laws of development and design and can be

arrayed in a systematic fashion manifested by correlated

trends among variables.

Extinction then occurs within the genera, the long-

term survivors of which will differ from more ephemeral

species in the same ways that r- and K- strategists differ.

Higher-level selection could also occur over short intervals

of time, as during mass extinctions. However, such selection

is difficult to separate from natural selection. By

contrast, long-term trends are largely attributable to

species- and higher-level selection; hence, the most

unequivocal examples of species- and higher-level selection

come from long-term trends, not from periods of mass

extinction. In the next three chapters I will explore

macroevolution in mammals and attempt to discern long-term

trends by comparing patterns among variables that arose over

a short time span with patterns that arose more quickly or

more recently.




In the previous chapter I speculated that adaptive

radiation produces speciose genera of many short-lived

species. Although the protracted nature of species selection

renders impractical the direct observations necessary for

its evaluation, in the next chapter I will test hypotheses

relevant to making inferences about the importance of this

process. First, however, I wanted to establish whether

prerequisites for the shotgun model are met. If the

prerequisites necessary for the process to occur do not

exist then I would be premature to invoke the model to

explain patterns I discern from the results of analyses.

One condition certain to be met for extensive species

selection within genera is that of heritability. Both

natural and species selection assume that in the absence of

mutation, genotypes of offspring are derived from their

parents. This assumption has been confirmed numerous times

and is the cornerstone of the science of genetics.

The second major assumption of a model that

incorporates extensive intrageneric selection, is that

there is considerable variation among species for selective

agents to act upon. In the simplest case, that is when there


is no variation in values for traits, then there is no

possibility for selection. Furthermore, it is intuitive that

the rate of selection is likely to be greater when the

variation is large than when it is small, because large

differences should be more readily discriminated by

selective agents than will small differences. However, even

when one allele is clearly optimal for a given population at

a certain place and time, the members of populations often

do not coverage on this optimum even after many generations.

Reasons for lack of fixation include gene flow, mutation,

changes in the environment that alter selective pressures,

and recombination, which will be discussed shortly.

Intrageneric species selection might, however, more

frequently result in optimal genotypes than will natural

selection. The reason for this is as follows.

Recombination among members of a species mixes optimal

and suboptimal alleles, whereas recombination does not occur

among species in a genus (unless they hybridize). Thus, a

large amount of variation within a species might not

necessarily enhance selection because much of it is masked

by dominant or codominant alleles. Since selection acts on

the phenotype, it is quite possible and frequently occurs

that deleterious alleles persist for many generations as

recessives. By contrast, since there is no recombination

among species, distinctions among them are probably more

apparent to selective agents than are many differences among


individuals in populations. Lack of recombination at higher

taxonomic levels probably also tends to make selection more

permanent than within populations. This notion is not new

and has been elaborated by some workers (e.g., Fowler and

MacMahon 1982) to explain the predominance of sexual over

asexual reproduction in nature. Briefly, the genetic

variation sexual species maintain by recombination and

dominance, serves to hedge bets against changes in selection

pressures. Asexual species, which cannot create new gene

combinations by recombination, suffer a higher extinction

rate than sexual species. Note that there is no mechanism to

allow the persistence of a species of low population size

analogous to the one that maintains recessive alleles in a

population. In a sense, then, the much greater species

richness of sexual than of asexual species can be attributed

to a form of reproduction that partially thwarts extinction

and species selection.

Nevertheless, the purported weaker correlation between

variation and rate of selection within populations should

not blind us to the likelihood that variation correlates

strongly with extinction rate among species or higher

categories. A positive correlation between amount of

variation and rate of species selection is intuitive and

will be assumed in this chapter. An extension of this

assumption can also be applied to the various taxonomic

levels. Taxonomic levels with large variances for characters


should be especially prone to species selection. Thus we

might consider a taxonomic level with high variance for

several characters to be a good place to look for the

effects of species selection. Although I believe this

assertion to be generally valid, it is also an


One complication is that lower taxa are nested within

higher taxa; hence, variance at one level is not independent

of variance at another level. Fortunately there is a

procedure, the nested analysis of variance, to measure the

variation within levels of a nested hierarchy while

controlling for other levels. I included the levels

infraclass or superorder (i.e., monotremes, marsupials and

placentals), order, family, genus and species in my nested

analyses of variance on North American and Australian

mammals. I followed Strahan (1983) in recognizing two orders

of marsupials, the Polyprotodonta and Diprotodonta. The

variables I analyzed for both continents were HBL, RS,

length of lactation and litter size. Additionally, for North

American mammals I included stratigraphic ranges of fossil

species that lived at some time during the interval from the

Hemphillian (Miocene) to the Recent. These data are from

Appendix 2 of Kurten and Anderson (1980).

The reader should be aware of certain subtleties in the

interpretation of the nested analysis of variance. The

variance at each taxonomic level is a measure of the amount


of variation that can be attributed to differences among,

not within, the units at that level. This can be illustrated

with a hypothetical example.

Suppose a nested analysis of variance, similar to the

ones I used, was performed on a data set containing body

size information (logarithmically transformed) on living

species of Nearctic mammals of the orders Insectivora and

Artiodactyla. The former order contains shrews and moles,

whereas ungulates comprise the latter. Thus there would be

no overlap in size among the two orders and a nested

analysis of variance would indicate that almost 100% of the

variation in body size occurred at the level of order. This

would be true even if there is considerable variation in

body size within these orders, because the interordinal

variation overwhelms the intraordinal variation. This same

principle applies, albeit to a lesser extent than in this

example, to the data sets I analyzed. Thus the reader should

not be surprised if the percent variance for some variables

is high at levels other than the genus.

Another consideration when interpreting nested analyses

of variance is that some variables are probably more subject

to species selection than others. Of the variables in my

data set, I expect variation in stratigraphic range to be

the best indicator that species selection might be rapid.

The reason for this is simple: of all the variables in my

data set, stratigraphic range is the only one with a


necessary connection to extinction. RS variation should also

set the stage for species selection, since species of very

small RS are likely to become extinct soon. Litter size

could also affect population size; and hence, probability of

extinction, albeit less so than RS because the magnitude of

variation in litter size is much less than in RS. Although

body size has been suggested to correlate positively with

extinction probability, this relation might be important

only when the species contrasted are of widely disparate

body sizes. Thus variation in HBL might be expected to

correlate more strongly in higher than in lower taxa because

there is so much more variation in HBL at higher taxa. For

example, the size difference between voles (Microtus) and

mammoths (Mammuthus) could differentially affect their

extinction probabilities, but size differences between two

species of Microtus might not.

The variable in my data set that probably is most

weakly correlated with extinction probability is length of

lactation. Although there might be a negative correlation

between length of lactation and reproductive rate, the

relationship at lower taxonomic levels is probably too weak

to substantially affect extinction probability. This is

probably at least in part because of the crudeness and

inaccuracy of measurement of this variable. In any case,

Predictions 4.1, a-c, are that stratigraphic range and RS

will have large variances among the species within genera,


that litter size and HBL will have somewhat smaller

intrageneric variances, and length of lactation will have

even less. I will now explain why I find intrageneric

variation is particularly interesting.

Although extinction can occur at any taxonomic level,

the greater age of higher taxa (Rensch 1960) suggests that

extinction is less common at higher levels. I therefore

expect extinctions of species to be more common than

extinctions of higher taxonomic levels. The lowest taxonomic

level in my analysis that is more inclusive than species is

the genus; hence, I infer a greater frequency for species

selection at the level of genus than for extinction of

higher levels. To put it more precisely, there have been

more extinctions of species than of genera, families or

orders. Hence, I predicted that characters highly correlated

with probability of extinction will exhibit large variation

at the level of genus.

The shotgun model also suggests that monospecific

genera are often the residue of extinctions among speciose

genera. This suggests that if we could somehow remove the

short-lived species from speciose genera, that the remaining

species would resemble monospecific genera. I was unable to

address this question rigorously, but I was at least able to

compare the variances of the two types of genera. Prediction

4.2 is thus that the variance among monospecific genera is

similar to that among speciose genera when variation among


the species in each speciose genus is controlled for


The shotgun model implies that with a greater passage

of time there is more opportunity for species selection.

Since higher taxa have greater stratigraphic ranges than

lower taxa (Rensch 1960; Van Valen 1973), we can infer that

they have, on average, been subject to more species

selection than the lower taxa contained within them. Thus

the relative importance of natural vs. species selection

could vary with taxonomic level, resulting in different

patterns of association among variables. Thus Prediction 4.3

was that signs of association will tend to differ among

taxonomic levels, and the differences will be greater with

widely-disparate levels than among taxa that are fewer

levels apart.

Materials and Methods

The nested analysis of variance technique used in this

chapter is available on the SAS statistical package (SAS

Institute 1985). The sources of data were described in

Chapter I, and the variables used were those for which

sample sizes were largest, and which were generally

comparable (except for stratigraphic range) between

Australia and North America. All of the nested analyses of

variance used only genera with more than two species. Some

of the so-called monospecific genera used to test Prediction

4.2 were not monospecific in the strict sense but were the


only Nearctic species in the genera. For example, the elk

(Cervus canadensis) was considered to be monospecific even

though there are several species of Old World Cervus. My

rationale for this is that the Old World Cervus belong to a

different evolutionary theatre; and hence, are irrelevant to

studies of Nearctic mammal evolution.

To compare the variances of monospecific and speciose

genera, I used an F statistic, with Satterthwaite's Formula

to calculate the degrees of freedom (Milliken and Johnson

1984). The mean square for the genera, mean square error,

coefficients of expected mean square, sample size and

variance for monospecific genera, were all calculated by the

PROC NESTED and PROC MEANS options of the SAS statistical

package. Since I had no reason to expect either type of

genus to have greater variance, I conducted two-tailed

tests. One might, however, hypothesize that monospecific

genera actually have greater variances, for reasons given in

the next chapter. Therefore I also calculated the F

statistics assuming a one-tailed test.

For my comparison of selection at different taxonomic

levels, several taxonomic levels were examined. The most-

inclusive taxonomic level available for mammals is the class

itself. Hence, the data set for the most-inclusive group

included all the species in my data set. The lowest

taxonomic level appropriate to this analysis is the genus;

hence, for this level I used species grouped by genera.