Population viability analysis (P.A.) is a structured and systematic analysis of the interacting factors, including abundance, rates of survival and productivity, demographic and environmental stochasticity, and catastrophes, that determine a population's risk of extinction. P.A.'s have a variety of applications, including, in recent years, use as tools in establishing recovery goals for some threatened and endangered species. General information on P.A.'s and their use is found in a large and growing body of scientific literature. Persons who want to learn about P.A. may find information in Shaffer (1987); Begon and Mortimer (1986), chapter 3; Lindenmayer et al. (1993); National Research Council (1995), chapter 7; and many other sources.
A draft of the following P.A. for the Atlantic Coast piping plover, dated 7 April, 1994, was sent to 13 experts outside the recovery team for review and comment. Five substantive responses were received. Three comment letters expressed overall support for data, methodology, and recommendations, but suggested that model parameters, especially survival rates and co-efficients of variation of survival and fecundity, might be excessively optimistic (i.e., the actual population is less secure than the model predicts). Two other commenters felt that survival rates for plovers in the southern part of the range might be higher than those observed in Massachusetts, perhaps due to shorter migration distances. One of these letters also stated that various model parameters, especially co-efficients of variation of survival and fecundity used to model catastrophic events, were overly pessimistic. Two commenters felt that more "sensitivity analyses" (to better gauge the factors that contribute most to population viability) would make the P.A. more useful. Finally, two letters indicated that a metapopulation model would more accurately reflect actual population dynamics than one which treats Atlantic Coast piping plovers as one panmictic(1) population.
In response to these comments and as a result of further discussions among the modelers, recovery team, and Fish and Wildlife Service biologists, refinements in the analysis were made and additional scenarios were modeled. However, a metapopulation model has yet to be developed.
Although the P.A. continues to treat Atlantic Coast piping plovers as a single population, S.M. Melvin and J.P. Gibbs (pers. comm. 1994) agree that a metapopulation model would be more predictive of actual population dynamics. A "metapopulation" comprises a number of smaller subpopulations distributed across separate habitat patches. Within a metapopulation, there are barriers that inhibit dispersal between subpopulations, and environmental conditions may vary between habitat patches.
A metapopulation structure may increase or decrease the extinction probability of the population as a whole. Each of the subpopulations, because of its smaller size, may be more susceptible to extirpation than the larger population. The potential for loss of small local populations is greater the smaller the subpopulation, the greater the distance between subpopulations, and the poorer the ability of the species to disperse between habitat patches to augment or re-colonize adjacent populations and habitat. On the other hand, a metapopulation may have a greater probability of persistence than a single large population, if subpopulations are relatively independent with regard to environmental conditions and if individuals can readily disperse between subpopulations. Thus, it is not possible to predict in advance if and how metapopulation modeling would change our understanding of piping plover population dynamics.
Development of a metapopulation model for the Atlantic Coast piping plover will be a near-term priority of the recovery program, and has been included in recovery task 3.7. This type of model will improve our understanding of population viability and will also assist biologists assessing the impacts of proposed projects undergoing Section 7 consultation and any Section 10(a)(1)(B) permit applications.
1. A "panmictic" breeding population is subject to random mating.
Scott M. Melvin, Massachusetts Division of Fisheries and Wildlife, Route 135, Westborough, Massachusetts 01581
James P. Gibbs, School of Forestry and Environmental Studies, Yale University, New Haven, Connecticut 06511
We developed a stochastic population growth model, based on age-specific survival rates and varying levels of fecundity and population size, to estimate probabilities that the Atlantic Coast population of Piping Plovers would fall to extinction or below various population thresholds during the next century. The model described below has been modified from our earlier draft (7 April 1994) as a result of comments received from U.S. Fish and Wildlife Service biologists and several reviewers. We present revised estimates of extinction probabilities and offer recommendations for delisting criteria for the Atlantic Coast population.
The Model
Gibbs performed initial analyses using Lotus Spreadsheet software with an @-Risk add-on, but then rewrote the model as a computer program in Turbo-Pascal, which greatly increased its simplicity, speed, and flexibility. The model recognizes 3 age classes (fledglings, adults 1 year old, and adults > 1 year old) and is based on an annual post-breeding census of the population. Only the female portion of the population is modeled; we assume a 1:1 sex ratio. The number of fledglings present in the population at the time of census is calculated as:
(1) F(t+1) = F(t)*SF*CP*PB + A(t)*SA*CP,
and the number of adults present as:
(2) A(t+1) = F(t)*SF + A(t)*SA,
where:
F = number of fledglings,
SF = annual survival rate of fledglings,
CP = female chicks fledged per female per year (chicks per pair divided by 2),
PB = proportion of 1-year old adults breeding,
A = number of adults,
SA = annual survival rate of adults
Equation (1) represents the production of fledglings in the census year. The first half of the equation represents the production of fledglings by 1 year-old birds (i.e., surviving fledglings produced the previous year). Note that the previous year's fledglings, F(t), survive their first winter (i.e., *SF) before they breed (i.e., *CP), and that only a portion of these 1 year-olds breed (i.e., *PB). Similarly, the second half of the equation represents adults alive the previous year that survive the winter (i.e., *SA) and then breed (i.e., *CP). All surviving adults > 1 year-old and 50% of 1 year-olds are assumed to breed if the population has not reached carrying capacity.
Equation (2) represents survival of fledglings through their first winter to adulthood, i.e., F(t)*SF, and survival of adults from one year to the next, i.e., A(t)*SA, and calculates the total number of adult females expected to be present at a post-breeding census of the population.
The effect of habitat limitation on the population is modeled by transforming breeding adults produced in excess of an input carrying capacity (K) into nonbreeding "floaters". Floaters experience the same survival rates as other adults, and reenter the breeding population during a subsequent season if a breeding opportunity becomes available (i.e., if the population falls below K).
Environmental-related variation is modeled in 2 ways. First, survival rates are permitted to vary annually according to normal distributions of means and coefficients of variation (CV) estimated from banding studies and truncated at 0 and 1. Annual variation in survival of adults 1 year-old and > 1 year-old is assumed to be perfectly correlated. Second, annual values of fecundity are permitted to vary according to a normal distribution of mean and CV estimated from field studies and truncated at 0. Demographic stochasticity is modeled by drawing a random number of individuals in any year from a binomial distribution of n = number of individuals alive the previous year and P = the probability of survival. Similarly, a number of St.-year breeders is determined from a binomial distribution of n = number of fledglings surviving to their St.-year and P = the proportion of 1 year-old birds breeding.
Each simulation consisted of 5,000 iterations. The number of breeding adults was tallied at year 100 of each iteration to calculate probabilities that the population (N) = 0 or < 50, 100, and 500 pairs.
The current model incorporates 2 additional scenarios that we believe are realistic: 1) reduced fecundity for pairs that exceed the recovery objective, and 2) Allee effects if the population falls below 100 pairs. Each is discussed briefly below.
1. Reduced fecundity for pairs that exceed recovery objective.
We assume that until the recovery objective for abundance is reached, maximum legal protection and "on-the-ground" management will be afforded to all breeding pairs in order to achieve some fecundity objective and sustain population growth. However, it is realistic to assume that if the population exceeds the recovery objective for abundance, protection and management will be relaxed for "surplus" pairs that exceed this objective. This could occur by reducing or eliminating efforts to monitor nesting plovers, manage pedestrians, vehicles, or predators, or protect habitat, and through "incidental take" allowed under Section 10 permits. We believe such reductions in management intensity would lead directly to reduced fecundity.
In the revised model, we assume that if the Atlantic Coast population increases above the recovery objective for abundance, mean fecundity for surplus pairs will drop to 0.5 chicks/pair. We believe that 0.5 chicks fledged/pair is a realistic and, perhaps, optimistic fecundity that could be expected for Atlantic Coast plovers if intensive management and legal protection were to be eliminated. For example, mean annual fecundity for Piping Plovers in North Carolina from 1988 to 1993 was only 0.54, in spite of increasingly intensive management.
2. Allee effect.
Allee effects are density dependent effects that draw small populations away from carrying capacity and toward extinction (Allee 1931, Allee et al. 1949, Ferson and Akcakaya 1990). Examples of Allee effects might include reduced reproductive output when population densities become so low that males and females have difficulty finding each other to breed, or reduced survival or fecundity caused by inbreeding.
We believe mean fecundity of the Atlantic Coast population could decrease substantially if the population declined to very low levels, simply as a result of increasing proportions of the population failing to reproduce because of their inability to find and successfully pair with a member of the opposite sex. On the breeding grounds, the Atlantic Coast population is distributed over > 3,000 km of coastline, from North Carolina to Newfoundland. Although Piping Plovers are very mobile and seem to be good dispersers, a population that fell below 100 pairs would be distributed over the landscape at a very low density and the probability of encountering and attracting an unpaired member of the opposite sex during any given 3-month nesting season might be low.
We have incorporated an Allee effect into the model by assuming that if the Atlantic Coast population declines below a threshold of 100 pairs, mean fecundity will decline at a linear rate from the input fecundity when N = 100 pairs to 0.0 when N = 0 pairs. We believe that, if anything, we have been conservative in our modeling of an Allee effect. If the Atlantic Coast population fell substantially below 100 pairs, we might expect additional increases in extinction probability caused by : 1) increased coefficients of variation for both fecundity and survival, and 2) increased negative effects of demographic stochasticity on fecundity (for example, if only 4 plovers returned to Maine or Maryland in a given year, there is a 12.5% probability that all 4 would be of the same sex).
Inputs
Fecundity
Mean and CV of fecundity (chicks fledged per pair) were calculated from data reported for the U.S. portion of the Atlantic Coast population (U.S. Fish and Wildlife Service 1993e). Mean and CV of fecundity in a given year were calculated as weighted averages across states, with population sizes as weights. These annual values were then averaged across years (unweighted) to calculate an overall mean and CV of fecundity. For the 5-year period 1989-1993, we calculated a mean fecundity of 1.21 chicks fledged per pair and CV of 0.15 for the U.S. portion of the Atlantic Coast population. However, we increased the CV of fecundity input to the model to 0.4, to represent greater variance in fecundity that might occur over the 100-year simulation period. We believe such long-term variance in fecundity is realistic and could be caused by catastrophes or long-term variation in quality or availability of breeding habitat, predator populations, or intensity and effectiveness of management on the breeding grounds.
We assumed that only 50% of 1 year-old birds breed, and that 100% of adults > 1 year-old breed. Small numbers of Piping Plovers have been reported to remain on wintering areas during the breeding season (Haig and Oring 1988b) and < 5-10% of plovers reported in Massachusetts during May and June appear unpaired. Cairns (1977) reported that 15-16% of the Piping Plovers at her study area in Nova Scotia appeared to be unpaired or did not nest. In Manitoba, Haig and Oring (1988a,b) reported that many adults did not find a mate or nest in a given year, but that 1 year-old birds "frequently bred".
Survival
We estimated mean annual survival rates for 2 age classes of piping plovers (fledgling to 1 year-old, and > 1 year-old), based on resightings of birds color-banded in Massachusetts (L.H. MacIvor, C.R. Griffin, and S.M. Melvin, University of Massachusetts-Amherst, unpubl. data). MacIvor et al. color-banded 103 breeding adults and 61 flightless chicks (aged 10 to 25 days) on beaches from Chatham to Provincetown on outer Cape Cod, Massachusetts, from 1985 to 1988. They captured incubating adults using wire box traps (Wilcox 1959) and captured chicks by hand. They banded all birds with a single aluminum legband and unique combinations of 2 or 3 plastic colored legbands. They searched for banded plovers on outer Cape Cod from mid March through the end of August or first week in September in 1986 through 1989, and solicited observations of color-banded plovers from other biologists in Massachusetts and elsewhere along the Atlantic Coast. They estimated mean annual survival rates and coefficients of variation for both fledglings and birds > 1 year-old, based on resightings of color-marked birds, using Program Jolly (Pollock et al. 1990). We input mean annual survival rates of 0.74 for adults > 1 year-old and 0.48 for fledglings (from fledging to 1 year old) (MacIvor et al. unpubl. data). We increased the coefficients of variation for survival input to the model to 0.20 for both age classes (Table 1), to account for potential long-term increases in variance of survival rates caused by catastrophes or other factors.
Carrying Capacity
We estimated the current carrying capacity (K) for the entire Atlantic Coast population (including Canada) at 2,000 pairs. This estimate was made by the Atlantic Coast Piping Plover Recovery Team following discussions with biologists coordinating plover efforts in all the Atlantic Coast states and provinces, and is felt to be conservative. Experience in New England, where plover numbers have doubled since 1986, has expanded our definition of suitable habitat and demonstrated that habitats may support far more pairs and higher productivity than previously estimated. Furthermore, efforts to assure dynamic functioning of plover habitat by allowing natural processes of erosion and accretion to occur could yield major improvements in habitat quality in some parts of the species' range.
Extinction Thresholds
In discussions during winter, 1994, the recovery team agreed that the recovery goal for the Atlantic Coast population of Piping Plovers should provide a > 95% probability of persistence (i.e., < 5% probability of extinction) for 100 years. Because extinction obviously represents the antithesis of recovery, the recovery team was also interested in estimating probabilities that the Atlantic Coast population would fall below thresholds of 50, 100, and 500 pairs during the next 100 years.
Table 1 summarizes the parameter estimates that we input to our model, and compares them with inputs used by Ryan et al. (1993) to model the Great Plains population of piping plovers.
Fecundity Needed For A Stationary Population
We estimated a mean annual fecundity of 1.245 chicks fledged per pair is needed to maintain a stationary population, based on empirical estimates of adult and immature survival and percentages of the 2 adult age classes that breed each year.
A review of census results for the Atlantic Coast population between 1989 and 1993 suggests that the actual fecundity needed to maintain a constant population may be slightly lower, perhaps 1.0 to 1.1 chicks /pair. Observed mean fecundity for the U.S. portion of the Atlantic Coast population between 1989 and 1993 was 1.21; during that time, population estimates increased by 21%, from 724 to 875 pairs (note, however, this increase resulted entirely from an 82% increase in the New England subpopulation driven by a mean fecundity of 1.69 during this period). Populations in New York and New Jersey remained relatively constant during this period, with mean fecundities of only 1.04 and 0.97, respectively. The Delaware to North Carolina subpopulation experienced a 10% population decline between 1989-1993; mean annual fecundity from 1988 to 1993 was 0.84.
There are several possible explanations for these apparent discrepancies between model results and actual observations:
Extinction Probabilities
We first calculated extinction probabilities for the entire Atlantic Coast population (U.S. and Canada combined) based on estimates of survival rates from MacIvor et al. (Table 2). When mean fecundity = 1.25 (our estimate needed for a stationary population), the goal of < 5 % extinction probability for 100 years was not met even when population size and carrying capacity were increased to 10,000 pairs.
When we increased fecundity to 1.50, a population of 2,000 pairs was needed to achieve the goal of < 5% extinction probability. Even at this level, however, the population had a 10% chance of falling below 50 pairs and a 26% chance of falling below 500 pairs (Table 2).
We next examined extinction probabilities for the entire Atlantic Coast population when mean survival rates decreased by 5 and 10 % for 1 year-old and > 1 year-old birds, respectively, during the first 50 years of the simulation, and then remained stable (within bounds set by coefficients of variation) for the remaining 50 years of the simulation period (Table 3). We suggest that declining survival rates over the next 50 years may represent a realistic scenario that should be considered in recovery planning. Such long-term declines in survival might be caused by one or more of the following:
Results of simulations presented in Table 3 demonstrate the sensitivity of extinction probabilities to even small changes in survival rates. With declining survival, a mean fecundity of 1.50 results in declining populations with high probabilities of extinction within 100 years. Even a population as large as 10,000 pairs has a 29% probability of extinction in 100 years.
Extinction probabilities for Atlantic Coast plovers were more sensitive to fecundity, survival rates, and variability in those parameters than to initial population size, at least within the narrow range of population sizes set by our estimate of carrying capacity. If it is unrealistic to substantially increase population size beyond 2,000 pairs, then the alternative must be to maintain fecundity at high enough levels to provide a margin of safety. This is not to say, however, that population size is not important. We believe the best ways to buffer against decreased fecundity and survival or increased variance in those parameters are to: (1) manage intensively to insure adequate fecundity and survival, and (2) maximize population size and number of breeding and wintering sites for each subpopulation. The larger and more evenly distributed the Atlantic Coast population is, both on the breeding and wintering grounds and during migration, the less will be the overall effects of environmental stochasticity, catastrophes, or reduced or inconsistent management. Given the difficulty of managing to improve survival, optimizing both abundance and distribution of all subpopulations would seem to be the best buffer against declines in mean survival for the population as a whole. Also, increasing population size may delay time to extinction, allowing managers more time to develop strategies to improve survival or fecundity.
Potential effects of population genetics on the long-term viability of the Atlantic Coast population of piping plovers are poorly understood. Haig and Oring (1988) used protein electrophoresis to examine genetic variability and differentiation between Piping Plover chicks (n=122) from Saskatchewan, Manitoba, North Dakota, Minnesota, and New Brunswick. For the 36 presumptive loci examined, they concluded that genetic variability within populations was comparable to other bird species, that inbreeding was not a significant factor within any of the populations sampled, and that little genetic differentiation had occurred between populations. Lack of differentiation between populations may be explained either by relatively recent declines and isolation of regional populations, or by adequate gene flow within and between populations to offset effects of genetic drift. Patterns of mating, dispersal, and distribution in Piping Plovers (Haig and Oring 1988a,b) are probably adequate to allow rates of gene flow > 1 individual/population/ generation between Atlantic Coast subpopulations, the most conservative estimate of amount of gene flow needed to offset effects of genetic drift (Wright 1931).
Effective population size (Ne) (Frankel and Soulé 1981) has not been estimated for the Atlantic Coast population. Demographic characteristics that undoubtedly reduce Ne below actual population size (N) for the Atlantic Coast population include:
However, Ne / N may be higher for piping plovers than for some other vertebrates because: (1) percentage of adults > 1 year-old not attempting to breed in a given year may be < 10%; (2) dispersal of > 1 individual > 100 km per generation probably occurs (Haig and Oring 1988b; MacIvor, Griffin and Melvin, unpubl. data); (3) sex ratio is approximately 1:1; and/or (4) variation in overall population size has been small, at least over the past 8 years of intensive monitoring and management.
Several workers have estimated Ne for vertebrates at 0.2-0.5 of actual population size (N) (Barrowclough and Coats 1985, Harris and Allendorf 1989, Mace and Lande 1991). If Ne for piping plovers falls within this range, then a recovery objective of a population of 1,200 pairs of Atlantic Coast piping plovers (U.S. Fish and Wildlife Service 1988e) would, at best, fall perilously close to the often-quoted minimum Ne of 500 individuals needed to preserve sufficient genetic variation in a population to maintain long-term fitness and evolutionary potential (Franklin 1980, Frankel and Soulé 1981). Hopefully, the demographic and behavioral characteristics of piping plovers are such that Ne / N is substantially > 0.5. We believe that an estimation of Ne for the Atlantic Coast population should be identified as a recovery task in the revised recovery plan.
Based on results of the viability analysis summarized and discussed above, we recommend the following recovery objectives for Atlantic Coast Piping Plovers to meet the conceptual goal of assuring > 95% probability of persistence for 100 years.
Throughout the year, the Atlantic Coast population should be as evenly dispersed as possible, distributed among many well-managed, productive nesting sites during the breeding season and many high-quality, secure sites during winter. Carrying capacity of winter habitat for Atlantic Coast Piping Plovers is unknown.
This recommendation increases by 800 pairs the population objective contained in the 1988 recovery plan for the Atlantic Coast population (U.S. Fish and Wildlife Service 1988e). That objective was established before estimates of survival rates were available, and without benefit of our current understanding of potential carrying capacity or responses of populations to management of predation, human disturbance, and off-road vehicles. That objective was also not based on any quantitative viability analysis, but simply sought to achieve a sizeable (50%) increase over the 1986 population estimate. At the time, such an increase was felt to be a reasonable compromise between what could actually be accomplished through management, and what historical populations had been. Analysis presented in this document (Table 2) suggests that, even when mean fecundity is 1.5, a population of 1,200 pairs has an 11% probability of extinction and a 55% chance of falling below 500 pairs, if variances of survival and fecundity are > 0.2 and 0.4, respectively.
We caution that a recovery objective of 2,000 pairs (4,000 individuals) falls within the range of minimum population size currently recommended for long-term viability in vertebrates. While population biologists have been reluctant or unable to establish definite rules-of-thumb for population sizes that insure viability over given time periods, several have suggested "several thousand" to > 10,000 individuals as minimum levels needed to insure 95% probability of persistence for 1 or more centuries (Soulé 1987, Belovsky 1987, Thomas 1990). Recent papers by Wilcove et al. (1993) and Tear et al. (1993) have criticized the U.S. Fish and Wildlife Service for not listing species earlier, before they decline to such low levels that recovery is more difficult or unlikely, and for establishing unrealistically low recovery goals.
We recognize that the Atlantic Coast population of Piping Plovers currently represents about 1/2 of the world's population of this species. However, at present we have little confidence that the Great Plains population will contribute to the viability of the Atlantic Coast population, given the lack of evidence of interchange between the 2 populations, and the current projections of rapid population decline recently predicted by Ryan et al. (1993) for the Great Plains population.
We caution that in a future scenario of declining survival and increased variance of survival and fecundity (Table 3), a population of 2,000 pairs with mean annual fecundity of 1.5 has an extinction probability of 31%, well above the <5% rule-of-thumb established by the recovery team. Managers must continue to vigilantly monitor critical demographic parameters of the Atlantic Coast population (see criterion 5), and be prepared to adjust abundance or fecundity objectives upward if declining survival or increased variances become evident.
We also recognize the possibility that survival rates for Atlantic Coast plovers may vary latitudinally, in which case adoption of subpopulation-specific fecundity objectives may be warranted in the future.
This analysis should be based on the best available data, and should seek to determine if a population size of 2,000 pairs is sufficient to maintain long-term genetic diversity.
Table A. Comparison of parameter estimates used in modeling Atlantic Coast and Great Plains populations of Piping Plovers.
Atlantic Coast
Parameter
Observed
Input
Great Plains1 Adult survival: Mean
0.7387
0.70-0.74
0.66 Adult survival: CV
0.0805
0.20
0.50 Imm. survival: Mean
0.4836
0.44-0.48
0.46 - 0.66 Imm. survival: CV
0.1011
0.20
0.50 - 0.71 Fecundity: Mean
1.21
variable
0.86 Fecundity: CV
0.15
0.40
0.59 Fecundity needed for stationary population
1.245
variable
1.13 Proportion of adults > 1 year-old breeding
_
1.00
1.00 Proportion of 1 year-olds breeding
_
0.50
1.00
1 Source: Ryan et al. 1993
Table B. Extinction probabilities for Atlantic Coast piping plover population.
Survival estimates for adults and fledglings are 0.7387 and 0.4836, respectively; these means remain stable during the simulation period, and vary randomly each year within bounds set by coefficients of variation (CV) of survival = 0.2 for both age classes. CV of fecundity is 0.4. Proportion of 1 year-old birds breeding = 0.5, proportion of > 1 year-old birds = 1.0. Number of iterations = 5000; simulation period = 100 years. Fecundity = mean number of chicks fledged per pair; K = carrying capacity; N = population size (number of pairs) = recovery objective. Fecundity is reduced for pairs that exceed the recovery objective; Allee effects are invoked if N < 100 pairs.
| Probability @ 100 years | ||||||
| Fecundity | K | N | N=0 | N<50 | N<100 | N<500 |
| 125 | 2,000 | 1,200 | 35 | 78 | 81 | 95 |
| 125 | 2,000 | 1,500 | 31 | 73 | 76 | 92 |
| 125 | 2,000 | 2,000 | 22 | 59 | 63 | 82 |
| 125 | 3,000 | 3,000 | 23 | 58 | 61 | 81 |
| 125 | 4,000 | 4,000 | 23 | 57 | 62 | 82 |
| 125 | 5,000 | 5,000 | 23 | 56 | 60 | 82 |
| 125 | 10,000 | 10,000 | 20 | 56 | 60 | 82 |
| 150 | 2,000 | 1,200 | 11 | 26 | 29 | 55 |
| 150 | 2,000 | 1,300 | 9 | 22 | 24 | 50 |
| 150 | 2,000 | 1,400 | 8 | 22 | 24 | 47 |
| 150 | 2,000 | 1,500 | 9 | 20 | 22 | 44 |
| 150 | 2,000 | 1,600 | 6 | 18 | 20 | 44 |
| 150 | 2,000 | 1,700 | 7 | 17 | 19 | 40 |
| 150 | 2,000 | 1,800 | 6 | 16 | 17 | 39 |
| 150 | 2,000 | 1,900 | 5 | 13 | 15 | 36 |
| 150 | 2,000 | 2,000 | 4 | 10 | 11 | 26 |
Table C. Extinction probabilities for Atlantic Coast piping plovers assuming declining survival.
Mean adult and fledgling survival rates begin at 0.74 and 0.48, respectively, then decline by 5 and 10% respectively, at a linear rate between year 1 and 50, then remain stable at 0.70 and 0.44, respectively, between year 50 and 100. Coefficients of variation (CV) of survival estimates are 0.2 for both age classes. CV of fecundity is 0.4. Proportion of 1 year-old birds breeding is 0.5; proportion of > 1 year-old birds breeding is 1.0. Number of iterations = 5000; simulation period = 100 years. Fecundity = mean number of chicks fledged per pair; K = carrying capacity; N = population size (number of pairs) = recovery objective. Fecundity is reduced for number of pairs that exceed the recovery objective, and Allee effects are invoked if N < 100 pairs.
|
Probability @ 100 years | ||||||
| Fecundity | K | N | N=0 | N<50 | N<100 | N<500 |
| 1.5 | 2,000 | 1,200 | 40 | 87 | 90 | 97 |
| 1.5 | 2,000 | 1,500 | 39 | 84 | 86 | 97 |
| 1.5 | 2,000 | 2,000 | 32 | 70 | 76 | 90 |
| 1.5 | 3,000 | 3,000 | 32 | 70 | 74 | 91 |
| 1.5 | 4,000 | 4,000 | 29 | 68 | 73 | 91 |
| 1.5 | 5,000 | 5,000 | 28 | 66 | 72 | 90 |
| 1.5 | 10,000 | 10,000 | 29 | 68 | 73 | 91 |
|
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Last updated March 15, 2000