Black Squirrels have been common in Westfield, Massachusetts and surrounding areas for many years, but Stanley Park seems to be where they are most abundant. Stanley Park in Westfield is both an urban park and a spectacular wildlife sanctuary which houses a wide variety of flora and fauna. Wildlife existing there ranges from ducks and geese to wildflowers and thick woodland, to grey squirrels and of course, black squirrels. The existence of these squirrels in such abundance compared to other surrounding areas begs many questions. Why are there black squirrels in Stanley Park? Where did they come from? How did they get there? How long have they been there? There are numerous black squirrel tales that further the enigmatic legend of their first appearence. Some of the more interesting explinations that hearsay brings are: They were introduced by Canadian hippies; they came from Alaska; from Russia; or even brought over by oil tankers from a number of foreign countries (Catalini, 1999). In reality, the black squirrels in Stanley Park are from Michigan. Tney were brought over 51 years ago in 1948 by the man who donated the land for Stanley Park, Frank Stanley Beveridge (Mitchell, 1989). They are neither an unique nor different species, rather just a melanistic color phase of the grey squirrel, Sciurus carolinensis. The first two black squirrels released into Stanley park, the day and month uncertain, did not survive, but a second group of six squirrels was introduced and proved to be prosperous in their new environment (Catalini, 1999).

The current study came about from the general questions above and has led us to a specific set of questions from which to work:

• How many black squirrels are in Stanley Park today?
• What is the current ratio of grey to black squirrels in Stanley Park?
• How has the population of black squirrels grown, both mathematically and biologically, since their introduction?

For this study we are looking to answer these questions and determine how our results could be enforced or argued with future observations of squirrels in Stanley Park. The documented squirrel density in an urban park is >21 per hectare (Koporowski, 1994) and the most accurate measure of Stanley Park is 275 acres, or 121.70664 ha. (Stanley Park, 1999). These documented values, along with the assumption that the squirrel density has not changed in 51 years throughout the land that is Stanley Park and that the birth rates for grey and black squirrels are identical, are factored into our hypothesis. Our hypothesis is: a discrete logistic growth curve could be used to demonstrate several scenarios regarding the population growth of black squirrels in Stanley Park. The two discrete mating seasons each year for the squirrels with females maturing after 14 months also has to be considered. A number of possibilities for the future ratio of the black squirrels are possible. The first possibility is that the current ratio is a stabalized ratio of grey to black squirrels within the total squirrel carrying capacity of Stanley Park. If this is the case, then at what year did this ratio reach stability? The second possibility is that other ratios of grey to black squirrels could exist. These ratios, however, would reach equilibrium in the future. Under this scenario, the observed ratio of two grey squirrels to one black represents a ratio which is moving towards balance. We have predicted several future ratios that represent a stablaized population of booth grey and black squirrels. These predictions cover a spectrum of potentioal population possibilites from ratios not far removed from the current, to a speculation of the population consisting almost entirely of black squirrels. All of the future-possible ratios will show different (r) values and carrying capacities for black squirrels.

We believe that this study of black and grey squirrels in Stanley Park is under ideal conditions for their observation. Throughout out observations of squirrels in the park we assumed ideal conditions for squirrel habitation. It was found that the two most important factors in the density of squirrels in wooded areas was the maturity of the wood as measured by the density of the trees, and the closeness of the woods to another woods of at least 0-5 ha (Fitzgibbon, 1997). Stanley park is made up of many areas of dense wood, in which the largest sample of squirrels was observed on a consistent basis. Stanley park is also in close proximity to other woods, the surrounding mountains.

Our field observation in Stanley Park involved walking a specific route while observing and recording the grey and black squirrels with the naked eye and field binoculars. This route and time of day was kept consistent throughout the four observations in attempt to keep our distance and amount of land observed consistent. The totals for these observations was calculated with 56 greys and 28 black, a total count of 84 squirrels. A ratio of grey to black squirrels was established by observing each days respective ratio and calculating the mean ratio from these four. We used this ratio to estimate the number of black and Grey squirrels in Stanley Park today. A number of other possible ratios was tested. The other ratios tested were 1:1, 5:4, 2:3, 1:2, 1:20, 1:50, 1:600, grey to black (Figure 1).

We estimated the total population of squirrels in Stanley park to be 2423. This number is based on a density of 20 squirrels/ha in urban parks (Koporowski, 1994). There are 121.71 hectares in Stanley park. Thus:

The number of estimated grey and black squirrels in Stanley park was calculated by dividing the total number of squirrels (2422) by three using our 2:1 ratio. This resulted in 807 black squirrels and 1615 grey squirrels.

We used a logistic growth curve as our mathematical model using the two to one grey to black ratio as our reference point in 1999. The equation we utilized was:

where (r) is the growth rate, (kc) is the carrying capacity and (N) is the number of individuals in any given generation. We used this equation with all of our predicted ratios of grey to black squirrels. These varied ratios produced varying (r) values from which we could use to predict the most accurate ratio for the present time. With our observed ratio of 2:1 at the present time, it was necessary to predict at what time in the past did Stanley park reach this ratio. To predict this we calculated the estimated (r) values for varying generations from the year they were introduced until the present, 101 generation (Figure 2). We could use these (r) values to predict at what time this ratio might have been met. We used Euler's equation and documented field squirrel data to establish an (r) value that we could compare to our (r) values computed with the logistic growth curve. Euler's equation is:

The parameters of Euler's equation are: (l_x) which is the possible offspring produced for the two mating seasons within a specific age cohort; (m_x) the survivorship of the individuals in their respective age classes; (e) the exponential function; (rx) the intrinsic rate of growth of an age cohort.

Figure 1 is the graph of a simulation of black squirrel populations utilizing the 8 different ratios of grey to black with all ratios passing through the 2:1 observed ratio in the year 1999, or 101st generation. With our observed 2:1 ratio a carrying capacity of black squirrels reached 807 around the 101st generation (Figure 1). This figure shows that all the ratios have different carrying capacities for black squirrels. If the population were to reach other ratios and different carrying capacities in the future, then the generation at which this were to occur could be predicted.

Figure 1. Simulated black squirrel populations with varying ratios of grey to black.

Figure 2 shows the estimated black squirrel populations at a 2:1 ratio with different (r) values for respective generations from 1948 until the present. An (r) value of 0.76038 was obtained by using Euler's equation (Table 2). This was included in Figure 2. This (r) value from Euler's equation shows that the population reached its carrying capacity of 807 black squirrels for a 2:1 ratio at about the 15th generation, or 7th year after they were introduced.

Figure 2. Estimated black squirrel populations at 2 grey to 1 black with varying r values.

The ratio we observed in Stanley Park was 2 greys to 1 black. It is possible that this ratio has been expressed for some time and that the carrying capacity of Stanley Park for black squirrels has been reached. If so, then in what generation did this occur? If the ratio is at 2 to1 now, it could change in the future. If this is the case, then what ratio can we predict to show in the future? We used a number of varying ratios with all of them showing a 2:1 ratio in the year 1999, generation 101. These ratios showed varying growth rates (r) and resulted in different carrying capacities for black squirrels in the future.

We used documented data to calculate a possible (r) value that is more scientifically based, utilizing factors such as survivorship and the production of offspring with two mating seasons. This equation allowed us to predict the best ratio by comparison of (r) values. The (r) values that were calculated from the various ratios implemented for future populations showed a broad range. The values were all much lower that that of the value from Euler's equation, none of them seemed logical. When observing the 2:1 ratio (r) values for specific years leading up to the 101st generation, we also see a wide range. By comparing Euler's equation to these (r) values, we see that it is very consistent with the time table. At ten years after the black squirrels were introduced the (r) value is 0.525 (Figure 2) for a 2:1 ratio, where as Euler's equation shows an (r) value of 0.76038. This suggests that the black squirrel population reached its carrying capacity at the 15th generation, or 7th year and has maintained this carrying capacity up until the 101st generation. This 2:1 ratio with the (r) value obtained using Euler's equation is well within the confines of researched (r) values for other like species. For example: the Red-Backed Voles, which are a feral species, were introduced on an island in Penobscot Bay in Maine have an (r) value of 1.17 in the natural environment (Crowell, 1973). And the first six years of the European rabbits in Australia from which an (r) value was calculated to be 1.21 (Fenner, 1965).

From our data it is necessary to reason whether or not this prediction is valid. If the ratio in Stanley Park is 2 grey to 1 black, why is this so? Why did it stop at this given ratio? It seems reasonable for the growth rate to be high since squirrels reproduce at prolific rates, 61% of females bearing litters averaging 2.75 each mating season (Koporowski, 1994). The grey squirrels would also be reproducing at this rate, so why was the black squirrel population allowed to rise? Possible increased predation on grey squirrels since there were simply more of them; predators tend to hunt what is in abundance. Grey squirrels were avidly hunted by children with BB guns in the early 1950s which may have contributed to their decline. This may have also assisted in the success of the black squirrels. It is possible that more grey squirrels are subject to becoming roadkill more often than black squirrels because grey squirrels blend into the pavement and are harder to see, where as black squirrels are easily visible on the road.

The best method for analyzing this data would be to count grey and black squirrels in Stanley Park in the future and compare the change in ratios, if any. If the observed ratio in ten years is two grey to one black, then our prediction of the black squirrel carrying capacity, having been reached sometime prior to 1999, would be enforced. This would also support our results derived from Euler's equation which places the stabilization of a 2 grey to 1 black ratio around the year 1955, about 15 generations after introduction. If a different ratio is observed then it can be compared to our predictions in figures 1 and 2 to estimate a population of black squirrels at that time.

1. Catalini, John. "Westfield's Black Squirrels." Focus Summer 1999:8-9

2. Crowell, K.C. 1973. Experimental zoogeography: Introduction of mice to small islands. American Naturalist, 107: 535

3. Fenner, F. 1965. Myxoma virus and Oryctolagus coniculus: Two colonizing species. pp 485-501, in The genetics of colonizing species (H.G Baker and G.C Stebbins, eds.). Academic Press, New York. 588pp.

4. Fitzbibbon, Claire D. "The Disrtibution of Grey Squirrel Dreys in Farm Woodland: The Influence of Wood Area, Isloation and Management." Journal of Applied Ecology 30 (1993): 736-742.

5. Hastings, Allan. Population Biology: Concepts and Models. New York: Springer, 1997.

6. Hedrick, Philip W. Population Biology: The Evolution and Ecology of Populations. Boston: Jones and Bartlett Publishers Inc., 1984.

7. Kelly, David. "Colorblind Squirrels Live in Peace." Union-News 10 December 199?: B2.

8. Koporowski, John, L. "Sciurus Carolinensis." Mammalian Species 480 (1994): 1-9.

9. Mitchell, Tom. "Westfield's Immigrant Black Squirrels...Firmly Established in Park, Beyond." Westfield Evening News 22 February 1989: A1+.

10. O'Brien, George. "Separating Fact From Legend on Westfield's Black Squirrels." Westfield Evening News 28 May 1983: A3+.

11. Rushton, S.P., et al. "Modeling the Distribution of the Red and Grey Squirrel at the Landscape Scale: A Combined GIS and Population Dynamics Approach." Journal of Applied Ecology 34 (1997): 1137-1154.

12. Stanley Park Nature Sanctuary. Online Last accessed 10/1/99

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