PROBLEM STATEMENT

The simulated ecosystem will have three components — an environment, a randomly chosen initial population of herbivores and carnivores with varied characteristics, and a set of rules governing the success or failure of organisms within the ecosystem.

The environment has two component values, carrying capacity and flora color. Carrying capacity refers to the kilograms of vegetative matter available for consumption by herbivores, and for purposes of the simulation is the product of random fluctuations of rainfall and temperature. Flora color refers to the predominant shade of the vegetation, and is expressed in terms of red, green, and blue primaries that allow for colors from black to white. Carrying capacity or flora color may be varied during the course of the simulation.

The population will consist of randomly chosen individuals with the following coding scheme:

Individuals are allowed to mate freely among all members of their respective herbivore or carnivore population, subject to the constraints of the fitness evaluation algorithm.

The fitness algorithm measures the competitiveness of an individual, measured against his peers. In predator/prey systems, prey animals in the absence of predators will show a proportional growth rate. Predators introduced into a prey-rich environment will show a high growth rate, and will slow the prey growth rate. An overabundance of predators will lead to declining numbers of prey, which will, in turn, reduce the number of predators. Lotka-Volterra’s equations illustrate the basic growth relationships between numbers of herbivores (H) and carnivores (C) [5]:

dH/dt = aH - bHC

dC/dT = -cC + dHC

where HC is the success rate of predation, and a,b,c,d are proportionality constants. HC, as defined by Kitching, is a function of several parameters such as detection success, learning by prey and predator, and hunger[4,5]. Therefore, our fitness algorithm must take into account the factors that lead to the success of predation. Four different functions are used to determine individual success.

(1) Herbivore feeding requirements – Herbivores require an amount of food proportional to their mass, m^.75. Food-rich environments favor larger animals, while food-poor environments will favor smaller animals. Accordingly, the success rate of foraging is:

f = (K / Eh)*(b * m^0.75)

This function determines the ability of the individual herbivore to successfully forage for food. Animals that are well fed are less likely to be caught by predators.

(2) Carnivore feeding requirements - Carnivores also require food proportional to their mass, m^0.75. Because they can convert 10% of herbivore mass into energy, their success rate for foraging is:

f = ((Mh/10) / Ec) * (d * m^0.75)

Similar to herbivores, this function also shows the success that a well fed predator is likely to have, vis-à-vis, his starving brethren.

(3) Detection success ratio - The ability of an animal to make or escape detection depends upon their sight (s), hearing (h), and camouflage (c) compared to their opponents.

Herbivore = x(s / S) + y(h / H) + zc

Carnivore = i(s / S) + j(h / H) + kc

S, H are mean population values for sight and hearing.

i,j,k,x,y,z are proportional constants

These factors play into the role of successful search and time of exposure. Again, both equations show how an individual must do better not only in absolute terms, but in terms of the competition.

(4) Intelligence success ratio - The intelligence of an individual relative to their opponents. Highly intelligent bipedal organisms are given additional credit for tool-use capability.

i = (b / B)(gc)

b is brain size of individual

B is average brain size of population

g is a proportionality constant

c is 1 for two legged animals, 0 for four legged animals

Intelligence is a grab-bag of all of the individual’s various abilities to out-wit the opponent.