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Viability analysis of endangered Gulf Coast beach mice (Peromyscus polionotus) populations
Biological Conservation 97 (2001) 107±118
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Viability analysis of endangered Gulf Coast beach mice (Peromyscus polionotus) populations Madan K. Oli a,*, Nicholas R. Holler a,b, Michael C. Wooten a a
Department of Biological Sciences, 331 Funchess Hall, Auburn University, Auburn, AL 36849-5414, USA Alabama Cooperative Fish and Wildlife Research Unit, Auburn University, Auburn, AL 36849-5414, USA
b
Received 6 December 1999; received in revised form 18 April 2000; accepted 31 May 2000
Abstract Beach mice, endangered subspecies of old®eld mice (Peromyscus polionotus), occur in a few, isolated populations along the Gulf Coast of Alabama and Florida, USA. To provide information needed for the management of these species, we conducted population viability analyses (PVA) using a stochastic dierential equation (Wiener-drift) model applied to long-term demographic data for four populations of beach mice. In the absence of catastrophic events, the probability that the mouse populations would decline to one mouse ranged from 0.002 for the population of Alabama beach mice (P. p. ammobates) at the Perdue unit of Bon Secour National Wildlife Refuge (BSPU) to 1.00 for the Perdido Key beach mouse (P. p. trissyllepsis) population at Gulf Island National Seashore (GINS). Modal time to extinction for those sample paths reaching extinction ranged from 5 years for the Fort Morgan population of Alabama beach mice to 21 years for the GINS population of Perdido Key beach mice. When the BSPU data set was extended to include data collected following Hurricane Opal, the probability of extinction increased to 0.479. If catastrophic events, which are frequent in the Gulf Coast habitats, are considered, virtually all populations of beach mice appear in substantial danger of extinction unless current levels of habitat fragmentation are reversed. In addition, ongoing development continues to reduce or fragment the habitat exacerbating the already precarious existence of these mice. It is our conclusion that the results obtained from the PVA analyses provide independent evidence that further loss of beach mouse habitat (including the scrub dune component) should be avoided, and that populations should be re-established within their historic range wherever feasible. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Alabama; Alabama beach mice; Conservation; Endangered species; Perdido Key beach mice; Peromyscus polionotus; Demography; Population dynamics; Population modelling; Population viability analysis (PVA)
1. Introduction Beach mice (Peromyscus polionotus ssp.) are inhabitants of coastal dune habitats along the northern Gulf Coast in the southeastern United States of America. Beach mice historically occurred throughout the coastal regions of the states of Alabama and western Florida. Five subspecies of beach mice are found along the Gulf Coast from Indian Pass in Gulf County, FL, west to the tip of the Fort Morgan peninsula in Baldwin County, AL, USA (Fig. 1). The increased pace of commercial and residential development in recent decades has resulted in substantial loss and fragmentation of habitat * Corresponding author at present address: Department of Wildlife Ecology and Conservation, University of Florida, 303 NewinsZiegler Hall, Gainesville, FL 32611-0430, USA. Fax: +1-352-3926984. E-mail address: [email protected]¯.edu (M.K. Oli).
available for these mice. Currently, beach mice occur in a few, isolated populations on a small portion of their historic range. Four of these subspecies, P. p. peninsularis, P. p. allophrys, P. p. trissyllepsis and P. p. ammobates, are listed as endangered. The remaining subspecies, the Santa Rosa beach mouse (P. p. leucocephalus), currently is not state or federally protected. An important element required for the management of any species at risk is an assessment of the viability of existing populations (Schaer, 1990). One approach to such assessment is through population viability analysis (PVA) (Gilpin and SouleÂ, 1986). PVA is a set of modelling techniques that utilize time-series data or basic life history parameters such as survival and fecundity rates as input variables for estimating risk of population extinction. The data requirements and range of results for these models are extremely varied and the techniques have been the subject of extensive research (Boyce,
0006-3207/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0006-3207(00)00104-X
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Fig. 1. Map illustrating locations of four populations of endangered beach mice that served as data sources for population viability analyses. The populations were located in coastal dune habitat in the states of Alabama and Florida, USA. Abbreviations for the study sites are: Fort Morgan Unit of Bon Secour National Wildlife Refuge (FTMO), Perdue Unit of Bon Secour National Wildlife Refuge (BSPU), Florida Point Unit of Gulf State Park (FPPK), and Johnson Beach Unit of Gulf Islands National Seashore (GINS). FTMO and BSPU represent populations of the Alabama beach mouse (Peromyscus polionotus ammobates). FPPK and GINS were the two last known populations of the Perdido Key beach mouse (P. p. trissyllepsis).
1992; Caughley, 1994; Mills et al., 1996; Beissinger and Westphal, 1998; Ludwig, 1999). Here, we present results of population viability analyses using a stochastic dierential equation (Wiener-drift; Dennis et al., 1991) model. Using this method, we estimated growth and extinction parameters for four populations of beach mice. Data for these analyses were derived from an extensive beach mouse population database. In 1986, personnel from the Alabama Cooperative Fish and Wildlife Research Unit began an ecological study of beach mice, including the Alabama and Perdido Key subspecies. Information on various aspects of population biology and life history obtained in these studies has been described in a series of publications (Hill, 1989; Holler et al., 1989; Holler and Rave, 1991; Holler, 1992a,b; Moyers, 1996; Novak, 1997; Swilling et al., 1998). After
reviewing the requirements for various PVA models, we determined that long-term demographic data from four populations of Alabama and Perdido Key beach mice provided the best estimates of parameters for use in conducting a comparative population viability analysis. Given the range of biotic and abiotic conditions experienced by these four populations, results from these analyses should serve as a reasonable starting point for evaluating viability of Gulf Coast populations. 2. Study area Data were obtained from mice representing four populations of two endangered subspecies. The four populations were situated west to east in what was
M.K. Oli et al. / Biological Conservation 97 (2001) 107±118
eectively linear dune habitat that is characteristic of the northern Gulf Coast (Fig. 1). The original ranges of the two subspecies were separated by a narrow outlet that drains the coastal bay. Housing and commercial development has resulted in extensive fragmentation of the dune habitat with a corresponding dramatic reduction in the known range. The two populations of Perdido Key beach mice (P. p. trissyllepsis) were separated by approximately 20 km of developed areas (Fig. 1) with no other populations known to exist. Scattered populations of Alabama beach mice (P. p. ammobates) were known to exist between the two study sites but trapping data indicate little probability of exchange. The two populations of Perdido Key beach mice studied were located within Gulf State Park, AL, USA. (Florida Point; FPPK), and within Gulf Islands National Seashore, FL, USA. (Johnson Beach; GINS). Florida Point is a small block of habitat at the extreme western end of Perdido Key (Fig. 1). The southern portion of the habitat block (separated by a coastal highway) is 1.9 km long, varies from about 30 m wide on the east to about 100 m wide at the western end, and consists of a line of primary dunes with a grassy ¯at or low secondary dunes landward. Some habitat north of the highway was intermittently used by beach mice but was not included in this study. Johnson Beach is located at the extreme eastern end of Perdido Key (Fig. 1). It has approximately 11 km of dune habitat which consists of primary and secondary dunes. Average width of the habitat is about 100 m. This habitat was extensively damaged by Hurricane Frederic in 1979, but showed good recovery by 1986. The mouse population was extirpated in 1979, but was re-established in 1986±1987 (Holler et al., 1989). Alabama beach mice were studied at the Perdue (BSPU) and Fort Morgan (FTMO) Units of the Bon Secour National Wildlife Refuge, Alabama, USA (Fig. 1). Habitat at the Perdue Unit is 5.5 km long and 260± 300 m wide, with good primary, secondary, and scrub dune habitat. It is the largest block of uninterrupted beach mouse habitat in Alabama. Habitat at Fort Morgan is 3.0 km long and 50±100 m wide (Fig. 1). It was heavily damaged by Hurricane Elena in 1985; when our study began only a few relict dunes remained. Dune restoration has been good and during most of our study there was a well-developed line of primary dunes with scattered relict secondary dunes to the rear. The study sites were described in detail by Holler et al. (1989), Rave and Holler (1992) and Swilling et al. (1998). 3. Methods 3.1. Data collection and estimation of population size Mice were captured using Sherman live traps (56.516.5 cm) set 10±15 m apart along trapping lines
109
in the dune habitat. The number of trapping stations varied between 150 at FPPK to 512 at GINS. Trapping transects consisted of single or double lines with each trapline con®gured to maximize capture probabilities at each site. Traps were opened in late evening and baited with dried oats or apple. Captured mice were weighed, and marked for individual identi®cation. Sex and reproductive status were determined by external criteria. Age was determined by pelage state. All mice were released at the sites of capture. The Jackknife estimator of program CAPTURE (Otis et al., 1978) was used to estimate population size within the trapped area using capture-recapture data. Trapping periods lasted for ®ve nights and were conducted two to six times per year. The Florida Point site was trapped in spring and autumn each year from spring 1986 through spring 1994. The three remaining sites were trapped four times per year between autumn 1988 and spring 1994. Data collected during 1987 and 1988 at the Perdue and Fort Morgan Units have been published previously (Rave and Holler, 1992). Studies at the Perdue Unit continued with bimonthly trapping starting the spring of 1994 and ending in February 1997. These studies were ongoing when Hurricane Opal made landfall on the Gulf Coast on 4 October 1995. We reanalyzed this extended set of data (BSPU2) to provide insight into the eects of a catastrophe on the probability of extinction. 3.2. Population viability analysis (PVA) Several methods are available for PVA (Boyce, 1992; Burgman et al., 1993; Caughley and Gunn, 1996; Beissinger and Westphal, 1998) including techniques that have been incorporated into computer programs such as the RAMAS family of software (Ferson, 1990; AkcËakaya et al., 1993; Burgman et al., 1993; Lindenmayer et al., 1995) and VORTEX (Lacy and Kreeger, 1992). Typically, analytical PVA models rely on estimated population growth rate and its variance, and can often be used without detailed knowledge of life history of study organisms (Beissinger and Westphal, 1998). These models, however, do not explicitly consider the eects of catastrophic events or other major environmental perturbations. Generic or custom simulation models, on the other hand, can capture the complexity of natural populations, including potential eects of catastrophic events. These models, however, are data-intensive and most require detailed life history and habitat data, eect of catastrophic events on life history variables, and other information that are not available for most endangered or threatened species. Thus, choice of a PVA model must be based on the availability of data. We have obtained reliable estimates of population size for our study populations based on 7±8 years of capture±recapture studies. We also have investigated various aspects of life history of these populations,
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including survival rates, dispersal, and prevalence and frequency of breeding (Rave and Holler, 1992; N. Holler, Alabama Cooperative Fish and Wildlife Research Unit, unpublished data). However, we lack data on several aspects of life history of beach mice, such as juvenile survival, fecundity (based on ®eld data), and potential eects of catastrophic events on life history variables. Considering the unavailability of these critical data and after careful review of available methods, we selected the stochastic dierential equation (Wienerdrift) model (Dennis et al. 1991) as the most appropriate for our data. Although the Wiener-drift model does not explicitly consider the direct eect of catastrophes and genetic stochasticity, it does incorporate environmental stochasticity which occurs within the sample period. Simple stochastic models, such as the Wiener-drift model, have been shown to adequately capture the dynamical properties of age- or stage-structured populations (Tuljapurkar and Orzack, 1980; Heyde and Cohen, 1985; Dennis et al., 1991; Lima et al., 1998). Most importantly, from our long-term studies we have reliable data to place parameters on the model (Dennis et al., 1991). While our ongoing studies continue to collect more data on the life history of beach mice, PVA results from the Wiener-drift model should provide insights into the relative risk faced by our study populations. Because only a portion of the habitat within each study site was sampled, population estimates for each study site were extrapolated for the total area of the suitable habitat. Multiplier factors were: 2 for GINS; 1 for FPPK; 2 for FTMO; and 5 for BSPU (Fig. 2A±D). Time series data on population size (extrapolated for the size of the study area) were used to estimate growth and extinction parameters for each study site. Census data were transformed as: yi=[ln(Ni /Niÿ1)]/ i , where Ni=population size at time i (i=0, 1, 2,. . .q), and ti is the time interval between successive censuses. A linear regression without intercept was performed with p yi as the dependent variable, and i as independent variable. The slope of the regression line has been shown to be an unbiased maximum likelihood estimator of the Wiener-drift mean parameter . Variance of the residuals can, thus, be taken as an unbiased maximum likelihood estimate of the model variance parameter, 2 (Dennis et al., 1991). The continuous rate of increase, r, was estimated as r 2 =2, and variance of r as Var r 2 =tq 4 =2 qÿ1, where q is the number of censuses, and tq is the time dierence between the ®rst and the last census. The probability of extinction (de®ned here as the probability of reaching the critical population size, Ncrit , at some future time), , was calculated as:
1; if40 exp ÿ2Xd = 2 ; if > 0
where Xd is the natural log of the ratio of population size at last census (Nq ) and the critical population size (Ncrit ; i.e. Xd =ln[Nq =Ncrit ]). Mean time to reach the critical population size () was calculated as Xd =jj, where jj is the absolute value of the model parameter, . Distribution of extinction time under the Wiener-drift model follows the inverse Gaussian distribution (Dennis et al., 1991). Thus, 100*p percentiles of the distribution are obtained by numerically ®nding the root of a nonlinear equation: G p ; Xd ; ; 2 ÿp 0, where, G p ; Xd ; ; 2 is the inverse Gaussian cumulative distribution function (cdf). Median time to extinction was calculated as the root of the above equation for p=0.5; other percentiles of the distribution can be calculated similarly by changing the value of p and numerically solving the equation. Most likely (mode) time to extinction (t*) is the value of t that maximizes the inverse Gaussian probability density function (pdf), g t; Xd ; ; 2 : ! xd 9 1=2 3 1 2 ÿ t j j 4v 2v where v Xd jj= 2 . Inverse Gaussian pdf was plotted as a function of time to produce a plot of probability distribution of extinction time given that the critical population size is reached. See Dennis et al. (1991) for full mathematical details and examples. The probability of extinction as calculated above does not have a time frame, and the probability of extinction before a given time calculated from inverse Gaussian cdf applies only to the sample paths that go extinct. It would, however, be helpful in reaching management decisions to know the risk faced by the populations within a given period of time. To provide this information, we utilized Monte Carlo simulations to calculate the probability of extinction before a given projected time. When assumptions of the Wiener-drift model are met, is normally distributed with mean and variance 2 =tq (i.e. normal (; 2 =tq )), and p an estimate of the standard error of is given by 2 =tq . Given this, we constructed 90% con®dence intervals of as p t0:05; qÿ1 2 =tq (Dennis et al., 1991). For our simulations, we sampled a random number from a normally distributed population with mean and variance 2 =tq . If the random number was within the 90% CI of , we used it as a model parameter and projected the natural log population size for a future time t as (Dennis et al., 1991): Xq t where is the natural log of population size at time t, Xq is the natural log of population size at the last census
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Fig. 2. Estimates of population size for: Bon Secour National Wildlife Refuge, Fort Morgan Unit (FTMO); Gulf State Park, Florida Point (FPPK); Gulf Islands National Seashore, Johnson Beach (GINS); and Bon Secour National Wildlife Refuge, Perdue Unit (BSPU). A. Fort Morgan (FTMO), B. Florida Point (FPPK), C. Gulf Islands National Seashore (GINS), and D. Bon Secour National Wildlife Refuge, Perdue Unit (BSPU). Data points represent jackknife population estimates (program CAPTURE) that were extrapolated for the total area of the suitable habitat. Census periods were: FTMO: October 1988±June 1994; FPPK: April 1986±May 1994; GINS: December 1988±June 1994; BSPU: October 1988±February 1997. Solid arrow indicates Hurricane Opal.
q; population size at time t was calculated as eU . If the random number was not within 90% CI of , another random number was drawn until one within 90% CI of was sampled. This process was repeated 50,000 times. The probability of extinction was calculated as the proportion of sample paths that were equal to or less than the critical population size. Given the critical population size (Ncrit ), the probability of extinction from the Wiener-drift model depends on , 2 , and Nq . Among our study populations, BSPU2 was monitored for the longest period and also included post-hurricane Opal data. We took the value of calculated from the BSPU2 data as the base parameter and investigated the sensitivity of extinction probabilities to changes in 2 and Nq for Ncrit =10 using Monte Carlo simulations. To investigate the sensitivity of extinction probabilities to 2 , and Nq were held constant (=0.072, Nq =465; Table 1), and 2 was allowed to vary. For each value of 2 , we constructed 90% con®dence interval on . To begin each simulation, a random number was drawn from a normally distributed population with mean and variance 2 =tq . If the random number was within the 90% CI of , it was used as the model parameter to project the natural log population size for 100 years as described above. This process was repeated 50,000 times
for each value of 2 . The probability of extinction was then calculated as the proportion of the sample paths with projected population size equal to or less than 10. The probability of extinction was then plotted as a function of 2 . The sensitivity of the probability of extinction to changes in Nq was investigated similarly, except that and 2 were held constant (=0.072, 2 =1.202; Table 1), and Nq was allowed to vary. One concern in all ecological analyses is that estimates of population size may be erroneous for a variety of reasons, and they may also be heavily in¯uenced by ®eld conditions as well as inadequacy of models used to analyze capture±recapture data. Although it is dicult to ascertain which observations are erroneous, the regression approach to estimating parameters for Wiener-drift model allows identi®cation of observations that exert unduly high in¯uence on estimated model parameters. Dennis et al. (1991) recommend identifying outlier transitions and excluding them from analyses. Following their approach, we de®ned an outlier as an observation that is not appropriately accommodated by a regression model, and which, when removed, can cause signi®cant change in the model parameters. Several in¯uence diagnostic statistics are available for identifying outlier observations in regression analysis, one of which is DFBETAS (Belsley et al., 1980; Myers,
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Table 1 Maximum likelihood estimates of growth and extinction parameters (Wiener-drift model) for four populations of endangered beach mice (Peromyscus polionotus)a Population
FTMOb FPPKc GINSd BSPUe BSPU2f
0.116 0.199 ÿ0.070 0.266 0.072
2
1.791 0.459 0.276 0.610 1.202
r
1.012 0.428 0.068 0.572 0.673
Var (r)
0.097 0.011 0.006 0.011 0.025
Nq
226 147 88 1155 465
Ncrit
t Ncrit
5 Ncrit
1
10
20
1
10
20
1
10
20
0.494 0.013 1.00 0.002 0.479
0.667 0.098 1.00 0.016 0.631
0.729 0.178 1.00 0.029 0.680
19.98 20.49 44.91 22.82 37.47
8.14 9.56 16.72 14.43 17.64
5.29 6.46 9.41 11.94 12.62
5.39 13.13 21.49 16.54 10.30
1.80 4.63 5.53 9.10 4.06
1.80 2.68 2.61 7.05 2.73
a
Extinction parameters are given for three values of critical population size (Ncrit=1, 10 and 20). Parameters were estimated after removing outlier observations. Values given for each population are: =Wiener-drift mean parameter, 2 =Wiener-drift variance parameter, r=estimated continuous annual rate of population growth, Var (r)=variance of the population growth rate, Nq=population size at last census, =probability that a population falls below the critical population size, 0:5 =median time (years) to reach the critical population size, and t =most likely (mode) time (years) to reach the critical population size. b Bon Secour National Wildlife Refuge, Fort Morgan Unit, AL. c Gulf State Park, Florida Point, AL. d Gulf Islands National Seashore, Johnson Beach (GINS), FL. e Bon Secour National Wildlife Refuge, Perdue Unit, AL, pre-hurricane Opal data. f Bon Secour National Wildlife Refuge, Perdue Unit, AL, pre- and post-hurricane Opal data.
1990). Typically, large absolute values of DFBETAS indicate outlier observations. Following the recommendation of Belsleyp et al. (1980), any observation with |DFBETAS|52/ N, where N is the number of transitions in a data set, was excluded from analysis. Once an outlier was removed, we re-analyzed the data, performed in¯uence diagnostics, and removed any remaining outliers; this process was repeated until none of the remaining transitions in the data set had |DFBEp TAS|52/ N. For our data, only 2±4 data points per data set were identi®ed as outliers and excluded from analysis. An important point is that each outlier was identi®ed by comparison to its nearest-neighbours which resulted in points being recommended for removal that are not necessarily at the extremes, as in more common variance based methods. 4. Results All of our study populations showed substantial changes in size during the study (Fig. 2). The number of transitions identi®ed as outliers in each of the four populations were: three (transitions following February, April and August 1992 censuses) for FTMO; two (transitions following April 1986 and November 1987 censuses) for FPPK; three (transitions following December 1988, November 1992 and October 1993 censuses) for GINS; and three (transitions following February 1990, June 1993 and October 1996 censuses) for BSPU. These transitions were dropped from the data sets prior to analyses. Although the FTMO population exhibited the highest growth rate of all study populations (Table 1), its longterm persistence is compromised by a substantial
¯uctuation in population size as re¯ected in high variance of population growth rate. Populations at FPPK and GINS were less variable, the latter with slow but declining trend in population size. During our study, the BSPU population grew steadily with a fairly low variance once outliers were removed from the data set (Table 1; Fig. 2D through the sample period (October 1988±February 1997). Long-term trends in population size [Fig. 2A±D] were clearly re¯ected in the estimated extinction parameters (Table 1). The GINS population, which showed an overall declining trend, was predicted by the model to be at the highest risk (Table 1). The FTMO population had the highest growth rate. This population was estimated to be at high risk of extinction, however, because of substantial ¯uctuation in population size. The prehurricane BSPU population had the highest population size and the lowest probability of extinction for any value of critical population size, and is, therefore, predicted to be at lowest risk among four study populations (Table 1). Distribution of time required to reach the critical population size, given that it is reached, may be used to assess the relative time frame of the extinction process. Median, and mode times to reach extinction are presented in Table 1. The highly skewed distribution of predicted extinction times (Fig. 3) invalidates the use of mean time to extinction as an appropriate measure of expected time to reach the critical population size; median and mode times to extinction and distribution of extinction time (Table 1) appear to be better indicators of the relative risk faced by each population. Our results indicate that the GINS population is certain to go extinct and is expected to decline to one mouse within 45 (median) or 21 (mode) years (Table 1).
M.K. Oli et al. / Biological Conservation 97 (2001) 107±118
Another population with severe risk of extinction is that at FTMO. The model predicts that this population has a 49% chance of declining to a single mouse at some future time, and if such a decline occurs it is likely to occur within 20 (median) or 5 (mode) years. Using only data through spring 1994 (i.e., pre-hurricane), the probability of extinction (Ncrit=1) was low for the BSPU population (=0.002). However, when post-Hurricane Opal data were included (BSPU2), probability of extinction rose to 0.479, and for those sample paths reaching Ncrit the median and mode times to extinction were 37 and 10 years, respectively. The predicted probability of extinction of the FPPK population is low (0.013). Given that the population declines to one mouse, it is expected to occur within 20 (median) or 13 (mode) years. Given that extinction occurs (Ncrit=10), there is a greater than 59% chance that it will occur within 25 years for all populations and a greater than 75% chance that it will occur within 50 years (Table 2a). Using results framed in more common terms (the overall probability of extinction before X years; Table 2b), there exists a substantial predicted probability of extinction within 100 years for all populations except FPPK, and for BSPU using only pre-hurricane data. However, inclusion of post-hurricane data (BSPU2) shows the population at BSPU also at substantial risk of extinction within 100 years. Overall, the BSPU population is predicted by the model to be the most viable of all study populations in the absence of catastrophic events, or when all populations are aected similarly by such events.
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5. Discussion Our analyses indicate that all study populations are at substantial risk of extinction. We believe this estimate of risk to be real. In fact, our estimates of extinction probabilities may be conservative. Severe population reduction or loss has occurred across all four sites since the data for this study were collected. However, care should be used in interpreting the results of our analyses. Estimates of extinction probabilities and times to extinction derived in analyses such as those used in this study may not be precise (cf. Beissinger and Westphal, 1998) and are clearly dependent on the information available for the starting parameters. Our data were collected during a period of general population growth following Hurricane Elena (1985), or in the case of GINS following reintroduction. All populations were substantially reduced following Hurricane Opal (1995), but we only had post-hurricane data adequate for analysis for BSPU2. In all other cases, our analyses do not consider the eects of a catastrophic event. Such events, however, are a normal aspect of long-term beach mouse population ecology. The population at BSPU was predicted to be much more viable than those at GINS or FTMO using the sample period prior to Hurricane Opal. We believe this derives from both the quantity and quality of habitat available to the population at that site. BSPU was considerably larger than FTMO and heterogeneity of habitat was greater than at either of the other sites. Nevertheless, when data were extended to include the
Fig. 3. Plots of inverse Gaussian probability density functions for each of four beach mouse populations, including pre- and post-hurricane Opal output for the Bon Secour National Wildlife Refuge (Perdue Unit; pre-hurricane: BSPU, pre- and post-hurricane: BSPU2). See text for details.
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Table 2 Probabilities of reaching critical population sizes in four populations of endangered beach micea Population t:
Probability of reaching Ncrit by (years): 25 50
75
Ncrit
1
1
10
500
1
10
1
10
1
10
A. Results based on inverse Gaussian cumulative distribution function FTMOb 0.569 0.763 0.754 0.871 0.837 FPPKc 0.621 0.871 0.918 0.977 0.981 GINSd 0.234 0.639 0.550 0.830 0.725 0.566 0.798 0.925 0.973 0.987 BSPUe BSPU2f 0.368 0.595 0.589 0.755 0.703
0.915 0.995 0.905 0.995 0.827
0.883 0.995 0.825 0.998 0.772
0.940 0.998 0.942 0.999 0.869
0.958 0.999 0.963 1.000 0.896
0.978 1.000 0.988 1.000 0.941
0.995 1.000 0.999 1.000 0.978
0.997 1.000 0.999 1.000 0.988
B. Results based FTMOb FPPKc GINSd BSPUe BSPU2f
0.381 0.137 0.587 0.217 0.359
0.378 0.127 0.565 0.126 0.358
0.389 0.144 0.599 0.140 0.376
0.396 0.156 0.605 0.153 0.388
0.398 0.163 0.625 0.157 0.398
0.399 0.167 0.633 0.171 0.405
0.409 0.172 0.639 0.174 0.403
0.342 0.082 0.489 0.080 0.299
10
200
10
on simulations 0.276 0.322 0.025 0.072 0.333 0.472 0.016 0.046 0.192 0.257
1
100
0.370 0.120 0.558 0.104 0.334
0.364 0.115 0.537 0.111 0.342
a Probabilities were derived using both analytical (inverse Gaussian cumulative distribution function) and simulation approaches for time periods ranging from 25 to 500 years. A: the probability of reaching the critical population size (Ncrit) before time t given that the critical population size is reached for Ncrit=1 and 10. All probabilities were calculated from the inverse Gaussian cumulative distribution function (cdf). B: the probability of reaching the critical population size (Ncrit) before a given time t based on 50,000 simulations. The probability of reaching Ncrit was calculated as the proportion of sample paths with population size at time t equal to or less than Ncrit. See text for full details. b Bon Secour National Wildlife Refuge, Fort Morgan Unit, AL. c Gulf State Park, Florida Point, AL. d Gulf Islands National Seashore, Johnson Beach (GINS), FL. e Bon Secour National Wildlife Refuge, Perdue Unit, AL, pre-hurricane Opal data. f Bon Secour National Wildlife Refuge, Perdue Unit, AL, pre- and post-hurricane Opal data.
period following Hurricane Opal, even BSPU was at substantial risk. Studies at BSPU clearly demonstrated the importance of scrub dune habitat to mice during a hurricane event (Swilling et al., 1998). Following the hurricane, numbers of mice occupying the scrub dunes increased, and mice remaining seaward of the scrub dunes made feeding forays into that habitat. Frontal dunes were essentially destroyed by the hurricane, but scrub dunes sustained mice permitting recolonization of the frontal dunes as the habitat recovered. This pattern was repeated following Hurricane Danny in 1997. Damage caused by Hurricane Opal at BSPU was considerably less than that caused in areas further east in Florida and closer to landfall (J. Moyers, personal communication). Thus, the increased probability of extinction estimated for BSPU2 does not re¯ect a worst case scenario. Also, because they have little or no scrub dune habitat, the eects of hurricanes on our other study sites would certainly be greater than those observed at BSPU. Recent reduction in the beach mouse population at GINS (M. C. Wooten, unpublished data.) may be related to this fact. The population at FPPK illustrates the caution which must be used in interpreting the results of population viability analyses based on data derived from sample periods too short to include normally recurring environmental catastrophes. Intuitively, we considered this population to be most at risk due to small size of the area sustaining the population, and lack of habitat heterogeneity, in particular the scrub dune component. The
model, however, indicated that probability of extinction for FPPK was low (0.013). This was a direct result of the data being collected between hurricane events during a period of population growth. Our data collection began soon after Hurricane Elena (1985) when mouse populations were low and habitat quality was poor. Except for one brief period of decline the population at FPPK was increasing and showed low variability. Habitat quality also showed continued improvement. Damage during Hurricane Opal was severe, especially on the eastern half of the area. Mice persisted in substantial numbers on the western portion immediately following the hurricane, but disappeared by the following summer (N.R. Holler, unpublished data). The population is now considered to be extirpated; this is consistent with our intuitive prediction. Overall, the results from this PVA are consistent in predicting that long-term viability of our study populations is questionable. The Perdido Key subspecies appears to be in immediate danger (Tables 1 and 2a, b and discussion re: FPPK). The probability that the two populations of the Alabama beach mouse will persist for 5100 years, a bench mark period for conservation, is lower than anticipated (Table 2a and 2b). The probability of extinction was generally insensitive to changes in current population size (Nq). Reasonable increases in Nq alone, given the observed and 2 from the BSPU population, would be unlikely to minimize the risk faced by this population (Fig. 4). The probability of extinction was very sensitive to changes in the
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variance parameter, 2 (Fig. 5). However, to maintain the probability that the BSPU population declines to 10 mice to 15% for 100 years, nearly an order of magnitude reduction in 2 would be required. Because of the frequency of catastrophic events in the Gulf Coast region, and existing limits on the size of available habitat, large increases in population size or substantial reduction in the variance of the population growth rate may not be attainable. Moderate increases in population size and decreases in the variance of the population growth rate may, however, be achievable by restoring populations on adjacent suitable habitats, increasing habitats area for the population to expand, and by promoting habitat heterogeneity (Drescher and Wissel, 1998). Two factors have frequently been emphasized as potential in¯uences in PVA models, density dependence and migration. In general, positive density-dependence and migration are suggested to increase persistence probabilities (Young, 1994). Our long term population data, however, provided little evidence for densitydependent responses, positive or negative, within any of the four populations during the years of our study. Admittedly, the sampling design was not adequate to detect small dierences but no obvious patterns of density dependency were noted. As an example during the peak reproductive periods, the percentage of females that were pregnant or pregnant/lactating varied little across years despite many-fold dierences in mouse density (M.C. Wooten, unpublished data). Reproductive output in these mice, by all measures available, was
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uncorrelated with population density during the period of this study. Most importantly, there was no evidence that density-dependent responses played a major role in buering severe population declines, the area of response that would be most critical in moderating extinction predictions. Immigration may have been an important component that was not included in our analyses. Each of our study populations was treated as an independent unit with no possibility of immigration from adjacent areas. This treatment was realistic for populations of the Perdido Key beach mouse because the two study sites were completely isolated by many kilometers of intense development creating a hostile environment for migration. In contrast, populations of Alabama beach mice at both the Perdue Unit and Fort Morgan may still be augmented by immigration from adjacent areas. Recent trapping data (1999±2000) indicated that movement of mice from scrub habitats contributed substantially to repopulation of the frontal dunes following population loss due to a series of severe storms (M. C. Wooten, unpublished data). Therefore, for these two populations it is important that migration between habitat patches be incorporated into future models. The adjacent areas have been developed to varying degrees and their ability to sustain populations of beach mice is unknown. The risk associated even with the BSPU population, our most secure population, clearly indicates the importance of maintaining multiple populations spread over as wide an area as possible. At present, we cannot provide estimates of the probability of losing all populations of a
Fig. 4. The sensitivity of the probability of extinction (probability that a population declines to 10 mice in 100 years) to changes in current population size (Nq) based on 50,000 simulations for each value of Nq. The mean and variance parameters were held constant at =0.072 and 2 =1.202.
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Fig. 5. The sensitivity of the probability of extinction (probability that a population declines to 10 mice in 100 years) to changes in variance parameter ( 2 ) based on 50,000 simulations for each value of 2 . The mean parameter and current population size were held constant at =0.072 and Nq =465. See text for full details.
subspecies simultaneously but clearly, application of a microgeographic metapopulation management design would be one approach to overcome the extinction dangers identi®ed by the PVA (Drechsler and Wissel, 1998). Studies are currently underway to assess Alabama beach mouse densities and population dynamics in areas outside of our original study sites. These studies should allow re®nement of future population viability estimates. Multiple populations do provide some protection against total loss, especially when migration or translocation among populations is possible. This has been directly demonstrated by the history of the Perdido Key beach mouse. When we began our work, the subspecies had been extirpated from all areas except FPPK. We reestablished mice on GINS in 1986±1987 (Holler et al., 1989). Following Hurricane Opal, the population at FPPK was lost, but mice still persist at GINS. This population has now recovered adequately to permit translocations to re-establish the subspecies at Perdido Key Recreation Area, Florida. Had the second population not been established earlier, the subspecies would now be extinct. Considerable research would be required to permit re®ned PVA for beach mice, and data on some critical variables (e.g. survival from birth to weaning) may never be obtainable. Furthermore, determining the variability in eects of hurricanes on life history parameters may not be possible due to the irregular frequency of hurricane events and the inherent variability
in their eects. We believe that our data are adequate to indicate that each of the four primary populations are at high, potentially unacceptable, levels of risk and require management attention. It is our recommendation that research eorts should be directed towards obtaining data permitting better management of existing habitat, and restoration of habitat following storm damage. In particular, areas presently developed that are subject to recurrent destruction by storms should be considered for possible return to natural beach habitat. Management strategies should focus on the preservation of remaining habitat, and restoration of habitat wherever possible. In particular, our ®ndings and those of Swilling et al. (1998) indicate that the zone of scrub dune habitat, where it occurs, helps to mitigate the deleterious eects of hurricanes. Preservation of the scrub dunes should be given high priority in conservation planning, and critical habitat should be rede®ned to include this zone where it presently exists. 6. Conclusion For many conservation biologists, results from population viability analyses are often disconcerting and, in some cases, outright discouraging. For small mammals in particular, their inherent tendencies to exhibit wide variation in life-history parameters frequently yield extreme persistence probabilities with large variances. In many cases, conclusions that populations will persist
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forever or go extinct in less time than is needed to publish the ®nding are not viewed as useful. Unfortunately, as we report for one population in this study, such conclusions may well be correct. In fact, given what is known about the ecology of Peromyscus polionotus, ``boom or bust'' models are fairly viable representations of nature. More often, however, reality is less extreme. Species do persist over extended time spans and no population lasts forever. For ``boom or bust'' species, what purpose, then, does a PVA serve? Hamilton and Moller (1995) argued that the value of many PVA analyses lies in the ``guidance to the relative ecacy of dierent management actions'' they provide, not in the accuracy of their predictions. PVA analyses serve as guideposts for re®ning critical questions. No matter the range of variance, they do provide a ranking of the relative danger of loss among populations or species, often in directions counter to existing management views. PVAs also help de®ne ``critical variables'' and allow researchers to focus limited resources on acquisition of the most critical data or habitat. The results for beach mice illustrate these qualities. For example, despite occurring on the largest uninterrupted habitat block of those studied, the GINS population appeared to be highly susceptible to loss. This information prompted acceleration of planned reestablishment eorts which have now been successfully completed (M. Wooten, unpublished data). The PVA results were instrumental in heightening awareness and cooperation among the multiple agencies involved. Findings that the now extirpated FPPK population, from a life-history perspective, had a relatively high probability of persistence has led to reconsideration of the value of this habitat block for re-introduction of mice. The dicult public relations problem of controlling free-ranging domestic cats, likely contributors to the population demise, has been given a strengthened focus by the agencies in charge. Clearly, even PVAs based on limited data that fail to give precise answers can be useful in the caldron of issues faced by conservationists. Acknowledgements This study was supported by the US Fish and Wildlife Service, through Agreement 1448-0004-94-9174. We gratefully acknowledge the personnel of the Bon Secour National Wildlife Refuge and the US Fish and Wildlife Service, especially Robbie Dailey, Lorna Patrick and Celeste South. Bill Lynn, Trent Farris, Denise Dailey, Steve Connick and Randy Swilling all contributed untold hours to the data collection eort. This manuscript was improved by insightful comments of Craig Guyer, Will McDearman, Mark Schwartz, and two anonymous reviewers.
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References AkcËakaya, H.R., McCarthy, M.A., Pearce, J., 1993. RAMAS/GIS: linking landscape data with population viability analysis. In: McAleer, M., Jakeman, A. (Eds.), Proceedings of the International Congress on Modelling and Simulation, Vol. 2. University of Western Australia, Australia, pp. 627±632. Beissinger, S.R., Westphal, M.I., 1998. On the use of demographic models of population viability in endangered species management. Journal of Wildlife Management 62, 821±841. Belsley, D.A., Kuh, E., Welsch, R.E., 1980. Regression Diagnostics: Identifying In¯uential Data and Sources of Collinearity, John Wiley, New York. Boyce, M.S., 1992. Population viability analysis. Annual Review of Ecology and Systematics 23, 481±506. Burgman, M.A., Ferson, S., AkcËakaya, H.R., 1993. Risk Assessment in Conservation Biology, Chapman & Hall, London. Caughley, G., 1994. Directions in conservation biology. Journal of Animal Ecology 63, 215±244. Caughley, G., Gunn, A., 1996. Conservation Biology in Theory and Practice. Blackwell Scienti®c, Cambridge, Massachusetts. Dennis, B., Munholland, P.L., Scott, J.M., 1991. Estimation of growth and extinction parameters for endangered species. Ecological Monographs 61, 115±143. Drechsler, M., Wissel, C., 1998. Trade-os between local and regional scale management of metapopulations. Biological Conservation 83, 31±41. Ferson, S., 1990. RAMAS/stage: generalized stage-based modeling for population dynamics. Applied Biomathematics, New York. Gilpin, M.E., SouleÂ, M.E., 1986. Minimum viable populations, processes of species extinction. In: Soule (Ed.), Conservation Biology, the Science of Scarcity and Diversity. Sinauer Associates, Sunderland, Massachusetts, pp. 19±34. Hamilton, S., Moller, H., 1995. Can PVA models using computer packages oer useful conservation advice? Sooty shearwaters Punus griseus in New Zealand as a case study. Biological Conservation 73, 107±117. Heyde, C.C., Cohen, J.E., 1985. Con®dence intervals for demographic projections based on products of random matrices. Theoretical Population Biology 27, 120±153. Hill, E.A., 1989. Population Dynamics, Habitat, and Distribution of the Alabama Beach Mouse. MS thesis. Auburn University, Alabama. Holler, N.R., 1992a. Choctawhatchee beach mouse. In: Humphrey, S.R. (Ed.), Rare and Endangered Biota of Florida, Volume 1. Mammals. University Presses of Florida, Tallahassee, Florida, pp. 76±86. Holler, N.R., 1992b. Perdido key beach mouse. In: Humphrey, S.R. (Ed.), Rare and Endangered Biota of Florida, Volume 1. Mammals. University Presses of Florida, Tallahassee, Florida, pp. 102±109. Holler, N.R., Mason, D.W., Dawson, R.M., Simons, T., Wooten, M.C., 1989. Reestablishment of the Perdido Key beach mouse (Peromyscus polionotus trissyllepsis) on Gulf Islands National Seashore. Conservation Biology 3, 397±404. Holler, N.R., Rave, E.H., 1991. Status of endangered beach mouse populations in Alabama. Journal of the Alabama Academy of Sciences 62, 18±27. Lacy, R., Kreeger, T., 1992. VORTEX users manual: a stochastic simulation of the extinction process, Chicago Zoological Society, Chicago Zoological Park, Brook®eld. Lima, M., Marquet, P.A., Jaksic, F.M., 1998. Population extinction risks of three Neotropical small mammal species. Oecologia 115, 120±126. Lindenmayer, D.B., Burgman, M.A., AkcËakaya, H.R., Lacy, R.C., Possingham, H.P., 1995. A review of the generic computer programs ALEX, RAMAS/space and VORTEX for modeling the viability of wildlife metapopulations. Ecological Modeling 82, 161±174. Ludwig, D., 1999. Is it meaningful to estimate probability of extinction? Ecology 80, 298±310.
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Mills, L.S., Hays, S.G., Baldwin, C., Wisdom, M.J., Cittaw, J., Mattson, D.J. et al., 1996. Factors leading to dierent viability of predictions for a grizzly bear data set. Conservation Biology 10, 863±873. Moyers, J.E., 1996. Food Habits of Gulf Coast Subspecies of Beach Mice (Peromyscus polionotus ssp.). MS thesis, Auburn University, Alabama, USA. Myers, R.H., 1990. Classical and Modern Regression with Applications, PWS-Kent, Boston. Novak, J.A., 1997. Home Range and Habitat use of Choctawhatchee Beach Mice. MS thesis Auburn University, Alabama. Otis, D.L., Burnham, K.P., White, G.C., Anderson, D.R., 1978. Statistical inference from capture data on closed animal populations. Wildlife Monographs 62, 1±135.
Rave, E.H., Holler, N.R., 1992. Population dynamics of beach mice (Peromyscus polionotus ammobates) in southern Alabama. Journal of Mammalogy 73, 347±355. Schaer, M.L., 1990. Population viability analysis. Conservation Biology 4, 39±40. Swilling, W.R., Wooten, M.C., Wooten, Holler, N.R., Lynn, W.J., 1998. Population dynamics of Alabama beach mice (Peromyscus polionotus ammobates) following Hurricane Opal. American Midland Naturalist 140, 287±298. Tuljapurkar, S., Orzack, S.H., 1980. Population dynamics in variable environments. Theoretical Population Biology 18, 314±342. Young, T.P., 1994. Natural die-os of large mammals: implications for conservation. Conservation Biology 8, 410±418.
www.elsevier.com/locate/biocon
Viability analysis of endangered Gulf Coast beach mice (Peromyscus polionotus) populations Madan K. Oli a,*, Nicholas R. Holler a,b, Michael C. Wooten a a
Department of Biological Sciences, 331 Funchess Hall, Auburn University, Auburn, AL 36849-5414, USA Alabama Cooperative Fish and Wildlife Research Unit, Auburn University, Auburn, AL 36849-5414, USA
b
Received 6 December 1999; received in revised form 18 April 2000; accepted 31 May 2000
Abstract Beach mice, endangered subspecies of old®eld mice (Peromyscus polionotus), occur in a few, isolated populations along the Gulf Coast of Alabama and Florida, USA. To provide information needed for the management of these species, we conducted population viability analyses (PVA) using a stochastic dierential equation (Wiener-drift) model applied to long-term demographic data for four populations of beach mice. In the absence of catastrophic events, the probability that the mouse populations would decline to one mouse ranged from 0.002 for the population of Alabama beach mice (P. p. ammobates) at the Perdue unit of Bon Secour National Wildlife Refuge (BSPU) to 1.00 for the Perdido Key beach mouse (P. p. trissyllepsis) population at Gulf Island National Seashore (GINS). Modal time to extinction for those sample paths reaching extinction ranged from 5 years for the Fort Morgan population of Alabama beach mice to 21 years for the GINS population of Perdido Key beach mice. When the BSPU data set was extended to include data collected following Hurricane Opal, the probability of extinction increased to 0.479. If catastrophic events, which are frequent in the Gulf Coast habitats, are considered, virtually all populations of beach mice appear in substantial danger of extinction unless current levels of habitat fragmentation are reversed. In addition, ongoing development continues to reduce or fragment the habitat exacerbating the already precarious existence of these mice. It is our conclusion that the results obtained from the PVA analyses provide independent evidence that further loss of beach mouse habitat (including the scrub dune component) should be avoided, and that populations should be re-established within their historic range wherever feasible. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Alabama; Alabama beach mice; Conservation; Endangered species; Perdido Key beach mice; Peromyscus polionotus; Demography; Population dynamics; Population modelling; Population viability analysis (PVA)
1. Introduction Beach mice (Peromyscus polionotus ssp.) are inhabitants of coastal dune habitats along the northern Gulf Coast in the southeastern United States of America. Beach mice historically occurred throughout the coastal regions of the states of Alabama and western Florida. Five subspecies of beach mice are found along the Gulf Coast from Indian Pass in Gulf County, FL, west to the tip of the Fort Morgan peninsula in Baldwin County, AL, USA (Fig. 1). The increased pace of commercial and residential development in recent decades has resulted in substantial loss and fragmentation of habitat * Corresponding author at present address: Department of Wildlife Ecology and Conservation, University of Florida, 303 NewinsZiegler Hall, Gainesville, FL 32611-0430, USA. Fax: +1-352-3926984. E-mail address: [email protected]¯.edu (M.K. Oli).
available for these mice. Currently, beach mice occur in a few, isolated populations on a small portion of their historic range. Four of these subspecies, P. p. peninsularis, P. p. allophrys, P. p. trissyllepsis and P. p. ammobates, are listed as endangered. The remaining subspecies, the Santa Rosa beach mouse (P. p. leucocephalus), currently is not state or federally protected. An important element required for the management of any species at risk is an assessment of the viability of existing populations (Schaer, 1990). One approach to such assessment is through population viability analysis (PVA) (Gilpin and SouleÂ, 1986). PVA is a set of modelling techniques that utilize time-series data or basic life history parameters such as survival and fecundity rates as input variables for estimating risk of population extinction. The data requirements and range of results for these models are extremely varied and the techniques have been the subject of extensive research (Boyce,
0006-3207/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0006-3207(00)00104-X
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Fig. 1. Map illustrating locations of four populations of endangered beach mice that served as data sources for population viability analyses. The populations were located in coastal dune habitat in the states of Alabama and Florida, USA. Abbreviations for the study sites are: Fort Morgan Unit of Bon Secour National Wildlife Refuge (FTMO), Perdue Unit of Bon Secour National Wildlife Refuge (BSPU), Florida Point Unit of Gulf State Park (FPPK), and Johnson Beach Unit of Gulf Islands National Seashore (GINS). FTMO and BSPU represent populations of the Alabama beach mouse (Peromyscus polionotus ammobates). FPPK and GINS were the two last known populations of the Perdido Key beach mouse (P. p. trissyllepsis).
1992; Caughley, 1994; Mills et al., 1996; Beissinger and Westphal, 1998; Ludwig, 1999). Here, we present results of population viability analyses using a stochastic dierential equation (Wiener-drift; Dennis et al., 1991) model. Using this method, we estimated growth and extinction parameters for four populations of beach mice. Data for these analyses were derived from an extensive beach mouse population database. In 1986, personnel from the Alabama Cooperative Fish and Wildlife Research Unit began an ecological study of beach mice, including the Alabama and Perdido Key subspecies. Information on various aspects of population biology and life history obtained in these studies has been described in a series of publications (Hill, 1989; Holler et al., 1989; Holler and Rave, 1991; Holler, 1992a,b; Moyers, 1996; Novak, 1997; Swilling et al., 1998). After
reviewing the requirements for various PVA models, we determined that long-term demographic data from four populations of Alabama and Perdido Key beach mice provided the best estimates of parameters for use in conducting a comparative population viability analysis. Given the range of biotic and abiotic conditions experienced by these four populations, results from these analyses should serve as a reasonable starting point for evaluating viability of Gulf Coast populations. 2. Study area Data were obtained from mice representing four populations of two endangered subspecies. The four populations were situated west to east in what was
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eectively linear dune habitat that is characteristic of the northern Gulf Coast (Fig. 1). The original ranges of the two subspecies were separated by a narrow outlet that drains the coastal bay. Housing and commercial development has resulted in extensive fragmentation of the dune habitat with a corresponding dramatic reduction in the known range. The two populations of Perdido Key beach mice (P. p. trissyllepsis) were separated by approximately 20 km of developed areas (Fig. 1) with no other populations known to exist. Scattered populations of Alabama beach mice (P. p. ammobates) were known to exist between the two study sites but trapping data indicate little probability of exchange. The two populations of Perdido Key beach mice studied were located within Gulf State Park, AL, USA. (Florida Point; FPPK), and within Gulf Islands National Seashore, FL, USA. (Johnson Beach; GINS). Florida Point is a small block of habitat at the extreme western end of Perdido Key (Fig. 1). The southern portion of the habitat block (separated by a coastal highway) is 1.9 km long, varies from about 30 m wide on the east to about 100 m wide at the western end, and consists of a line of primary dunes with a grassy ¯at or low secondary dunes landward. Some habitat north of the highway was intermittently used by beach mice but was not included in this study. Johnson Beach is located at the extreme eastern end of Perdido Key (Fig. 1). It has approximately 11 km of dune habitat which consists of primary and secondary dunes. Average width of the habitat is about 100 m. This habitat was extensively damaged by Hurricane Frederic in 1979, but showed good recovery by 1986. The mouse population was extirpated in 1979, but was re-established in 1986±1987 (Holler et al., 1989). Alabama beach mice were studied at the Perdue (BSPU) and Fort Morgan (FTMO) Units of the Bon Secour National Wildlife Refuge, Alabama, USA (Fig. 1). Habitat at the Perdue Unit is 5.5 km long and 260± 300 m wide, with good primary, secondary, and scrub dune habitat. It is the largest block of uninterrupted beach mouse habitat in Alabama. Habitat at Fort Morgan is 3.0 km long and 50±100 m wide (Fig. 1). It was heavily damaged by Hurricane Elena in 1985; when our study began only a few relict dunes remained. Dune restoration has been good and during most of our study there was a well-developed line of primary dunes with scattered relict secondary dunes to the rear. The study sites were described in detail by Holler et al. (1989), Rave and Holler (1992) and Swilling et al. (1998). 3. Methods 3.1. Data collection and estimation of population size Mice were captured using Sherman live traps (56.516.5 cm) set 10±15 m apart along trapping lines
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in the dune habitat. The number of trapping stations varied between 150 at FPPK to 512 at GINS. Trapping transects consisted of single or double lines with each trapline con®gured to maximize capture probabilities at each site. Traps were opened in late evening and baited with dried oats or apple. Captured mice were weighed, and marked for individual identi®cation. Sex and reproductive status were determined by external criteria. Age was determined by pelage state. All mice were released at the sites of capture. The Jackknife estimator of program CAPTURE (Otis et al., 1978) was used to estimate population size within the trapped area using capture-recapture data. Trapping periods lasted for ®ve nights and were conducted two to six times per year. The Florida Point site was trapped in spring and autumn each year from spring 1986 through spring 1994. The three remaining sites were trapped four times per year between autumn 1988 and spring 1994. Data collected during 1987 and 1988 at the Perdue and Fort Morgan Units have been published previously (Rave and Holler, 1992). Studies at the Perdue Unit continued with bimonthly trapping starting the spring of 1994 and ending in February 1997. These studies were ongoing when Hurricane Opal made landfall on the Gulf Coast on 4 October 1995. We reanalyzed this extended set of data (BSPU2) to provide insight into the eects of a catastrophe on the probability of extinction. 3.2. Population viability analysis (PVA) Several methods are available for PVA (Boyce, 1992; Burgman et al., 1993; Caughley and Gunn, 1996; Beissinger and Westphal, 1998) including techniques that have been incorporated into computer programs such as the RAMAS family of software (Ferson, 1990; AkcËakaya et al., 1993; Burgman et al., 1993; Lindenmayer et al., 1995) and VORTEX (Lacy and Kreeger, 1992). Typically, analytical PVA models rely on estimated population growth rate and its variance, and can often be used without detailed knowledge of life history of study organisms (Beissinger and Westphal, 1998). These models, however, do not explicitly consider the eects of catastrophic events or other major environmental perturbations. Generic or custom simulation models, on the other hand, can capture the complexity of natural populations, including potential eects of catastrophic events. These models, however, are data-intensive and most require detailed life history and habitat data, eect of catastrophic events on life history variables, and other information that are not available for most endangered or threatened species. Thus, choice of a PVA model must be based on the availability of data. We have obtained reliable estimates of population size for our study populations based on 7±8 years of capture±recapture studies. We also have investigated various aspects of life history of these populations,
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including survival rates, dispersal, and prevalence and frequency of breeding (Rave and Holler, 1992; N. Holler, Alabama Cooperative Fish and Wildlife Research Unit, unpublished data). However, we lack data on several aspects of life history of beach mice, such as juvenile survival, fecundity (based on ®eld data), and potential eects of catastrophic events on life history variables. Considering the unavailability of these critical data and after careful review of available methods, we selected the stochastic dierential equation (Wienerdrift) model (Dennis et al. 1991) as the most appropriate for our data. Although the Wiener-drift model does not explicitly consider the direct eect of catastrophes and genetic stochasticity, it does incorporate environmental stochasticity which occurs within the sample period. Simple stochastic models, such as the Wiener-drift model, have been shown to adequately capture the dynamical properties of age- or stage-structured populations (Tuljapurkar and Orzack, 1980; Heyde and Cohen, 1985; Dennis et al., 1991; Lima et al., 1998). Most importantly, from our long-term studies we have reliable data to place parameters on the model (Dennis et al., 1991). While our ongoing studies continue to collect more data on the life history of beach mice, PVA results from the Wiener-drift model should provide insights into the relative risk faced by our study populations. Because only a portion of the habitat within each study site was sampled, population estimates for each study site were extrapolated for the total area of the suitable habitat. Multiplier factors were: 2 for GINS; 1 for FPPK; 2 for FTMO; and 5 for BSPU (Fig. 2A±D). Time series data on population size (extrapolated for the size of the study area) were used to estimate growth and extinction parameters for each study site. Census data were transformed as: yi=[ln(Ni /Niÿ1)]/ i , where Ni=population size at time i (i=0, 1, 2,. . .q), and ti is the time interval between successive censuses. A linear regression without intercept was performed with p yi as the dependent variable, and i as independent variable. The slope of the regression line has been shown to be an unbiased maximum likelihood estimator of the Wiener-drift mean parameter . Variance of the residuals can, thus, be taken as an unbiased maximum likelihood estimate of the model variance parameter, 2 (Dennis et al., 1991). The continuous rate of increase, r, was estimated as r 2 =2, and variance of r as Var r 2 =tq 4 =2 qÿ1, where q is the number of censuses, and tq is the time dierence between the ®rst and the last census. The probability of extinction (de®ned here as the probability of reaching the critical population size, Ncrit , at some future time), , was calculated as:
1; if40 exp ÿ2Xd = 2 ; if > 0
where Xd is the natural log of the ratio of population size at last census (Nq ) and the critical population size (Ncrit ; i.e. Xd =ln[Nq =Ncrit ]). Mean time to reach the critical population size () was calculated as Xd =jj, where jj is the absolute value of the model parameter, . Distribution of extinction time under the Wiener-drift model follows the inverse Gaussian distribution (Dennis et al., 1991). Thus, 100*p percentiles of the distribution are obtained by numerically ®nding the root of a nonlinear equation: G p ; Xd ; ; 2 ÿp 0, where, G p ; Xd ; ; 2 is the inverse Gaussian cumulative distribution function (cdf). Median time to extinction was calculated as the root of the above equation for p=0.5; other percentiles of the distribution can be calculated similarly by changing the value of p and numerically solving the equation. Most likely (mode) time to extinction (t*) is the value of t that maximizes the inverse Gaussian probability density function (pdf), g t; Xd ; ; 2 : ! xd 9 1=2 3 1 2 ÿ t j j 4v 2v where v Xd jj= 2 . Inverse Gaussian pdf was plotted as a function of time to produce a plot of probability distribution of extinction time given that the critical population size is reached. See Dennis et al. (1991) for full mathematical details and examples. The probability of extinction as calculated above does not have a time frame, and the probability of extinction before a given time calculated from inverse Gaussian cdf applies only to the sample paths that go extinct. It would, however, be helpful in reaching management decisions to know the risk faced by the populations within a given period of time. To provide this information, we utilized Monte Carlo simulations to calculate the probability of extinction before a given projected time. When assumptions of the Wiener-drift model are met, is normally distributed with mean and variance 2 =tq (i.e. normal (; 2 =tq )), and p an estimate of the standard error of is given by 2 =tq . Given this, we constructed 90% con®dence intervals of as p t0:05; qÿ1 2 =tq (Dennis et al., 1991). For our simulations, we sampled a random number from a normally distributed population with mean and variance 2 =tq . If the random number was within the 90% CI of , we used it as a model parameter and projected the natural log population size for a future time t as (Dennis et al., 1991): Xq t where is the natural log of population size at time t, Xq is the natural log of population size at the last census
M.K. Oli et al. / Biological Conservation 97 (2001) 107±118
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Fig. 2. Estimates of population size for: Bon Secour National Wildlife Refuge, Fort Morgan Unit (FTMO); Gulf State Park, Florida Point (FPPK); Gulf Islands National Seashore, Johnson Beach (GINS); and Bon Secour National Wildlife Refuge, Perdue Unit (BSPU). A. Fort Morgan (FTMO), B. Florida Point (FPPK), C. Gulf Islands National Seashore (GINS), and D. Bon Secour National Wildlife Refuge, Perdue Unit (BSPU). Data points represent jackknife population estimates (program CAPTURE) that were extrapolated for the total area of the suitable habitat. Census periods were: FTMO: October 1988±June 1994; FPPK: April 1986±May 1994; GINS: December 1988±June 1994; BSPU: October 1988±February 1997. Solid arrow indicates Hurricane Opal.
q; population size at time t was calculated as eU . If the random number was not within 90% CI of , another random number was drawn until one within 90% CI of was sampled. This process was repeated 50,000 times. The probability of extinction was calculated as the proportion of sample paths that were equal to or less than the critical population size. Given the critical population size (Ncrit ), the probability of extinction from the Wiener-drift model depends on , 2 , and Nq . Among our study populations, BSPU2 was monitored for the longest period and also included post-hurricane Opal data. We took the value of calculated from the BSPU2 data as the base parameter and investigated the sensitivity of extinction probabilities to changes in 2 and Nq for Ncrit =10 using Monte Carlo simulations. To investigate the sensitivity of extinction probabilities to 2 , and Nq were held constant (=0.072, Nq =465; Table 1), and 2 was allowed to vary. For each value of 2 , we constructed 90% con®dence interval on . To begin each simulation, a random number was drawn from a normally distributed population with mean and variance 2 =tq . If the random number was within the 90% CI of , it was used as the model parameter to project the natural log population size for 100 years as described above. This process was repeated 50,000 times
for each value of 2 . The probability of extinction was then calculated as the proportion of the sample paths with projected population size equal to or less than 10. The probability of extinction was then plotted as a function of 2 . The sensitivity of the probability of extinction to changes in Nq was investigated similarly, except that and 2 were held constant (=0.072, 2 =1.202; Table 1), and Nq was allowed to vary. One concern in all ecological analyses is that estimates of population size may be erroneous for a variety of reasons, and they may also be heavily in¯uenced by ®eld conditions as well as inadequacy of models used to analyze capture±recapture data. Although it is dicult to ascertain which observations are erroneous, the regression approach to estimating parameters for Wiener-drift model allows identi®cation of observations that exert unduly high in¯uence on estimated model parameters. Dennis et al. (1991) recommend identifying outlier transitions and excluding them from analyses. Following their approach, we de®ned an outlier as an observation that is not appropriately accommodated by a regression model, and which, when removed, can cause signi®cant change in the model parameters. Several in¯uence diagnostic statistics are available for identifying outlier observations in regression analysis, one of which is DFBETAS (Belsley et al., 1980; Myers,
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Table 1 Maximum likelihood estimates of growth and extinction parameters (Wiener-drift model) for four populations of endangered beach mice (Peromyscus polionotus)a Population
FTMOb FPPKc GINSd BSPUe BSPU2f
0.116 0.199 ÿ0.070 0.266 0.072
2
1.791 0.459 0.276 0.610 1.202
r
1.012 0.428 0.068 0.572 0.673
Var (r)
0.097 0.011 0.006 0.011 0.025
Nq
226 147 88 1155 465
Ncrit
t Ncrit
5 Ncrit
1
10
20
1
10
20
1
10
20
0.494 0.013 1.00 0.002 0.479
0.667 0.098 1.00 0.016 0.631
0.729 0.178 1.00 0.029 0.680
19.98 20.49 44.91 22.82 37.47
8.14 9.56 16.72 14.43 17.64
5.29 6.46 9.41 11.94 12.62
5.39 13.13 21.49 16.54 10.30
1.80 4.63 5.53 9.10 4.06
1.80 2.68 2.61 7.05 2.73
a
Extinction parameters are given for three values of critical population size (Ncrit=1, 10 and 20). Parameters were estimated after removing outlier observations. Values given for each population are: =Wiener-drift mean parameter, 2 =Wiener-drift variance parameter, r=estimated continuous annual rate of population growth, Var (r)=variance of the population growth rate, Nq=population size at last census, =probability that a population falls below the critical population size, 0:5 =median time (years) to reach the critical population size, and t =most likely (mode) time (years) to reach the critical population size. b Bon Secour National Wildlife Refuge, Fort Morgan Unit, AL. c Gulf State Park, Florida Point, AL. d Gulf Islands National Seashore, Johnson Beach (GINS), FL. e Bon Secour National Wildlife Refuge, Perdue Unit, AL, pre-hurricane Opal data. f Bon Secour National Wildlife Refuge, Perdue Unit, AL, pre- and post-hurricane Opal data.
1990). Typically, large absolute values of DFBETAS indicate outlier observations. Following the recommendation of Belsleyp et al. (1980), any observation with |DFBETAS|52/ N, where N is the number of transitions in a data set, was excluded from analysis. Once an outlier was removed, we re-analyzed the data, performed in¯uence diagnostics, and removed any remaining outliers; this process was repeated until none of the remaining transitions in the data set had |DFBEp TAS|52/ N. For our data, only 2±4 data points per data set were identi®ed as outliers and excluded from analysis. An important point is that each outlier was identi®ed by comparison to its nearest-neighbours which resulted in points being recommended for removal that are not necessarily at the extremes, as in more common variance based methods. 4. Results All of our study populations showed substantial changes in size during the study (Fig. 2). The number of transitions identi®ed as outliers in each of the four populations were: three (transitions following February, April and August 1992 censuses) for FTMO; two (transitions following April 1986 and November 1987 censuses) for FPPK; three (transitions following December 1988, November 1992 and October 1993 censuses) for GINS; and three (transitions following February 1990, June 1993 and October 1996 censuses) for BSPU. These transitions were dropped from the data sets prior to analyses. Although the FTMO population exhibited the highest growth rate of all study populations (Table 1), its longterm persistence is compromised by a substantial
¯uctuation in population size as re¯ected in high variance of population growth rate. Populations at FPPK and GINS were less variable, the latter with slow but declining trend in population size. During our study, the BSPU population grew steadily with a fairly low variance once outliers were removed from the data set (Table 1; Fig. 2D through the sample period (October 1988±February 1997). Long-term trends in population size [Fig. 2A±D] were clearly re¯ected in the estimated extinction parameters (Table 1). The GINS population, which showed an overall declining trend, was predicted by the model to be at the highest risk (Table 1). The FTMO population had the highest growth rate. This population was estimated to be at high risk of extinction, however, because of substantial ¯uctuation in population size. The prehurricane BSPU population had the highest population size and the lowest probability of extinction for any value of critical population size, and is, therefore, predicted to be at lowest risk among four study populations (Table 1). Distribution of time required to reach the critical population size, given that it is reached, may be used to assess the relative time frame of the extinction process. Median, and mode times to reach extinction are presented in Table 1. The highly skewed distribution of predicted extinction times (Fig. 3) invalidates the use of mean time to extinction as an appropriate measure of expected time to reach the critical population size; median and mode times to extinction and distribution of extinction time (Table 1) appear to be better indicators of the relative risk faced by each population. Our results indicate that the GINS population is certain to go extinct and is expected to decline to one mouse within 45 (median) or 21 (mode) years (Table 1).
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Another population with severe risk of extinction is that at FTMO. The model predicts that this population has a 49% chance of declining to a single mouse at some future time, and if such a decline occurs it is likely to occur within 20 (median) or 5 (mode) years. Using only data through spring 1994 (i.e., pre-hurricane), the probability of extinction (Ncrit=1) was low for the BSPU population (=0.002). However, when post-Hurricane Opal data were included (BSPU2), probability of extinction rose to 0.479, and for those sample paths reaching Ncrit the median and mode times to extinction were 37 and 10 years, respectively. The predicted probability of extinction of the FPPK population is low (0.013). Given that the population declines to one mouse, it is expected to occur within 20 (median) or 13 (mode) years. Given that extinction occurs (Ncrit=10), there is a greater than 59% chance that it will occur within 25 years for all populations and a greater than 75% chance that it will occur within 50 years (Table 2a). Using results framed in more common terms (the overall probability of extinction before X years; Table 2b), there exists a substantial predicted probability of extinction within 100 years for all populations except FPPK, and for BSPU using only pre-hurricane data. However, inclusion of post-hurricane data (BSPU2) shows the population at BSPU also at substantial risk of extinction within 100 years. Overall, the BSPU population is predicted by the model to be the most viable of all study populations in the absence of catastrophic events, or when all populations are aected similarly by such events.
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5. Discussion Our analyses indicate that all study populations are at substantial risk of extinction. We believe this estimate of risk to be real. In fact, our estimates of extinction probabilities may be conservative. Severe population reduction or loss has occurred across all four sites since the data for this study were collected. However, care should be used in interpreting the results of our analyses. Estimates of extinction probabilities and times to extinction derived in analyses such as those used in this study may not be precise (cf. Beissinger and Westphal, 1998) and are clearly dependent on the information available for the starting parameters. Our data were collected during a period of general population growth following Hurricane Elena (1985), or in the case of GINS following reintroduction. All populations were substantially reduced following Hurricane Opal (1995), but we only had post-hurricane data adequate for analysis for BSPU2. In all other cases, our analyses do not consider the eects of a catastrophic event. Such events, however, are a normal aspect of long-term beach mouse population ecology. The population at BSPU was predicted to be much more viable than those at GINS or FTMO using the sample period prior to Hurricane Opal. We believe this derives from both the quantity and quality of habitat available to the population at that site. BSPU was considerably larger than FTMO and heterogeneity of habitat was greater than at either of the other sites. Nevertheless, when data were extended to include the
Fig. 3. Plots of inverse Gaussian probability density functions for each of four beach mouse populations, including pre- and post-hurricane Opal output for the Bon Secour National Wildlife Refuge (Perdue Unit; pre-hurricane: BSPU, pre- and post-hurricane: BSPU2). See text for details.
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Table 2 Probabilities of reaching critical population sizes in four populations of endangered beach micea Population t:
Probability of reaching Ncrit by (years): 25 50
75
Ncrit
1
1
10
500
1
10
1
10
1
10
A. Results based on inverse Gaussian cumulative distribution function FTMOb 0.569 0.763 0.754 0.871 0.837 FPPKc 0.621 0.871 0.918 0.977 0.981 GINSd 0.234 0.639 0.550 0.830 0.725 0.566 0.798 0.925 0.973 0.987 BSPUe BSPU2f 0.368 0.595 0.589 0.755 0.703
0.915 0.995 0.905 0.995 0.827
0.883 0.995 0.825 0.998 0.772
0.940 0.998 0.942 0.999 0.869
0.958 0.999 0.963 1.000 0.896
0.978 1.000 0.988 1.000 0.941
0.995 1.000 0.999 1.000 0.978
0.997 1.000 0.999 1.000 0.988
B. Results based FTMOb FPPKc GINSd BSPUe BSPU2f
0.381 0.137 0.587 0.217 0.359
0.378 0.127 0.565 0.126 0.358
0.389 0.144 0.599 0.140 0.376
0.396 0.156 0.605 0.153 0.388
0.398 0.163 0.625 0.157 0.398
0.399 0.167 0.633 0.171 0.405
0.409 0.172 0.639 0.174 0.403
0.342 0.082 0.489 0.080 0.299
10
200
10
on simulations 0.276 0.322 0.025 0.072 0.333 0.472 0.016 0.046 0.192 0.257
1
100
0.370 0.120 0.558 0.104 0.334
0.364 0.115 0.537 0.111 0.342
a Probabilities were derived using both analytical (inverse Gaussian cumulative distribution function) and simulation approaches for time periods ranging from 25 to 500 years. A: the probability of reaching the critical population size (Ncrit) before time t given that the critical population size is reached for Ncrit=1 and 10. All probabilities were calculated from the inverse Gaussian cumulative distribution function (cdf). B: the probability of reaching the critical population size (Ncrit) before a given time t based on 50,000 simulations. The probability of reaching Ncrit was calculated as the proportion of sample paths with population size at time t equal to or less than Ncrit. See text for full details. b Bon Secour National Wildlife Refuge, Fort Morgan Unit, AL. c Gulf State Park, Florida Point, AL. d Gulf Islands National Seashore, Johnson Beach (GINS), FL. e Bon Secour National Wildlife Refuge, Perdue Unit, AL, pre-hurricane Opal data. f Bon Secour National Wildlife Refuge, Perdue Unit, AL, pre- and post-hurricane Opal data.
period following Hurricane Opal, even BSPU was at substantial risk. Studies at BSPU clearly demonstrated the importance of scrub dune habitat to mice during a hurricane event (Swilling et al., 1998). Following the hurricane, numbers of mice occupying the scrub dunes increased, and mice remaining seaward of the scrub dunes made feeding forays into that habitat. Frontal dunes were essentially destroyed by the hurricane, but scrub dunes sustained mice permitting recolonization of the frontal dunes as the habitat recovered. This pattern was repeated following Hurricane Danny in 1997. Damage caused by Hurricane Opal at BSPU was considerably less than that caused in areas further east in Florida and closer to landfall (J. Moyers, personal communication). Thus, the increased probability of extinction estimated for BSPU2 does not re¯ect a worst case scenario. Also, because they have little or no scrub dune habitat, the eects of hurricanes on our other study sites would certainly be greater than those observed at BSPU. Recent reduction in the beach mouse population at GINS (M. C. Wooten, unpublished data.) may be related to this fact. The population at FPPK illustrates the caution which must be used in interpreting the results of population viability analyses based on data derived from sample periods too short to include normally recurring environmental catastrophes. Intuitively, we considered this population to be most at risk due to small size of the area sustaining the population, and lack of habitat heterogeneity, in particular the scrub dune component. The
model, however, indicated that probability of extinction for FPPK was low (0.013). This was a direct result of the data being collected between hurricane events during a period of population growth. Our data collection began soon after Hurricane Elena (1985) when mouse populations were low and habitat quality was poor. Except for one brief period of decline the population at FPPK was increasing and showed low variability. Habitat quality also showed continued improvement. Damage during Hurricane Opal was severe, especially on the eastern half of the area. Mice persisted in substantial numbers on the western portion immediately following the hurricane, but disappeared by the following summer (N.R. Holler, unpublished data). The population is now considered to be extirpated; this is consistent with our intuitive prediction. Overall, the results from this PVA are consistent in predicting that long-term viability of our study populations is questionable. The Perdido Key subspecies appears to be in immediate danger (Tables 1 and 2a, b and discussion re: FPPK). The probability that the two populations of the Alabama beach mouse will persist for 5100 years, a bench mark period for conservation, is lower than anticipated (Table 2a and 2b). The probability of extinction was generally insensitive to changes in current population size (Nq). Reasonable increases in Nq alone, given the observed and 2 from the BSPU population, would be unlikely to minimize the risk faced by this population (Fig. 4). The probability of extinction was very sensitive to changes in the
M.K. Oli et al. / Biological Conservation 97 (2001) 107±118
variance parameter, 2 (Fig. 5). However, to maintain the probability that the BSPU population declines to 10 mice to 15% for 100 years, nearly an order of magnitude reduction in 2 would be required. Because of the frequency of catastrophic events in the Gulf Coast region, and existing limits on the size of available habitat, large increases in population size or substantial reduction in the variance of the population growth rate may not be attainable. Moderate increases in population size and decreases in the variance of the population growth rate may, however, be achievable by restoring populations on adjacent suitable habitats, increasing habitats area for the population to expand, and by promoting habitat heterogeneity (Drescher and Wissel, 1998). Two factors have frequently been emphasized as potential in¯uences in PVA models, density dependence and migration. In general, positive density-dependence and migration are suggested to increase persistence probabilities (Young, 1994). Our long term population data, however, provided little evidence for densitydependent responses, positive or negative, within any of the four populations during the years of our study. Admittedly, the sampling design was not adequate to detect small dierences but no obvious patterns of density dependency were noted. As an example during the peak reproductive periods, the percentage of females that were pregnant or pregnant/lactating varied little across years despite many-fold dierences in mouse density (M.C. Wooten, unpublished data). Reproductive output in these mice, by all measures available, was
115
uncorrelated with population density during the period of this study. Most importantly, there was no evidence that density-dependent responses played a major role in buering severe population declines, the area of response that would be most critical in moderating extinction predictions. Immigration may have been an important component that was not included in our analyses. Each of our study populations was treated as an independent unit with no possibility of immigration from adjacent areas. This treatment was realistic for populations of the Perdido Key beach mouse because the two study sites were completely isolated by many kilometers of intense development creating a hostile environment for migration. In contrast, populations of Alabama beach mice at both the Perdue Unit and Fort Morgan may still be augmented by immigration from adjacent areas. Recent trapping data (1999±2000) indicated that movement of mice from scrub habitats contributed substantially to repopulation of the frontal dunes following population loss due to a series of severe storms (M. C. Wooten, unpublished data). Therefore, for these two populations it is important that migration between habitat patches be incorporated into future models. The adjacent areas have been developed to varying degrees and their ability to sustain populations of beach mice is unknown. The risk associated even with the BSPU population, our most secure population, clearly indicates the importance of maintaining multiple populations spread over as wide an area as possible. At present, we cannot provide estimates of the probability of losing all populations of a
Fig. 4. The sensitivity of the probability of extinction (probability that a population declines to 10 mice in 100 years) to changes in current population size (Nq) based on 50,000 simulations for each value of Nq. The mean and variance parameters were held constant at =0.072 and 2 =1.202.
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Fig. 5. The sensitivity of the probability of extinction (probability that a population declines to 10 mice in 100 years) to changes in variance parameter ( 2 ) based on 50,000 simulations for each value of 2 . The mean parameter and current population size were held constant at =0.072 and Nq =465. See text for full details.
subspecies simultaneously but clearly, application of a microgeographic metapopulation management design would be one approach to overcome the extinction dangers identi®ed by the PVA (Drechsler and Wissel, 1998). Studies are currently underway to assess Alabama beach mouse densities and population dynamics in areas outside of our original study sites. These studies should allow re®nement of future population viability estimates. Multiple populations do provide some protection against total loss, especially when migration or translocation among populations is possible. This has been directly demonstrated by the history of the Perdido Key beach mouse. When we began our work, the subspecies had been extirpated from all areas except FPPK. We reestablished mice on GINS in 1986±1987 (Holler et al., 1989). Following Hurricane Opal, the population at FPPK was lost, but mice still persist at GINS. This population has now recovered adequately to permit translocations to re-establish the subspecies at Perdido Key Recreation Area, Florida. Had the second population not been established earlier, the subspecies would now be extinct. Considerable research would be required to permit re®ned PVA for beach mice, and data on some critical variables (e.g. survival from birth to weaning) may never be obtainable. Furthermore, determining the variability in eects of hurricanes on life history parameters may not be possible due to the irregular frequency of hurricane events and the inherent variability
in their eects. We believe that our data are adequate to indicate that each of the four primary populations are at high, potentially unacceptable, levels of risk and require management attention. It is our recommendation that research eorts should be directed towards obtaining data permitting better management of existing habitat, and restoration of habitat following storm damage. In particular, areas presently developed that are subject to recurrent destruction by storms should be considered for possible return to natural beach habitat. Management strategies should focus on the preservation of remaining habitat, and restoration of habitat wherever possible. In particular, our ®ndings and those of Swilling et al. (1998) indicate that the zone of scrub dune habitat, where it occurs, helps to mitigate the deleterious eects of hurricanes. Preservation of the scrub dunes should be given high priority in conservation planning, and critical habitat should be rede®ned to include this zone where it presently exists. 6. Conclusion For many conservation biologists, results from population viability analyses are often disconcerting and, in some cases, outright discouraging. For small mammals in particular, their inherent tendencies to exhibit wide variation in life-history parameters frequently yield extreme persistence probabilities with large variances. In many cases, conclusions that populations will persist
M.K. Oli et al. / Biological Conservation 97 (2001) 107±118
forever or go extinct in less time than is needed to publish the ®nding are not viewed as useful. Unfortunately, as we report for one population in this study, such conclusions may well be correct. In fact, given what is known about the ecology of Peromyscus polionotus, ``boom or bust'' models are fairly viable representations of nature. More often, however, reality is less extreme. Species do persist over extended time spans and no population lasts forever. For ``boom or bust'' species, what purpose, then, does a PVA serve? Hamilton and Moller (1995) argued that the value of many PVA analyses lies in the ``guidance to the relative ecacy of dierent management actions'' they provide, not in the accuracy of their predictions. PVA analyses serve as guideposts for re®ning critical questions. No matter the range of variance, they do provide a ranking of the relative danger of loss among populations or species, often in directions counter to existing management views. PVAs also help de®ne ``critical variables'' and allow researchers to focus limited resources on acquisition of the most critical data or habitat. The results for beach mice illustrate these qualities. For example, despite occurring on the largest uninterrupted habitat block of those studied, the GINS population appeared to be highly susceptible to loss. This information prompted acceleration of planned reestablishment eorts which have now been successfully completed (M. Wooten, unpublished data). The PVA results were instrumental in heightening awareness and cooperation among the multiple agencies involved. Findings that the now extirpated FPPK population, from a life-history perspective, had a relatively high probability of persistence has led to reconsideration of the value of this habitat block for re-introduction of mice. The dicult public relations problem of controlling free-ranging domestic cats, likely contributors to the population demise, has been given a strengthened focus by the agencies in charge. Clearly, even PVAs based on limited data that fail to give precise answers can be useful in the caldron of issues faced by conservationists. Acknowledgements This study was supported by the US Fish and Wildlife Service, through Agreement 1448-0004-94-9174. We gratefully acknowledge the personnel of the Bon Secour National Wildlife Refuge and the US Fish and Wildlife Service, especially Robbie Dailey, Lorna Patrick and Celeste South. Bill Lynn, Trent Farris, Denise Dailey, Steve Connick and Randy Swilling all contributed untold hours to the data collection eort. This manuscript was improved by insightful comments of Craig Guyer, Will McDearman, Mark Schwartz, and two anonymous reviewers.
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