Incorporate Density Dependence Research Articles

Population consequences of chronic toxicity: incorporating density dependence into the analysis of life table response experiments

Data from chronic toxicity tests are usually analysed by calculating how the toxicant reduces population growth rate. The contribution of effects on different parts of the life history to this reduction can be determined using sensitivity analyses and life table response experiments (LTREs). These provide a convenient descriptor of what happens within the laboratory toxicity test, but are only a good predictor of likely consequences in the field if density dependence of population dynamics can be ignored. Here I show how sensitivity analysis and LTREs can be applied to density dependent populations and illustrate the methods with data on the toxicity of dieldrin to Eurytemora affinis. I also outline the extension of the approach to populations which experience variations in vital rates. Stationary population sizes in density dependent populations at equilibrium mean that vital rates late in life are usually more important than in the density independent analysis. Substantial reductions in some vital rates can have little impact on the population if they are compensated by reductions in the intensity of density dependence. This represents one aspect of the assimilative capacity of ecological systems.

A Hypothesis Regarding the Abruptness of Density Dependence and the Growth Rate of Populations

Most population models incorporate density dependence in a manner that implies the effects of density set in at increasingly higher rates as population densities decrease to zero. For many populations, it may be more plausible to assume that the effects of density set in at a maximum rate around some characteristic density K > 0: that is, the per capita rate of increase of the population has an inverted sigmoidal form as a function of population density. In the model discussed here, the rate at which density dependence sets in around K is governed by a parameter γ, which I refer to as the "abruptness" parameter: the larger the parameter γ, the weaker the effects of density dependence are for population densities below K, the more rapidly density dependence sets in around K, and the more severe the effects of density dependence are beyond K. Results obtained from an Evolutionary Stable Strategy (ESS) analysis of the abruptness parameter γ suggest the hypothesis that populations with a density‐independent growth rate of <100% from one generation to the next (i.e., a reproductive value of <2) will exhibit a relatively high level of abruptness in their response to density, while the reverse will be true for populations with a density‐independent growth rate of >100%. Further, if true, this hypothesis suggests that females with high reproductive rates who deposit young on resources and provide no further maternal care should clump their young to reduce the level of abruptness in density dependence. Also, this hypothesis, together with the fact that high levels of abruptness promote oscillations in populations, implies that we are more likely to observe cyclic and chaotic behavior in relatively slower growing populations than previously thought.

On robust weed population models

SummaryDifference equation models incorporating density dependence are considered in the context of the description of the dynamics of weed populations over discrete generations. Their applicability is assessed in relation to modelling yield loss, two species and three species interactions and the influence of density independent control practices. Analysis indicates that whilst plant populations may show simple dynamical properties around equilibrium levels, convergent oscillations to equilibrium may result from the application of control measures. Such models are argued to have potential as robust qualitative predictors of weed species abundance.

Stability of Real Interacting Populations in Space and Time: Implications, Alternatives and the Negative Binomial kc

(1) Data are examined that relate to two-population interaction models based on the negative binomial parameter, k, and the resulting 'empty-cell' probability (e.g. probability of host escaping parasitoid attack). As predicted (Taylor, Woiwod & Perry 1979) estimates of k were non-linearly related to population density for samples of Drosophila melanogaster eggs, predator Phytoseiulus persimilis adults (among its prey, Tetranychus urticae), parasitoid Ooencyrtus kuvanae adults (among eggs of its host, Lymantria dispar) and parasitoid A laptusfusculus eggs (in eggs of its host Mesopsocus immunis). (2) Contagion did not increase with k, in contrast to conventional expectations, and k was highly variable as found by Elliot (1982) for the parasitoid Agriotypus armatus. There was no constant (kc) value. Hence, the criterion required for stability in May's (1978) phenomenological model did not exist. (3) This and similar two-population interaction models dependent on the 'empty-cell' probability, p0, will overestimate p0 unless they incorporate density dependence of k. They will also overestimate equilibrium densities. Stability analyses for May's phenomenological and related models, performed about these equilibrium densities, are not reliable. (4) An alternative simple host-parasitoid model is examined in which heterogeneity is built into the basic Nicholson-Bailey model by allowing parasitoid and host to respond to one another by movement; this model also applies if the host has a partial refuge from the parasitoid. (5) Models involving two interacting species should not depend upon the premise that the two species are distributed independently of one another.

Delayed germination of seeds: Cohen's model revisited

D. Cohen's (1966, J. Theor. Biol., 12, 110–129) model of delayed germination of seeds in a variable environment is extended to incorporate density dependence. It is shown that this has a considerable impact on the optimal germination rate, and the results are interpreted in terms of bet-hedging behavior. The effect of spatial dispersal is briefly considered.

Dynamic complexity in predator-prey models framed in difference equations

THE complicated dynamics associated with simple first-order, nonlinear difference equations have received considerable attention (refs 1–4 and R. M. May and G. F. Oster, unpublished). In an ecological context, equations of this type provide a powerful and realistic means of modelling the behaviour of animal populations with ron-overlapping generations, typified by many arthropods in temperate regions. May4 has shown that such models, incorporating density dependence, have three regimes of dynamic solution in their parameter space, namely (1) a stable equilibrium point; (2) bifurcating cycles of period 2n, 0<n< ∞, where n is a positive integer and (3) behaviour which has been termed chaotic, that is, cycles of any integral period or complete aperiodicity, depending on the initial conditions. May4 has indicated that such complexity can also occur in the wider context of competition between two species, described by two first-order, nonlinear difference equations of similar form to those governing single-species growth.