Submitted by Joan Pereverzoff

Student Number 8474

Submitted to Dr. J. Ackerman

Class: ENVS 406 Ecological Modelling

University of Northern British Columbia

8 April 1998

A dynamic model was designed to examine the endangered Florida panther (Felis concolor coryi) population. The objective of the model was to examine the causes of the populations growth and decline. The model calculated the current status of the population at 50 panthers to be above the model’s carrying capacity of 20 panthers. The factors in the model that were inputs into the population were births and a captive breeding program while the factors that were outputs for the population were the loss of habitat, as well as road kills, kitten mortality, and disease. Florida panthers showed a strong correlation to increasing habitat size (Carrying Capacity = 0.0055 x Land Area + 0.0577, R² = 1) and decreasing road kill rate (Population Size = -504.66 x Road Kill Rate + 297.76, R² = 0.83). The effect of a captive breeding program did not show any effect on the population. A random element was added into disease rate section of the model and resulted in greater population size fluctuations.

The applications of this study’s results suggest that increasing suitable habitat areas, decreasing road kills, disease and kitten mortality will enable the Florida panther to increase its population to a sustainable size.

The Florida panther (Felis concolor coryi) population is a small, isolated population in the southern tip of Florida. The population size has decreased steadily since the 1920's due to land development and hunting (Dold, 1995). As a result, in 1967, the subspecies was put on the endangered species list. Stemming from the new status of the subspecies, several research projects have been carried out to predict the future of the population.

There are approximately 30 to 50 panthers in the Big Cypress Swamp and Everglades area in southern Florida (Belden and Hagendorn, 1993) and they occupy a range of approximately 10000 km². The home range was determined for male panthers to be 435 +/- 231 km² while the female panthers occupy 202 +/- 141 km² (Belden et al., 1988). The research by Belden et al. (1988) found that the population is currently near carrying capacity for the area it occupies.

The Florida panther has several sources for population sources for population growth. They are primarily births and immigration from controlled breeding programs. The birth rate has not been documented in previous studies, but is assumed to be similar to the North American cougar’s birth rate of 1 to 6 kittens every other year (Jackson and Petticrew, 1980). Panthers tend to have their first reproduction near 36 months although reproduction has been documented as early as 18 months (Maehr et al., 1989). The gestation period for Florida panthers is 90 to 96 days (Maehr et al., 1989). Due to inbreeding effects, 50% of the kittens do not survive (Fergus, 1991). Thus, the net birth input into the population is 50% of the births. The second source of growth for the Florida panthers is a controlled breeding program that increases the panther population by breeding panthers from Florida as well as Texas and Arizona and releasing them in southern Florida. There are two benefits to the program. Firstly, the population grows from increasing the number of individuals in the population and secondly, the new individuals bring new genes that will increase the genetic diversity of the population, thereby reducing the negative effects of inbreeding.

The Florida panther population also has several sources that lead to its decline. They are lack of habitat, deaths that result from conflicts with humans including hunting and road kills, disease and inbreeding effects.

The lack of habitat is the primary source of the population’s decline. This factor forces the home range of the Florida panthers to be smaller than other panther and cougar populations. With increased densities, disease and parasites can spread more easily through the population and conflicts among panthers escalates. Even with increased densities, the total available suitable habitat size limits the number of Florida panthers that survive in the area.

The next major source of decline for the Florida panthers is conflicts with humans. This category can be divided into road kills along state highways which resulted in seven panther deaths between 1972 and 1985 (Dold, 1995) and hunting. Hunting of the panthers was declared illegal several decades ago yet the study by Belden and Hagedorn (1993) found that of seven panthers released in northern Florida, three were killed directly by bullets or suffered infection from bullet wounds.

Disease and the negative effects of inbreeding comprise the last category for the decline of the Florida panthers. Inbreeding leaves an unhealthy panther population because 80% of the panthers have heart murmurs and other heart deformities, 90% of the males have one undescended testicle, 22% are sterile and 90% of the sperm are malformed (Dold, 1995; Barone et al., 1994). Inbreeding can lead to reduced fecundity, birth defects, higher mortality among newborns, slower growth and a homogeneous immune system that could leave the entire population vulnerable to a single pathogenic strain (Fergus, 1991). Parasites common to the Florida panthers include: ixodid ticks present on the entire population (Wehinger et al., 1995), notoendric mange (Maehr et al., 1995), Sarococystis sp. (Greiner et al., 1989), and the intestinal nematode Ancyclostoma pluridentatum (Maehr et al., 1989).

A computer model was designed to study the Florida panther population over time. There are several objectives for the model: 1) determine the importance of the factors that contribute to its growth and decline, 2) determine the carrying capacity of the Florida panther range, and 3) make predictions for the future status of the Florida panthers. This paper will examine the outline the methodology for the design of the model, evaluate the outputs of the model and apply the results to the management of the Florida panthers.

The null hypothesis tested in this model is that the Florida panther population will grow to larger population size over time based on the current conditions. The alternate hypothesis is that the population will not grow based on current conditions and will remain an endangered species. Within the main null hypothesis was tested: Habitat size, road kills, kitten mortality, disease and the captive breeding program do not restrict the growth of the panther population. The alternate hypothesis was that any or all of the above parameters restrict the growth of the panther population.

The model was constructed in the Stella 5.0 modelling environment and the various runs including the sensitivity analysis were performed within Stella for a time period of 50 years. The statistical analysis and graphs of the data were carried out in EXCEL. The model was designed where there were inputs into and outputs out of the Florida panther population.

The parameters chosen were to evaluate the panther population were:

The initial population size was entered as 50 panthers. Births were two kittens per year per female (females account for 60% of the population). Captive breeding panther population was 50 panthers with an input of 10% of its size into the Florida panther population per year. Disease deaths and road kill deaths were entered as 20% and 1% of the panther population size respectively. Kitten mortality was determined to be 50% of the panther births. The density of the panther population was calculated as the land area of suitable habitat divided by the panther population size. The deaths from lack of suitable habitat were calculated to lower the population size to the home range size of 250 kms/panther. If the density of the panthers was already below the home range size, there were no deaths from lack of suitable habitat until the population grew to greater than the home range size.

See Figure 1 for the flow chart of the model program of the Florida panthers, Appendix 1 for the source code and Stella printout of the model.

Sensitivity analysis of the model was carried out in the Sensi-specs section of the Stella program using 10 values of the parameter being tested. The parameters of land area, captive breeding panther population, and road kill rate were varied to test the robustness of the model. A random element was placed into the kitten mortality rate using the RANDOM function in Stella.

The model was run with the initial values for 100 years. See Figure 2 for the change in population size with respect to time.

When the model was run with the initial parameter values for 100 years, the population decreased from 50 panthers to a stable 20 panthers in 30 years (mean for n = 23 panthers, standard error = 0.38).

The model’s robustness was tested with several sensitivity analysis tests. Ten values of land area were evaluated in the model ranging from 1,000 m² to 150,000 km². See Figure 3 for the effect of land area on the population size and Figure 4 for the effect of land area on the carrying capacity of the area.

The model is very sensitive to the land area. There is a perfect correlation (R² = 1) between the carrying capacity of the land and the habitat size described by the equation: Carrying Capacity = 0.0055 x Land Area + 0.0577. The population growth is logistic in that it grows to carrying capacity then levels off.

The effect of the captive breeding program panther population on the model was evaluated for 10 initial values of the population ranging from 0 to 200 panthers. They were input into the Florida panther population at a rate of 10% per year. See Figure 5 for the effect of the captive breeding program on the Florida panthers and Figure 6 for the effect of immigration on the rate to reach carrying capacity (stabilization rate).

It took an average of 38 +/- 3.5 years to reach carrying capacity. The captive breeding program did not enhance the size of Florida panther population, it only affected the amount of time needed to reach the carrying capacity population size.

The effect of the rate of road kills was also analysed for 10 different values ranging from 0% to 50% mortality of the Florida panther population from road kills. See Figure 7 for the effect of road kills on the population size and Figure 8 for the effect of road kill rates on the carrying capacity population size.

The model is sensitive to the rate of road kills. A rate higher than approximately 0.4 (i.e. 40% of the population) results in the decline of the population to extinction. In fact, for any road kill rate greater than 0.0 results in reducing the panther population as described by: Population Size = -504.66 x Road Kill Rate + 297.76 (R² = 0.83).

A random element was inserted into the model in the disease rate. The random number produced was between the range of 0.0 and 1.0 fraction of the population (i.e. between 0 and 100% of the population). The results are presented in Figure 9 (Effect of Disease Rates on Population Growth) and Figure 10 (Effect of Disease Rate on Deaths).

When a random element is inserted into the model, the panther population does not grow as smoothly as when the disease rate remains constant. There are more fluctuations in the population size from year to year when the random element is inserted. Also, there only a weak correlation between the disease rate and the number of panther deaths (R² = 0.45).

Statistical analysis was conducted using EXCEL’s descriptive statistics option and are listed in Appendix 2.

The null hypothesis that the Florida panther population would increase based on current conditions was evaluated. It was found that the panthers decreased in numbers using the current conditions. The population size started at 50 panthers and decreased steadily to 20 panthers where it leveled off. This indicated that 20 panthers was the carrying capacity.

By increasing the land area, the population showed logistic growth (rapid growth until it leveled off to a carrying capacity value). There was a direct correlation between the increase in the carrying capacity of the population and the land area. It can be described by: Carrying Capacity = 0.0055 x Land Area + 0.0577 (R² = 1). By increasing the captive breeding program panther population, the population growth would not increase beyond the same carrying capacity value. However, the rate to reach the carrying capacity increased with increasing captive breeding program population size based on the polynomial equation: Years to reach carrying capacity = 0.001 x (Captive breeding program population size)2 + 0.3559 x (Captive breeding program population size) + 16.8 (R² = 0.96). The road kill rate affected the population size by decreasing the population with increasing road kill rates. It can be described by: Population Size = -504.66 x Road Kill Rate + 297.76 (R² = 0.83).

The inclusion of a random element increased the fluctuations in the population. The model based on current conditions steadily decreased to carrying capacity, where it remained constant for 70 years, whereas the random element run showed continual fluctuations over the time period. This is more representative of the population’s size changes with respect to time because random events like a disease sweeping through a population are more realistic than a constant population size that does not experience these events.

There are several limitations to the model. The model cannot take into account the effects of inbreeding on the population, nor can it measure the relative health of the population. The model does not divide the population into age classes. The model is also limited because it does not compute the interactions with other predators.

The following assumptions were made for the Florida panther model. The initial population size was assumed to be 50, which the high end of the estimate range of 30 to 50 panthers. The birth fraction was assumed to be two kittens per female per year to simplify the model input instead of the actual one to six kittens per female per year. Additionally, the female population fraction was estimated to be 60% of the population (this value was used in the calculations of the births). Kitten mortality was assumed to be 50% of the births even when the population size grew beyond the size where inbreeding could impact the kitten mortality rate.

The most significant assumption for the Florida panther model was that small population sizes would not be affected by inbreeding. This assumption simplified the model because the modeller was unable to find nor estimate the dividing population size to separate the population not affected by inbreeding from the population affected by inbreeding.

The captive breeding program was assumed to manage 50 panthers with an immigration rate of 10% of the captive breeding program population size into the Florida panthers. The home range was averaged to be 275 km² per panther and the land area was assumed to be 4000 km². Prey (i.e. food source) was assumed to not be a limiting factor for the Florida panthers. Finally, it was assumed that there were no panther losses in the model due to hunting or emigration despite the fact that illegal hunting has occurred in the past.

There are several future improvements that could be made for the model. The most important addition would be adding the genetic component into the model. The effects of inbreeding would decrease the healthiness of the population once the population went below a certain genetic diversity limit. Factors such as the fact that 22% of the males are sterile could be added into the model. Another interesting addition would be removing the privileges of the endangered species status once the panther population became large. This would mean including hunting rates and less protected areas. Another recommendation for future models would be to track the individuals by age class. One of the benefits would indicate if the individuals merely died from natural causes (not accounted for in the present model). Also, the interaction within the species and with other predators could be examined (e.g., deaths due to panther fights). Finally, the addition of prey interactions could be added if the population grew to the point where food sources could be limiting in their growth.

This study found that the null hypothesis is rejected because the population does not grow based on current conditions. The population declines steadily until it reaches the land’s carrying capacity of 20 panthers. There is a strong correlation between the growth of the land area to be occupied by panthers and the growth of the population. There is also a strong correlation between increasing the road kill rates and the decline of the Florida panther population. The captive breeding program did not show any effect on the Florida panther population because regardless of how many panthers are added into the Florida panther population, there is a limit to how many can survive in the land area. Unless the land area is increased to accept new panthers, the addition of captive breeding program panthers is futile.

Random events like disease that can destroy between 0 and 100% of the population had a strong effect on the population growth of the Florida panthers. The population would grow and decline with greater fluctuation, showing a more dynamic population trajectory than the steady state style of the current model.

There are several applications for this model. The model can be used to evaluate closed system populations, especially small size populations. The findings of this model can be applied to the management of the Florida panther. If offers clear guidelines as to which parameters are the most important to the growth of this endangered species. It is recommended that increasing the land area inhabited by the Florida panther will have the greatest effect on the recovery of the population. Other results that can be applied are to decrease the road kill, disease and kitten mortality rates. The captive breeding program could serve to enhance the population only in conjunction with increasing land area.

Barone, Mark A., Roelke, M. Howard, J. Brown, J. Anderson, A. and Wildt, D. 1994. Reproductive Characteristics of Male Florida Panthers, Comparative Studies from Florida, Texas, Colorado, Latin America, and North American Zoos. Journal of Mammalogy, 75(1): 150-162.

Belden, Robert C., Frankenberger, W., McBride, R. and Schwikert, S. 1988. Panther Habitat use in Southern Florida. Journal of Wildlife Management 52(4): 660-663.

Belden, Robert C. and Hagendorn, B. 1993. Feasibility of Translocating Panthers into Northern Florida. Journal of Wildlife Management 57(2): 388-397.

Dold, Catherine. 1995. Florida Panthers Get Some Outside Genes. New York Times 20:C1-4.

Fergus, Chuck. 1991. The Florida Panther Verges on Extinction. Science 251:1178-1180.

Greiner, E., Roelke, M., Atkinson, C., Dubey, J., and Wright, S. 1989. Sarcocystis sp. in Muscles of Free-ranging Florida Panthers and Cougars (Felis concolor). Journal of Wildlife Diseases 25(4): 623-628.

Jackson L. and Petticrew, P. for Ministry of Environment 1980. Preliminary Cougar Management Plan for British Columbia. 23 pp.

Maehr, David S., Land, E., Roof, J. and McCown, W. 1989. Early Maternal Behavior in the Florida Panther (Felis concolor coryi). America Midland National 122: 34-43.

Maehr, David S., Greiner, E. Lanier, J. and Murphy, D. 1995. Notoedric Mange in the Florida panther. Journal of Wildlife Diseases. 31(2):251-254.

Wehinger, Kimberly, Roelke, Melody, Grenier, Ellis. 1995. Ixodid Ticks from Panthers and Bobcats in Florida. Journal of Wildlife Diseases. 31(4):480-485.

Captive_Breeding_Program_Panther_Population(t) =

Captive_Breeding_Program_Panther_Population(t - dt) + (- Immigration) * dt

INIT Captive_Breeding_Program_Panther_Population = 50

OUTFLOWS:

Immigration = Captive_Breeding_Program_Panther_Population*.1

Panther_Population(t) = Panther_Population(t - dt) + (Births + Immigration - Deaths) * dt

INIT Panther_Population = 50

INFLOWS:

Births = Panther_Population*.6 *Birth_Fraction

Immigration = Captive_Breeding_Program_Panther_Population*.1

OUTFLOWS:

Deaths =

Panther_Population*Disease+Panther_Population*Road_Kills+Kitten_Mortality+Lack_of

_Habitat*Panther_Population

Birth_Fraction = 2

Density + Land_Area/Panther_Population

Disease = 0.2

Kitten_Mortality = 5*Births

Land_Area = 50000

Road_Kills = .01

Lack_of_Habitat = GRAPH(Density)

(0.00, 0.9), (50.0, 0.8), (100,0.66), (150, 0.5), (200, 0.33), (250, 0.2), (300, 0.00), (350, 0.00), (400, 0.00), (450, 0.00), (500, 0.00)

Figure A1: Schematic Model from Stella 50 of Honda Panther Population

The focus of this term paper prospectus is the analysis of the endangered Florida Panther (Felis concolor coryi) population. There are several components that must be examined before a proper model can be developed. The Florida Panther population is an isolated population in the Southern part of Florida primarily occupying the Big Cypress Swamp and Everglades area (Belden and Hagedorn, 1993). There are approximately 30 to 50 panthers in the area (Fergus, 1991) and each panther occupies a home range of approximately 435 +/- 231 km² (male) or 202 +/- 141 km² (female) (Belden et al., 1988). It is believed that the population is near carrying capacity for the area it currently occupies (Belden et al., 1988). The climate is tropical savannah (Hela, 1952 as cited in Belden et al., 1988) and the majority of the rainfall occurs between May and October.

The sources of population growth for the panthers are births, at a rate comparable to North American cougars of 1 to 6 kittens/year every other year (Jackson and Petticrew, 1980) and limited immigration from controlled breeding projects (Fergus, 1991). Panthers tend to have their first reproduction near 36 months although reproduction has been documented at as early as 18 months (Maehr, 1992) and will have an average of 4 litters in a lifetime. The gestation period for Florida panthers is 90 - 96 days (Maehr and Moore, 1989). In 1991, there was a 50% mortality in kittens (Fergus, 1991). The controlled breeding program aims to improve the genetic diversity by breeding less genetically similar panthers. Panthers are captured and the offspring are released in a controlled fashion.

The main cause of the decline of the Florida panthers is loss of suitable habitat (Belden et al., 1988). This figure is difficult to estimate because it is based on direct and indirect mechanisms that effect the panther population. Once, the Florida panthers occupied nearly the entire state. Currently, they occupy 1. X 104 km² area.

The second highest cause of death is from highway kills. Between 1972 and 1985, seven panthers have died on state roads. The next cause of death for panthers is from conflicts with humans including hunting. Of seven panthers released in Northern Florida, 3 were either killed directly by bullets or suffered infection from bullet wounds (Belden and Hagedorn, 1993).

Diseases, parasites also effect the population. Specimens of Dermacentor variabilis, Ixodes spacularis, I. affinis, Ambylomma maculatum and A. americanum were found to be present on samples taken from Florida panthers and Ixodid ticks were present on all 53 panthers (Wehinger et al., 1995). Other studies have discovered Notoedric Mange (Maehr et al., 1995) and Sarcocystis sp. (Greiner et al., 1989). These parasites lead to immune compromise and weaken the health of individuals, hence the population of the panthers. The intestinal nematode, Ancylostoma pluridentatum, may be a significant mortality factor in juvenile Florida panthers (Maehr, 1989).

The last major source of decline of panthers is from genetic deformities and lack of genetic diversity. Inbreeding can lead to reduced fecundity, birth defects, higher mortality among newborns, slower growth and a homogeneous immune system that could leave the entire panther population vulnerable to a single pathogenic strain (Fergus, 1991). Maehr supports this claim with evidence that inbreeding may contribute to the mortality of juveniles during the first six months of life (Maehr et al., 1989). The study by Barone in 1994 found that only 7% of male Florida panther sperm was normal. The deformities were attributed to genetic links caused by severe inbreeding within the population. These results indicate that there is a reduced chance of reproduction for the Florida panthers. The computer program VORTEX forecast an 85% probability that the Florida panther population would die out in 25 years unless captive breeding programs were introduced to increase the genetic diversity of the population.

Maehr et al. (1990) lists the wild hog (Sus scrofa) to be the most common prey for the Florida panthers followed by white-tailed deer (Odocoileus virginianus), raccoon (Procyon lotor), and 9-banded armadillo (Dasypus novemcinctus). There was found to be no seasonal variation in diet. Prey was concentrated in areas with better soils and panthers were found to prefer hunting in the mixed swamp and hammock forests because they provide cover and food for the primary choices of prey (Belden et al., 1988). Florida panthers make on average 1 kill/9.3 days (Belden and Hagedorn, 1993). Belden et al. (1988) developed a predictive model of energy cost required by panthers. It was found that one kill of mule deer is required per 8 - 11 days for a male and 14 to 17 days for a female. A female with kittens would require 1 deer kill every 3.3 days to satisfy energy needs (Belden and Hagedorn, 1993). In northern Florida, the deer population is at a density of 1 deer/12.1 ha. A 15% annual harvest by panthers would be sustainable for both the deer and panther population (Belden and Hagedorn, 1993).

Barone, Mark A. Roelke, M. Howard, J. Brown, J. Anderson, A. and Wildt, D. 1994. Reproductive Characteristics of Male Florida Panthers, Comparative Studies from Florida, Texas, Colorado, Latin America, and North American Zoos, Journal of Mammalogy, 75(1): 150-162.

Belden, Robert C., Frankenberger, W., McBride, R. and Schwikert, S. 1988. Panther Habitat use in Southern Florida. Journal of Wildlife Management 52(4):660-663.

Belden, Robert C. and Hagedorn, B. 1993. Feasibility of Translocating Panthers into Northern Florida. Journal of Wildlife Management 57(2): 388-397.

Fergus, Chuck. 1991. The Florida Panther Verges on Extinction. Science 251:1178-1180.

Greiner, E., Roelke, M., Atkinson, C., Dubey, J., and Wright, S. 1989. Sarcocystis sp. in Muscles of Free-ranging Florida Panthers and Cougars (Felis concolor). Journal of Wildlife Diseases 25(4): 623-628.

Jackson L. and Petticrew, P. for Ministry of Environment. 1980. Preliminary Cougar Management Plan for British Columbia. 23 pp.

Maehr, David S., Land, E., Roof, J. and McCown, W. 1989. Early Maternal Behavior in the Florida Panther (Felis concolor coryi). America National 122:34-43.

Maehr, David S., Belden, R. Land, E. and Wilkins, L. 1990. Food Habits of Panthers in Southwest Florida. Journal of Wildlife Management (3): 420-423.

Maehr, David S. and Moore, C. 1992. Models of Mass Growth for 3 North American Cougar Populations. Journal of Wildlife Management. 56(4):700-707.

Maehr, David S., Greiner, E. Lanier, J. and Murphy, D. 1995. Notoedric Mange in the Florida panther. Journal of Wildlife Diseases. 31(2):251-254.

Smallwood, K. Shawn. 1997. Interpreting pump (Puma concolor) population estimates for theory and management. Environmental Conservation 24(3)283-289.

Wehinger, Kimberly, Roelke, Melody, Grenier, Ellis. 1995. Ixodid Ticks from Panthers and Bobcats in Florida. Journal of Wildlife Diseases. 31(4):480-485.