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—independe...

Red environmental noise and the appearance of delayed density dependence in age–structured populations

“…In keeping with predictions from unstructured population models (Royama 1981;Williams & Leibhold 1995;Jiang & Shao 2003), our simulations demonstrate that both negative and positive spurious DDD could arise in age-structured populations subjected to red environmental noise. We have also demonstrated that different densitydependent scenarios can lead to qualitatively different patterns of spurious DDD in age-structured populations.…”

“…Previous studies on this topic have focused on unstructured models of homogenous populations (Royama 1981;Williams & Liebhold 1995;Jiang & Shao 2003), despite the fact that many organisms go through multiple stages during their life cycle or have spatially structured populations. We focus on age-structured populations here.…”

Population dynamics of the major North American needle-eating budworms.

“…For the eastern budworm, the points represent generation survival in a single plot (plot G4), but for the western and jack pine budworms, they represent mean values for all the plot-years in OREG and the Michigan populations described in Foltz (1969), respectively. Because the author of figure 43B noted that "...the rise and fall of population density in...[plot G4] followed much the same pattern as...other areas...." (Royama 1984), and because he repeatedly used the numerical trend in this plot as an example (Royama 1981(Royama , 1984, I assume that this trend represents typical numerical behavior for the eastern budworm during an outbreak. As the outbreak progressed, S G systematically declined in both the eastern and western species.…”

Will Sympatric Speciation Fail due to Stochastic Competitive Exclusion?

“…More precisely, we assume these random deviations are additive on a log scale, a common assumption in population modeling and ecological time series analysis (e.g., Royama 1981;Turchin and Taylor 1992;Bjørnstad et al 1995;Ives et al 1999). Populations with identical traits can be expected to respond to environmental fluctuations in a similar way; that is, we expect a high-correlation r between their respective deviations from the deterministic growth rate.…”