Meaning of density-dependence and related terms in population dynamics.
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To better understand the role of habitat quality and boundaries on population dynamics at the landscape scale, we develop a model combining a spatially implicit approach, a spatial population Leslie-type model and an implicit model of habitat fragmentation. An original approach of elasticity permits to identify which types of element and boundary influence the most population viability according to the wood fragmentation degree. The studied species is a corridor forest insect sensitive to fragmentation (Abax parallelepipedus, Coleoptera, Carabidae). We show that a single large patch of wood is better than several small patches for the population viability.
Simple discrete time models of population growth admit a wide variety of dynamic behaviors, including population cycles and chaos. Yet studies of natural and laboratory populations typically reveal their dynamics to be relatively stable. Many explanations for the apparent rarity of unstable or chaotic behavior in real populations have been developed, including the possible stabilizing roles of migration, refugia, abrupt density-dependence, and genetic variation in sensitivity to density. We develop a theoretical framework for incorporating random spatial variation in density into simple models of population growth, and apply this approach to two commonly used models in ecology: the Ricker and Hassell maps. We show that the incorporation of spatial density variation into both these models has a strong stabilizing influence on their dynamic behavior, and leads to their exhibiting stable point equilibria or stable limit cycles over a relatively much larger range of parameter values. We suggest that one reason why chaotic population dynamics are less common than the simple models indicate is, these models typically neglect the potentially stabilizing role of spatial variation in density.
Population dynamical parameters of Trichuris trichiura infections in children were estimated from longitudinal intensity and prevalence data from a population (n = 23) in a children's home in Jamaica. The theoretical predictions of a deterministic model incorporating these parameters were approximated to observed horizontal-age prevalence data from a naturally infected population (n = 203) of children in a St. Lucian village, and a rough estimate of the basic reproductive rate (Ro = 8-10) of T. trichiura obtained. The findings suggest that T. trichiura populations are intrinsically more difficult to control by traditional mass-treatment chemotherapy (eradication requires greater than 91% of the population to be treated every 6 months for greater than 5 years) than are populations of Ascaris, but may be more susceptible to selective chemotherapy programmes which aim to treat only the most heavily infected individuals.
BACKGROUND: Malaria is one of the oldest and deadliest infectious diseases in humans. Many mathematical models of malaria have been developed during the past century, and applied to potential interventions. However, malaria remains uncontrolled and is increasing in many areas, as are vector and parasite resistance to insecticides and drugs. METHODS: This study presents a simulation model of African malaria vectors. This individual-based model incorporates current knowledge of the mechanisms underlying Anopheles population dynamics and their relations to the environment. One of its main strengths is that it is based on both biological and environmental variables. RESULTS: The model made it possible to structure existing knowledge, assembled in a comprehensive review of the literature, and also pointed out important aspects of basic Anopheles biology about which knowledge is lacking. One simulation showed several patterns similar to those seen in the field, and made it possible to examine different analyses and hypotheses for these patterns; sensitivity analyses on temperature, moisture, predation and preliminary investigations of nutrient competition were also conducted. CONCLUSIONS: Although based on some mathematical formulae and parameters, this new tool has been developed in order to be as explicit as possible, transparent in use, close to reality and amenable to direct use by field workers. It allows a better understanding of the mechanisms underlying Anopheles population dynamics in general and also a better understanding of the dynamics in specific local geographic environments. It points out many important areas for new investigations that will be critical to effective, efficient, sustainable interventions.
An induced outbreak of a bovine herpesvirus 1 (BHV1) infection in a dairy herd is described. The outbreak was induced by injecting three BHV1 seropositive cows with dexamethasone. Within 7 weeks all seronegative cows had seroconverted. Also some seropositive animals showed a significant increase in serum antibody titre. Using these data, parameters of population dynamics such as R0, the basic reproduction ratio, could be estimated. The basic reproduction ratio is a threshold value describing infection dynamics in a population. This parameter is defined as the average number of secondary cases generated by one primary case in a wholly susceptible population of defined density. In this population R0 was estimated to be at least 7. The importance of these findings, and implications for eradication of BHV1 are discussed.
The population dynamics of five synanthropic fly species, Chrysomyia rufifacies, Musca d. domestica Muscina stabulans F. Sarcophaga haemorrhoidalis, and Stomoxys calcitrans, were studied at three different habitats in Buraydah, Saudi Arabia. The chosen habitats were the slaughter house, the cattle market and the rubbish dumps. The number of flies caught per twenty sticky bands was taken monthly, for a whole year, as an index to the fly population at that habitat during that month. M. d. domestica was the most abundant fly species; it made up nearly 98%, 81% and 75% of the total synanthropic fly population at the rubbish dumps, the cattle market and the slaughter house, respectively. It reached its maximum abundance in May and minimum occurrence in January. House flies were collected throughout the year and survived conditions seemed to be unsuitable for other species.
1. One of the most difficult problems in developing spatially explicit models of population dynamics is the validation and parameterization of the movement process. We show how movement models derived from capture-recapture analysis can be improved by incorporating them into a spatially explicit metapopulation model that is fitted to a time series of abundance data. 2. We applied multisite capture-recapture analysis techniques to photo-identification data collected from female grey seals at the four main breeding colonies in the North Sea between 1999 and 2001. The best-fitting movement models were then incorporated into state-space metapopulation models that explicitly accounted for demographic and observational stochasticity. 3. These metapopulation models were fitted to a 20-year time series of pup production data for each colony using a Bayesian approach. The best-fitting model, based on the Akaike Information Criterion (AIC), had only a single movement parameter, whose confidence interval was 82% less than that obtained from the capture-recapture study, but there was some support for a model that included an effect of distance between colonies. 4. The state-space modelling provided improved estimates of other demographic parameters. 5. The incorporation of movement, and the way in which it was modelled, affected both local and regional dynamics. These differences were most evident as colonies approached their carrying capacities, suggesting that our ability to discriminate between models should improve as the length of the grey seal time series increases.
"An age-structured model of population dynamics with age-dominance is proposed and analyzed. Existence and uniqueness of solutions are established as well as the uniqueness and local asymptotic stability of steady-states. Conditions for convergence to or oscillation about the steady-state are specified in some cases." (SUMMARY IN FRE)
Stratified squamous epithelia, such as those covering the skin, esophagus, and cervix, are normally in a dynamic steady state: production of new cells (proliferation) is matched by loss of terminally differentiated cells into the environment (desquamation). The parameters that describe population dynamics in stratified epithelia--number of dividing cells, number of cell layers, transit time, and rate of desquamation--can be closely monitored in cultures of stratified epithelial cells. Analysis of these data show that cultures of stratified epithelial cells can be maintained in a dynamic steady state for at least 1 month and thus have a dynamic behavior similar to stratified epithelia in vivo. Although this in vitro behavior may be intuitively reasonable based on the in vivo behavior of these cells, it is remarkable in that it is contrary to the general experience with other normal cell types in culture. The usefulness of measuring population dynamics in cultures is demonstrated by an analysis of the actions of retinoids on human keratinocytes. In addition, we show that because of favorable geometry and ease of manipulation, these cultures are well-suited to the analysis of heterogeneity in the proliferating population of cells.
The population dynamics of Trichostrongylus colubriformis larvae were compared over two years on contrasting topographical aspects north (warm and dry) and south-facing (cool and moist) hill slopes) on paddocks which form part of the 'non-chemical' and conventional' farm systems at the AgResearch Ballantrae Hill Country Station located in a summer-moist region of New Zealand. Sheep faeces containing 50,000 Trichostrongylus eggs were incubated for 4 days at 25 degrees C and then deposited on each of 36 sub-plots in each of 8 plots in a 2 x 2 factorial design in the summer (summer trial) and again in autumn (autumn trial). Pasture was removed to ground level and larvae extracted from six sub-plots from each plot 2, 4, 6, 8, 11 and 14 weeks after contamination in all trials. Larvae were recovered from two strata, 0-5 cm above the soil surface and > 5 cm above the soil surface. Fewer (p < 0.001) larvae were recovered from herbage (47 vs. 118) and residual faeces (28 vs. 246) from the autumn than from the summer trials. This coincided with more rapid (p < 0.001) faecal disappearance in the autumn trials. In the summer trials, fewer (p < 0.003) larvae were recovered from the herbage (101 vs. 182) and residual faeces (140 vs. 352) from plots on the south than the north facing aspect. In the autumn trials there was a rapid (p < 0.0001) faecal disappearance from the south-facing aspect. In the autumn trials there was a non-significant (p < 0.10) trend for fewer larvae to be recovered from the south-facing aspect (2 vs. 54). This also coincided with more rapid faecal disappearance from the south-facing aspect. There was no effect of farm system on the number of larvae recovered. Despite greater (p < 0.0001) numbers of larvae recovered from the bottom stratum of herbage, the density of larvae (L3/kg DM) tended (p < 0.12) to be higher in the top stratum of herbage. It was concluded that season and aspect have a marked effect on the number of larvae recovered from herbage and that this was inversely related to the rate of faecal disappearance.
How do the behavioural interactions between individuals in an ecological system produce the global population dynamics of that system? We present a stochastic individual-based model of the reproductive cycle of the mite Varroa jacobsoni, a parasite of honeybees. The model has the interesting property in that its population level behaviour is approximated extremely accurately by the exponential logistic equation or Ricker map. We demonstrated how this approximation is obtained mathematically and how the parameters of the exponential logistic equation can be written in terms of the parameters of the individual-based model. Our procedure demonstrates, in at least one case, how study of animal ecology at an individual level can be used to derive global models which predict population change over time.
In this article, we develop population game theory, a theory that combines the dynamics of animal behavior with population dynamics. In particular, we study interaction and distribution of two species in a two-patch environment assuming that individuals behave adaptively (i.e., they maximize Darwinian fitness). Either the two species are competing for resources or they are in a predator-prey relationship. Using some recent advances in evolutionary game theory, we extend the classical ideal free distribution (IFD) concept for single species to two interacting species. We study population dynamical consequences of two-species IFD by comparing two systems: one where individuals cannot migrate between habitats and one where migration is possible. For single species, predator-prey interactions, and competing species, we show that these two types of behavior lead to the same population equilibria and corresponding species spatial distributions, provided interspecific competition is patch independent. However, if differences between patches are such that competition is patch dependent, then our predictions strongly depend on whether animals can migrate or not. In particular, we show that when species are settled at their equilibrium population densities in both habitats in the environment where migration between habitats is blocked, then the corresponding species spatial distribution need not be an IFD. Thus, when species are given the opportunity to migrate, they will redistribute to reach an IFD (e.g., under which the two species can completely segregate), and this redistribution will also influence species population equilibrial densities. Alternatively, we also show that when two species are distributed according to the IFD, the corresponding population equilibrium can be unstable.
Heterogeneous access to sanitation services is a characteristic of communities in Brazil. This heterogeneity leads to different patterns of hepatitis A endemicity: areas with low infection rates have higher probability of outbreaks, and areas with higher infection rates have high prevalence and low risk of outbreaks. Here we develop a mathematical model to study the effect of variable exposure to infection on the epidemiological dynamics of hepatitis A. Differential equations were used to simulate population dynamics and were numerically solved using the software Stella. The model uses parameters from serological surveys in the Greater Metropolitan Rio de Janeiro, in areas with different sanitation conditions. Computer simulation experiments show that the range of infection rates observed in these communities are characteristic of high and low levels of hepatitis A endemicity. We also found that the functional relationship between sanitation and exposure to infection is an important component of the model. The analysis of the public health impact of partial sanitation requires a better understanding of this relationship.
This paper describes a mathematical model which allows us to compare the data collected from short-term cross-sectional surveys with the population dynamics of host and parasite populations over longer periods of time. The model extends an earlier framework for two parasite species in one host, to one for an arbitrary number of parasite species. We show that the conditions necessary for the coexistence of two parasite species extend to expressions for the coexistence of three or more parasite species. Furthermore, the model suggests that those species which form the 'core' of the parasite community are those whose high fecundity and transmission efficiency permit them to colonize hosts readily. In contrast, those species which are classified as 'satellite' species of the community are either species with low fecundity, or low transmission efficiencies. This work confirms earlier studies that suggest that increasing degrees of aggregation are crucial in allowing several species of parasites to coexist in the same species of hosts. The properties of the model are compared with patterns observed in data collected for helminth parasites of Anolis lizards, wood mice and eels. This combined theoretical and empirical approach confirms the importance of the life history strategies of the parasite in determining the abundance of each species in the community. It suggests that studies of parasite community structure have to pay more attention to the strategies pursued by each individual species before interactions between species are considered.