Models of growth with density regulation in more than one life stage

On a population model with density dependence and Allee effect

We study the dynamics of a discrete model with two different stages of the population, the pre-adult stage governed by a Beverton-Holt-type map and the adult stage by a [Formula: see text]-Ricker map. The composition of both maps gives the dynamics. The existence of the Allee effect is easily observed. We check that the model can evolve from a sure extinction to complicated dynamics. The presence of an almost sure extinction is proved to exist when the dynamical complexity is the highest possible.

On the proper periodic Ricker model

The periodic Ricker equation has been studied by several authors, including the present one. However, the periodic model derived from the original one has not been studied in detail. We show that the model often taken as a periodic Ricker model is a particular case of the original one and compare their dynamics. In particular, we characterize the parameter region where the model has a periodic point of period two, which is globally stable. We also compute the parameter regions where complex behavior is exhibited.

Climate change and highland malaria: fresh air for a hot debate

In recent decades, malaria has become established in zones at the margin of its previous distribution, especially in the highlands of East Africa. Studies in this region have sparked a heated debate over the importance of climate change in the territorial expansion of malaria, where positions range from its neglect to the reification of correlations as causes. Here, we review studies supporting and rebutting the role of climatic change as a driving force for highland invasion by malaria. We assessed the conclusions from both sides of the argument and found that evidence for the role of climate in these dynamics is robust. However, we also argue that over-emphasizing the importance of climate is misleading for setting a research agenda, even one which attempts to understand climate change impacts on emerging malaria patterns. We review alternative drivers for the emergence of this disease and highlight the problems still calling for research if the multidimensional nature of malaria is to be adequately tackled. We also contextualize highland malaria as an ongoing evolutionary process. Finally, we present Schmalhausen's law, which explains the lack of resilience in stressed systems, as a biological principle that unifies the importance of climatic and other environmental factors in driving malaria patterns across different spatio-temporal scales.

When density dependence is not instantaneous: theoretical developments and management implications

Most organisms live in changing environments or do not use the same resources at different stages of their lives or in different seasons. As a result, density dependence will affect populations differently at different times. Such sequential density dependence generates markedly different population responses compared to the unrealistic assumption that all events occur simultaneously. Various field studies have also shown that the conditions that individuals experience during one period can influence success and per capita vital rates during the following period. These carry-over effects further complicate any general principles and increase the diversity of possible population dynamics. In this review, we describe how studies of sequential density dependence have diverged in directions that are both taxon-specific and have non-overlapping terminology, despite very similar underlying problems. By exploring and highlighting these similarities, we aim to improve communication between fields, clarify common misunderstandings, and provide a framework for improving conservation and management practices, including sustainable harvesting theory.

Density dependence in the terrestrial life history stage of two anurans

Populations of species with complex life cycles have the potential to be regulated at multiple life history stages. However, research tends to focus on single stage density-dependence, which can lead to inaccurate conclusions about population regulation and subsequently hinder conservation efforts. In amphibians, many studies have demonstrated strong effects of larval density and have often assumed that populations are regulated at this life history stage. However, studies examining density regulation in the terrestrial stages are rare, and the functional relationships between terrestrial density and vital rates in amphibians are unknown. We determined the effects of population density on survival, growth and reproductive development in the terrestrial stage of two amphibians by raising juvenile wood frogs (Rana sylvatica) and American toads (Bufo americanus) at six densities in terrestrial enclosures. Density had strong negative effects on survival, growth and reproductive development in both species. We fitted a priori recruitment functions to describe the relationship between initial density and the density of survivors after one year, and determined the functional relationship between initial density and mass after one year. Animals raised at the lowest densities experienced growth and survival rates that were over twice as great as those raised at the highest density. All female wood frogs in the lowest density treatment showed signs of reproductive development, compared to only 6% in the highest density treatment. Female American toads reached minimum reproductive size only at low densities, and male wood frogs and American toads reached maturity only in the three lowest density treatments. Our results demonstrate that in the complex life cycle of amphibians, density in the terrestrial stage can reduce growth, survival and reproductive development and may play an important role in amphibian population regulation. We discuss the implications of these results for population regulation in complex life cycles and for amphibian conservation.

Two-species asymmetric competition: effects of age structure on intra- and interspecific interactions

1. The patterns of density-dependent resource competition and the mechanisms leading to competitive exclusion in an experimental two-species insect age-structured interaction were investigated. 2. The modes of competition (scramble or contest) and strength of competition (under- to overcompensatory) operating within and between the stages of the two species was found to be influenced by total competitor density, the age structure of the competitor community and whether competition is between stages of single or two species. 3. The effect of imposed resource limitation on survival was found to be asymmetric between stages and species. Environments supporting both dominant and subordinate competitors were found to increase survival of subordinate competitors at lower total competitor densities. Competitive environments during development within individual stage cohorts (i.e. small or large larvae), differed from the competitive environment in lumped age classes (i.e. development from egg-->pupae). 4. Competition within mixed-age, stage or species cohorts, when compared with uniform-aged or species cohorts, altered the position of a competitive environment on the scramble-contest spectrum. In some cases the competitive environment switched from undercompensatory contest to overcompensatory scramble competition. 5. Such switching modes of competition suggest that the relative importance of the mechanisms regulating single-species population dynamics (i.e. resource competition) may change when organisms are embedded within a wider community.

Signature Function for Predicting Resonant and Attenuant Population 2-cycles

Populations are either enhanced via resonant cycles or suppressed via attenuant cycles by periodic environments. We develop a signature function for predicting the response of discretely reproducing populations to 2-periodic fluctuations of both a characteristic of the environment (carrying capacity), and a characteristic of the population (inherent growth rate). Our signature function is the sign of a weighted sum of the relative strengths of the oscillations of the carrying capacity and the demographic characteristic. Periodic environments are deleterious for populations when the signature function is negative. However, positive signature functions signal favorable environments. We compute the signature functions of six classical discrete-time single species population models, and use the functions to determine regions in parameter space that are either favorable or detrimental to the populations. The two-parameter classical models include the Ricker, Beverton-Holt, Logistic, and Maynard Smith models.

Theoretical estimates of consumable food and probability of acquiring food in larvae of Chrysomya putoria (Diptera: Calliphoridae)

An indirect estimate of consumable food and probability of acquiring food in a blowfly species, Chrysomya putoria, is presented. This alternative procedure combines three distinct models to estimate consumable food in the context of the exploitative competition experienced by immature individuals in blowfly populations. The relevant parameters are derived from data for pupal weight and survival and estimates of density-independent larval mortality in twenty different larval densities. As part of this procedure, the probability of acquiring food per unit of time and the time taken to exhaust the food supply are also calculated. The procedure employed here may be valuable for estimations in insects whose immature stages develop inside the food substrate, where it is difficult to partial out confounding effects such as separation of faeces. This procedure also has the advantage of taking into account the population dynamics of immatures living under crowded conditions, which are particularly characteristic of blowflies and other insects as well.

Periodic solutions to nonautonomous difference equations

A technique is presented for determining when periodic solutions to nonautonomous periodic difference equations exist. Under certain constraints, stable periodic solutions can be guaranteed to exist, and this is used to compare the analogous behavior of a nonautonomous periodic hyperbolic difference equation to that of the nonautonomous periodic Pearl-Verhulst logistic differential equation.