Fundamental Concepts and Methodology for the Analysis of Animal Population Dynamics, with Particular Reference to Univoltine Species

Abstract

This paper presents some concepts and methodology essential for the analysis of population dynamics of univoltine species. Simple stochastic difference equations, comprised of endogenous and exogenous components, are introduced to provide a basic structure for density—dependent population processes. The endogenous component of a population process is modelled as a function of density in the past p generations, including the most recent. The exogenous component of the process consists of all density—independent components of the ecological factors involved, including enhance variations. The model is called a pth order density—dependent process. For a successful analysis of a population process by the above model, it is important that the process be in a state of statistical equilibrium, or stationarity. The simplest notion of stationarity is introduced, and the average behavior of the process, under this assumption, discussed. The order of density dependence in the population process of a given species depends on its interaction with other species involved in the food web. Considering certain attributes of the food web, in particular the limited number of trophic levels, the pyrmaid of numbers, the linear linkages between closely interacting species, and niche separation among competing species, it is argued that the order of density dependence is probably not much higher than three. A second—order model is perhaps adequate in many practical cases. The dynamics of some lower order density—dependent processes are compared by simulations, with a view to showing the effect of density—dependent and density—independent components at different orders. Several types of density dependence are discussed. If a given factor influencing the temporal variation in density is by itself influenced by density, it is called "causally density—dependent," which may reveal itself by some degree of correlation with density. A density—independent factor, however, may also show some sort of correlation with density in the recent past. This is called "statistically density—dependent." Such statistical density dependence may be due to: (1) spurious correlation, (2) bias in an estimator of the correlation coefficient, (3) autocorrelations in the density—independent factor, and (4) an intriguing mathematical property of the stochastic process. Particularly because of the last two reasons, it is often difficult to distinguish, by correlation method, between causal and statistical density dependence. Distinction also exists between temporal and spatial density dependence, the latter not necessarily implying the involvement of the former. The importance of the distinction between these types of density dependence is discussed in relation to the data analysis and model building. A Statistical analysis of the effect of ecological factors on population dynamics is attempted. Since it is often difficult to determine, by correlation, the causally density—dependent structure of a population process under the influence of some unknown density—independent factors, it is suggested that we reverse the procedure to determine the effect of the density—independent factors first. To confirm the involvement of some suspected density—independent factors in the species dynamics, I propose several methods of correlation between annual fluctuations in some population parameters, such as density, rate of change in density, and their transforms, and those in suitable indices of the suspected factors. Merits, demerits, and limitations of these methods are also discussed. To simplify the arguments, the correlation models are set up first without stage division, and then are elaborated to those in which the whole generation span is divided into several life—cycle stages, so that life table information can be used effectively for the identification of the density—independent factors involved in each stage. A set of life tables of the spruce budworm, Choristoneura fumiferana (Clem.), is analyzed to provide an example of the application of the above concepts and methods. Concluding remarks include some notes on designing life table studies.