Differentiation and Frequency Distributions of Body Weights in Plants and Animals

J. Uchmanski

Abstract

The basic and simplest system that one can consider in ecology is a group of individuals of equal age and representing one species, that is, a cohort. This paper is an attempt to show that analysis of such a system may be of great importance to understanding basic ecological problems, such as, intraspecific competition and the dynamics of a single population. It is easy to observe that in even-aged populations individuals differ in weights. A close look can show that weight distributions in even-aged populations may have different skewness. Most common are distributions with coefficients of skewness greater than zero. Sometimes weight distributions are symmetrical or with skewness coefficients less than zero. In a cohort of growing individuals the coefficient of skewness changes with time: most often starting from zero (symmetrical distribution), it increases in time; sometimes after an initial increase it can decrease in the final stage of growth, which is related to an increased mortality of individuals. The rate of change in skewness, and the skewness itself depend on the density of individuals in a cohort and on food conditions. They are greater at higher densities and increase with deteriorating food conditions. Weight distributions are symmetrical at low densities and optimal food conditions. The differences in individual weights measured by variance of weight distributions or coefficient of variation follow the same pattern, but observed changes with time, density and food conditions are not so clear. These conclusions rest upon the review of numerous papers concerning both plants and animals, which is presented in this paper. In the past, the properties of weight disributions in even-aged populations were explained not by interactions between individuals, but rather as a natural outcome of the growth process of non-interacting individuals. The exponential equation of growth, with relative growth rate having a normal distribution in populations, was used to support this hypothesis. Obtained weight distributions were of positive skewness; however, this model, which in fact is able to describe the growth process only in its initial stage, cannot explain the changes of skewness of weight distributions with density and food conditions. A model has been developed which includes competitive interactions among members of even-aged populations to explain observed properties of weight distributions in them. The basic assumption is that intraspecific competition leads to uneven partitioning of resources, which are the object of competition. Functions describing resource partitioning among individuals are included into the model. Two versions of the model are considered: deterministic and stochastic. The first one assumes that the fate of an individual is determined in the early stages of growth and its relative position in the population does not change in time. This corresponds with the situation, for instance, of terrestrial plants or sedentary animals living in a heterogeneous environment. In particular, the mathematical form of the growth model, the so-called balance equation of growth, modified by including a resource-partitioning function, was used. The deterministic model is considered with constant and variable food conditions. In the latter case two situations were analysed: constant in-flow of food and its exponential growth. In the stochastic model of growth it is assumed that for each individual there exists a probability of increasing weight, which depends on past increases in weight. This probability plays the role of the resource-partitioning function. The stochastic model can describe an animal actively hunting for its prey. In both versions, the deterministic and the stochastic one, the dependence of resource intake on the amount of available resource is included. The skewness of weight distributions given by these models is analysed. It is shown that these models describe and explain all properties of weight distributions in even-aged populations: their skewness and changes in skewness with time, density and food conditions. A set of assumptions on resource-partitioning functions is formulated to obtain observed properties of weight distributions. These assumptions are analysed in detail. An attempt was made to answer the question of whether or not competition is really responsible for differentiation of weights and skewness of their distributions. Restrictions of the models and kinds of organisms described by them are also discussed and ways of verification of the models are presented. Finally, the application of these models of differentiation of individual weights to the construction of non-volterrian models of number dynamics of a single population is suggested.

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