Equations Used in the Squirrel Model

Adult squirrel population equations

Each year, the number of squirrels changed due to immigration, emigration, roadkilldeaths of mature squirrels, and survival of yearlings to their second year. The equation for the change is:

squirrels = squirrels + (survive - deaths + immigration - emigration + immigration - roadkill)

The survival rate is described in the yearling equation section. The death rate of mature squirrels was based on the amount of food present per squirrel ("food level"): 5% of the adults died when the food level was "high" (greater than 1.2 units per squirrel), 40% died when the food level was average (between 0.8 and 1.2 inclusive), and 70% died when the food level was low (less than 0.8).

Immigration and emigration were more complex; they took into account both the food level and area per squirrel. When the food level was high and there was a lot of area (at least 0.6 acre) per squirrel, immigration was highest, defined by:

int(.5 + (.8+.4*random) * (a_sq-.45)*total)

(Note the use of int(.5 + x) to round the values to the nearest integer.) When there was adequate area (0.4 to 0.6 acre) per squirrel, immigration was somewhat less:

int(.5 + (.8+.4*random) * (a_sq-.4)/2*total)

When the food level was not high or the area per squirrel was low (less than 0.4 acre per squirrel), there was no immigration.

Emigration, on the other hand, was highest when there was little food or area. If the food level or area per squirrel was low, emigration was defined as:

    min(squirrels-deaths, int(.5 + (.8+random*.4) *
            (squirrels-deaths) * ((.8-flev)/.8 + (.4-a_sq)/.4) / 2))
The value "(squirrels-deaths)" had to be used because dead squirrels are not allowed to emigrate. Under other circumstances (at least adequate food and area), there was no emigration.

Roadkill was based on emigration and the total squirrel population; 60-90% of the emigrating squirrels and 10-30% of the other squirrels became roadkill.

Yearling population equations

The yearling model was simpler than the adult squirrel model. The only things affecting the yearling population were births and deaths. Also, since no yearlings remain such for more than a year, the population always clears out at the end of each year. The overall equation is:

yearlings = yearlings + (births - survive - deaths1)

Deaths1 is simply the old yearling population less the surviving yearlings.

The survival rate for yearlings depended on the food level. When the food level was high, 55% of the yearlings survived to become adults; when the food level was medium, 20% survived; and when the food level was low, only 1% survived.

The birth rate depended on the food level as well as the number of adult and yearling squirrels. When the food level was high, 90% of all pairs of squirrels (assuming a 50/50 male/female split) had a litter; adult pairs had 4.7 squirrels per litter, and yearling pairs had 3.9 squirrels per litter. In addition, 10-40% of adult pairs had a second litter (also with 4.7 squirrels per litter). However, with average or little food, 88% of the adult pairs had litters of 3.4 squirrels each, and 51% of the yearling pairs had litters, averaging only .7 squirrels per litter.

Food equations

The food submodel was fairly simple, involving only production and consumption of food and rotting of leftovers. Each year, the food produced was 250 units per acre multiplied by the "weather factor", a value indicating how good the weather was each year; a weather factor of 1 meant "normal" weather, values above 1 were "good" weather, and values below 1 meant "bad" weather. These corresponded to average, more than average, and less than average food production.

Each year, squirrels were assumed to eat either all of the food or 100 units per squirrel, whichever was less. (100 units is an arbitrary number; it is the "adequate amount of food per squirrel", i.e. the amount of food a squirrel needs to live comfortable.) Any food left over was assumed to rot by the end of the year, so no food was left over from previous years.

The weather factor was defined as follows:

	Year	Weather
	----	-------
	1989	2.00
	1990	1.00
	1991	0.98
	1992	1.01
	1993	0.20
	1994	1.05
	1995	0.98
	1996	0.97
	1997	1.00
	1998	1.04
	1999	1.02
	2000	1.00
	2001	1.00
	2002	1.02
	2003	0.97
	2004	0.95
	2005	1.01
	2006	0.97
	2007	1.03
	2008	0.97
	2009	1.03
	2010	1.05
In summary, the weather was unusually good in 1989, unusually bad in 1993, and approximately normal otherwise.