An adapted form of the Lotka-Volterra predator-prey model is employed here to explore the interactive and symbiotic effects between human foragers and Zea in the Soconusco region. This model was originally designed to explore the synergistic population effects between predators and their prey. The basic assumption of the model is that predator population sizes are related to prey population sizes, and vice versa, and that a functional response occurs between the two—the rate of prey capture by a predator is a function of prey abundance (Gotelli 1998).
The Lotka-Volterra model is the simplest model of predator-prey interactions and was developed independently by Lotka and Volterra.8 It has two variables, P and V, and several parameters: V is the density of prey, P is the density of predators, r is the intrinsic rate of prey population increase, 8 is the capture efficiency coefficient, b is the reproduction rate of predators per prey eaten, and m is the predator mortality rate. This mathematical model shows how predator populations keep populations of prey species in check. If the predator population is relatively low, the prey population will increase in size, and often results in population cycles that are stochastic in form.
In order to better match reality in terms of human/environmental interactions, we adapted the Lotka-Volterra model to the cultivator (human)-cultigen (maize) relationship that developed in the Soconusco region. Cultivator-cultigen interactions are unlike the relationship between predator and prey because plants, particularly potential cultigens, respond differently to human predation, intensified collection, and consumption. Cultivation and consumption can lead to selective increases in seed size, greater plant densities, and overall increases in cultigen productivity (e.g., Rindos 1984), rather than decreases in density or size. The cutting and burning of forest habitat and the creation of fields also increases the overall density and yield of cultigens due to economies of scale and sometimes creates a functional increase in cultivator population levels. This idea is supported by the close correlation between maize productivity and population densities in the Valley of Oax-aca, Mexico (Kirkby 1973). We argue that this model is appropriate for exploring the interactive processes at work in proto-agricultural bi-otic communities because net increases in culti-gen acquisition, leading to more intensified food producing practices, are a function of changes in the rate of harvesting efficiency and cultigen density rather than intrinsic increases in cultivator population; although the context for adopting these cultigens in the first place may be related to population-dependent reductions in higher ranked prey. Further, the density and rate of cultigen harvest are also dependent on the food-quality being produced due to the demands of the cultivator.
We employ one variant of the Lotka-Volterra model known as the type III functional response. This model allows for changes in feeding be
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