SAMPLE SIZE ESTIMATES
A Preliminary Analysis of Sample Sizes
Required for MarkRecovery and MarkResighting Studies
of Manatees (Trichechus manatus) in Florida
1983
Jane M. Packard
and
James D. Nichols2
IFlorida Cooperative Fish and Wildlife Research Unit
School of Forest Resources and Conservation
117 NewinsZiegler Hall
University of Florida
IFAS
Gainesville, FL 32611
2Patuxent Wildlife Research Center
U.S, Fish and Wildlife Service
Laurel, Maryland 20811
Prepared for:
U.S. Fish and Wildlife Service
75 Spring Street, S.W.
Atlanta, GA 30303
Cooperative Agreement No. 141600091544
Research Work Order No. 2
Citation should read: Packard, J. M. and J. D. Nichols. 1983. Sample size
estimates: A preliminary analysis of sample sizes required for markrecovery
and markresighting studies of manatees (Trichechus manatus) in Florida.
Manatee Population Research Report No. 4. Technical Report No. 8. Florida
Cooperative Fish and Wildlife Research Unit. University of Florida,
Gainesville, Florida. 14 pp.
TABLE OF CONTENTS PAGE
RECOMMENDATIONS 1
INTRODUCTION 2
METHODS 2
Tags Recovered in Carcasses 2
Multiple Tagging Periods and Resighting 3
Single Tagging Period and Resighting 3
RESULTS 4
Tags Recovered in Carcasses 4
Multiple Tagging Periods and Resighting 4
Single Tagging Period and Resighting 11
DISCUSSION 11
CONCLUSIONS 13
LITERATURE CITED. 13
RECOMMENDATIONS
1. Estimation of survival rates by means of tags recovered from carcasses
should be a longterm (10 years) project. The estimate obtained would be
a mean annual rate for the duration of the study. The sample sizes
required to obtain yearly survival rate estimates (in contrast to a mean
rate) with the desired precision would be too high to be feasible.
About 40 to 210 manatees would need to be marked annually under a
10year program to obtain a mean survival rate with a coefficient of
variation of 0.05. A shorter program would require a larger sample size
to achieve the same level of precision. If a lower level of precision
is acceptable, additional analysis would be needed to estimate sample
size. However, a lower level of precision is not recommended.
2. Prior to the planning of markresighting studies, better estimates of
rates of emigration and sighting are needed. If emigration is high and
probability of sighting is low, an unreasonable number of manatees would
need to be marked to obtain estimates with the desired coefficient
of variation. Under conditions of low emigration and high sighting
probability, about 20 to 30 manatees would need to be captured during
each of five periods for JollySeber estimates of manatee abundance
and survival at a warmwater refuge. Under similar favorable
conditions, about 35 to 40 manatees would need to be marked at the
beginning of the season if marking occurred during only one capture
period.
3. Due to the relatively high numbers of animals that would need to be
marked at warmwater refuges, the possibility of using natural scar
patterns as marks needs to be further examined. However, since not all
animals can be identified in this manner, it would involve some changes
in assumptions and definitions of variables in the models currently
used. Appropriate models should be developed to approximate sample
sizes required for markresighting studies based on scar patterns.
2
INTRODUCTION
Approximate sample sizes that would be required to estimate abundance
and survival rates are needed to plan markrecovery studies of manatees
(Trichechus manatus) in Florida (Eberhardt 1982). Computer programs that
have been developed to estimate sample sizes required for waterfowl studies
are generally applicable to this question. Using these programs, sample
sizes have been estimated for three potential research projects: (a)
estimates of annual survival rates based on recovery of tagged.manatees via
the salvage of carcasses, (b) estimates of abundance and shortterm survival
based on repeated marking and resighting of manatees at a warmwater refuge,
and (c) estimates of abundance and shortterm survival based on one marking
effort and subsequent resightings at a warmwater refuge.
METHODS
Computer programs used in this analysis have been developed and are
available at Patuxent Wildlife Research Center (J. D. Nichols and J. E.
Hines, May 6, 1981 and August 27, 1979 Memoranda to Chief, Game Section,
Migratory Bird Habitat Research Laboratory). The analyses performed for each
potential project are as follows.
Tags Recovered in Carcasses
Models of birdband recoveries used to estimate survival rates of
waterfowl have been described by Brownie et al. (1978). The model used in
the present analysis (Model 1) is based on the situation where a sample of
adults is tagged and released into the population at roughly the same months,
for each of several successive years. Models permitting the inclusion of
young animals are also available, but we consider only the singleage model
for simplicity. The model also assumes that survival (S) and tag recovery
rates (f) are yearspecific but independent of the year of tagging.
Application of this model to the manatee situation is based on recovery
of tags by salvage of carcasses. Therefore, in the manatee situation,
recovery rate (f) is the product of annual mortality (1S) and a salvage rate
(q = probability that a dead manatee is salvaged). Salvage rates are not
precisely known and are likely to vary in different areas of Florida (O'Shea,
pers. comm.), so a range of values was used (q = 0.6, 0.7, 0.8). Survival
rates of manatees are not known, but probably are above 90% (Eberhardt 1982).
A range of survival rates (S = 0.80, 0.85, 0.90, 0.95) was used in this
analysis. Thus, the recovery rates (f = q(1S)) ranged from 0.03 to 0.16.
It is not necessary to specify expected population size when planning band
recovery experiments designed to estimate survival rates.
Estimates were calculated for research projects of three durations (4, 7
and 10 years). The sample sizes were computed to yield a desired coefficient
of variation ((CV(Si) = 0.10) for estimates of survival rates corresponding
to specific years. Sample sizes required to estimate the mean survival rate
over all years were computed to yield a coefficient of variation (CV(c)) of
0.05. The coefficient of variation of an estimator is the standard error of
the estimator divided by the estimator itself, so CV (S) = SE (S)/S. A small
coefficient of variation indicates a narrow confidence interval on the
estimator, while a large value indicates a wide confidence interval.
2
INTRODUCTION
Approximate sample sizes that would be required to estimate abundance
and survival rates are needed to plan markrecovery studies of manatees
(Trichechus manatus) in Florida (Eberhardt 1982). Computer programs that
have been developed to estimate sample sizes required for waterfowl studies
are generally applicable to this question. Using these programs, sample
sizes have been estimated for three potential research projects: (a)
estimates of annual survival rates based on recovery of tagged.manatees via
the salvage of carcasses, (b) estimates of abundance and shortterm survival
based on repeated marking and resighting of manatees at a warmwater refuge,
and (c) estimates of abundance and shortterm survival based on one marking
effort and subsequent resightings at a warmwater refuge.
METHODS
Computer programs used in this analysis have been developed and are
available at Patuxent Wildlife Research Center (J. D. Nichols and J. E.
Hines, May 6, 1981 and August 27, 1979 Memoranda to Chief, Game Section,
Migratory Bird Habitat Research Laboratory). The analyses performed for each
potential project are as follows.
Tags Recovered in Carcasses
Models of birdband recoveries used to estimate survival rates of
waterfowl have been described by Brownie et al. (1978). The model used in
the present analysis (Model 1) is based on the situation where a sample of
adults is tagged and released into the population at roughly the same months,
for each of several successive years. Models permitting the inclusion of
young animals are also available, but we consider only the singleage model
for simplicity. The model also assumes that survival (S) and tag recovery
rates (f) are yearspecific but independent of the year of tagging.
Application of this model to the manatee situation is based on recovery
of tags by salvage of carcasses. Therefore, in the manatee situation,
recovery rate (f) is the product of annual mortality (1S) and a salvage rate
(q = probability that a dead manatee is salvaged). Salvage rates are not
precisely known and are likely to vary in different areas of Florida (O'Shea,
pers. comm.), so a range of values was used (q = 0.6, 0.7, 0.8). Survival
rates of manatees are not known, but probably are above 90% (Eberhardt 1982).
A range of survival rates (S = 0.80, 0.85, 0.90, 0.95) was used in this
analysis. Thus, the recovery rates (f = q(1S)) ranged from 0.03 to 0.16.
It is not necessary to specify expected population size when planning band
recovery experiments designed to estimate survival rates.
Estimates were calculated for research projects of three durations (4, 7
and 10 years). The sample sizes were computed to yield a desired coefficient
of variation ((CV(Si) = 0.10) for estimates of survival rates corresponding
to specific years. Sample sizes required to estimate the mean survival rate
over all years were computed to yield a coefficient of variation (CV(c)) of
0.05. The coefficient of variation of an estimator is the standard error of
the estimator divided by the estimator itself, so CV (S) = SE (S)/S. A small
coefficient of variation indicates a narrow confidence interval on the
estimator, while a large value indicates a wide confidence interval.
2
INTRODUCTION
Approximate sample sizes that would be required to estimate abundance
and survival rates are needed to plan markrecovery studies of manatees
(Trichechus manatus) in Florida (Eberhardt 1982). Computer programs that
have been developed to estimate sample sizes required for waterfowl studies
are generally applicable to this question. Using these programs, sample
sizes have been estimated for three potential research projects: (a)
estimates of annual survival rates based on recovery of tagged.manatees via
the salvage of carcasses, (b) estimates of abundance and shortterm survival
based on repeated marking and resighting of manatees at a warmwater refuge,
and (c) estimates of abundance and shortterm survival based on one marking
effort and subsequent resightings at a warmwater refuge.
METHODS
Computer programs used in this analysis have been developed and are
available at Patuxent Wildlife Research Center (J. D. Nichols and J. E.
Hines, May 6, 1981 and August 27, 1979 Memoranda to Chief, Game Section,
Migratory Bird Habitat Research Laboratory). The analyses performed for each
potential project are as follows.
Tags Recovered in Carcasses
Models of birdband recoveries used to estimate survival rates of
waterfowl have been described by Brownie et al. (1978). The model used in
the present analysis (Model 1) is based on the situation where a sample of
adults is tagged and released into the population at roughly the same months,
for each of several successive years. Models permitting the inclusion of
young animals are also available, but we consider only the singleage model
for simplicity. The model also assumes that survival (S) and tag recovery
rates (f) are yearspecific but independent of the year of tagging.
Application of this model to the manatee situation is based on recovery
of tags by salvage of carcasses. Therefore, in the manatee situation,
recovery rate (f) is the product of annual mortality (1S) and a salvage rate
(q = probability that a dead manatee is salvaged). Salvage rates are not
precisely known and are likely to vary in different areas of Florida (O'Shea,
pers. comm.), so a range of values was used (q = 0.6, 0.7, 0.8). Survival
rates of manatees are not known, but probably are above 90% (Eberhardt 1982).
A range of survival rates (S = 0.80, 0.85, 0.90, 0.95) was used in this
analysis. Thus, the recovery rates (f = q(1S)) ranged from 0.03 to 0.16.
It is not necessary to specify expected population size when planning band
recovery experiments designed to estimate survival rates.
Estimates were calculated for research projects of three durations (4, 7
and 10 years). The sample sizes were computed to yield a desired coefficient
of variation ((CV(Si) = 0.10) for estimates of survival rates corresponding
to specific years. Sample sizes required to estimate the mean survival rate
over all years were computed to yield a coefficient of variation (CV(c)) of
0.05. The coefficient of variation of an estimator is the standard error of
the estimator divided by the estimator itself, so CV (S) = SE (S)/S. A small
coefficient of variation indicates a narrow confidence interval on the
estimator, while a large value indicates a wide confidence interval.
Multiple Tagging Periods and Resighting
To evaluate sampling intensity needed to estimate average population
size (N) using the JollySeber model (Jolly 1965, Seber 1965), coefficients
of variation for this parameter (N) were determined for a range of capture
probabilities (PC = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0) and
population sizes (N = 100, 200, 300, 400, 500). The population sizes were
chosen to correspond to the number of manatees that might be present at a
warmwater refuge. Maximum aerial counts at six sites over five years ranged
from 30 to 270 manatees (Eberhardt 1982). Considering that methods
independent of aerial surveys have yielded preliminary estimates nearly
double the maximum aerial count (Shane 1981, Packard 1981), the potential
range of population sizes could thus be 60 to 540 manatees, and we rounded it
to a range of 100 to 500 manatees.
The model assumes that manatees can be marked with individually
recognizable tags at five periods during a winter (assuming there will be
five cold spells) and that sampling is done by sighting of marked and
unmarked individuals at these periods. The probability of sighting is
unknown, but will presumably be a function of effort, so a range of values
was used (PS = 0.2, 0.4, 0.6, 0.8). The rate at which manatees leave
warmwater refuges (via death or emigration) between sampling periods is also
unknown, so calculations were performed for two shortterm survival rates
(PHI = 0.7, 0.9). Note that PHI corresponds to short time periods between
samplings and includes emigration loss, whereas S corresponds to 1 year and
includes only mortality.
For each value of survival (PHI) and population size (N), the
coefficient of variation of f (the mean estimate of population size) at each
of the values of sighting probability (PS) was plotted against sample size
(N PC). A level of precision indicated by a coefficient of variation less
than 0.10 is generally acceptable for such studies. Therefore, values
yielding an estimated coefficient of variation of 0.08 or less were
considered within the desired level of precision. Approximate sample sizes
required to obtain the desired coefficient of variation were identified by
interpolation of the point where the line (CV = 0.08) intersected the curve
for each probability of sighting (PS = 0.2, 0.4, 0.6, 0.8). These minimum
sample sizes were plotted against population size for each value of survival
rate (PHI = 0.7, 0.9). Sample sizes are the number of manatees that must be
captured for tagging at each cold spell, not all of which will be unmarked.
Single Tagging Period and Resighting
The computer program used was the same as for the multipletagging
project described above, but it was assumed that marks were applied on only
the first capture (cold spell) and only resightings were obtained at
subsequent cold spells. The same values for parameters were used. Rather
than extrapolating minimum sample sizes from plots as described above, the
lowest (to the nearest 0.01) capture probability (PCm) with a coefficient of
variation less than 0.10 was identified from examination of the output
tables. The minimum sample sizes were thus calculated as the product of the
population size and the capture probability (N PCm).
Multiple Tagging Periods and Resighting
To evaluate sampling intensity needed to estimate average population
size (N) using the JollySeber model (Jolly 1965, Seber 1965), coefficients
of variation for this parameter (N) were determined for a range of capture
probabilities (PC = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0) and
population sizes (N = 100, 200, 300, 400, 500). The population sizes were
chosen to correspond to the number of manatees that might be present at a
warmwater refuge. Maximum aerial counts at six sites over five years ranged
from 30 to 270 manatees (Eberhardt 1982). Considering that methods
independent of aerial surveys have yielded preliminary estimates nearly
double the maximum aerial count (Shane 1981, Packard 1981), the potential
range of population sizes could thus be 60 to 540 manatees, and we rounded it
to a range of 100 to 500 manatees.
The model assumes that manatees can be marked with individually
recognizable tags at five periods during a winter (assuming there will be
five cold spells) and that sampling is done by sighting of marked and
unmarked individuals at these periods. The probability of sighting is
unknown, but will presumably be a function of effort, so a range of values
was used (PS = 0.2, 0.4, 0.6, 0.8). The rate at which manatees leave
warmwater refuges (via death or emigration) between sampling periods is also
unknown, so calculations were performed for two shortterm survival rates
(PHI = 0.7, 0.9). Note that PHI corresponds to short time periods between
samplings and includes emigration loss, whereas S corresponds to 1 year and
includes only mortality.
For each value of survival (PHI) and population size (N), the
coefficient of variation of f (the mean estimate of population size) at each
of the values of sighting probability (PS) was plotted against sample size
(N PC). A level of precision indicated by a coefficient of variation less
than 0.10 is generally acceptable for such studies. Therefore, values
yielding an estimated coefficient of variation of 0.08 or less were
considered within the desired level of precision. Approximate sample sizes
required to obtain the desired coefficient of variation were identified by
interpolation of the point where the line (CV = 0.08) intersected the curve
for each probability of sighting (PS = 0.2, 0.4, 0.6, 0.8). These minimum
sample sizes were plotted against population size for each value of survival
rate (PHI = 0.7, 0.9). Sample sizes are the number of manatees that must be
captured for tagging at each cold spell, not all of which will be unmarked.
Single Tagging Period and Resighting
The computer program used was the same as for the multipletagging
project described above, but it was assumed that marks were applied on only
the first capture (cold spell) and only resightings were obtained at
subsequent cold spells. The same values for parameters were used. Rather
than extrapolating minimum sample sizes from plots as described above, the
lowest (to the nearest 0.01) capture probability (PCm) with a coefficient of
variation less than 0.10 was identified from examination of the output
tables. The minimum sample sizes were thus calculated as the product of the
population size and the capture probability (N PCm).
RESULTS
Large sample sizes would be required to estimate survival by means of
carcass recovery, but the sampling effort per year may be reduced by
extending the tagging and recovery over a longer period. Sample sizes
required for JollySeber estimates of abundance and survival at warmwater
refuges are dependent on the probability of sighting and survival rate (the
probability that an animal in the area at sampling period i is still in the
area in period i + 1). Thus, possible values for these variables should be
determined prior to designing markresighting programs.
Tags Recovered in Carcasses
For annual survival estimates from a 4year tagging and recovery program
(Table 1), sample sizes range from 380 to 2200 animals for first year
estimates, depending on salvage and survival rates. If a precise estimate of
survival rate for the final year of the program (i.e. the survival rate for
year 3) is desired, then thousands of animals would have to be marked each
year. If an average survival estimate over all years is desired, annual
sample sizes would range from 450 to 2360 animals.
If tagging and recovery are extended over 7 years (Table 2), the range
of sample sizes for first year survival rate estimates drops to 1801090
animals tagged annually. Sample sizes required for a mean estimate of
survival range from 100 to 500 animals.
Over a 10year period (Table 3), sample sizes required for a firstyear
estimate would range from 130 to 730 manatees. Sample sizes required to
estimate survival rate for the last year of a 10year study would range from
870 to 5090 manatees. For an estimate of the mean survival rate over 10
years, annual sample sizes would range from 40 to 210 animals.
Multiple Tagging Periods and Resighting
For fixed PS, N, and PHI, the coefficient of variation of N declines as
a curvilinear function of sample size (Figure 1). The range of the
coefficient of variation is greater for small populations (N = 100) than for
large populations (N = 500) at capture probabilities between 0.1 and 1.0
(0.1 <.PC .1.0). If a coefficient of variation less than 0.1 is desired,
the probability of sighting is a critical variable. With a sighting
probability of PS = 0.2, the desired level of precision can not be achieved
within the ranges of parameters specified in this model. At a higher
survival rate (Figure 2), sample sizes can be smaller to achieve the desired
coefficient of variation.
When the sighting probability is high (PS > 0.6), the size of the
population has little influence on the minimum sample size required to obtain
the desired level of precision (Figure 3). At a low survival rate (PHI =
0.7) and sighting probability (PS = 0.4), required sample sizes range from
about 140 to 180 manatees, depending on population size. If the probability
of sighting is as high as 0.6 or 0.8, sample sizes must be about 60 or 20
manatees, respectively. At a higher survival (PHI = 0.9), required sample
sizes range from about 10 to about 90, depending on the sighting probability
(Figure 3).
RESULTS
Large sample sizes would be required to estimate survival by means of
carcass recovery, but the sampling effort per year may be reduced by
extending the tagging and recovery over a longer period. Sample sizes
required for JollySeber estimates of abundance and survival at warmwater
refuges are dependent on the probability of sighting and survival rate (the
probability that an animal in the area at sampling period i is still in the
area in period i + 1). Thus, possible values for these variables should be
determined prior to designing markresighting programs.
Tags Recovered in Carcasses
For annual survival estimates from a 4year tagging and recovery program
(Table 1), sample sizes range from 380 to 2200 animals for first year
estimates, depending on salvage and survival rates. If a precise estimate of
survival rate for the final year of the program (i.e. the survival rate for
year 3) is desired, then thousands of animals would have to be marked each
year. If an average survival estimate over all years is desired, annual
sample sizes would range from 450 to 2360 animals.
If tagging and recovery are extended over 7 years (Table 2), the range
of sample sizes for first year survival rate estimates drops to 1801090
animals tagged annually. Sample sizes required for a mean estimate of
survival range from 100 to 500 animals.
Over a 10year period (Table 3), sample sizes required for a firstyear
estimate would range from 130 to 730 manatees. Sample sizes required to
estimate survival rate for the last year of a 10year study would range from
870 to 5090 manatees. For an estimate of the mean survival rate over 10
years, annual sample sizes would range from 40 to 210 animals.
Multiple Tagging Periods and Resighting
For fixed PS, N, and PHI, the coefficient of variation of N declines as
a curvilinear function of sample size (Figure 1). The range of the
coefficient of variation is greater for small populations (N = 100) than for
large populations (N = 500) at capture probabilities between 0.1 and 1.0
(0.1 <.PC .1.0). If a coefficient of variation less than 0.1 is desired,
the probability of sighting is a critical variable. With a sighting
probability of PS = 0.2, the desired level of precision can not be achieved
within the ranges of parameters specified in this model. At a higher
survival rate (Figure 2), sample sizes can be smaller to achieve the desired
coefficient of variation.
When the sighting probability is high (PS > 0.6), the size of the
population has little influence on the minimum sample size required to obtain
the desired level of precision (Figure 3). At a low survival rate (PHI =
0.7) and sighting probability (PS = 0.4), required sample sizes range from
about 140 to 180 manatees, depending on population size. If the probability
of sighting is as high as 0.6 or 0.8, sample sizes must be about 60 or 20
manatees, respectively. At a higher survival (PHI = 0.9), required sample
sizes range from about 10 to about 90, depending on the sighting probability
(Figure 3).
Table 1. Number of tags required for a 4year recovery program at several
rates of survival (S) and carcass recovery (q) .
YEAR
(i)
1
2
3
Mean
1
2
3
Mean
1
2
3
Mean
SALVAGE
RATE(q)
0.6
0.7
0.8
REQUIRED TAGS
S = U.80
570
740
1330
640
460
600
1110
530
380
500
950
450
S = 0.85
740
980
1790
820
610
810
1500
690
510
690
1290
590
S = 0.90
1100
1480
2700
1200
910
1240
2290
1020
770
1060
1980
880
S = 0.95
2200
3000
5470
2360
1860
2540
4660
2010
1600
2200
4060
1750
aTo obtain estimates for each year with a coefficient of variation
of 0.10 and mean annual estimates with a coefficient of variation
of 0.05. The sample sizes corresponding to the annual estimates (e.g.
for year i) reflect the number of animals to be marked in each year of the
study in order to estimate Si with the desired level of precision. For
example, if S = 0.80 and q = 0.60, then approximately 570 animals should
be marked during each of the 4 years of the study in order to estimate
S such that CV (S ) = 0.10. To estimate S approximately 1330
animals should be marked during each of the 4 years of the study.
^ ^^^ ^ = 
Table 2. Number of tags required for a 7year recovery program at several
rates of survival (S) and carcass recovery (q) .
YEAR
(i)
1
2
3
4
5
6
Mean
1
2
3
4
5
6
Mean
1
2
3
4
5
6
Mean
SALVAGE
RATE(q)
0.6
0.7
0.8
REQUIRED TAGS
S = 0.80
310
320
370
470
680
1250
140
240
250
290
380
550
1050
120
180
190
230
310
460
890
100
S = 0.85
380
410
490
630
910
1680
180
300
330
390
510
750
1410
150
240
260
320
420
630
1210
130
S = 0.90
550
610
740
960
1380
2550
260
440
500
610
790
1150
2160
220
360
410
510
670
990
1860
190
S = 0.95
1090
1240
1510
1960
2820
5180
500
910
1040
1260
1650
2390
4410
430
770
880
1080
1420
2060
3840
370
aTo obtain estimates for each year with a coefficient of variation of
0.10 and mean annual estimates with a coefficient of variation of
0.05. The sample sizes corresponding to the annual estimates (e.g.
for year i) reflect the number of animals to be marked in each year of the
study in order to estimate S. with the desired level of precision. For
example, if S = 0.80 and q = 0.60, then approximately 310 animals should
be marked during each of the 7 years of the study in order to estimate
S such that CV (S ) = 0.10. To estimate S approximately 1250
animals should be marked during each of the 7 years of the study.
__ __ __
Table 3. Number of tags required for a 10year recovery program at several
rates of survival (S) and carcass recovery (q)a.
YEAR
(i)
1
2
3
4
5
6
7
8
9
Mean
1
2
3
4
5
6
7
8
9
Mean
1
2
3
4
5
6
7
8
9
Mean
SALVAGE
RATE(q)
0.6
0.7
0.8
REQUIRED TAGS
S = 0.80
230
230
240
260
300
360
460
660
1230
60
170
160
180
200
230
280
370
540
1030
50
120
120
130
150
170
220
300
450
870
40
S = 0.85
270
270
300
340
390
480
620
890
1650
80
210
210
230
260
310
380
500
730
1390
60
150
160
170
200
240
310
410
620
1190
50
S = 0.90
370
390
440
500
590
720
940
1360
2500
110
290
310
340
400
470
590
780
1130
2120
90
230
240
280
320
390
490
650
970
1830
80
S = 0.95
730
780
880
1010
1200
1480
1920
2770
5090
210
590
640
720
840
1000
1240
1620
2350
4330
180
490
540
610
710
850
1060
1390
2030
3760
150
aTo obtain estimates for each year with a coefficient of variation of
0.10 and mean annual estimates with a coefficient of variation of
0.05. The sample sizes corresponding to the annual estimates (e.g.
for year i) reflect the number of animals to be marked in each year of the
study in order to estimate Si with the desired level of precision. For
example, if S = 0.80 and q = 0.60, then approximately 230 animals should
be marked during pach of the 10 years of the study in order to estimate
S such that CV (S ) = 0.10. To estimate S9, approximately 1230
animals should be marked during each of the 10 years of the study.
_ __ ~
N=100
40 60
SAMPLE SIZE
0.2
I
0.4
0.8
z
80 100 L
lU
0.4 \ N=200
0.3
0.2 Ps.
0.2
0.1
0.4
40 80 120 160 200
SAMPLE SIZE
I 0.3
> 0.2
I 
0.1
0
h
N=300
0.2
PS=
0.2
0.4
S0.6
0.8
60 120 180 240 300
SAMPLE SIZE
SN=400
0.2
80 160 240 320 400
SAMPLE SIZE
N=500
PS=
100 200 300 400 500
SAMPLE SIZE
Assuming manatee survival rate of 0.7, curves show the relation
of sample size to the coefficient of variation of population
estimates, dependent on population size (N) and probability of
sighting (PS).
SURVIVAL=0.7
z
0
S0.4
z
0
S0.2
Figure 1.
z 0.3
0.2
W 0.1
U.
N=100
PS=
0.2
0.6
:0.8
I,
f
z
U
LL
u
(J
U
20 40 60 80 100
SAMPLE SIZE
N=200
PS.
0.2
0.4
40 80 120 160 200
SAMPLE SIZE
N=300
PS=
0.2
_____ ___ io0.8
60 120 180 240 300
SAMPLE SIZE
N=400
PS=
 0__.2
0.46
0.8
80 160 240 320 400
SAMPLE SIZE
N=500
PS6
0 0 6
^ ::::="1 1'! ,I IaB06
100 200 300
SAMPLE SIZE
400 500
Figure 2. Assuming manatee survival rate of 0.9, curves show the relation
of sample size to the coefficient of variation of population
estimates, dependent on population size (N) and probability of
sighting (PS).
SURVIVAL= 0.9
Z 0.4
0
O
0.3
5 0.2
C,
U
0 0.1
U
SURVIVAL = 0.7
PROBABILITY OF
SIGHTING (PS)=
160 
a 0.4
120 1
801
o 0.6
40 1
* 0.8
100 200 300 400 500
POPULATION SIZE (N)
160 F SURVIVAL= 0.9
PROBABILITY OF
SIGHTING (PS)=
a 0.4
o 0.6
* 0.8
100 200 300 400 500
POPULATION SIZE (N)
Sample sizes required to obtain population estimates with a
coefficient of variation below 0.1, dependent on survival rate
and probability of sighting.
120 1
80 1
40 
Figure 3.
200 
Single Tagging Period and Resighting
To obtain the desired coefficient of variation, sample sizes would need
to be higher if manatees are tagged during one period at the beginning of a
winter compared to multiple tagging periods during the winter. At a high
sighting probability (PS = 0.8), an initial sample of about 15 manatees would
have to be marked at a high survival rate (PHI = 0.9) and about 35 manatees
for a lower survival rate (PHI = 0.7) (Table 4). Required sample sizes
increase substantially as the probability of sighting decreases.
DISCUSSION
Sample sizes calculated in these analyses indicate that under certain
conditions, it will be impractical to tag enough manatees to obtain estimates
of population parameters that are within the desired level of precision. For
example, under the best recovery conditions (S = 0.8, q = 0.8) large numbers
of manatees (950 manatees per year) would have to be marked over 4 years to
obtain precise annual survival rate estimates for all years of a 4year
program of carcass recovery. Over 10 years, annual sample sizes for
estimates of annual survival rate through the eighth year will still be large
(450 manatees per year) to obtain the same level of precision. Because the
total population may be as low as 1,000 to 3,000 manatees (Eberhardt 1982),
annual estimates of survival rates within the desired coefficient of
variation (CV = 0.1) may not be feasible. Because of the low tag recovery
rates and relatively small population size, band recovery models such as
those used for waterfowl populations will not provide precise annual survival
rate estimates for Florida manatees.
If a mean estimate of survival is adequate and recovery conditions are
good, about 40 manatees would need to be tagged each year of a 10year
program, and 450 manatees would need to be marked each year of a 4year
program. However, if recovery conditions are poor (q = 0.6, S = 0.95), it
would not be possible to mark enough manatees to obtain mean survival
estimates with the desired precision. Therefore, before initiating a program
of tagrecovery via salvage of carcasses, it is necessary to decide whether a
lower level of precision is acceptable and whether estimates of mean annual
survival rates will yield the information needed for management purposes.
Emigration rates (1 PHI) and probability of sighting (PS) need to be
determined before evaluating the feasibility of obtaining estimates of
population parameters via tagging and resighting at warmwater refuges. If
emigration is high (PHI = 0.7), the probability of sighting must be as high
as PS = 0.8 for a multipletagging program to be feasible; about 20 animals
would have to be captured at each tagging period. If emigration is low (PHI
= 0.9) it might be possible to conduct the studies even if the sighting
probability is as low as PS = 0.6; however, sample sizes would need to be
about 30 manatees. At sighting probabilities lower than PS = 0.6, sample
sizes would have to be too large to be feasible.
If tags are put out only at the beginning of a season, the probability
of sighting must be high (PS = 0.8) for the project to be feasible. At a low
rate of emigration (PHI = 0.9), at least 15 to 20 manatees should be tagged.
If the emigration rate is higher (PHI = 0.7), at least 35 to 40 manatees
should be tagged.
Table 4. Sample sizes
(N), probabil
PS = 0.2
PC (N*PC)
(N*PC) required for a range of population size
ities of sighting (PS) and survival rate (PHI).
PS = 0.4
PC (N*PC)
PS = 0.6
PS = 0.8
PC (N*PC)
PHI = 0.9
100
200
300
400
500
PHI = 0.7
100
200
300
400
500
.16
.07
.05
.04
.03
.34
.16
.11
.08
.07
aCalculated from the minimum probability of
an estimate of mean population size with a
than 0.10.
capture (PC) that will yield
coefficient of variation less
The potential disturbance associated with tagging large numbers of
manatees at a warm water refuge should be considered, because markrecovery
models assume the behavior of marked animals (specifically, probability of
emigrating and of being sighted) is not changed. Under optimal conditions,
the number of tagged manatees required may be within the range that could be
obtained by recognition of distinct scar patterns. However, slightly
different assumptions would be involved in a markrecognition program based
on distinct scar patterns, and sample sizes would need to be calculated
specifically for such a program.
CONCLUSIONS
1. Precise estimation of annual survival rates by tag recovery from
carcasses is not feasible due to the large sample sizes that would be
required.
2. An estimate of the mean annual survival rate over 10 years would be
feasible by means of tag recovery in carcasses if the recovery rate
(product of mortality and salvage rates) is high. About 40 to 210
manatees would need to be tagged each year.
3. A high rate of emigration and low probability of sighting tags would
make a program involving multiple marking periods infeasible, due to
large sample sizes. However, if the probability of sighting is high,
about 10 to 30 manatees would need to be captured at each marking
period, depending on emigration rates.
4. If sighting probability is high, about 15 to 40 manatees would need to
be marked for estimates from a markresighting program that involved
only one initial tagging period. When total marking effort is
considered, a singletaggingperiod program is more efficient than a
program relying on multiple tagging periods. However, the potentially
greater disturbance associated with tagging many manatees at one time
should be considered.
LITERATURE CITED
Brownie, D., D. R. Anderson, K. P. Burnham, and D. S. Robson. 1978.
Statistical inference from band recovery data: A handbook. U.S.
Fish and Wildlife Service, Resource Publication No. 130. 212 pp.
Eberhardt, L. L. 1982. Censusing Manatees. Prepared for U.S. Fish and
Wildlife Service, P.O. No. 401810414. Manatee Population Research
Report No. 1. Technical Repoft No. 81. Florida Cooperative Fish and
Wildlife Research Unit, GainesvilTe, FL. 18 pp.
Jolly, G. M. 1965. Explicit estimates from capturerecapture data with
both death and immigrationstochastic model. Biometrika 52(1/2):
225247.
The potential disturbance associated with tagging large numbers of
manatees at a warm water refuge should be considered, because markrecovery
models assume the behavior of marked animals (specifically, probability of
emigrating and of being sighted) is not changed. Under optimal conditions,
the number of tagged manatees required may be within the range that could be
obtained by recognition of distinct scar patterns. However, slightly
different assumptions would be involved in a markrecognition program based
on distinct scar patterns, and sample sizes would need to be calculated
specifically for such a program.
CONCLUSIONS
1. Precise estimation of annual survival rates by tag recovery from
carcasses is not feasible due to the large sample sizes that would be
required.
2. An estimate of the mean annual survival rate over 10 years would be
feasible by means of tag recovery in carcasses if the recovery rate
(product of mortality and salvage rates) is high. About 40 to 210
manatees would need to be tagged each year.
3. A high rate of emigration and low probability of sighting tags would
make a program involving multiple marking periods infeasible, due to
large sample sizes. However, if the probability of sighting is high,
about 10 to 30 manatees would need to be captured at each marking
period, depending on emigration rates.
4. If sighting probability is high, about 15 to 40 manatees would need to
be marked for estimates from a markresighting program that involved
only one initial tagging period. When total marking effort is
considered, a singletaggingperiod program is more efficient than a
program relying on multiple tagging periods. However, the potentially
greater disturbance associated with tagging many manatees at one time
should be considered.
LITERATURE CITED
Brownie, D., D. R. Anderson, K. P. Burnham, and D. S. Robson. 1978.
Statistical inference from band recovery data: A handbook. U.S.
Fish and Wildlife Service, Resource Publication No. 130. 212 pp.
Eberhardt, L. L. 1982. Censusing Manatees. Prepared for U.S. Fish and
Wildlife Service, P.O. No. 401810414. Manatee Population Research
Report No. 1. Technical Repoft No. 81. Florida Cooperative Fish and
Wildlife Research Unit, GainesvilTe, FL. 18 pp.
Jolly, G. M. 1965. Explicit estimates from capturerecapture data with
both death and immigrationstochastic model. Biometrika 52(1/2):
225247.
14
Packard, J. M. 1981. Abundance, distribution, and feeding habits of
manatees (Trichechus manatus) wintering between St. Lucie and Palm Beach
Inlets, Florida. Report prepared for the U.S. Fish and Wildlife Service
under contract No. 141600480105. 142 pp.
Seber, G. A. 1965. A note on the multiplerecapture census. Biometrika
52(1/2):249259.
Shane, S. H. 1981. Abundance, distribution and use of power plant effluents
by manatees (Trichechus manatus) in Brevard County, Florida. NTIS No.
PB81147019. Dept. of Comm. Springfield, VA. 244 pp.
