Density-dependence in the bird populations of anoak wood over 22 years

Annual counts of the five commonest bird species in an oak wood in southeastern England over 22 years showed evidence for density-dependent feedback in their year-to-year fluctuations. The counts also showed evidence for effects of winter weather in two species (Wren Troglodytes troglodytes and Robin Erithacus rubecula ). Evidence for density-dependence in the Wren was greatly strengthened when effects of winter weather were included in the analysis.     

Effects of survival thresholds upon one-dimensional dynamics of single-species populations

A simple one-dimensional model of single-species populations is studied by means of computer simulations. Although the model has a rich spectrum of dynamics including chaotic behavior, the introduction of survival thresholds makes the chaotic region so small that it can be hardly observed. Stochastic fluctuations further reduce the chaotic region because they accidentally lead populations to extinction. The model thus naturally explains the observation that the majority of natural populations do not show chaotic behavior but a monotonic return to a stable equilibrium point following a disturbance.     

Density-dependence in parasite transmission dynamics

The transmission of vector-borne parasites is complex, yet to a large extent this complexity can be unravelled through the insights gained from simple mathematical models of the transmission system. The principle is simple because the key question is merely "what is the rate of increase in numbers of hosts affected?" Clearly, if this rate of increase is greater than unity then the infection can spread, while if it is less than unity it will decline. Ronald Ross in 1911 was the first to formulate this idea for malarial(1) and malaria transmission has since attracted most attention from modellers of parasitic diseases(2-4). But although it is implicitly recognized that nothing- not even parasitic transmission - can increase indefinitely, the importance of some degree of density-dependence in regulating the system tends to be neglected (see Box 1). In this article, Klaus Dietz explores some classical ideas of modelling parasitic disease transmission, emphasizing not only the importance of density dependence but also the importance of knowing exactly where such effects operate in the system.     

Equilibrium populations of heterostylous plants

A general relation is derived which must be satisfied by the equilibrium frequencies of the incompatibility types occurring in populations of heterostylous plants. Specific assumptions are made about the underlying genetic mechanism, but these are fulfilled in practically all relevant cases. With usual mating systems corresponding to pollen or zygote elimination and no fitness differences, it follows that all incompatibility types must be equally frequent. Given different fitness values, the general relation leads to more complex equations determining the frequencies. These equations are used for estimating fitness values of the Long, Mid and Short types in Lythrum salicaria. Expressions for the equilibrium frequencies are also found for a special mating system in Oxalis alpina.     

Sustainability in single-species population models

In this paper, we review the concept of sustainability with regard to a single-species, age-structured fish population with density dependence at some stage of its life history. We trace the development of the view of sustainability through four periods.The classical view of sustainability, prevalent in the 1970s and earlier, developed from deterministic production models, in which equilibrium abundance or biomass is derived as a function of fishing mortality. When there is no fishing mortality, the population equilibrates about its carrying capacity. We show that carrying capacity is the result of reproductive and mortality processes and is not a fixed constant unless these processes are constant. There is usually a fishing mortality, F(MSY), which results in MSY, and a higher value, F(ext), for which the population is eventually driven to extinction. For each F between 0 and F(ext), there is a corresponding sustainable population. From this viewpoint, the primary tool for achieving sustainability is the control of fishing mortality.The neoclassical view of sustainability, developed in the 1980s, involved population models with depensation and stochasticity. This view point is in accord with the perception that a population at a low level is susceptible to collapse or to a lack of rebuilding regardless of fishing. Sustainability occurs in a more restricted range from that in the classical view and includes an abundance threshold. A variety of studies has suggested that fishing mortality should not let a population drop below a threshold at 10-20% of carrying capacity.The modern view of sustainability in the 1990s moves further in the direction of precaution. The fishing mortality limit is the former target of F(MSY) (or some proxy), and the target fishing mortality is set lower. This viewpoint further reduces the range of permissible fishing mortalities and resultant desired population sizes. The objective has shifted from optimizing long-term catch to preserving spawning biomass and egg production for the future. The use of discount rates in objective functions involving catch is not a suitable alternative to protecting reproductive value.As we move into the post-modern time period, new definitions of sustainability will attempt to incorporate he economic and social aspects of fisheries and/or ecosystem and habitat requirements. These definitions now involve "warm and fuzzy" notions (healthy ecosystems and fishing communities, the needs of future generations, diverse fish communities) and value judgements of desired outcomes. Additional work is needed to make these definitions operational and to specify quantitative objectives to be achieved. In addition, multiple objectives may be incompatible, so trade-offs in what constitutes sustainability must be made. The advances made under the single-species approach should not be abandoned in the post-modern era, but rather enhanced and combined with new approaches in the multi-species and economic realms.     

Density-dependence as a size-independent regulatory mechanism

The growth function of populations is central in biomathematics. The main dogma is the existence of density-dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the theta-logistic, which generalizes the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter rho and a competition coefficient theta. Distinct sign combinations of these parameters reproduce not only the family of theta-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population.     

Equilibrium stability of single-species metapopulations

We investigate the effect of migration between local populations of a single discrete-generation species living in a ring or an array of habitats. The commonly used symmetric dispersal assumption is relaxed to include the biologically more reasonable asymmetric dispersion. It is demonstrated analytically that density independent migration has no effect on the equilibrium stability of individual populations. However, the positive equilibrium may be destabilizing if the migration is density dependent in such a way that it increases with increasing population density at the source patch.     

Permanence of single-species stage-structured models

In this paper, we consider population survival by using single-species stage-structured models. As a criterion of population survival, we employ the mathematical notation of permanence. Permanence of stage-structured models has already been studied by Cushing (1998). We generalize his result of permanence, and obtain a condition which guarantees that population survives. The condition is applicable to a wide class of stage-structured models. In particular, we apply our results to the Neubert-Caswell model, which is a typical stage-structured model, and obtain a condition for population survival of the model.The research is partially supported by the Ministry of Education, Science and Culture, Japan, under Grant in Aid for Scientific Research (A) 13304006.     

Density-dependence of functional development in spiking cortical networks grown in vitro

During development, the mammalian brain differentiates into specialized regions with distinct functional abilities. While many factors contribute to functional specialization, we explore the effect of neuronal density on the development of neuronal interactions in vitro. Two types of cortical networks, namely, dense and sparse with 50,000 and 12,500 total cells, respectively, are studied. Activation graphs that represent pairwise neuronal interactions are constructed using a competitive first response model. These graphs reveal that, during development in vitro, dense networks form activation connections earlier than sparse networks. Link entropy analysis of dense network activation graphs suggests that the majority of connections between electrodes are reciprocal in nature. Information theoretic measures reveal that early functional information interactions (among three electrodes) are synergetic in both dense and sparse networks. However, during later stages of development, previously synergetic relationships become primarily redundant in dense, but not in sparse networks. Large link entropy values in the activation graph are related to the domination of redundant ensembles in late stages of development in dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specializations of nervous system tissue in vivo.     

Inbreeding depression in small populations of self-incompatible plants.

Self-incompatibility (SI) is a widespread mechanism that prevents inbreeding in flowering plants. In many species, SI is controlled by a single locus (the S locus) where numerous alleles are maintained by negative frequency-dependent selection. Inbreeding depression, the decline in fitness of selfed individuals compared to outcrossed ones, is an essential factor in the evolution of SI systems. Conversely, breeding systems influence levels of inbreeding depression. Little is known about the joint effect of SI and drift on inbreeding depression. Here we studied, using a two-locus model, the effect of SI (frequency-dependent selection) on a locus subject to recurrent deleterious mutations causing inbreeding depression. Simulations were performed to assess the effect of population size and linkage between the two loci on the level of inbreeding depression and genetic load. We show that the sheltering of deleterious alleles linked to the S locus strengthens inbreeding depression in small populations. We discuss the implications of our results for the evolution of SI systems.     

Persistence and extinction in single-species reaction-diffusion models

Single-species reaction-diffusion models are analyzed to determine the effect of various diffusion mechanisms on species persistence or extinction.     

Density-dependence and within-host competition in a semelparous parasite of leaf-cutting ants

Background  

Parasite heterogeneity and within-host competition are thought to be important factors influencing the dynamics of host-parasite relationships. Yet, while there have been many theoretical investigations of how these factors may act, empirical data is more limited. We investigated the effects of parasite density and heterogeneity on parasite virulence and fitness using four strains of the entomopathogenic fungus, Metarhizium anisopliae var. anisopliae, and its leaf-cutting ant host Acromyrmex echinatior as the model system.     

Global asymptotic behavior in single-species discrete diffusion systems

We consider a single-species dynamical system which is composed of several patches connected by discrete diffusion. Based on recently developed cooperative system theory and the property of a cooperative matrix, we obtain sufficient and necessary conditions for the system with linear diffusion to be extinct and for one with nonlinear diffusion to be globally stable. We also obtain a critical patch number in the system with linear diffusion for the species to go extinct. These results extend some recent known ones for discrete diffusion systems.Research partly supported by the Ministry of Education, Science and Culture, Japan, under Grant 01540177     

Models for the effect of toxicant in single-species and predator-prey systems

Models of single-species and predator-prey systems in a polluted closed environment are developed and partially analyzed. Three cases are considered: a single influx of toxicant, a constant influx of toxicant, and a periodic pollution of the environment. In the case of single-species growth we are able to determine some local and global dynamics. In the case of predator-prey systems, we investigate the existence of steady states for a small constant influx of toxicant.On leave from Department of Mathematics, Indian Institute of Technology, Kanpur, IndiaResearch partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A4823     

Stochastic analogues of deterministic single-species population models

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models--additive normally distributed noise and multiplicative lognormally distributed noise--generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.     

Nuclear power plants and natural populations of Mexican Drosophila

With the worldwide proliferation of nuclear power plants has come the need to study the biological effects of the operation of the reactors on surrounding populations. We have begun a long-term study of the sibling species Drosophila melanogaster and D. simulans in the area of Laguna Verde in the state of Veracruz in Mexico. Laguna Verde, on the Gulf of Mexico about 75 km north of the city of Veracruz, is the location of the country's first nuclear power plant. This plant has not yet gone "on-line." The species have been collected from two sites, one of which is south of the reactor and is in the path of the prevailing north to south wind flow. The other collecting site is west of the plant. The species are being studied for the following: species frequency, desiccation resistance, vagility, proportion of larvae pupating, pupation height, and egg to adult survival after irradiation. To date we have noted both spatial and seasonal differences in a number of these characteristics. The information being gathered will serve as base-line data for monitoring the future operation of the nuclear power plant.     

Density-dependence by habitat heterogeneity: individual quality versus territory quality

The aim of this comment is to review the ecological issues concerning the role of individual and habitat heterogeneity as possible mechanisms explaining density-dependent fecundity in animal populations. Our intention is to discuss different approaches to determine whether or not studied populations are subjected to density-dependent processes and which mechanisms are involved. We show that because individual quality (e.g. measured in terms of age of breeding individuals) and territory quality can be correlated, untangling both effects on fecundity is frequently a difficult task. We discuss the misuse of statistical methods and other problems related to the specific characteristics of the studied populations that can have a strong influence on the conclusions reached by researchers working in this field.