• TABLE OF CONTENTS
HIDE
 Title Page
 Table of Contents
 Recommendations
 Introduction
 Methods
 Results
 Discussion
 Conclusions
 Acknowledgements
 Reference






Group Title: Florida Cooperative Fish and Wildlife Research Unit Technical report 8-9
Title: Preliminary assessment of uncertainty involved in modeling manatee populations
CITATION PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00073818/00001
 Material Information
Title: Preliminary assessment of uncertainty involved in modeling manatee populations final report, 1985
Series Title: Technical report
Physical Description: 19 p. : ill. ; 28 cm.
Language: English
Creator: Packard, Jane M
U.S. Fish and Wildlife Service
Florida Cooperative Fish and Wildlife Research Unit
Publisher: Florida Cooperative Fish and Wildlife Research Unit, University of Florida
Place of Publication: Gainesville Fla
Publication Date: [1985]
 Subjects
Subject: Manatees   ( lcsh )
Manatee populations -- Mathematical models   ( lcsh )
West Indian manatee   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Includes bibliographical references (p. 18-19).
Statement of Responsibility: Jane M. Packard.
General Note: "Prepared for U.S. Fish and Wildlife Service under cooperative agreement no. 14-16-0009-1544."
General Note: " Research work order no. 2."
Funding: This collection includes items related to Florida’s environments, ecosystems, and species. It includes the subcollections of Florida Cooperative Fish and Wildlife Research Unit project documents, the Sea Grant technical series, the Florida Geological Survey series, the Coastal Engineering Department series, the Howard T. Odum Center for Wetland technical reports, and other entities devoted to the study and preservation of Florida's natural resources.
 Record Information
Bibliographic ID: UF00073818
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: aleph - 001135515
oclc - 24415363
notis - AFN4706

Table of Contents
    Title Page
        Title page
    Table of Contents
        Table of contents
    Recommendations
        Page 1
    Introduction
        Page 2
    Methods
        Page 2
        The models
            Page 2
            Page 3
            Page 4
        Assumptions involved
            Page 5
            Page 6
            Page 7
            Page 8
    Results
        Page 9
        Range of projected growth rates
            Page 9
            Page 10
            Page 11
            Page 12
            Page 13
            Page 14
    Discussion
        Page 15
        Maximum growth rates
            Page 15
        Uncertainty in estimated values
            Page 15
        Future research directions
            Page 16
    Conclusions
        Page 17
    Acknowledgements
        Page 17
    Reference
        Page 18
        Page 19
Full Text




PRELIMINARY ASSESSMENT OF UNCERTAINTY INVOLVED

IN MODELING MANATEE POPULATIONS



FINAL REPORT

1985





Jane M. Packard
Department of Wildlife and Fisheries Sciences
Texas A&M University
College Station, Texas 77843-2258


Under subcontract from:

Florida Cooperative Fish and Wildlife Research Unit
117 Newins-Ziegler Hall
University of Florida
Gainesville, Florida 32611




Prepared for:

U.S. Fish and Wildlife Service
75 Spring St. S.E.
Atlanta, GA 30303

Cooperative Agreement No. 14-16-0009-1544
Research Work Order No. 2




Citation should read: Packard, J.M. 1985. Preliminary assessment of
uncertainty involved in modeling manatee populations. Manatee Population
Research Report No. 9. Technical Report No. 8-9. Florida Cooperative
Fish and Wildlife Research Unit. University of Florida, Gainesville,
Florida 19 pp.








TABLE OF CONTENTS PAGE


RECOMMENDATIONS 1

INTRODUCTION 2

METHODS 2

The Models 2

Assumptions Involved 5

RESULTS 9

Range of Projected Growth Rates 9

Sensitivity of the 10-age Class Model 9

DISCUSSION 15

Maximum Growth Rates 15

Uncertainty in Estimated Values 15

Future Research Directions 16

CONCLUSIONS 17

ACKNOWLEDGMENTS 17

REFERENCES 18








RECOMMENDATIONS

1. As modeled in this study, the maximum potential rate of increase of
manatee populations is likely to be as low as 2-7%. Given the available
data and uncertainties involved in estimating population parameters, the
possibility of a current negative rate of change in the Florida manatee
population (e.g. a population decline) cannot be ruled out. This suggests
that management policies are well justified in being conservative about
reducing risks to the population. The rate of recovery from a catastrophic
event would be very slow. The margin for error. in managing the population
is thus narrow. Even gradual, cumulative changes reducing the growth rate
by a few percentage points could make a difference between population
growth and decline.


2. The rate of population change is likely to be most sensitive to changes
in the adult survival rate. Management efforts should thus focus on
reducing adult mortality. Considered separately, each of the factors of
post-weaning survival, subadult survival and proportion of females breeding
had relatively more effect on sensitivity of the model than variations in
the age structure.


3. Additional effort is needed in developing a working model suitable for
projecting manatee population changes. The uncertainty involved in
estimating the values for population parameters needs to be reduced by
analysis of existing data, collection of additional data, and development
of appropriate techniques for estimating values from incomplete data. The
available computer programs suitable for manatee population modeling
efforts were identified in the current study. However, additional effort
is needed to modify the programs used, or to acquire and compile the
programs that were developed on hardware not available to manatee
researchers at the time of this study.








INTRODUCTION

Development of a population model for the West Indian manatee
(Trichechus manatus) could contribute substantially to understanding the
life history pattern, demography and implications of alternative management
actions considered for this endangered species. Although considerable
effort has been focused on developing models to evaluate population
dynamics of cetaceans and pinnipeds (DeMaster 1981, Gerrodette et.al. in
press), until recently relatively little has been done to model sirenia
populations. A recent application of modeling techniques to evaluate the
effect of calving intervals, mortality rates, and age of first calving on
population growth rates projected for dugongs (Dugong dugon) has
illustrated the value of the modeling approach (Marsh and Marsh, unpub.
manus.).

Particularly for endangered species, an understanding of demography
derived from population models can provide insight into appropriate
management practices where the risks of error are considered great. For
example, an evaluation of the demography and life-history pattern of the
Everglade Kite (Rostrhamus sociabilis plumbeus) indicated high adult
survival rates were important to growth and persistence of the population,
and provided recommendations as to where emphasis should be placed in
collection of further data and in management efforts (Nichols et. al.
1980).

In the initial stages of evaluating the population dynamics of a
species, modeling techniques can provide valuable tools to assess the
internal consistency of field data, the expected range of population growth
rates, and the relative sensitivity of those rates to changes in each of
the basic population parameters. In the later stages of modeling a
population, the model is tested against actual data and revised until it
provides valid projections. A tested model may then be used to project the
effects of actual or potential events and management actions.

Sufficient life-history data now exist to begin the process of
constructing a general model based on the manatee life-history pattern.
The purpose of this paper is to compile available data on the estimated
values of manatee population parameters, to evaluate the uncertainty
inherent in these estimates, and to identify future research needed to
construct and validate more specific models.


METHODS

The Models

The age-structured models employed in this study were based on the
Leslie matrix approach and were used to project population changes at
discrete time intervals, as described by Goodman (1978). The values for
age specific rates were collapsed within 6-year age classes to enter the
data into an available model constructed to manipulate 10 age classes. A
model manipulating 50 1-year age classes was used for one simulation to
verify that the data in the simpler model had been collapsed in a
reasonable manner.








INTRODUCTION

Development of a population model for the West Indian manatee
(Trichechus manatus) could contribute substantially to understanding the
life history pattern, demography and implications of alternative management
actions considered for this endangered species. Although considerable
effort has been focused on developing models to evaluate population
dynamics of cetaceans and pinnipeds (DeMaster 1981, Gerrodette et.al. in
press), until recently relatively little has been done to model sirenia
populations. A recent application of modeling techniques to evaluate the
effect of calving intervals, mortality rates, and age of first calving on
population growth rates projected for dugongs (Dugong dugon) has
illustrated the value of the modeling approach (Marsh and Marsh, unpub.
manus.).

Particularly for endangered species, an understanding of demography
derived from population models can provide insight into appropriate
management practices where the risks of error are considered great. For
example, an evaluation of the demography and life-history pattern of the
Everglade Kite (Rostrhamus sociabilis plumbeus) indicated high adult
survival rates were important to growth and persistence of the population,
and provided recommendations as to where emphasis should be placed in
collection of further data and in management efforts (Nichols et. al.
1980).

In the initial stages of evaluating the population dynamics of a
species, modeling techniques can provide valuable tools to assess the
internal consistency of field data, the expected range of population growth
rates, and the relative sensitivity of those rates to changes in each of
the basic population parameters. In the later stages of modeling a
population, the model is tested against actual data and revised until it
provides valid projections. A tested model may then be used to project the
effects of actual or potential events and management actions.

Sufficient life-history data now exist to begin the process of
constructing a general model based on the manatee life-history pattern.
The purpose of this paper is to compile available data on the estimated
values of manatee population parameters, to evaluate the uncertainty
inherent in these estimates, and to identify future research needed to
construct and validate more specific models.


METHODS

The Models

The age-structured models employed in this study were based on the
Leslie matrix approach and were used to project population changes at
discrete time intervals, as described by Goodman (1978). The values for
age specific rates were collapsed within 6-year age classes to enter the
data into an available model constructed to manipulate 10 age classes. A
model manipulating 50 1-year age classes was used for one simulation to
verify that the data in the simpler model had been collapsed in a
reasonable manner.








INTRODUCTION

Development of a population model for the West Indian manatee
(Trichechus manatus) could contribute substantially to understanding the
life history pattern, demography and implications of alternative management
actions considered for this endangered species. Although considerable
effort has been focused on developing models to evaluate population
dynamics of cetaceans and pinnipeds (DeMaster 1981, Gerrodette et.al. in
press), until recently relatively little has been done to model sirenia
populations. A recent application of modeling techniques to evaluate the
effect of calving intervals, mortality rates, and age of first calving on
population growth rates projected for dugongs (Dugong dugon) has
illustrated the value of the modeling approach (Marsh and Marsh, unpub.
manus.).

Particularly for endangered species, an understanding of demography
derived from population models can provide insight into appropriate
management practices where the risks of error are considered great. For
example, an evaluation of the demography and life-history pattern of the
Everglade Kite (Rostrhamus sociabilis plumbeus) indicated high adult
survival rates were important to growth and persistence of the population,
and provided recommendations as to where emphasis should be placed in
collection of further data and in management efforts (Nichols et. al.
1980).

In the initial stages of evaluating the population dynamics of a
species, modeling techniques can provide valuable tools to assess the
internal consistency of field data, the expected range of population growth
rates, and the relative sensitivity of those rates to changes in each of
the basic population parameters. In the later stages of modeling a
population, the model is tested against actual data and revised until it
provides valid projections. A tested model may then be used to project the
effects of actual or potential events and management actions.

Sufficient life-history data now exist to begin the process of
constructing a general model based on the manatee life-history pattern.
The purpose of this paper is to compile available data on the estimated
values of manatee population parameters, to evaluate the uncertainty
inherent in these estimates, and to identify future research needed to
construct and validate more specific models.


METHODS

The Models

The age-structured models employed in this study were based on the
Leslie matrix approach and were used to project population changes at
discrete time intervals, as described by Goodman (1978). The values for
age specific rates were collapsed within 6-year age classes to enter the
data into an available model constructed to manipulate 10 age classes. A
model manipulating 50 1-year age classes was used for one simulation to
verify that the data in the simpler model had been collapsed in a
reasonable manner.








10-age Class Model

The computer program used for population simulations based on 10 age
classes was written by Nichols and Hines (unpub. manus.). It provides for
simulation of demographic and environmental stochasticity. In this
application, only the demographic stochasticity was considered, referring
to the type of variation that could be expected due to the error in
measuring values of population parameters.

The input parameters that were modified in the present application of
the computer program are listed in Table 1. The program calculated age-
specific reproductive rates from the proportion of breeding females in each
age class and the number of calves per age class interval. The program
accounts for mortality at the beginning of each age class interval, that
is, before reproduction has occurred. The input population structure is
used in calculation of reproduction in the initial year of the simulation.
Subsequently, each age class is incremented, mortality calculated, then
age-specific reproduction is calculated.

A total of 17 simulations were conducted. Of these, 14 consisted of
10 replicates over 10 time periods, and the rest consisted of 6 replicates
over 20 time periods. The former all utilized the "initial" age structure
while changing values for each parameter, and the latter utilized default
values while varying the age structure.

The moderate parameter values were used as default values.
Simulations were run with all values set high, all values set moderate,
then all values set low. The results of the simulation with all values set
moderate was used as a standard for comparison of the effect of varying the
other values. Separate simulations were then run for each parameter in
turn, setting it at high and low values, with other parameters at default
values.

The 3 simulations in which the age structure was varied were run with
all other parameters set at default values. These simulations were run for
more time periods to assess the cumulative effect of variation in the age
structure.


50-age Class Model

The computer program written for simulations using 50 age classes was
provided by \!.E. Grant and modified by J. Wilber (Department of Wildlife
and Fisheries Sciences, Texas A&M University). The program calculates the
primary eigenvalue and associated eigenvector, projecting age structures
for a specified number of years. It does not provide for replicated
simulations, nor for efficient ways of changing the population parameters
for such a large matrix. Thus, it was not as well suited for running the
number of simulations required for sensitivity testing as described above
for the 10-age class model. On the other hand, it was more
straightforward and did not require complicated assumptions (specified
below) for collapsing the values within age classes. It was used to verify
that the general magnitude of the results from the 10-age class model was
appropriate.



























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Assumptions Involved

In this initial stage of model development, insufficient data are
available to assign values to parameters in a manner that is expected to be
predictive of actual population change. Rather, the approach was to
specify the assumptions used in estimating the range of values that
reasonably could be expected in simulations. Each assumption may then be
evaluated and revised to increase the validity of the model in the future.

Subpopulations of manatees in different areas of Florida cannot be
assumed to be homogeneous with respect to population parameters. Trends
indicated by manatee counts at warm-water refuges have varied among six
areas (Eberhardt 1982). The values for mortality differ among four
geographic regions of Florida (O'Shea et. al. 1985). Therefore, a future
predictive model of the entire Florida population would probably consist of
submodels for each distinct area, or would somehow account for the range in
estimated parameter values. Conceptually, the present study focuses on a
subpopulation of the size (100-200 manatees) representative of manatees
attracted to each winter refuge. The following assumptions were used to
assign values to parameters in the simulations.


Age specific mortality

The longevity of manatees was assumed to be 50-60 years, based on
their similarity to dugongs and maximum known age of dugongs. Techniques
for aging manatees are currently in the process of development. The oldest
living known-age manatee has been in captivity since 1947, thus, is at
least 38 years old.

Very little information exists regarding age-specific mortality rates
of manatees, although there are some indications of relative differences
between immature and mature age classes in susceptibility to mortality
factors (O'Shea et al. 1985). High, moderate and low survival values used
in the 10-age class model are summarized in Table 1. The model specified
survival to weaning (ages 1-2, age class (0)), survival to subadult (ages
3-4, age class (0)), survival to adult (ages 5-6, age class (0)), and adult
survival (ages 7-66, age classes (1) to (10)).

The range of values for high, moderate, and low estimates of survival
rates were calculated in a manner that considered the number of carcasses
recovered in each age category, the effect of winter severity, and a range
of possible current population levels. The average number of carcasses
retrieved per year over 10 years (1975-1984) has been 28, 31, and 16 for
adults, subadults and calves, respectively (O'Shea et. al. 1985, Sirenia
Project, unpublished data). For three years (1977, 1981, 1982) identified
as having severely cold winters, the averages have been 39, 47, and 18 for
the same categories. Upper and lower limits of mortality rates were
estimated by dividing the number of carcasses by the upper and lower
estimate of the number of manatees in each category. Estimates assumed
that the population consists of 60% adults, 26% subadults, and 14% calves
(based on the initial age structure in Table 2), and that the population
may range from 1,000 to 3,000 manatees (Eberhardt 1982). The mortality
rates estimated for average years was 0.02-0.05 for adults, 0.04-0.12 for


























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subadults, and 0.04-0.11 for calves. The range of mortality rates for bad
years was 0.02-0.07 for adults, 0.06-0.18 for subadults, and 0.04-0.13 for
calves. Thus the range of mortality rates for adults was chosen as 0.02 to
0.07 with an intermediate value of 0.045. The range of mortality rates for
subadults was 0.04 to 0.18 with 0.08 as an intermediate value. The range
of mortality rates for calves was 0.04 to 0.13 with 0.08 as an intermediate
value.

Survival to weaning (2 yrs) was calculated as the square of the
probability of surviving each year, (p4), with p estimated as 0.96, 0.92,
and 0.87, respectively for high, moderate, and low estimates. These
estimates assume that 4 to 13% of calves die each year during the first two
years of dependency on the mother based on the number of carcasses
recovered and the range of estimated number of calves in the population.

Survival from weaning to subadult was calculated as tie square of the
probability of surviving each of the 3rd and 4th years, (p4), with p
estimated as 0.96, 0.92, and 0.82, respectively. The high and moderate
estimates assume that there is no reduction in the survival probability of
calves during the first two years after weaning. The low estimate assumes
that survival probability of weaned calves is lower than of dependent
calves. This assumption is based on the indication that independent
juveniles may be more succeptible to cold induced or other mortality,
compared to calves accompanying and nursing from their mothers.

Survival of subadults to age class (1) was calculated with the same
values as survival from weaning to subadult status. There was no
information indicating that a change in assumptions should be made between
the ages 3-4 and 5-6.

Annual adult survival was assumed to be 0.98, 0.955, 0.93, from the
ages 7-60, and 0.0 for the age class. 10 (61-66 yrs). There were no data
to indicate that adjustments should be made for age-specific differences in
the survival rate of adults.

A second approach using the collapsed 10-age class model was based on
a generalized curve for mammalian survival rates. The generalized
mammalian survivorship curve constructed by Barlow (unpub. manus.) was used
to derive survival probabilities per age class, with rates specified in
Table 2. Age-specific rates were collapsed for 6-year age classes by
multiplying the survival probabilities of all six ages within each age
class.

For the 50-age class model, survival rates were 0.92 for the years 1-6
and 0.955 for subsequent ages. These values were the same as the moderate
estimates used for the 10-age class model.


Age specific reproduction rates

Reproductive rates were assumed to differ only between immature and
mature manatees (Table 1). In the initial age class (1-6 years), females
were assumed not to reproduce. Although the minimum recorded age of first
parturition is 5 years, the probability of calf survival for such young








primiparous mothers is considered low (Rathbun., pers. commun.). In
captivity, age of first reproduction has been recorded at 8 years (Odell
1978).

The uncertainty regarding age-specific reproductive rates is high. In
this study, age was assumed to make no difference once females began
reproducing at age 6 years. The proportion of breeding females was chosen
as 0.70, 0.61 and 0.56 for high, moderate and low estimates, respectively.
There was internal inconsistency in the data used to calculate these
values, as follows.

The observed ratio of calves to adults counted on aerial surveys
ranges from 0.09 to 0.14 with a mean of 0.11 (Rathbun, pers. commun.). Out
of a population of 100 manatees, 50 can be assumed to be female. Of those
50, we can assume 60-70% or 30-35 manatees are of breeding age. If the
inter-birth interval is 2 years, half of those females would have calves
each year, so the expected number of calves would be 15-17. However, calf
mortality must be considered. Given the assumed calf survival rates, then
14-16 calves would be expected to be alive, and the females that lost
calves would be expected to cycle again, adding an additional 2-4 calves.
Thus the expected number of calves per 100 adults would be 16-20. Since
the actual number observed is lower, this may mean that not all females are
breeding at every opportunity. To estimate breeding proportions, the
observed over expected number of calves was calculated using high (14/20),
moderate (11/18) and low (9/16) values.

The litter size was assumed to be 1 manatee, although there is some
evidence that about 5% of litters are twins (Rathbun, pers. commun.). This
proportion seemed inconsequential for this preliminary general model. As
the interbirth interval is generally 2 years, it was assumed that those
females breeding within an age class would produce 3 calves over 6 years.
The probability of producing three calves per simulated time period (6
years) was set at 1.0.

Reproductive rates entered into the 50-age class model were in a
different format. The model required specification of the number of female
calves per adult female. A moderate value for the proportion of breeding
females was chosen (0.61). The sex ratio of calves was assumed to be 0.5
and the interbirth interval was assumed to be 2 years, resulting in a value
of 0.1525 female calves per adult female (0.5 x 0.5 x 0.61). As in the 10-
age class model, the assumption was no reproduction through age 6 and no
age-specific changes in reproductive rates in ages 7-50.


Age structure

Simulations were run with three age structures for the 10-age class
model (Table 2). The initial age structure was derived from the expected
survival of a cohort using an assumed constant survival rate of 0.92. This
age structure was biased more toward younger age classes, and would be
characteristic of a growing population. An even age structure was chosen
as a condition that might exist if recruitment was low and the population
was heavily biased toward adults. The adjusted age structure was derived
from the average final simulation using moderate values for all parameters.









It was assumed to be close to a stable age distribution.

The age structure used in the 50-age class model simulation is
specified in Table 3. It was derived such that the proportion of manatees
within each 6-year age class was comparable to the initial age structure
used in the 10-age class model. For example, the sum of manatees age 1-6
years was 39, the same as the proportion of manatees in the first (0) age
class of the 10-age class model.


RESULTS


Range of Projected Growth Rates

The average final rate of increase was chosen as an index of the
relative effect of the range in parameter values. The projected average
rates of population change using the 10-age class model ranged from 0.8476
to 1.3943 per 6-year period (Table 4). If we can assume all high estimates
for population parameters are valid, then manatee populations could
increase at a rate of 6.6% per year (Table 4). If all low estimates are
valid, the populations could decline at 2.5% per year. Medium values
indicate that the population could increase by 2% per year.

The growth rate calculated using the 50-age class model was
comparable. The primary eigenvalue was 1.0232, indicating that the
population was simulated to change at a rate of 2.3% per year. The final
total population size after 50 years was similar to that projected by the
10-age class model; however, the initial starting size was lower. (Figure 1).


Sensitivity of the 10-age Class Model

The relative sensitivity of the model to changes in parameter values
is summarized in Figure 2. The model appears to be most sensitive to
changes in adult survival probabilities. If the assumptions regarding
post-weaning survival are correct, then subadult survival has relatively
more effect on potential population declines than breeding proportions and
survival to weaning.

If the actual survival probabilities are closer to those typical of
large mammals in general, then the average rate of increase would be
somewhere between that obtained from simulations using the moderate and low
estimates for all parameters (Table 4). The survivorship curves resulting
from the estimated values were not sigmoid, in contrast to the generalized
mammal survivorship curve (Figure 3). However, the effect of this
difference did not appear to substantially affect results.

The simulated variations in age structure had relatively little effect
on average growth rates (Figure 1). The final total population projected
using the initial age structure differed from that using the adjusted, but
not the even age structures.









It was assumed to be close to a stable age distribution.

The age structure used in the 50-age class model simulation is
specified in Table 3. It was derived such that the proportion of manatees
within each 6-year age class was comparable to the initial age structure
used in the 10-age class model. For example, the sum of manatees age 1-6
years was 39, the same as the proportion of manatees in the first (0) age
class of the 10-age class model.


RESULTS


Range of Projected Growth Rates

The average final rate of increase was chosen as an index of the
relative effect of the range in parameter values. The projected average
rates of population change using the 10-age class model ranged from 0.8476
to 1.3943 per 6-year period (Table 4). If we can assume all high estimates
for population parameters are valid, then manatee populations could
increase at a rate of 6.6% per year (Table 4). If all low estimates are
valid, the populations could decline at 2.5% per year. Medium values
indicate that the population could increase by 2% per year.

The growth rate calculated using the 50-age class model was
comparable. The primary eigenvalue was 1.0232, indicating that the
population was simulated to change at a rate of 2.3% per year. The final
total population size after 50 years was similar to that projected by the
10-age class model; however, the initial starting size was lower. (Figure 1).


Sensitivity of the 10-age Class Model

The relative sensitivity of the model to changes in parameter values
is summarized in Figure 2. The model appears to be most sensitive to
changes in adult survival probabilities. If the assumptions regarding
post-weaning survival are correct, then subadult survival has relatively
more effect on potential population declines than breeding proportions and
survival to weaning.

If the actual survival probabilities are closer to those typical of
large mammals in general, then the average rate of increase would be
somewhere between that obtained from simulations using the moderate and low
estimates for all parameters (Table 4). The survivorship curves resulting
from the estimated values were not sigmoid, in contrast to the generalized
mammal survivorship curve (Figure 3). However, the effect of this
difference did not appear to substantially affect results.

The simulated variations in age structure had relatively little effect
on average growth rates (Figure 1). The final total population projected
using the initial age structure differed from that using the adjusted, but
not the even age structures.
































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class model (open circles), and the 10-age class model starting
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Relative effect of varying the values of population parameters.
The relative change in population growth rate (delta r) is the
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in parameters. Shaded bars indicate parameters set at high
values and white bars indicate parameters set at low values.


0.2
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1 00C0





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10


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Survivorship curves for four sets of survival values used in
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(squares) and low (crosses).


Figure 3.








DISCUSSION

Maximum Growth Rates

If the assumptions upon which this study was based are correct, the
maximum potential growth rate of manatee populations is very slow, on the
order of 2-6.6% per year. Given the uncertainty involved in estimating
population parameters, it is even possible that the Florida manatee
population currently has a negative growth rate (-2.5% per year).

These results are consistent with other studies of marine mammals.
Marsh and Marsh (unpub. manus.) found that the maximum projected dugong
population growth rates would be 10% per year, with more probable rates on
the order of 2-8% per year. Reilly and Barlow (in press) systematically
varied values for the parameters of calf survival, age at first
reproduction and calving interval in a study of potential rates of increase
for dolphin populations. Populations with a 2-3 year calving interval and
age of first reproduction at 7-9 years are not likely to experience growth
rates greater than 8% per year.

The low maximum potential rate of increase of manatee populations has
several management implications. If a catastrophic event occurred, the
population would take many years to recover. Trends in population growth
will be detectable only over several decades, given the current level of
error associated with measuring population indices (Packard, Siniff and
Cornell, in press). The balance between growth and decline of the
population is sensitive to changes of less than 10% in the annual adult and
subadult mortality rates.

The sensitivity of projected manatee population growth rates to adult
and subadult survival is consistent with assessments of other marine mammal
populations. The importance of adult survival rates to population growth
of species with the life history characteristics of marine mammals was
predicted by Eberhardt and Siniff (1977), and has been supported by the
studies of DeMaster (1981), Reilly and Barlow (in press).

The status of the Florida manatee population has been in question
since the apparent mortality rate (based on carcasses recovered) appears to
be close to 10% of the minimum estimated population size. The relation
between carcass recovery rates and population growth rate is likely to be
complex. In a general sense, mortality is offset by reproductive rates.
However, the age of first reproduction, and differences in mortality rates
among age classes can influence population growth rates in a manner that is
not intuitively obvious. Further development of age-structured models such
as those utilized in this study are essential to fully evaluate the status
of the population.


Uncertainty in Estimated Values

The survival rates used in the present study are more likely to be
biased high than low. The estimated values were based on recovery of
manatee carcasses, undoubtedly not representing all the manatee mortality
occurring each year. The high estimates of survival were based, in part,








DISCUSSION

Maximum Growth Rates

If the assumptions upon which this study was based are correct, the
maximum potential growth rate of manatee populations is very slow, on the
order of 2-6.6% per year. Given the uncertainty involved in estimating
population parameters, it is even possible that the Florida manatee
population currently has a negative growth rate (-2.5% per year).

These results are consistent with other studies of marine mammals.
Marsh and Marsh (unpub. manus.) found that the maximum projected dugong
population growth rates would be 10% per year, with more probable rates on
the order of 2-8% per year. Reilly and Barlow (in press) systematically
varied values for the parameters of calf survival, age at first
reproduction and calving interval in a study of potential rates of increase
for dolphin populations. Populations with a 2-3 year calving interval and
age of first reproduction at 7-9 years are not likely to experience growth
rates greater than 8% per year.

The low maximum potential rate of increase of manatee populations has
several management implications. If a catastrophic event occurred, the
population would take many years to recover. Trends in population growth
will be detectable only over several decades, given the current level of
error associated with measuring population indices (Packard, Siniff and
Cornell, in press). The balance between growth and decline of the
population is sensitive to changes of less than 10% in the annual adult and
subadult mortality rates.

The sensitivity of projected manatee population growth rates to adult
and subadult survival is consistent with assessments of other marine mammal
populations. The importance of adult survival rates to population growth
of species with the life history characteristics of marine mammals was
predicted by Eberhardt and Siniff (1977), and has been supported by the
studies of DeMaster (1981), Reilly and Barlow (in press).

The status of the Florida manatee population has been in question
since the apparent mortality rate (based on carcasses recovered) appears to
be close to 10% of the minimum estimated population size. The relation
between carcass recovery rates and population growth rate is likely to be
complex. In a general sense, mortality is offset by reproductive rates.
However, the age of first reproduction, and differences in mortality rates
among age classes can influence population growth rates in a manner that is
not intuitively obvious. Further development of age-structured models such
as those utilized in this study are essential to fully evaluate the status
of the population.


Uncertainty in Estimated Values

The survival rates used in the present study are more likely to be
biased high than low. The estimated values were based on recovery of
manatee carcasses, undoubtedly not representing all the manatee mortality
occurring each year. The high estimates of survival were based, in part,








DISCUSSION

Maximum Growth Rates

If the assumptions upon which this study was based are correct, the
maximum potential growth rate of manatee populations is very slow, on the
order of 2-6.6% per year. Given the uncertainty involved in estimating
population parameters, it is even possible that the Florida manatee
population currently has a negative growth rate (-2.5% per year).

These results are consistent with other studies of marine mammals.
Marsh and Marsh (unpub. manus.) found that the maximum projected dugong
population growth rates would be 10% per year, with more probable rates on
the order of 2-8% per year. Reilly and Barlow (in press) systematically
varied values for the parameters of calf survival, age at first
reproduction and calving interval in a study of potential rates of increase
for dolphin populations. Populations with a 2-3 year calving interval and
age of first reproduction at 7-9 years are not likely to experience growth
rates greater than 8% per year.

The low maximum potential rate of increase of manatee populations has
several management implications. If a catastrophic event occurred, the
population would take many years to recover. Trends in population growth
will be detectable only over several decades, given the current level of
error associated with measuring population indices (Packard, Siniff and
Cornell, in press). The balance between growth and decline of the
population is sensitive to changes of less than 10% in the annual adult and
subadult mortality rates.

The sensitivity of projected manatee population growth rates to adult
and subadult survival is consistent with assessments of other marine mammal
populations. The importance of adult survival rates to population growth
of species with the life history characteristics of marine mammals was
predicted by Eberhardt and Siniff (1977), and has been supported by the
studies of DeMaster (1981), Reilly and Barlow (in press).

The status of the Florida manatee population has been in question
since the apparent mortality rate (based on carcasses recovered) appears to
be close to 10% of the minimum estimated population size. The relation
between carcass recovery rates and population growth rate is likely to be
complex. In a general sense, mortality is offset by reproductive rates.
However, the age of first reproduction, and differences in mortality rates
among age classes can influence population growth rates in a manner that is
not intuitively obvious. Further development of age-structured models such
as those utilized in this study are essential to fully evaluate the status
of the population.


Uncertainty in Estimated Values

The survival rates used in the present study are more likely to be
biased high than low. The estimated values were based on recovery of
manatee carcasses, undoubtedly not representing all the manatee mortality
occurring each year. The high estimates of survival were based, in part,









on the assumption that the population was 3,000 manatees, and the low
survival estimates were based on the assumption that the population was
1,000 manatees.

The reproductive rates used in the present study were derived with
considerable uncertainty. If the ratios of calves to adults sighted on
aerial surveys are representative of reproduction within the total
population, then there is internal inconsistency in some of the assumptions
adopted with respect to manatee reproduction. These assumptions were that
the mean inter-birth interval is 2 years, that 60% of the population is of
reproductive age, that the sex ratio is 1:1, and that all females of
reproductive age reproduce. In the Crystal River area, the percentage of
females that are sexually mature has been estimated at 43.7% of known
individuals (Rathbun, pers. commun.). The percent females sexually mature
can be influenced by age at first reproduction, as well as the age
structure of the population. Reproductive rates will also be influenced by
calf mortality, as the inter-birth interval is likely to be reduced when a
female loses her calf prior to weaning.


Future Research Directions

Considering the results of this study, emphasis should be placed on
reducing the uncertainty associated with estimates of subadult and adult
survival, and the proportion of females reproducing each year. Given the
sensitivity of projected manatee population growth rates to adult survival,
mortality rates will have to be measured at an accuracy greater than 10%
prior to development of specific models that can be tested and used for
prediction of population change. This suggests that techniques yielding
estimates of average survival rates over a decade will not be suitable for
providing the degree of accuracy required (Packard and Nichols 1983).

The required data could be obtained by following marked individuals
over time. The data base already accumulated for Crystal River and Blue
Spring manatees provides a good start. However, it needs to be analyzed in
a manner that more directly provides the information required as input to
age-structured population models. The data base needs to be expanded to
include areas such as the Indian River, Riviera Beach, and Fort Myers.
Even if techniques for tagging manatees are not employed, useful
information can be obtained from following the individual reproductive
histories of scarred and naturally marked manatees.

To obtain estimates of survival rates, large numbers of manatees will
need to be identified. Out of a sample of 100 identified manatees, one
would expect only about 4-18 deaths to occur each year. If emigration is
occurring to a large extent it will be very difficult to detect whether the
disappearance of an individual is due to mortality or to movement out of a
study area. However, it would be very useful to determine if mortality is
greater than 10% per year; if it is, then the population is likely to be
very close to a negative growth rate that would indicate decline.

Additional work is needed to develop a computer program that can be
easily manipulated to explore the effects of changes in parameter values
for manatee populations. The 10-age structure model used in the present









study required several calculations to collapse the data from age-specific
data (in terms of years) to age-classes (in terms of 6-year categories).
The techniques for collapsing age-structured data involve several
considerations (Goodman, unpub. manus.), and more attention should be given
to the manner in which incomplete data are treated in development of a
working manatee population model. The program could be altered to provide
for more age classes, or a subprogram that calculates values collapsed
across age-classes could be added. Other alternatives include the use of
programs developed for other marine mammal populations (e.g. Gerrodette et.
al. 1983, Marsh and Marsh, unpub. manus.). The 10-age class model used in
the present study was designed for a seasonally breeding species. For
marine mammals without a breeding season, an element of adult female
mortality should be included in the calculation of natality (J. Barlow,
pers. commun.).


CONCLUSIONS

The maximum potential rate of increase for manatee populations is
likely to be within the range of 2-7% per year. If low estimates of
population parameters are valid, the Florida manatee population could be in
a state of decline (negative rate of change). In order of decreasing
relative effect on population growth rates, population parameters are adult
survival, post-weaning survival, proportion breeding females, survival to
weaning and the age structure. Each of the assumptions used in estimation
of population parameter values needs to be evaluated with respect to field
data before specific models projecting actual population changes can be
developed.


ACKNOWLEDGMENTS

This .study was supported by the U.S. Fish and Wildlife Service under
Cooperative Agreement No. 14-16-0009-1544, Research Work Order No.2, with
the Florida Cooperative Fish and Wildlife Research Unit. The work was
subcontracted to the Texas Agricultural Experiment Station (TAES), Texas
A&M University (TAMU). Administrative support has been provided by TAES,
the Department of Wildlife and Fisheries Sciences, TAMU, and the School of
Forest Resources and Conservation, Institute of Food and Agricultural
Sciences, University of Florida. I am grateful to L. Procarione for
assistance in running the simulations, to J. D. Nichols, J. E. Hines, W. E.
Grant and J. Wilber for providing the computer programs that were used for
the simulations, and to G. B. Rathbun, T. J. O'Shea, and R. K. Bonde for
providing the information used in estimating parameter values. In the
initial stages of the project, J. Barlow, D. P. DeMaster, J. D. Nichols,
and D. B. Siniff kindly shared with .me their knowledge of current modeling
techniques and provided guidance. J. Christian, E. Possardt, H. F.
Percival, and D. Wesley deserve special acknowledgment for their wisdom in
supporting my request for a micro-computer to conduct this work. I
appreciate the assistance of L. Giffen in preparation of the manuscript and
the reviews by J. Barlow, L. W. Lefebvre, T. J. O'Shea and E. E. Possardt.









study required several calculations to collapse the data from age-specific
data (in terms of years) to age-classes (in terms of 6-year categories).
The techniques for collapsing age-structured data involve several
considerations (Goodman, unpub. manus.), and more attention should be given
to the manner in which incomplete data are treated in development of a
working manatee population model. The program could be altered to provide
for more age classes, or a subprogram that calculates values collapsed
across age-classes could be added. Other alternatives include the use of
programs developed for other marine mammal populations (e.g. Gerrodette et.
al. 1983, Marsh and Marsh, unpub. manus.). The 10-age class model used in
the present study was designed for a seasonally breeding species. For
marine mammals without a breeding season, an element of adult female
mortality should be included in the calculation of natality (J. Barlow,
pers. commun.).


CONCLUSIONS

The maximum potential rate of increase for manatee populations is
likely to be within the range of 2-7% per year. If low estimates of
population parameters are valid, the Florida manatee population could be in
a state of decline (negative rate of change). In order of decreasing
relative effect on population growth rates, population parameters are adult
survival, post-weaning survival, proportion breeding females, survival to
weaning and the age structure. Each of the assumptions used in estimation
of population parameter values needs to be evaluated with respect to field
data before specific models projecting actual population changes can be
developed.


ACKNOWLEDGMENTS

This .study was supported by the U.S. Fish and Wildlife Service under
Cooperative Agreement No. 14-16-0009-1544, Research Work Order No.2, with
the Florida Cooperative Fish and Wildlife Research Unit. The work was
subcontracted to the Texas Agricultural Experiment Station (TAES), Texas
A&M University (TAMU). Administrative support has been provided by TAES,
the Department of Wildlife and Fisheries Sciences, TAMU, and the School of
Forest Resources and Conservation, Institute of Food and Agricultural
Sciences, University of Florida. I am grateful to L. Procarione for
assistance in running the simulations, to J. D. Nichols, J. E. Hines, W. E.
Grant and J. Wilber for providing the computer programs that were used for
the simulations, and to G. B. Rathbun, T. J. O'Shea, and R. K. Bonde for
providing the information used in estimating parameter values. In the
initial stages of the project, J. Barlow, D. P. DeMaster, J. D. Nichols,
and D. B. Siniff kindly shared with .me their knowledge of current modeling
techniques and provided guidance. J. Christian, E. Possardt, H. F.
Percival, and D. Wesley deserve special acknowledgment for their wisdom in
supporting my request for a micro-computer to conduct this work. I
appreciate the assistance of L. Giffen in preparation of the manuscript and
the reviews by J. Barlow, L. W. Lefebvre, T. J. O'Shea and E. E. Possardt.








REFERENCES

Barlow, J. Unpublished manuscript. Biological limits on current growth
rate of a spotted dolphin population (Stenella attenuata). National
Marine Fisheries Service. La Jolla, California. June 1984. 23 pp.

DeMaster, D. P. 1981. Incorporation of density dependence and harvest
into a general population model for seals. In: C. W. Fowler, ed.
Dynamics of Large Mammal Populations. J. Wiley & Sons, Inc.: New
York. pp.389-401.

Eberhardt, L. L. 1982. Censusing manatees. Manatee Population Research
Report No. 1. Tech. Rep. No. 8-1. Fl. Coop. Fish and Wildl. Res.
Unit. Univ. of Fl., Gainesville, Florida. 18pp.

Eberhardt, L. L., and D. B. Siniff. 1977. Population dynamics and marine
mammal management. J. Fish. Res. Board Can. 34:183-190. 18pp.

Gerrodette, T., D. Goodman, and J. Barlow. 1983. Two computer programs to
project populations with time-varying vital rates. NOAA Technical
Memorandum. NOAA-TM-NMFS-SWFC-28. 52pp.

Goodman, D. Unpublished manuscript. Discrete time parameterizations of
the life history. Montana State University, Bozeman, Montana.
September 1983. 65pp.

Goodman, D. 1978. Management implications of the mathematical demography
of marine mammals. NTIS PB-289678. 80pp.

Hines, J. E. and J. D. Nichols. Unpublished manuscript. Users manual for
SIMU.MENU and SIMU.PGM. Patuxent Wildlife Research Center, Laurel,
Md. 1984. 6pp.

Marsh, H., and L..M. Marsh. Unpublished manuscript. Population biology of
sirenia: implications for conservation. Paper presented at the IVth
International Theriological Congress. Edmonton, Alberta. 13-20
August 1985.

Nichols, J. D., G. L. Hensler, and P. W. Sykes. 1980. Demography of the
Everglade Kite: implications for population management. Ecol. Model.
9:215-232.

O'Shea, T. J., C. A. Beck, R. K. Bonde, H. I. Kochman, and D. K. Odell.
1985. An analysis of manatee mortality patterns in Florida, 1976-81.
J. Wildl. Manager 49:1-11.

Packard, J. M. and J. D. Nichols. 1983. Sample size estimates: a
preliminary analysis of sample sizes required for mark-recovery and
mark-resighting studies of manatees (Trichechus manatus) in Florida.
Manatee Population Research Report No. 4. Technical Report No. 8-4.
Fl. Coop. Fish and Wildl. Res. Unit. Univ. of Fl., Gainesville, Fla.
15pp.






19


Packard, J. M., D. B. Siniff, and J. A. Cornell. In press. Use of
replicate counts to improve indices of trends in manatee abundance.
Wildl. Soc. Bull.

Reilly, S. B., and J. Barlow. In press. Rates of increase in dolphin
population size. Fish. Bull.




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