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Recovery of the whooping crane Grus americana
Biological Conservation 45 (1988) 11-20
Recovery of the Whooping Crane Grus americana
Clark S. Binkley & Richard S. Miller School of Forestry and Environmental Studies, Yale University, 205 Prospect Street, New Haven, Connecticut 06511, USA (Received 28 August 1987; accepted 30 August 1987)
A BSTRA CT Officially listed as 'endangered', the whooping crane Grus americana currently receives strong legal protection under the Endangered Species Act of 1973. To remove it from endangered status, the official Whooping Crane Recovery Plan requires 40 nesting pairs in the main population which migrates from Wood Buffalo National Park, NWT, Canada to the Aransas National Wildlife refuge on the Texas gulf coast. Two demographic models of the migratory population indicate that this criterion for recovery is likely to be met within the next decade.
INTRODUCTION The primary, wild population of the whooping crane Grus americana nests in W o o d Buffalo National Park (WBNP), NWT, Canada and winters at the Aransas National Wildlife Refuge (ANWR) and on a few associated islands on the gulf coast of Texas. The total population of this species has probably never been large, but it did have a wide distribution in North America before European colonisation of the continent (Allen, 1952). Fossil remains have been found from the Upper Pliocene in Idaho (Miller, 1944) and the Pleistocene in California, Kansas and Florida (Wetmore, 1931, 1956). Its decline in numbers coincided with the agricultural development of its traditional breeding areas in the prairies in the 1800s and early 1900s. The last nesting pair of whooping cranes in the prairies was recorded at Muddy Lake, Saskatchewan, Canada in 1922. 11 Biol. Conserv. 0006-3207/88/$03"50 © 1988 Elsevier Applied Science Publishers Ltd, England. Printed in Great Britain
12
Clark S. Binkley, Richard S. Miller
Legislation protecting the whooping crane was first enacted with the ratification of the Migratory Bird Treaty between the United States and Great Britain (Canada) in 1916. In 1937 the Aransas National Wildlife Refuge was established on the gulf coast of Texas to protect its only known wintering grounds, but it was not until 1954 that the nesting area was discovered at WBNP, which had been set aside by the Canadian government as a reserve and management area for the wood bison Bison bison athabascae in 1922 (Raup, 1933). After the establishment of the Aransas National Wildlife Refuge, an annual census of wintering whooping cranes was begun in 1938 and has continued with annual counts of young birds and birds with adult plumage. A total of 18 birds was counted in the winter of 1938, the number dropped to 16 in 1941, and increased to 110 in 1986 (E. Kuyt, pers. comm.). However, this overall increase has been accompanied by a 10-year periodicity in the relative abundance of whooping cranes (Boyce & Miller, 1985; Boyce, 1987), beginning with the decrease to 16 birds in 1941. The cause of this periodicity is not known, although it may be related to rainfall and predation on the nesting grounds. Passage of the Endangered Species Act of 1973 resulted in the listing of the whooping crane as an endangered species and the establishment of a Whooping Crane Recovery Team to formulate a Recovery Plan. A goal of this plan is to remove the whooping crane from the endangered category to the threatened category. The criteria for 'downlisting' are (i) a population of 40 nesting pairs at Wood Buffalo National Park and (ii) a population of 25 nesting pairs at each of 2 other sites (USFWS, 1986). In previous work we estimated the survivorship curve for the migratory whooping crane population (Binkley & Miller, 1980), and demonstrated that a demographic model based on this curve is consistent with other observed life history information about the population, including rate of increase, size of the breeding population and annual recruitment (Binkley & Miller, 1983). Taking advantage of nine additional years of data, this paper first revises these estimates and then uses the revised estimates to forecast the future population levels and to infer when the Recovery Team's target of 40 nesting pairs in the W B N P - A N W R population will be reached.
THE MODELS
A single equation model A simple projection can be based on a single equation depicting the population development over time. We previously found that the
The whooping crane
13
p o p u l a t i o n trace for the w h o o p i n g crane population separates into two periods during the mid-1950s. A simple model to account for this shift is In N(t) = In N(0) + rlt + r2t'
(1)
where
N(t) = p o p u l a t i o n size at time t r 1 = growth rate prior to t* r 2 = growth rate after t* t' - ~'0
It - -
t < t* t*
t >_ t*
In other words, the p o p u l a t i o n grows at rate rl until t* and then at a rate of r~ + r 2 after that time. A l t h o u g h the parameters of this equation can be estimated in m a n y ways, ordinary least squares regression (corrected for first-order serial correlation a m o n g the residuals) gave a better fit than did either a m a x i m u m likelihood procedure or nonlinear least squares. Fitting eqn (1) using an iterative generalised least squares procedure to account for first order autocorrelation in the residuals produced the following model: In N(t) = - 35"82 + 0-020 02r I + 0"021 60r 2 (--2"64) (2-87) (2"21)
(2)
where t * = 1 9 5 7 , R = 0 . 8 3 1 , F ( 2 , 4 6 ) = 1 1 3 . 2 and a serial correlation coefficient = 0.4459 (t-statistics are in parentheses). The current p o p u l a t i o n growth rate is thus 0.0416 or slightly less t h a n the figure of 0.0425 we f o u n d previously (Binkley & Miller, 1983). A t-test of the hypothesis that the growth rate has declined since 1978 is rejected (t = - 0 . 0 2 9 2 with 45df.) Figure 1 shows a projection of this model to 2020 along with the 90% confidence intervals. These data can be used to infer the year of recovery. The age of first breeding in captive females is about five years (Erickson, 1976), and this age has been confirmed for the wild W B N P - A N W R population by Kuyt & Goossen (1987).~ The n u m b e r of nesting pairs can be estimated by assuming a 1:1 sex ratio 2 and that all sexually m a t u r e birds form pairs. A l t h o u g h this model of pair formation overstates the h u m b e r of nesting pairs by 14.6%, 1 In a sample o f banded birds in the W B N P - A N W R population, Kuyt & Goossen (1987) found first nesting occurring at 5-0 +__ 1.18 years (n = 14) and first fertile eggs occurring at 5-4 + 0.84years (n = 10). Our fecundity estimates are based on nesting pairs so the younger age is the more appropriate estimate of the age at first breeding to use in our demographic model. 2 In a sample of 22 banded young in 1980, 1981 and 1984, Kuyt & Goossen (1987) found the sex ratio at the age o f 2 months to be exactly 1:1.
14
Clark S. Binkley, Richard S. Miller ~ °
!
0
10
I"
!
i
i i i i i i i i iii
i i i i i i i i i i i i i
1967
1950
1960
I I I I
I I I I I I I I I I I I
WIT
1979 y ~
1990
2000
2010
2020
Fig. 1. History and projection of the whooping crane population, 1938-2020. The growth rate of the W B N P - A N W R population increased from 0-0200 prior to 1957 to 0.0416 after that time. The vertical dashed line shows the beginning of the forecast period. The heavy solid line shows the mean estimates of population numbers, and the lighter lines show the smoothed upper and lower 90% confidence intervals for the forecast. The heavy horizontal line is drawn at 153 birds, the size of the population needed to produce 40 nesting pairs. Achieving 40 nesting pairs in the W B N P - A N W R population is a primary criterion established by the Whooping Crane Recovery Team for downlisting the species from endangered to threatened status. The population forecast indicates that this recovery target will be reached in 1997. The upper and lower confidence bands reach this level in 1991 and 2005, respectively.
the bias is not statistically significant (Binkley & Miller, 1983). The stationary age distribution of the population can be estimated from the survivorship curve presented below (Table 1). Using this age distribution and model of nesting pairs, we can conclude that a total population of 153 will provide 40 breeding pairs. 3 Figure 1 shows that this population level will be reached in 1997. The upper 90% confidence interval reaches this level in 1991, and the lower 90% confidence interval reaches this level in 2005.
The whooping crane
15
TABLE 1 Estimated Age-specific Survivorship/(x), Mortality q(x), and Age Distribution C(x) for the Migratory Whooping Crane Population X
(Age in years)
l(x)
SE[I(x)]
q(x)
C(x)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
1-000 0 0-9425 0.8923 0.842 8 0-794 2 0.746 5 0.699 6 0-653 5 0.608 3 0.564 0 0.520 5 0.477 8 0.4360 0.3950 0.3548 0.3156 0.277 1 0-2395 0-2028 0-t669 0.131 8 0.097 58 0.064 21 0.031 68
-0.1554 0-1266 0,101 40 0.080 58 0.065 38 0.057 35 0.056 80 0.061 72 0-069 24 0-077 23 0.084 51 0-09043 0-09465 0-09694 0-09719 0.095 32 0-091 28 0.08502 0.07653 0-06578 0-052 76 0.037 46 0.019 88
0.057 5 0.0533 0.0555 0-057 7 0-060 1 0.062 8 0.065 9 0-069 2 0-072 8 0.077 1 0.082 0 0.087 5 0.0940 0.101 8 0-1105 0.1220 0-135 7 0-1532 0.1770 0-2103 0.2596 0-342 0 0.506 6 1.000
0.115 2 0-1042 0.0946 0.085 7 0-0775 0.069 8 0.062 8 0-056 3 0.050 2 0.044 7 0.039 6 0.034 8 0-0305 0.0265 0-0228 0.0195 0-0164 0-0136 0.0110 0-0087 0-0066 0-004 7 0.003 0 0.001 4
x refers to the age of the cohort. Because the survivorship curve is estimated using census data taken at ANWR, the actual age of the cohort is approximately 1/2 year older than the value of x given in this table. l(x) is the fraction of a cohort which survives to age x. q(x) = [l(x) - l(x + l)]/l(x), q(x) is the fraction of the population in age class x which dies prior to reaching age x + 1. C(x) =l(x)exp(-rx)/~S=ol(i)exp(-ri) (Krebs, 1972). C(x) is the proportion of the population between age x and .~ + 1 in the stationary age distribution.
3 From Table 1, the fraction of the population in non-breeding ages (less than 5) equals 0.4771. The fraction of the population in breeding ages is then 1 -0.4771 = 0'5229. Forty breeding pairs requires 80 birds of breeding age, or a total population of 80/.0-5229 = 153 birds. K uyt & Goossen (1987) estimate that the non-breeding individuals comprise only 34.2% of the population, implying that a total population of 122 will produce 40 breeding pairs.
16
Clark S. Binkley, Richard S. Miller
An age-class model T h e e n d a n g e r e d status o f the w h o o p i n g crane, a n d its c o n s e q u e n t p r o t e c t i o n , has m a d e it difficult to o b t a i n the d a t a n e e d e d to estimate key p o p u l a t i o n p a r a m e t e r s . Y o u n g - o f - t h e - y e a r can be r e c o g n i s e d b y their juvenile plumage, b u t after their first winter m o u l t c a n n o t be distinguished f r o m the white adults. T h e a n n u a l w i n t e r census at A N W R r e c o r d s first-year juveniles s e p a r a t e l y f r o m birds in adult p l u m a g e which m a y o r m a y n o t be sexually m a t u r e . A l t h o u g h b a n d i n g studies have been c o n d u c t e d o n the m i g r a t o r y p o p u l a t i o n o n l y since 1977, the age s t r u c t u r e o f the entire p o p u l a t i o n is implicitly k n o w n because the n u m b e r o f y o u n g each y e a r has been r e c o r d e d since 1938. Binkley & Miller (1980) e x p l o i t e d this implicit a g e - s t r u c t u r e i n f o r m a t i o n to estimate the s u r v i v o r s h i p c u r v e for the m i g r a t o r y p o p u lation. Since t h a t time, nine m o r e years o f census d a t a have b e c o m e available, a n d some o f the earlier d a t a h a v e been revised. T a b l e 1 shows a revised estimate o f the survivorship curve 4 a l o n g with the s t a n d a r d e r r o r s o f the estimates, the implied age-specific m o r t a l i t y rates a n d the f r a c t i o n o f the p o p u l a t i o n in e a c h age class. 4 Following Binkley & Miller (1980), the survivorship curve was estimated as follows. Ifa(t) is the number of birds in adult plumage observed in year t,y(t) is the number ofyoung observed in year t and T is the maximum longevity, then by definition T
a( t)
= ) , l(x)j,(t - x)
(F1)
x=l
All of the variables in this expression are known except the T values of l(x) The number of observations in the census is inadequate to estimate the l(x) values directly, so instead the functional relationship between x and l(x) is approximated by l(x) = a 0 + a l x + a2 X2
(F2)
The power series approximation to the true l(x) curve was truncated at three terms on the basis of statistical fit and conformance to prior expectations about the shape of l(x) (i.e. l(x) is non-increasing). Substituting F2 into F1 gives an expression, linear in the parameters ao, a~ and a2, which can then be estimated using ordinary least squares regression. This technique is known as polynomial distributed lags (or Almon lags) in the econometrics literature (Johnston, 1972). Because of serial correlation in the residuals, the model was estimated using an iterative generalised least squares procedure. The lag-one serial correlation coefficient is estimated from the residuals and then is used to modify the variance--covariance matrix in a GLS estimate. The process is iterated until the desired convergence in the coefficients is obtained. The value of Twas estimated as follows. The l(x) curve was constrained so that I(T) = 0. The l(x) curve was estimated for several values of 7",and then the maximum likelihood estimate of T was found by inspection. The resulting equation has T=24, R2=0.6077, and F(I, 24) = 37-2. Table I gives the estimated values of I(x).
The whooping crane
17
The estimated m a x i m u m longevity T remains at 24years. Juvenile mortality has apparently declined, f r o m 0.375 in the earlier sample to 0.0575 when the more recent data are included in the estimate. As a consequence, the entire l(x) curve has shifted upwards, indicating improved survivorship of recent cohorts. Using a different estimation technique, N e d e l m a n et al. (1986) found similar trends of improving survivorship over time. Because juvenile mortality declined, the fraction of the population in nonbreeding age classes has risen, from 43.0% to 47.8%. Young-of-the-year comprise 18-2% of the 1986 population, in constrast to 11-5%, which would be expected in the stationary age distribution. The survivorship curve forms the basis of a population projection model. Taking n(x,t) to be the n u m b e r o f individuals in age class x at time t, and m(x) to be the age-specific fecundity schedule, the following recursion relations hold
n(x, t) = n(O, t -- x)l(x)
x= 1,...,T
T
n(O, t) = ~
(3)
m(x)n(x, t)
x=l
A plausible fecundity schedule can be developed from the data on nesting pairs and offspring. 5 Assuming a 1:1 sex ratio and that all breeding adults appear as nesting pairs at WBNP, the average fecundity for adults is 0-229 with a standard deviation of0.110 (n = 20). Since the age at first breeding is 5, we take f0-0 0"229
re(x)
l
x< 5 x> 5
(4)
A Monte Carlo projection of the population can be constructed using the m e a n and standard errors of the estimated survivorship and fecundity schedules. The age-class structure of the 1986 population was reconstructed by 'ageing' the young reported each year from 1963 to 1985 using the s The Euler equation T
S = ~ ' l(x)m(x) exp(-- rx) = 1
(F3)
x=O
gives a check on the consistency of the estimate ofr and the l(x) and re(x) schedules.Using the values for these parameters presented in this paper gives S = !.039.. Because the fecundity schedule is based on the number of young counted in the ANWR census, it incorporates all causes of mortality between hatching and arrival at ANWR.
18
Clark S. Binkley, Richard S. Miller 10.|
~.~.~o-~-~-o=~
............................
./
e-
;-~, ~O'~O
./
,/
./ 0,1 . . . . . . . .
O-q)-e'~/- e.i. "i . • 1990
1995
" ' 1
.
2000
.
.
.
I
2005
.
.
.
.
I
~
I
2015
Fig. 2. Cumulative distribution of recovery date from Monte Carlo simulation of the ageclass model. The age structure of the 1986 population was reconstructed by 'ageing' the young born between 1963 and 1985 according to the estimated I(x) schedule. This initial age structure was projected forward using the recursion relations given in equation (3). Normal random numbers with the appropriate means and standard deviations were drawn to reproduce the estimated uncertainty in the l(x) and re(x) schedules. Fifty-year population projections were replicated 100 times. This figure shows the fraction of the replicates where the recovery target of 40 pairs (153 in the total population) was reached by the year specified on the horizontal axis. In half the replicates, recovery was achieved by 1998. In 90% of the replicates recovery was reached by 2003, and in all cases the requisite number of birds to produce 40 nesting pairs occurred before 2014. survivorship curve s h o w n in T a b l e 1. T h e n e q u a t i o n (3) was s i m u l a t e d 100 times for 50-year p r o j e c t i o n period. F i g u r e 2 shows the c u m u l a t i v e d i s t r i b u t i o n for the y e a r in which r e c o v e r y is r e a c h e d (defined as 40 pairs using the same m o d e l o f pair f o r m a t i o n as discussed above). T h e m e d i a n estimate o f r e c o v e r y for the W B N P - A N W R p o p u l a t i o n is 1998. In 10% o f the replicates, r e c o v e r y was achieved b y 1994 a n d in 9 0 % o f the replicates r e c o v e r y was achieved by 2003.
The whooping crane
19
CONCLUSIONS A principal criterion for reducing the statutory protection o f the whooping crane 40 breeding pairs in the main migratory p o p u l a t i o n - - i s likely to be reached within the next decade. Both population projection models used to reach this conclusion are conservative in the sense that both tend to underestimate the current population levels (the 1986 population is 110; the single-equation model estimates it to be 98.1 and the age-class model estimates it to be 102.3). 6 Establishment of two additional populations comprising at least 25 nesting pairs appears to be the greater hurdle to downlisting the whooping crane from endangered to threatened status. Observed variations in the survivorship and fecundity schedules presumably arise from variations in environmental factors. The main migratory population apparently has suffered no major environmental catastrophe since the annual census began in 1938. S i t u a t e d o n the G u l f Coast close to a major, heavily used barge canal, the wintering population at A N W R is susceptible to oil spills which could destroy its primary food supply. The wintering population could also be directly damaged by a late hurricane. W B N P is vulnerable to periods of low rainfall which could allow dry-season fires or high rates o f predation on nests and prefledged y o u n g (Boyce, 1987; K u y t & Goossen, 1987). However, barring such major environmental catastrophes, the biological recovery of the W B N P - A N W R whooping crane population is progressing as well as could be expected for a K-selected species with its population characteristics. While the short-term outlook for the W B N P - A N W R population is good, its longer term prospects turn on the political problems o f delisting the species from 'endangered' to 'threatened' status, and accommodating the projected population increases on its G u l f Coast wintering grounds. ACKNOWLEDGEMENT We thank Ernie Kuyt, o f the Canadian Wildlife Service, for the use of unpublished data. 6 Two other attempts to forecast the WBNP-ANWR population understate the recent population levels even more than the models presented in this paper. Miller et ak's 0974) stochastic birth-death model estimated a 1986 population of 89 with lower and upper 95% confidence limits of 39 and 138 birds, respectively.Using data through 1984, Boyce's 0987) ARIMA model estimates the 1986 population as 90 with lower and upper confidence limits of 79 and 102 birds, respectively. ARIMA models typically provide very good short-term forecasts. Hence the large error in Boyce's (1987) forecast after only two years indicates an unanticipated structural shift in the model towards better survivorship, greater reproductive success or both.
20
Clark S. Binkley, Richard S. Miller REFERENCES
Allen, R. P. (1952). The whooping crane. Natl. Audubon Soc. Res. Rep., 3. Binkley, C. S. & Miller, R. S. (1983). Population characteristics of the whooping crane Grus americana. Can. J. ZooL, 61, 2768-76. Binkley, C. S. & Miller, R. S. (1980). Survivorship of the whooping crane Grus americana. Ecology, 16, 434-7. Boyce, M. S. (1987). Time-series analysis and forecasting of the Aransas/Wood Buffalo whooping crane population. Proceedings 1985 Crane Workshop, ed. by J. C. Lewis, 1-9. Grand Isle, NE, Platt River Whooping Crane Maintenance Trust. Boyce, M. S. & Miller, R. S. (1985). Ten-year periodicity in whooping crane census. Auk, 102, 658-60. Erickson, R. C. (1976). Whooping crane studies at the Patuxent Wildlife Research Center. Proc. int. Crane Workshop, held at Baraboo, Wisconsin, 26 Sept. 1975, 1, 166-76. Johnston, J. (1972). Econometric methods. New York, McGraw-Hill. Krebs, C. I. (1972). Ecology: The experimental analysis of distribution and abundance. Scranton, PA, Harper and Row. Kuyt, E. & Goossen, J. P. (1987). Survival, age composition and age at first breeding of whooping cranes at Wood Buffalo National Park, Canada. In Proceedings 1985 Crane Workshop, ed. by J. C. Lewis, 230-44, held at Grand Isle, NE, Platt River Whooping Crane Maintenance Trust. Miller, L. (1944). Some Pliocene birds from Oregon and Idaho. Condor, 46, 25-32. Miller, R. S., Botkin, D. B. & Mendelssohn, R. (1974). The whooping crane Grus americana population of North America. Biol. Conserv., 6, 106-11. Nedelman, J., Thompson, J. A. & Taylor, R. J. (1986). The statistical demography of whooping cranes. Clemson University Dep. of Mathematical Sciences Tech. Rep., 505. Raup, H. M. (1933). Range conditions in the Wood Buffalo Park of western Canada with notes on the history of the wood bison. Am. Comm. for Int. Wildl. Protection. Spec. Pubis, 1, 2-16. US Fish and Wildlife Service (1986). Whooping crane recovery plan. Albuquerque, NM, US Fish and Wildlife Service. Wetmore, A. (1931). The avifauna of the Pleistocene of Florida. Smithsonian Misc. Collect., 85, 35-6. Wetmore, A. (1956). A check-list of the fossil and pre-historic birds of North America and the West Indies. Smithsonian Misc. Collect., 131.
Recovery of the Whooping Crane Grus americana
Clark S. Binkley & Richard S. Miller School of Forestry and Environmental Studies, Yale University, 205 Prospect Street, New Haven, Connecticut 06511, USA (Received 28 August 1987; accepted 30 August 1987)
A BSTRA CT Officially listed as 'endangered', the whooping crane Grus americana currently receives strong legal protection under the Endangered Species Act of 1973. To remove it from endangered status, the official Whooping Crane Recovery Plan requires 40 nesting pairs in the main population which migrates from Wood Buffalo National Park, NWT, Canada to the Aransas National Wildlife refuge on the Texas gulf coast. Two demographic models of the migratory population indicate that this criterion for recovery is likely to be met within the next decade.
INTRODUCTION The primary, wild population of the whooping crane Grus americana nests in W o o d Buffalo National Park (WBNP), NWT, Canada and winters at the Aransas National Wildlife Refuge (ANWR) and on a few associated islands on the gulf coast of Texas. The total population of this species has probably never been large, but it did have a wide distribution in North America before European colonisation of the continent (Allen, 1952). Fossil remains have been found from the Upper Pliocene in Idaho (Miller, 1944) and the Pleistocene in California, Kansas and Florida (Wetmore, 1931, 1956). Its decline in numbers coincided with the agricultural development of its traditional breeding areas in the prairies in the 1800s and early 1900s. The last nesting pair of whooping cranes in the prairies was recorded at Muddy Lake, Saskatchewan, Canada in 1922. 11 Biol. Conserv. 0006-3207/88/$03"50 © 1988 Elsevier Applied Science Publishers Ltd, England. Printed in Great Britain
12
Clark S. Binkley, Richard S. Miller
Legislation protecting the whooping crane was first enacted with the ratification of the Migratory Bird Treaty between the United States and Great Britain (Canada) in 1916. In 1937 the Aransas National Wildlife Refuge was established on the gulf coast of Texas to protect its only known wintering grounds, but it was not until 1954 that the nesting area was discovered at WBNP, which had been set aside by the Canadian government as a reserve and management area for the wood bison Bison bison athabascae in 1922 (Raup, 1933). After the establishment of the Aransas National Wildlife Refuge, an annual census of wintering whooping cranes was begun in 1938 and has continued with annual counts of young birds and birds with adult plumage. A total of 18 birds was counted in the winter of 1938, the number dropped to 16 in 1941, and increased to 110 in 1986 (E. Kuyt, pers. comm.). However, this overall increase has been accompanied by a 10-year periodicity in the relative abundance of whooping cranes (Boyce & Miller, 1985; Boyce, 1987), beginning with the decrease to 16 birds in 1941. The cause of this periodicity is not known, although it may be related to rainfall and predation on the nesting grounds. Passage of the Endangered Species Act of 1973 resulted in the listing of the whooping crane as an endangered species and the establishment of a Whooping Crane Recovery Team to formulate a Recovery Plan. A goal of this plan is to remove the whooping crane from the endangered category to the threatened category. The criteria for 'downlisting' are (i) a population of 40 nesting pairs at Wood Buffalo National Park and (ii) a population of 25 nesting pairs at each of 2 other sites (USFWS, 1986). In previous work we estimated the survivorship curve for the migratory whooping crane population (Binkley & Miller, 1980), and demonstrated that a demographic model based on this curve is consistent with other observed life history information about the population, including rate of increase, size of the breeding population and annual recruitment (Binkley & Miller, 1983). Taking advantage of nine additional years of data, this paper first revises these estimates and then uses the revised estimates to forecast the future population levels and to infer when the Recovery Team's target of 40 nesting pairs in the W B N P - A N W R population will be reached.
THE MODELS
A single equation model A simple projection can be based on a single equation depicting the population development over time. We previously found that the
The whooping crane
13
p o p u l a t i o n trace for the w h o o p i n g crane population separates into two periods during the mid-1950s. A simple model to account for this shift is In N(t) = In N(0) + rlt + r2t'
(1)
where
N(t) = p o p u l a t i o n size at time t r 1 = growth rate prior to t* r 2 = growth rate after t* t' - ~'0
It - -
t < t* t*
t >_ t*
In other words, the p o p u l a t i o n grows at rate rl until t* and then at a rate of r~ + r 2 after that time. A l t h o u g h the parameters of this equation can be estimated in m a n y ways, ordinary least squares regression (corrected for first-order serial correlation a m o n g the residuals) gave a better fit than did either a m a x i m u m likelihood procedure or nonlinear least squares. Fitting eqn (1) using an iterative generalised least squares procedure to account for first order autocorrelation in the residuals produced the following model: In N(t) = - 35"82 + 0-020 02r I + 0"021 60r 2 (--2"64) (2-87) (2"21)
(2)
where t * = 1 9 5 7 , R = 0 . 8 3 1 , F ( 2 , 4 6 ) = 1 1 3 . 2 and a serial correlation coefficient = 0.4459 (t-statistics are in parentheses). The current p o p u l a t i o n growth rate is thus 0.0416 or slightly less t h a n the figure of 0.0425 we f o u n d previously (Binkley & Miller, 1983). A t-test of the hypothesis that the growth rate has declined since 1978 is rejected (t = - 0 . 0 2 9 2 with 45df.) Figure 1 shows a projection of this model to 2020 along with the 90% confidence intervals. These data can be used to infer the year of recovery. The age of first breeding in captive females is about five years (Erickson, 1976), and this age has been confirmed for the wild W B N P - A N W R population by Kuyt & Goossen (1987).~ The n u m b e r of nesting pairs can be estimated by assuming a 1:1 sex ratio 2 and that all sexually m a t u r e birds form pairs. A l t h o u g h this model of pair formation overstates the h u m b e r of nesting pairs by 14.6%, 1 In a sample o f banded birds in the W B N P - A N W R population, Kuyt & Goossen (1987) found first nesting occurring at 5-0 +__ 1.18 years (n = 14) and first fertile eggs occurring at 5-4 + 0.84years (n = 10). Our fecundity estimates are based on nesting pairs so the younger age is the more appropriate estimate of the age at first breeding to use in our demographic model. 2 In a sample of 22 banded young in 1980, 1981 and 1984, Kuyt & Goossen (1987) found the sex ratio at the age o f 2 months to be exactly 1:1.
14
Clark S. Binkley, Richard S. Miller ~ °
!
0
10
I"
!
i
i i i i i i i i iii
i i i i i i i i i i i i i
1967
1950
1960
I I I I
I I I I I I I I I I I I
WIT
1979 y ~
1990
2000
2010
2020
Fig. 1. History and projection of the whooping crane population, 1938-2020. The growth rate of the W B N P - A N W R population increased from 0-0200 prior to 1957 to 0.0416 after that time. The vertical dashed line shows the beginning of the forecast period. The heavy solid line shows the mean estimates of population numbers, and the lighter lines show the smoothed upper and lower 90% confidence intervals for the forecast. The heavy horizontal line is drawn at 153 birds, the size of the population needed to produce 40 nesting pairs. Achieving 40 nesting pairs in the W B N P - A N W R population is a primary criterion established by the Whooping Crane Recovery Team for downlisting the species from endangered to threatened status. The population forecast indicates that this recovery target will be reached in 1997. The upper and lower confidence bands reach this level in 1991 and 2005, respectively.
the bias is not statistically significant (Binkley & Miller, 1983). The stationary age distribution of the population can be estimated from the survivorship curve presented below (Table 1). Using this age distribution and model of nesting pairs, we can conclude that a total population of 153 will provide 40 breeding pairs. 3 Figure 1 shows that this population level will be reached in 1997. The upper 90% confidence interval reaches this level in 1991, and the lower 90% confidence interval reaches this level in 2005.
The whooping crane
15
TABLE 1 Estimated Age-specific Survivorship/(x), Mortality q(x), and Age Distribution C(x) for the Migratory Whooping Crane Population X
(Age in years)
l(x)
SE[I(x)]
q(x)
C(x)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
1-000 0 0-9425 0.8923 0.842 8 0-794 2 0.746 5 0.699 6 0-653 5 0.608 3 0.564 0 0.520 5 0.477 8 0.4360 0.3950 0.3548 0.3156 0.277 1 0-2395 0-2028 0-t669 0.131 8 0.097 58 0.064 21 0.031 68
-0.1554 0-1266 0,101 40 0.080 58 0.065 38 0.057 35 0.056 80 0.061 72 0-069 24 0-077 23 0.084 51 0-09043 0-09465 0-09694 0-09719 0.095 32 0-091 28 0.08502 0.07653 0-06578 0-052 76 0.037 46 0.019 88
0.057 5 0.0533 0.0555 0-057 7 0-060 1 0.062 8 0.065 9 0-069 2 0-072 8 0.077 1 0.082 0 0.087 5 0.0940 0.101 8 0-1105 0.1220 0-135 7 0-1532 0.1770 0-2103 0.2596 0-342 0 0.506 6 1.000
0.115 2 0-1042 0.0946 0.085 7 0-0775 0.069 8 0.062 8 0-056 3 0.050 2 0.044 7 0.039 6 0.034 8 0-0305 0.0265 0-0228 0.0195 0-0164 0-0136 0.0110 0-0087 0-0066 0-004 7 0.003 0 0.001 4
x refers to the age of the cohort. Because the survivorship curve is estimated using census data taken at ANWR, the actual age of the cohort is approximately 1/2 year older than the value of x given in this table. l(x) is the fraction of a cohort which survives to age x. q(x) = [l(x) - l(x + l)]/l(x), q(x) is the fraction of the population in age class x which dies prior to reaching age x + 1. C(x) =l(x)exp(-rx)/~S=ol(i)exp(-ri) (Krebs, 1972). C(x) is the proportion of the population between age x and .~ + 1 in the stationary age distribution.
3 From Table 1, the fraction of the population in non-breeding ages (less than 5) equals 0.4771. The fraction of the population in breeding ages is then 1 -0.4771 = 0'5229. Forty breeding pairs requires 80 birds of breeding age, or a total population of 80/.0-5229 = 153 birds. K uyt & Goossen (1987) estimate that the non-breeding individuals comprise only 34.2% of the population, implying that a total population of 122 will produce 40 breeding pairs.
16
Clark S. Binkley, Richard S. Miller
An age-class model T h e e n d a n g e r e d status o f the w h o o p i n g crane, a n d its c o n s e q u e n t p r o t e c t i o n , has m a d e it difficult to o b t a i n the d a t a n e e d e d to estimate key p o p u l a t i o n p a r a m e t e r s . Y o u n g - o f - t h e - y e a r can be r e c o g n i s e d b y their juvenile plumage, b u t after their first winter m o u l t c a n n o t be distinguished f r o m the white adults. T h e a n n u a l w i n t e r census at A N W R r e c o r d s first-year juveniles s e p a r a t e l y f r o m birds in adult p l u m a g e which m a y o r m a y n o t be sexually m a t u r e . A l t h o u g h b a n d i n g studies have been c o n d u c t e d o n the m i g r a t o r y p o p u l a t i o n o n l y since 1977, the age s t r u c t u r e o f the entire p o p u l a t i o n is implicitly k n o w n because the n u m b e r o f y o u n g each y e a r has been r e c o r d e d since 1938. Binkley & Miller (1980) e x p l o i t e d this implicit a g e - s t r u c t u r e i n f o r m a t i o n to estimate the s u r v i v o r s h i p c u r v e for the m i g r a t o r y p o p u lation. Since t h a t time, nine m o r e years o f census d a t a have b e c o m e available, a n d some o f the earlier d a t a h a v e been revised. T a b l e 1 shows a revised estimate o f the survivorship curve 4 a l o n g with the s t a n d a r d e r r o r s o f the estimates, the implied age-specific m o r t a l i t y rates a n d the f r a c t i o n o f the p o p u l a t i o n in e a c h age class. 4 Following Binkley & Miller (1980), the survivorship curve was estimated as follows. Ifa(t) is the number of birds in adult plumage observed in year t,y(t) is the number ofyoung observed in year t and T is the maximum longevity, then by definition T
a( t)
= ) , l(x)j,(t - x)
(F1)
x=l
All of the variables in this expression are known except the T values of l(x) The number of observations in the census is inadequate to estimate the l(x) values directly, so instead the functional relationship between x and l(x) is approximated by l(x) = a 0 + a l x + a2 X2
(F2)
The power series approximation to the true l(x) curve was truncated at three terms on the basis of statistical fit and conformance to prior expectations about the shape of l(x) (i.e. l(x) is non-increasing). Substituting F2 into F1 gives an expression, linear in the parameters ao, a~ and a2, which can then be estimated using ordinary least squares regression. This technique is known as polynomial distributed lags (or Almon lags) in the econometrics literature (Johnston, 1972). Because of serial correlation in the residuals, the model was estimated using an iterative generalised least squares procedure. The lag-one serial correlation coefficient is estimated from the residuals and then is used to modify the variance--covariance matrix in a GLS estimate. The process is iterated until the desired convergence in the coefficients is obtained. The value of Twas estimated as follows. The l(x) curve was constrained so that I(T) = 0. The l(x) curve was estimated for several values of 7",and then the maximum likelihood estimate of T was found by inspection. The resulting equation has T=24, R2=0.6077, and F(I, 24) = 37-2. Table I gives the estimated values of I(x).
The whooping crane
17
The estimated m a x i m u m longevity T remains at 24years. Juvenile mortality has apparently declined, f r o m 0.375 in the earlier sample to 0.0575 when the more recent data are included in the estimate. As a consequence, the entire l(x) curve has shifted upwards, indicating improved survivorship of recent cohorts. Using a different estimation technique, N e d e l m a n et al. (1986) found similar trends of improving survivorship over time. Because juvenile mortality declined, the fraction of the population in nonbreeding age classes has risen, from 43.0% to 47.8%. Young-of-the-year comprise 18-2% of the 1986 population, in constrast to 11-5%, which would be expected in the stationary age distribution. The survivorship curve forms the basis of a population projection model. Taking n(x,t) to be the n u m b e r o f individuals in age class x at time t, and m(x) to be the age-specific fecundity schedule, the following recursion relations hold
n(x, t) = n(O, t -- x)l(x)
x= 1,...,T
T
n(O, t) = ~
(3)
m(x)n(x, t)
x=l
A plausible fecundity schedule can be developed from the data on nesting pairs and offspring. 5 Assuming a 1:1 sex ratio and that all breeding adults appear as nesting pairs at WBNP, the average fecundity for adults is 0-229 with a standard deviation of0.110 (n = 20). Since the age at first breeding is 5, we take f0-0 0"229
re(x)
l
x< 5 x> 5
(4)
A Monte Carlo projection of the population can be constructed using the m e a n and standard errors of the estimated survivorship and fecundity schedules. The age-class structure of the 1986 population was reconstructed by 'ageing' the young reported each year from 1963 to 1985 using the s The Euler equation T
S = ~ ' l(x)m(x) exp(-- rx) = 1
(F3)
x=O
gives a check on the consistency of the estimate ofr and the l(x) and re(x) schedules.Using the values for these parameters presented in this paper gives S = !.039.. Because the fecundity schedule is based on the number of young counted in the ANWR census, it incorporates all causes of mortality between hatching and arrival at ANWR.
18
Clark S. Binkley, Richard S. Miller 10.|
~.~.~o-~-~-o=~
............................
./
e-
;-~, ~O'~O
./
,/
./ 0,1 . . . . . . . .
O-q)-e'~/- e.i. "i . • 1990
1995
" ' 1
.
2000
.
.
.
I
2005
.
.
.
.
I
~
I
2015
Fig. 2. Cumulative distribution of recovery date from Monte Carlo simulation of the ageclass model. The age structure of the 1986 population was reconstructed by 'ageing' the young born between 1963 and 1985 according to the estimated I(x) schedule. This initial age structure was projected forward using the recursion relations given in equation (3). Normal random numbers with the appropriate means and standard deviations were drawn to reproduce the estimated uncertainty in the l(x) and re(x) schedules. Fifty-year population projections were replicated 100 times. This figure shows the fraction of the replicates where the recovery target of 40 pairs (153 in the total population) was reached by the year specified on the horizontal axis. In half the replicates, recovery was achieved by 1998. In 90% of the replicates recovery was reached by 2003, and in all cases the requisite number of birds to produce 40 nesting pairs occurred before 2014. survivorship curve s h o w n in T a b l e 1. T h e n e q u a t i o n (3) was s i m u l a t e d 100 times for 50-year p r o j e c t i o n period. F i g u r e 2 shows the c u m u l a t i v e d i s t r i b u t i o n for the y e a r in which r e c o v e r y is r e a c h e d (defined as 40 pairs using the same m o d e l o f pair f o r m a t i o n as discussed above). T h e m e d i a n estimate o f r e c o v e r y for the W B N P - A N W R p o p u l a t i o n is 1998. In 10% o f the replicates, r e c o v e r y was achieved b y 1994 a n d in 9 0 % o f the replicates r e c o v e r y was achieved by 2003.
The whooping crane
19
CONCLUSIONS A principal criterion for reducing the statutory protection o f the whooping crane 40 breeding pairs in the main migratory p o p u l a t i o n - - i s likely to be reached within the next decade. Both population projection models used to reach this conclusion are conservative in the sense that both tend to underestimate the current population levels (the 1986 population is 110; the single-equation model estimates it to be 98.1 and the age-class model estimates it to be 102.3). 6 Establishment of two additional populations comprising at least 25 nesting pairs appears to be the greater hurdle to downlisting the whooping crane from endangered to threatened status. Observed variations in the survivorship and fecundity schedules presumably arise from variations in environmental factors. The main migratory population apparently has suffered no major environmental catastrophe since the annual census began in 1938. S i t u a t e d o n the G u l f Coast close to a major, heavily used barge canal, the wintering population at A N W R is susceptible to oil spills which could destroy its primary food supply. The wintering population could also be directly damaged by a late hurricane. W B N P is vulnerable to periods of low rainfall which could allow dry-season fires or high rates o f predation on nests and prefledged y o u n g (Boyce, 1987; K u y t & Goossen, 1987). However, barring such major environmental catastrophes, the biological recovery of the W B N P - A N W R whooping crane population is progressing as well as could be expected for a K-selected species with its population characteristics. While the short-term outlook for the W B N P - A N W R population is good, its longer term prospects turn on the political problems o f delisting the species from 'endangered' to 'threatened' status, and accommodating the projected population increases on its G u l f Coast wintering grounds. ACKNOWLEDGEMENT We thank Ernie Kuyt, o f the Canadian Wildlife Service, for the use of unpublished data. 6 Two other attempts to forecast the WBNP-ANWR population understate the recent population levels even more than the models presented in this paper. Miller et ak's 0974) stochastic birth-death model estimated a 1986 population of 89 with lower and upper 95% confidence limits of 39 and 138 birds, respectively.Using data through 1984, Boyce's 0987) ARIMA model estimates the 1986 population as 90 with lower and upper confidence limits of 79 and 102 birds, respectively. ARIMA models typically provide very good short-term forecasts. Hence the large error in Boyce's (1987) forecast after only two years indicates an unanticipated structural shift in the model towards better survivorship, greater reproductive success or both.
20
Clark S. Binkley, Richard S. Miller REFERENCES
Allen, R. P. (1952). The whooping crane. Natl. Audubon Soc. Res. Rep., 3. Binkley, C. S. & Miller, R. S. (1983). Population characteristics of the whooping crane Grus americana. Can. J. ZooL, 61, 2768-76. Binkley, C. S. & Miller, R. S. (1980). Survivorship of the whooping crane Grus americana. Ecology, 16, 434-7. Boyce, M. S. (1987). Time-series analysis and forecasting of the Aransas/Wood Buffalo whooping crane population. Proceedings 1985 Crane Workshop, ed. by J. C. Lewis, 1-9. Grand Isle, NE, Platt River Whooping Crane Maintenance Trust. Boyce, M. S. & Miller, R. S. (1985). Ten-year periodicity in whooping crane census. Auk, 102, 658-60. Erickson, R. C. (1976). Whooping crane studies at the Patuxent Wildlife Research Center. Proc. int. Crane Workshop, held at Baraboo, Wisconsin, 26 Sept. 1975, 1, 166-76. Johnston, J. (1972). Econometric methods. New York, McGraw-Hill. Krebs, C. I. (1972). Ecology: The experimental analysis of distribution and abundance. Scranton, PA, Harper and Row. Kuyt, E. & Goossen, J. P. (1987). Survival, age composition and age at first breeding of whooping cranes at Wood Buffalo National Park, Canada. In Proceedings 1985 Crane Workshop, ed. by J. C. Lewis, 230-44, held at Grand Isle, NE, Platt River Whooping Crane Maintenance Trust. Miller, L. (1944). Some Pliocene birds from Oregon and Idaho. Condor, 46, 25-32. Miller, R. S., Botkin, D. B. & Mendelssohn, R. (1974). The whooping crane Grus americana population of North America. Biol. Conserv., 6, 106-11. Nedelman, J., Thompson, J. A. & Taylor, R. J. (1986). The statistical demography of whooping cranes. Clemson University Dep. of Mathematical Sciences Tech. Rep., 505. Raup, H. M. (1933). Range conditions in the Wood Buffalo Park of western Canada with notes on the history of the wood bison. Am. Comm. for Int. Wildl. Protection. Spec. Pubis, 1, 2-16. US Fish and Wildlife Service (1986). Whooping crane recovery plan. Albuquerque, NM, US Fish and Wildlife Service. Wetmore, A. (1931). The avifauna of the Pleistocene of Florida. Smithsonian Misc. Collect., 85, 35-6. Wetmore, A. (1956). A check-list of the fossil and pre-historic birds of North America and the West Indies. Smithsonian Misc. Collect., 131.