Dynamics of age- and size-structured populations in fluctuating environments: Applications of stochastic matrix models to natural populations

Recent developments of the theory of stochastic matrix modeling have made it possible to estimate general properties of age- and size-structured populations in fluctuating environments. However, applications of the theory to natural populations are still few. The empirical studies which have used stochastic matrix models are reviewed here to examine whether predictions made by the theory can be generally found in wild populations. The organisms studied include terrestrial grasses and herbs, a seaweed, a fish, a reptile, a deer and some marine invertebrates. In all the studies, the stochastic population growth rate (ln λ _s ) was no greater than the deterministic population growth rate determined using average vital rates, suggesting that the model based only on average vital rates may overestimate growth rates of populations in fluctuating environments. Factors affecting ln λ _s include the magnitude of variation in vital rates, probability distribution of random environments, fluctuation in different types of vital rates, covariances between vital rates, and autocorrelation between successive environments. However, comprehensive rules were hardly found through the comparisons of the empirical studies. Based on shortcomings of previous studies, I address some important subjects which should be examined in future studies.     

Ergodicity and extinction in a stochastic susceptible-infected-recovered-susceptible epidemic model with influence of information

An epidemic model with stochastic contact transmission coefficient takes into account white noise and the influence of information. Sufficient conditions for the extinction and persistence of the disease are expressed. The existence of a stationary distribution and the ergodic property are proved. The peak of infected population can be decreased by information. The analytical results are showed by simulations and the influence of white noise and information on the dynamics of epidemics are evaluated.     

A simple evolutionary model of dormancy and dispersal in heterogeneous patches with special reference to phytophagous lady beetles: I. Stable environments

Summary A simple evolutionary model of dormancy and dispersal is presented with special reference to phytophagous lady beetles. In order to investigate spatially heterogeneous environments, we assume the simplest patch structure, that is, there are only two patches, main and sub. Environments are also assumed to be temporally constant. The main patch is superior to the sub patch, but density effect at the main patch is higher than at the sub patch. Optimal dormancy and dispersal are obtained at the same time by the method of evolutionarily stable strategy (ESS). In the univoltine life cycle, dormancy strategy vanishes because dormant individuals do not reproduce at all but suffer from a certain mortality rate during winter hibernation. In the bivoltine life cycle, the dormancy and dispersal rates constitute a trade-off: the rates change together with a negative correlation when the mortality rate during dispersal or during winter hibernation changes. When suitability of the main patch gradually deteriorates, the optimal strategy changes as follows: neither dormancy nor dispersal is adopted at the most suitable condition, the dispersal rate is increased without dormancy in the intermediate condition, and then the dormancy rate is increased with a constant dispersal rate. We discuss the field observation data of lady beetles in the light of results of our model.     

Population dynamics in Germany: the role of immigration and population momentum

The effects of changes in rates of mortality, fertility, and migration depend not only on the age-specific patterns and levels of these rates, but on the age structure of the population. In order to remove the influences of the age structure and concentrate on the effects of the demographic rates themselves, a common practice is to analyze the influences of the rates for a standard age structure. This paper analyzes current and future population changes in Germany, using a stationary population equivalent model (SPE) that shows long-term effects of current fertility, mortality, and international migration patterns. Results indicate that the German population will eventually decline because of below replacement fertility, if net immigration does not counteract this decrease. This means, for instance, that the long-term stationary population levels for Germany will decrease by approximately 6.5 million during a decade in which current fertility, mortality, and international migration levels prevail. The paper also reports how various other assumptions for mortality, fertility, and international migration affect the SPE model for Germany.     

Host-feeding and oviposition by parasitoids in relation to host stage: Consequences for parasitoid-host population dynamics

Summary Among parasitoids which host-feed destructively, there is a tendency for females to partition their feeding and oviposition behaviour in relation to different host stages, feeding preferentially or exclusively on earlier host stages and ovipositing preferentially or exclusively in (or on) later ones. We explored the dynamic implications of this behaviour for parasitoid-host population dynamics, using modifications of the age-structured simulation models of Kidd and Jervis (1989, 1991). Using the new versions of the models, we compared the situation where parasitoids practice host stage discrimination with respect to feeding and oviposition, with the situation where they do not. Additionally, we examined the effects of host stage discrimination on populations by (a) having generations either discrete or overlapping, (b) varying initial age structure, (c) having varying degrees of density dependence acting on host adult mortality, and (d) varying parasitoid develoment times in relation to the length of host development. With either discrete or overlapping generations of the host population, a reduction in the parasitoid development time had a destabilizing influence on the parasitoid-host population interaction. With discrete generations stage discrimination had no effect on the risk of extinction, irrespective of either the degree of density dependence acting on the host population, or the initial age structure of the host population. When parasitoid search was uncoupled from the insect's adult energy requirements, the interaction was always unstable. With continuous generations, stage discrimination affected stability at certain parasitoid development times, but not at others. The relative lengths of parasitoid and host development times also influenced the tendency of the host population to show discrete or overlapping generations.     

The effect of long-term migration dynamics on population structure in England & Wales and Scotland

We investigated the effect of migration on population dynamics in England & Wales and Scotland from the mid-nineteenth century to the present by comparing actual population size and structure with estimates based on zero net migration from a range of starting dates. In this period, Scotland had the largest net outflow among countries in Europe for which detailed information is available, whereas overall net migration in England & Wales was close to zero. In the absence of migration, population would have been over twice as large in Scotland in 2013 as the actual value, but similar to its actual value in England & Wales. Levels and pace of population ageing have been broadly similar in both countries, so the major impact of differential migration has been on population size rather than structure. We discuss these findings in relation to the debate on migration policy between political parties supporting and opposing independence in the 2014 Scottish referendum.     

A stochastic version of the malthusian trap model: Consequences for the empirical relationship between economic growth and population growth in LDC's

A stochastic version of the Malthusian trap model relating the growth rate of income per capita to the population growth rate of a given country is described. This model is applied to the a priori evaluation of the cross‐sectional correlation between these two growth rates under two additional assumptions: i) the relations in the model at national levels include country‐specific and time‐invariant random components, and ii) these growth rates are measured with a certain degree of temporal aggregation. It is shown that these two assumptions can explain near‐zero correlations between the two growth rates even if there exist a strongly negative effect of population growth on economic growth. However it is not clear whether these assumptions fully explain such insignificant correlations. Indeed, the implementation of the model is complicated by the structural shifts which are likely to occur in the equations over the course of the demographic transition.     

Yearly variation in recruitment and its effect on population dynamics inYoldia notabilis (Mollusca: Bivalvia), analyzed using projection matrix model

Summary Long-term variation in recruitment was estimated by constructing projection matrices for a marine bivalve,Yoldia notabilis, at two stations in Otsuchi Bay, northeastern Japan, and the effects of its variation on population dynamics were examined using a simple matrix model. The matrix model was developed from the Leslie matrix, in which the population growth rate λ was expressed as a function of recruitment rater ₀. The equilibrium recruitment rater _s, or the recruitment rate required to maintain population at constant size (λ=1), was expressed by the reciprocal of the reproductive value of a newly recruited individual. The estimates ofr _s for the field population were lower at the shallower station than at the deeper station, reflecting higher survivorship and fecundity. Past recruitment rate estimated both by the field samplings for 3 years and by the back-calculation from the current age structure for over 10 years showed large yearly variation, ranging between 0 and 58.6×10⁻⁴. The estimates were larger thanr _s, and hence, large enough to increase population size (λ>1) only in approximately one-third of the estimated years. This suggests that the population has been maintained by occasional successful recruitment occurring once every few years.