The population dynamics of outbred laboratory mice in indoor enclosures in the absence and presence of a naturally transmitted direct life-cycle nematode Heligmosomoides polygyrus Dujardin 1845 were reported previously. This manuscript presents further information on the age and sex structure of the populations, results of experiments designed to estimate the density-dependent effect of the parasite on host survival and reproduction, and a mathematical model of both uninfected and infected mouse populations. In the uninfected mouse population, survival of female mice was age- and density-independent, survival of male mice was age-dependent and density-independent, and recruitment was density-dependent. Independent experiments revealed that the parasite had no density-dependent effect on mouse reproduction, but had density-dependent effects on both acute and chronic survival of mice. An age-structured Leslie matrix model captured the exponential growth and plateau of the uninfected mouse population. Modification of the model to incorporate the effects of the parasite provided a good fit to the data from the infected populations, supporting the hypothesis that density-dependent effects of the parasite on host survival could lead to regulation of host abundance.

Nosema pyrausta is an important microsporidian pathogen of the European corn-borer, Ostrinia nubilalis (Pyralidae), a major pest of corn (maize). The population dynamics of the interaction between the moth and its pathogen have been studied previously using simple models phrased as coupled differential equations, and using large simulation models containing over 150000 coupled equations. A middle approach is adopted here and the interaction studied using an age-structured model written as a system of delay-differential equations. Although the model contains twenty four parameters, estimates for twenty of these were available in the literature. Our model provides a good qualitative match to observed within and between season dynamics and suggests which aspects of the interaction are most important in determining the nature of the system's population dynamics. More generally, we argue that in the absence of better data on insect-disease interactions in natural habitats, valuable insights can be gained by studying equivalent systems in agro-ecosystems. We also argue that models of intermediate complexity that incorporate considerable detail about the natural history of individual interactions, but which are derived from the classical models of animal ecology and epidemiology, offer the most profitable way of modelling insect-pathogen interactions in the wild.

The Sharpe-Lotka-McKendrick (or von Foerster) equations for an age-structured population, with a nonlinear term to represent overcrowding or competition for resources, are considered. The model is extended to include a growth term, allowing the population to be structured by size or weight rather than age, and a general solution is presented. Various examples are then considered, including the case of cell growth where cells divide at a given size.

We develop the qualitative theory of thesolutions of the McKendrick partial differential equation ofpopulation dynamics. We calculate explicitly the weak solutionsof the McKendrick equation and of the Lotka renewal integralequation with time and age dependent birth rate. Mortality modulusis considered age dependent. We show the existence of demographycycles. For a population with only one reproductive age class,independently of the stability of the weak solutions and after atransient time, the temporal evolution of the number ofindividuals of a population is always modulated by a time periodicfunction. The periodicity of the cycles is equal to the age ofthe reproductive age class, and a population retains the memoryfrom the initial data through the amplitude of oscillations. For apopulation with a continuous distribution of reproductive ageclasses, the amplitude of oscillation is damped. The periodicityof the damped cycles is associated with the age of the firstreproductive age class. Damping increases as the dispersion of thefertility function around the age class with maximal fertilityincreases. In general, the period of the demography cycles isassociated with the time that a species takes to reach thereproductive maturity.

In this work, we introduce a new software created to study hematopoiesis at the cellpopulation level with the individually based approach. It can be used as an interface between theoreticalworks on population dynamics and experimental observations. We show that this softwarecan be useful to study some features of normal hematopoiesis as well as some blood diseases suchas myelogenous leukemia. It is also possible to simulate cell communication and the formation ofcell colonies in the bone marrow.

Estimates of births and standing age-distributions were combined to estimate the size of the southern elephant seal population at Marion Island at various times during its decline. To estimate births each year from 1986 through 1997 we used the number of adult females hauled out on 15 October, which is the peak haulout date for breeding elephant seal females at all breeding sites in the Indian Ocean. A conversion factor (3.15) was derived from the standing age-distributions, and applied to estimates of annual births to yield total population size. The population at Marion Island declined 37.5% overall from 1986–97 at an annual rate of 4.3% from 1986–91 and c. 2.5% yr−1 afterwards.

We analyze a two species discrete predator-prey model inwhich the prey disperses between two patches of a heterogeneous environmentwith barriers and the mature predator disperses between thepatches with no barrier. By using the discrete dynamical system generated by a monotone, concavemaps for subcommunity of prey, we obtain the subcommunity of preyexists an equilibrium which attracts all positive solutions, andusing the stability trichotomy results on the monotone andcontinuous operator, we obtain some sufficient conditions for thepermanence of species. These results are applied to the modelswith rational growth functions and exponential growth functions.We also present numerical examples to illustrate the dynamiccomplexity of systems.

The impact of deliberate culling of fox populations has been much debated. Although a local (< 10 km2) impact has been accepted, previous authors have denied that culling has any impact on a larger scale because local losses are compensated through immigration. Rather, it has been claimed that at this scale fox density is determined by resources, mediated through social behaviour and breeding suppression. We determined the impact of culling on a regional scale (> 1000 km2), using data on culling (Heydon & Reynolds, 2000), fox density (Heydon, Reynolds & Short, 2000) and productivity. The three U.K. study regions (size 1238–2322 km2) were in mid-Wales (A), the east Midlands (B) and East Anglia (C). High productivity in regions A and C was associated with low density, high culling mortality and high overall mortality (all relative to region B), indicating that density was suppressed by culling. In region B (moderate) breeding suppression was associated with a higher density and lower cull than in regions A and C, implying that fox density was closer to the maximum sustainable by resources. We conclude that the impact of culling in different regions of Britain is variable, dependent on the regional prevalence, methods, and history of culling. However, it is clear that in a range of circumstances culling can substantially depress fox numbers, and that current fox densities reflect a history of culling. This conclusion is fundamental in considering the management of fox predation in farming and conservation contexts.