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

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.     

Temporal Allele Frequency Change and Estimation of Effective Size in Populations with Overlapping Generations

In this paper we study the process of allele frequency change in finite populations with overlapping generations with the purpose of evaluating the possibility of estimating the effective size from observations of temporal frequency shifts of selectively neutral alleles. Focusing on allele frequency changes between successive cohorts (individuals born in particular years), we show that such changes are not determined by the effective population size alone, as they are when generations are discrete. Rather, in populations with overlapping generations, the amount of temporal allele frequency change is dependent on the age-specific survival and birth rates. Taking this phenomenon into account, we present an estimator for effective size that can be applied to populations with overlapping generations.     

The effects of seasonality on discrete models of population growth

The effects of seasonality on the dynamics of a bivoltine population with discrete, nonoverlapping generations are examined. It is found that large seasonality is inevitably destabilizing but that mild seasonality may have a pronounced stabilizing effect. Seasonality also allows for the coexistence of alternative stable states (equilibria, cycles, chaos). These solutions may be seasonally in-phase, out-of-phase, or asynchronous. In-phase solutions correspond to winter regulation of population density, whereas out-of-phase solutions correspond to summer regulation. Analysis suggests that summer regulation is possible only in mildly seasonal habitats.     

Continuous-discrete models of the dynamics of an isolated population and of 2 competing species

The paper presents the analysis of various mathematical models for dynamics of isolated population and for competition between two species. It is assumed that mortality is continuous and birth of individuals of new generations takes place in certain fixed moments. Influence of winter upon the population dynamics and conditions of classic discrete model "deduction" of population dynamics (in particular, Moran-Ricker and Hassel's models) are investigated. Dynamic regimes of models under various assumptions about the birth and death rates upon the population states are also examined. Analysis of models of isolated population dynamics with nonoverlapping generations showed the density changes regularly if the birth rate is constant. Moreover, there exists a unique global stable level and population size stabilizes asymptotically at this equilibrium, i.e. cycle and chaotic regimes in various discrete models depend on correlation between individual productivity and population state in previous time. When the correlation is exponential upon mean population size the discrete Hassel model is realized. Modification of basis model, based on the assumption that during winter survival/death changes are constant, showed that population size at global level is stable. Generally, the dependence of population rate upon "winter parameters" has nonlinear character. Nonparametric models of competition between two species does not vary if the individual productivity is constant. In a phase space there are several stable stationary states and population stabilizes at one or other level asymptotically. So, in discrete models of competition between two species oscillation can be explained by dependence of population growth rate on the population size at previous times.     

Mathematical modelling of host-parasitoid systems: effects of chemically mediated parasitoid foraging strategies on within- and between-generation spatio-temporal dynamics.

In this paper we develop a novel discrete, individual-based mathematical model to investigate the effect of parasitoid foraging strategies on the spatial and temporal dynamics of host-parasitoid systems. The model is used to compare na?ve or random search strategies with search strategies that depend on experience and sensitivity to semiochemicals in the environment. It focuses on simple mechanistic interactions between individual hosts, parasitoids, and an underlying field of a volatile semiochemical (emitted by the hosts during feeding) which acts as a chemoattractant for the parasitoids. The model addresses movement at different spatial scales, where scale of movement also depends on the internal state of an individual. Individual interactions between hosts and parasitoids are modelled at a discrete (micro-scale) level using probabilistic rules. The resulting within-generation dynamics produced by these interactions are then used to generate the population levels for successive generations. The model simulations examine the effect of various key parameters of the model on (i) the spatio-temporal patterns of hosts and parasitoids within generations; (ii) the population levels of the hosts and parasitoids between generations. Key results of the model simulations show that the following model parameters have an important effect on either the development of patchiness within generations or the stability/instability of the population levels between generations: (i) the rate of diffusion of the kairomones; (ii) the specific search strategy adopted by the parasitoids; (iii) the rate of host increase between successive generations. Finally, evolutionary aspects concerning competition between several parasitoid subpopulations adopting different search strategies are also examined.     

On the impact of winter conditions on the dynamics of a population with non-overlapping generations: a model approach

The authors propose new type of models with non-overlapping generations. It is assumed that during winter period individuals are not active (as, for example, in insect populations in boreal forests) and some portion of population dyes. However the portion of population, that survives, Q, indirectly depends on feeding conditions in previous growing season. In the formal terms, Q = Q(u) is a decreasing function of the mean population size u (i.e., of the integral) over the growing period, and traditional discrete-time model therefore turns into a discrete-continuous one. Under any constant birth rate Y, the model is reduced to a discrete one in its general form, and a general result consists in global stability of the zero solution for any Y < 1, e.t., in population extinction from any initial state. In particular cases of dependence of Q(u) and different types of population self-limitation during growing season the general model results in a great variety of discrete models (including well known Moran-Ricker and Skellam models). For logistic growth of population during the growing season and exponential decrease in Q(u), the condition is obtained for a non-trivial steady state to exist, and the outcome is presented for bifurcation analysis with regard to parameter Y: cycles with typical period-doubling and chaotic dynamics.     

Effective Size and F-Statistics of Subdivided Populations. I. Monoecious Species with Partial Selfing

Assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, we have derived recurrence equations for the inbreeding coefficient and coancestry between individuals within and among subpopulations for a subdivided monoecious population with arbitrary distributions of male and female gametes per family, variable pollen and seed migration rates, and partial selfing. From the equations, formulas for effective size and expressions for F-statistics are obtained. For the special case of a single unsubdivided population, our equations reduce to the simple expressions derived by previous authors. It is shown that population structure (subdivision and migration) is important in determining the inbreeding coefficient and effective size. Failure to recognize internal structures of populations may lead to considerable bias in predicting effective size. Inbreeding coefficient, coancestry between individuals within and among subpopulations accrue at different and variable rates over initial generations before they converge to the same asymptotic rate of increase. For a given population, the smaller the pollen and seed migration rates, the more generations are required to attain the asymptotic rate and the larger the asymptotic effective size. The equations presented herein can be used for the study of evolutionary biology and conservation genetics.     

Effective Size and F-Statistics of Subdivided Populations. II. Dioecious Species

Assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, we have derived recurrence equations for the inbreeding coefficient and coancestry between individuals within and among subpopulations for a subdivided monoecious population with arbitrary distributions of male and female gametes per family, variable pollen and seed migration rates, and partial selfing. From the equations, formulas for effective size and expressions for F-statistics are obtained. For the special case of a single unsubdivided population, our equations reduce to the simple expressions derived by previous authors. It is shown that population structure (subdivision and migration) is important in determining the inbreeding coefficient and effective size. Failure to recognize internal structures of populations may lead to considerable bias in predicting effective size. Inbreeding coefficient, coancestry between individuals within and among subpopulations accrue at different and variable rates over initial generations before they converge to the same asymptotic rate of increase. For a given population, the smaller the pollen and seed migration rates, the more generations are required to attain the asymptotic rate and the larger the asymptotic effective size. The equations presented herein can be used for the study of evolutionary biology and conservation genetics.     

Genetic steady-state under BLUP selection for an infinite and homogeneous population with discrete generations

A matrix derivation is proposed to analytically calculate the asymptotic genetic variance-covariance matrix under BLUP selection according to the initial genetic parameters in a large population with discrete generations. The asymptotic genetic evolution of a homogeneous population with discrete generations is calculated for a selection operating on an index including all information (pedigree and records) from a non-inbred and unselected base population (BLUP selection) or on an index restricted to records of a few ancestral generations. Under the first hypothesis, the prediction error variance of the selection index is independent of selection and is calculated from the genetic parameters of the base population. Under the second hypothesis, the prediction error variance depends on selection. Furthermore, records of several generations of ancestors of the candidates for selection must be used to maintain a constant prediction error variance over time. The number of ancestral generations needed depends on the population structure and on the occurrence of fixed effects. Without fixed effects to estimate, accounting for two generations of ancestors is sufficient to estimate the asymptotic prediction error variance. The amassing of information from an unselected base population proves to be important in order not to overestimate the asymptotic genetic gains and not to underestimate the asymptotic genetic variances.     

Temporal estimates of effective population size in species with overlapping generations

The standard temporal method for estimating effective population size (N(e)) assumes that generations are discrete, but it is routinely applied to species with overlapping generations. We evaluated bias in the estimates N(e) caused by violation of this assumption, using simulated data for three model species: humans (type I survival), sparrow (type II), and barnacle (type III). We verify a previous proposal by Felsenstein that weighting individuals by reproductive value is the correct way to calculate parametric population allele frequencies, in which case the rate of change in age-structured populations conforms to that predicted by discrete-generation models. When the standard temporal method is applied to age-structured species, typical sampling regimes (sampling only newborns or adults; randomly sampling the entire population) do not yield properly weighted allele frequencies and result in biased N(e). The direction and magnitude of the bias are shown to depend on the sampling method and the species' life history. Results for populations that grow (or decline) at a constant rate paralleled those for populations of constant size. If sufficient demographic data are available and certain sampling restrictions are met, the Jorde-Ryman modification of the temporal method can be applied to any species with overlapping generations. Alternatively, spacing the temporal samples many generations apart maximizes the drift signal compared to sampling biases associated with age structure.     

CAN A PATCHY POPULATION STRUCTURE AFFECT THE EVOLUTION OF COMPETITION STRATEGIES?

Simulation models are described that examine the effect of a patchy population structure on the evolution of competition strategies. The results of the models suggest that a patchy population structure will make the evolution of scramble competition strategies more likely than in a single undivided population. The outcome of the models depends on the details of the population structure, in particular the number of individuals that found patches, the number of generations of competition within a patch, and the point at which founding females mate can all affect the evolutionary outcome. The results of the models are compared to those of previous models examining the effects of a structured population on the evolution of female-biased sex ratios, and altruistic behavior. The results of the model may help to explain the patterns of larval competition strategies observed in bruchid beetles.     

Effective size and F-statistics of subdivided populations for sex-linked loci.

For a population subdivided into an arbitrary number (s) of subpopulations, each consisting of different numbers of separate sexes, with arbitrary distributions of family size and variable migration rates by males (dm) and females (df), the recurrence equations for inbreeding coefficient and coancestry between individuals within and among subpopulations for a sex-linked locus are derived and the corresponding expressions for asymptotic effective size are obtained by solving the recurrence equations. The usual assumptions are made which are stable population size and structure, discrete generations, the island migration model, and without mutation and selection. The results show that population structure has an important effect on the inbreeding coefficients in any generation, asymptotic effective size, and F-statistics. Gene exchange among subpopulations inhibits inbreeding in initial generations but increases inbreeding in later generations. The larger the migration rate, the greater the final inbreeding coefficients and the smaller the effective size. Thus if the inbreeding coefficient is to be restricted to a specific value within a given number of generations, the appropriate population structure (the values of s, dm, and df) can be obtained by using the recurrence equations. It is shown that the greater the extent of subdivision (large s, small dm and df), the larger the effective size. For a given subdivided population, the effective size for a sex-linked locus may be larger or smaller than that for an autosomal locus, depending on the sex ratio, variance and covariance of family size, and the extend of subdivision. For the special case of a single unsubdivided population, our recurrence equations for inbreeding coefficient and coancestry and formulas for effective size reduce to the simple expressions derived by previous authors.     

Note : Genetic and biochemical characterization of nisin Z produced by Lactococcus lactis ssp. lactis biovar. diacetylactis UL 719

The bacteriocin produced by Lactococcus lactis ssp. lactis biovar. diacetylactis UL 719 was purified and characterized. Two peaks exhibiting antimicrobial activity were obtained after purification. Primary structure of the peptide of major peak 2 was identical to that of nisin Z when determined by Edman degradation and confirmed by DNA sequence analysis. The molecular mass as determined by mass spectrometry was 3346·39 ± 0·40 Da for peak 1 and 3330·39 ± 0·27 Da for peak 2, which suggests that peak 1 may correspond to an oxidized form of nisin Z. The two purified peaks exhibiting xrantimicrobial activity appear to correspond with the oxidized and native forms of nisin Z.     

Toward a theory of marker-assisted gene pyramiding

We investigate the best way to combine into a single genotype a series of target genes identified in different parents (gene pyramiding). Assuming that individuals can be selected and mated according to their genotype, the best method corresponds to an optimal succession of crosses over several generations (pedigree). For each pedigree, we compute the probability of success from the known recombination fractions between the target loci, as well as the number of individuals (population sizes) that should be genotyped over successive generations until the desired genotype is obtained. We provide an algorithm that generates and compares pedigrees on the basis of the population sizes they require and on their total duration (in number of generations) and finds the best gene-pyramiding scheme. Examples are given for eight target genes and are compared to a reference genotype selection method with random mating. The best gene-pyramiding method combines the eight targets in three generations less than the reference method while requiring fewer genotypings.     

From local interactions to population dynamics in site-based models of ecology

A central problem in ecology is relating the interactions of individuals-described in terms of competition, predation, interference, etc.-to the dynamics of the populations of these individuals-in terms of change in numbers of individuals over time. Here, we address this problem for a class of site-based ecological models, where local interactions between individuals take place at a finite number of discrete resource sites over non-overlapping generations and, between generations, individuals move randomly between sites over the entire system. Such site-based models have previously been applied to a wide range of ecological systems: from those involving contest or scramble competition for resources to host-parasite interactions and meta-populations. We show how the population dynamics of site-based models can be accurately approximated by and understood through deterministic and stochastic difference equations. Conversely, we use the inverse of this approximation to show what implicit assumptions are made about individual interactions by modelling of population dynamics in terms of difference equations. To this end, we prove a useful and general theorem: that any model in our class of site-based models has a corresponding stochastic difference equation population model, by which it can be approximated. This theorem allows us to calculate long-term population dynamics, evolutionary stable strategies and, by extending our theory to account for large deviations, extinction probabilities for a wide range of site-based systems. Our methodology is then illustrated to various examples of between species competition, predator-prey interactions and co-operation.     

A note on effective population size with overlapping generations

A simple derivation is given for a formula obtained previously for the effective size of random-mating populations with overlapping generations. The effective population size is the same as that for a population with discrete generations having the same variance of lifetime family size and the same number of individuals entering the population per generation.     

Estimating the survival rate and mean longevity for adults in a field population of the green rice leafhopper,Nephotettix cincticeps Uhler,by the application ofHokyo andKiritani’s method

Application of the female dissection method proposed byHokyo andKiritani (1967) was attempted in both 1968 and 1969 to estimate the daily survival rate and the mean longevity for the adult population of the green rice leafhopper, Nephotettix cincticeps, in a paddy field. The estimated mean longevity for females was far shorter than the physiological longevity of this species, ranging from 4 to 7 days with some variation between different generations. This could explain the remarkable discontinuity among successive generations which proved to form an important feature of the pattern of seasonal population changes of this insect. Between the two years, the estimated survival rate (and hence the mean longevity also) was negatively correlated to the estimated population size of adults that emerged in either of the two successive generations. This apparent density dependence suggests the possibility that the adult survival, including the effect of dispersal, plays some critical role in bringing about the remarkable population stability from year to year shown by the field population of N. cincticeps.     

Age dependent dispersal is not a simple process: Density dependence, stability, and chaos

I present both discrete and continuous models for a single species with overlapping generations, density dependence, and movement rates that vary with age. In the discrete time and space model, I show that if the strongly density dependent age class(es) are stationary, the spatially structured model may exhibit instabilities or even chaos which are not present in the corresponding model without spatial structure. I argue that the conditions which lead to these diffusive instabilities are likely to be met in natural populations. Thus it is important to consider the interaction between age structure and spatial structure in both experimental and theoretical work. In particular, the conditions leading to chaos are more common than would be predicted in models which ignore structure.     

Dynamical facilitation of the ideal free distribution in nonideal populations

The ideal free distribution (IFD) requires that individuals can accurately perceive density‐dependent habitat quality, while failure to discern quality differences below a given perception threshold results in distributions approaching spatial uniformity. Here, we investigate the role of population growth in restoring a nonideal population to the IFD. We place a simple model of discrete patch choice under limits to the resolution by which patch quality is perceived and include population growth driven by that underlying quality. Our model follows the population's distribution through both breeding and dispersal seasons when perception limits differ in their likely influence. We demonstrate that populations of perception limited movers can approximate an IFD provided sufficient population growth; however, the emergent IFD would be temporally inconstant and correspond to reproductive events. The time to emergence of the IFD during breeding is shorter under exponential growth than under logistic growth. The IFD during early colonization of a community persists longer when more patches are available to individuals. As the population matures and dispersal becomes increasingly random, there is an oscillation in the observance of IFD, with peaks most closely approximating the IFD occurring immediately after reproductive events, and higher reproductive rates producing distributions closer to the IFD.     

Projecting insect voltinism under high and low greenhouse gas emission conditions

We develop individual-based Monte Carlo methods to explore how climate change can alter insect voltinism under varying greenhouse gas emissions scenarios by using input distributions of diapause termination or spring emergence, development rate, and diapause initiation, linked to daily temperature and photoperiod. We show concurrence of these projections with a field dataset, and then explore changes in grape berry moth, Paralobesia viteana (Clemens), voltinism that may occur with climate projections developed from the average of three climate models using two different future emissions scenarios from the International Panel of Climate Change (IPCC). Based on historical climate data from 1960 to 2008, and projected downscaled climate data until 2099 under both high (A1fi) and low (B1) greenhouse gas emission scenarios, we used concepts of P. viteana biology to estimate distributions of individuals entering successive generations per year. Under the low emissions scenario, we observed an earlier emergence from diapause and a shift in mean voltinism from 2.8 to 3.1 generations per year, with a fraction of the population achieving a fourth generation. Under the high emissions scenario, up to 3.6 mean generations per year were projected by the end of this century, with a very small fraction of the population achieving a fifth generation. Changes in voltinism in this and other species in response to climate change likely will cause significant economic and ecological impacts, and the methods presented here can be readily adapted to other species for which the input distributions are reasonably approximated.