Appendix B
Wolf Viability Analysis
By Robert E. Rolley, Adrian P. Wydeven,
Ronald N. Schultz, Richard T. Thiel and
Bruce E. Kohn.

Population Viability Analysis (PVA) is the estimation of extinction probabilities by analyses that incorporate identifiable threats to population survival into models of the extinction process (Lacy, R. C. 1993. VORTEX: a computer simulation model for population viability analysis. Wildlife Research 20:45-65). The extinction process involves both deterministic processes (eg. over-harvest, habitat destruction, competition or predation from introduced species) and stochastic processes (random variation of demographic and genetic events and the effect of environmental variation on demographic and genetic events).

Stochastic processes are especially important for small populations. Demographic variation is the normal variation in the population's birth and death rates and sex ratio caused by random differences among individuals. For example, in extremely small populations, it is possible through random chance for all offspring born during one generation to be of one sex. Variation in environmental conditions (eg. periodic favorable or severe weather conditions) often cause variation in reproduction and survival rates. In addition, rare catastrophic events, such as disease epidemics, fires, or floods, can greatly affect small populations. Lastly, small populations can be affected by the loss of genetic variation through genetic drift and inbreeding.

Computer simulation modelling provides a tool for exploring the viability of populations subjected to many complex, interacting deterministic and stochastic processes. We used the VORTEX simulation model (Lacy, R. C., K. A. Hughes, and P. S. Miller. 1995. VORTEX: a stochastic simulation of the extinction process. Version 7 User's Manual. IUCN/SSC Conservation Breeding Specialist Group, Apple Valley, MN, USA.) to estimate the viability of the gray wolf population in Wisconsin. VORTEX is an individual-based model that simulates birth and death processes as discrete, sequential events, with probabilistic outcomes. The model generates random numbers to determine whether individual animals lives or dies and the number of progeny produced by each female each year. The model can simulate inbreeding depression as a decrease in viability of inbred animals.

Model Inputs and Assumptions

We modeled the Wisconsin wolf population as a single interbreeding population with no ingress from or egress to other populations. Based on observed litter sizes in Wisconsin, as well as literature records, we assumed a mean litter size of 5.3 pups/litter and the sex ratio at birth of 50:50. We further assumed a Poisson distribution of litter sizes, with a maximum of 11 pups. We assumed that the proportion of females breeding was density dependent. However, due to uncertainty of the proportion of females breeding, we evaluated possible 2 reproductive scenarios. In the high reproduction scenario, we assumed the age of first breeding was 2 years, 90% of females bred when population size was low, and 60% of females bred when the population was at biological carrying capacity. In the low reproduction scenario, we assumed the age of first breeding was 3 years, 80% of female bred when population size was low, and 50% of females bred when the population was at biological carrying capacity. Based on the observed survival rates of radio-collared wolves in Wisconsin, we assumed mean annual pup mortality was 70%, mean annual mortality of yearling and adult females was 16%, and mean annual mortality of yearling and adult males was 30%.

Based on 17 annual estimates, we estimated the standard deviation (SD) of pup mortality was approximately 10%. However, data were not available to estimate the effect of environmental variability on adult mortality rates or the proportion of females producing pups. We believe it is likely that environmental variation has a greater effect on pup survival than on adult survival or the proportion of females breeding. Due to the uncertainty of the effects of environmental variation on survival and reproductive rates, we evaluated 3 scenarios. In the low environmental variation scenario, we assumed the SD in the percentage of females producing was 2%, the SD of pup survival was 5%, and the SD of adult survival was 3%. In the moderate environmental variation scenario, we assumed the SD in the percentage of females producing was 4%, the SD of pup survival was 10%, and the SD of adult survival was 6%. In the high environmental variation scenario, we assumed the SD in the percentage of females producing was 6%, the SD of pup survival was 15%, and the SD of adult survival was 12%. We assumed that variation in survival was concordant with variation in reproduction, i.e., years of poor reproduction were associated with years of poor survival and years of good reproduction were associated with years of good survival.

Few data are available to estimate the frequency of catastrophic events in wolf populations. The Wisconsin wolf population has experienced 2 epidemics during the past 17 years. To assess the effect of catastrophic events on the viability of wolf populations we evaluated 3 scenarios. We simulated population trends assuming a 0, 5, and 10% probability of a catastrophic event per year. We assumed that a catastrophic event reduced both reproduction and survival by 50%.

We assessed the effect of initial population size on viability by simulating trends with initial populations of 100, 200, 300, 400, and 500 wolves. The age distribution of starting populations were set to reflect stable age distributions based on the reproduction and survival rates.

In the initial series of analyses we assumed a biological carrying capacity (BCC) of 500 wolves and that BCC was stable over time. Whenever simulated populations exceed the biological carrying capacity, additional mortality was imposed to reduce the population back to carrying capacity. For each of the 90 combinations of the 2 reproductive, 3 environmental variation, 3 catastrophic event, and 5 initial scenarios we calculated 100 iterations of simulated population change over 100 years. We estimated the probability of extinction (PE) as the proportion of the 100 iterations in with the number of individuals of one sex declined to 0. In addition, we estimated the probability of relisting (PR) wolves as endangered as the proportion of the 100 iterations that declined to less than 80 individuals at least once during the 100-year simulations. In all simulations, we assumed that the population was not harvested or augmented. We did not attempt to simulate the effect of inbreeding depression in these analyses.

We conducted a second series of simulations to assess the effect of managing the population at a level below that of the assumed BCC of 500. For these analyses, we assumed a cultural carrying capacity (CCC) of 300. Because the hypothetical CCC was lower than the BCC set by food availability, we assumed that the percentage of females breeding when the population was at CCC only declined to 80% in the high reproduction scenario and to 70% in the low reproduction scenario. In these analyses, we used initial population sizes of 100, 200, and 300 wolves; assumed a 5% probability of catastrophe; and evaluated the 2 reproduction and 3 environmental variability scenarios described above.

Results

Most simulated populations increased rapidly from the initial size to BCC and fluctuated around BCC, occasionally decreasing due to unfavorable environmental conditions or catastrophic events. Within the range evaluated, initial population size had little effect on the probability of extinction (Tables B1-B6). Averaging across reproductive levels, environmental variability, and the probability of catastrophic events, PE for initial populations of 100 was 0.086, compared to 0.061 for initial populations of 500. In contrast, initial population size did effect the probability that simulated populations would decline below 80 wolves and be relisted as endangered. Mean PR decreased from 0.48 for initial populations of 100 to 0.31 for initial populations of 500.

The probability of catastrophic events greatly affected the probability of extinction. When the probability of catastrophic events was 0, PE was less than or equal to 0.02 for all initial population sizes in all reproduction and environmental variability scenarios evaluated. When the probability of catastrophes was 0.05, PE was less than 0.05 for all initial population sizes in the low and moderate environmental variability scenarios, regardless of reproduction. When environmental variability was high and the probability of catastrophe was 5%, PE was 0.05-0.09 in the high reproduction simulations and 0.09-0.20 in the low reproduction simulations. When the probability of catastrophe was 10%, PE increased markedly as environmental variability increased.

Probability of extinction differ among the 3 levels of environmental variability. Mean PE was 0.013 for low environmental variability, 0.036 for moderate environmental variability, and 0.153 for high environmental variability. The effect of environmental variability differed among levels of reproduction and probability of catastrophes. The increase in PE as environmental variability increased was 2 times greater for low levels of reproduction than for high levels of reproduction. Similarly, the increase in PE as environmental variability increased was markedly greater when the chance of catastrophic events was 10% than when the chance of catastrophes was lower. The proportion of females breeding affected the probability of extinction. Mean PE under the high reproduction scenario was 0.04, compared to 0.09 under the low reproduction scenario. The effect of reproduction differed depending on levels of environmental variation and the probability of catastrophe. The difference in PE between reproductive levels was substantially greater with the high environmental variation scenarios than with the low environmental variation scenarios. Likewise, increasing the probability of catastrophe increased the difference in PE between the two levels of reproduction.

With low to moderate environmental variability and probability of catastrophe less than or equal to 0.05, less then 5% of the simulated populations when extinct (Tables B1, B2, B4, and B5). However, with a 5% chance of catastrophe, the proportion of simulated populations that declined below 80 wolves varied from 0.02 to 0.38 (mean = 0.15) in the low to moderate environmental variation scenarios. The risk of extinction and relisting increased considerably under the high environmental variability and 10% chance of catastrophe scenarios.

Managing wolves at a hypothetical cultural carrying capacity of 300 instead of allowing the population reach a biological carrying capacity of 500 had little effect on the risk of extinction (Tables B7 and B8). However, managing for a lower population approximately doubled the proportion of simulated populations that declining below 80 individuals under the low and moderate environmental variability scenarios. Virtually all simulated populations declined below 80 individuals in the high environmental variability scenarios.

Discussion

PVA is a process of assembling all available demographic information, explicitly incorporating what we do know into an overall model, and evaluating the impact of what we do not know on the predictions from the model. Computer simulation modeling is a tool that permits estimation of the approximate probability of population extinction and facilitates testing of various hypotheses about the viability of small populations. The estimates and predictions are only as good as the data and assumptions input to the model. Because many population processes are stochastic, a PVA can never specify what will happen to a population. Instead, PVA forecasts the likely effects of those factors incorporated into the model.

An essential component of PVA is sensitivity testing, evaluating ranges of plausible values for uncertain parameters to determine the effects of uncertainty on model predictions. Our analyses suggest that estimates of the probability of extinction and relisting are very sensitive to uncertainty about environmental variation and the probability of catastrophes.

PVA is, by definition, an assessment of the probability of persistence of a population over some specified number of years. However, prevention of extinction is only the first step for effective conservation of a species. Management goals may need to be greater than simply preventing extinction if wolves are to be functional members of Wisconsin's biological communities.

In these analyses, we assumed no ingres to determine viable levels for a Wisconsin wolf population that would be independent of wolf population states in adjacent states. We had included ingress in some preliminary analyses, but by definition, a population with constant ingress would never go extinct. Therefore, we believed that including ingress in the model provided little useful information on long-term viability.

The main objective of the management plan is to ensure that wolves will not have to be relisted or endangered. Our current (1998) population estimate is 178 to 184 wolves. This PVA suggests that a population of 300 to 500 wolves would have a high probability of persisting for 100 years under most of the scenarios evaluated. However, given the information currently available we cannot exclude the possibility that a population of 300 to 500 wolves may decline to the point that relisting as endangered will be necessary in the future. In fact, with onlly moderate environmental variability and a 5 percent chance of catastrophic events 10 to 40 percent of simulated population declined below 80 wolves.

Given the effect of uncertainties on model predictions, this PVA should be viewed as a component of an adaptive management process. In adaptive management, the lack of knowledge adequate to predict with certainty the best course of action is acknowledged, management actions are designed in such a way that monitoring will generate new understanding and refinement of the model, and corrective adjustments to management plans are made whenever accumulated data suggest that the present course is inadequate to achieve the goals and a better strategy exists.

Our uncertainty about the magnitude of environmental variation and the frequency and severity of catastrophic events emphasizes the importance of continued monitoring of the Wisconsin gray wolf population to insure its long-term persistence. As additional information becomes available the model can be revised and if necessary corrective management can be implemented.