One- and multi-locus multi-allele selection models in a random environment

Summary We deduce conditions for stochastic local stability of general perturbed linear stochastic difference equations widely applicable in population genetics. The findings are adapted to evaluate the stability properties of equilibria in classical one- and multi-locus multi-allele selection models influenced by random temporal variation in selection intensities. As an example of some conclusions and biological interpretations we analyse a special one-locus multi-allele model in more detail.This work was supported in part by Stiftung Volkswagenwerk.     

The Ross-Macdonald model in a patchy environment

We generalize to n patches the Ross-Macdonald model which describes the dynamics of malaria. We incorporate in our model the fact that some patches can be vector free. We assume that the hosts can migrate between patches, but not the vectors. The susceptible and infectious individuals have the same dispersal rate. We compute the basic reproduction ratio R(0). We prove that if R(0)1, then the disease-free equilibrium is globally asymptotically stable. When R(0)>1, we prove that there exists a unique endemic equilibrium, which is globally asymptotically stable on the biological domain minus the disease-free equilibrium.     

Coexistence in a fluctuating environment by the effect of relative nonlinearity: A minimal model

The minimal model of the “relative nonlinearity” type fluctuation-maintained coexistence is investigated. The competing populations are affected by an environmental white noise. With quadratic density dependence, the long-term growth rates of the populations are determined by the average and the variance of the (fluctuating) total density. At most two species can coexist on these two “regulating” variables; competitive exclusion would ensue in a constant environment. A numerical study of the expected time until extinction of any of the two species reveals that the criterion of mutual invasibility predicts the parameter range of long-term coexistence correctly in the limit of zero extinction threshold. However, any extinction threshold consistent with a realistic population size will allow only short-term coexistence. Therefore, our simulations question the biological relevance of mutual invasibility, as a sufficient condition of coexistence, for large density fluctuations. We calculate the average and the variance of the fluctuating density of the coexisting populations analytically via the moment-closure approximation; the results are reasonably close to the simulated behavior. Based on this treatment, robustness of coexistence is studied in the limit of infinite population size. We interpret the results of this analysis in the context of necessity of niche segregation with respect to the regulating variables using a framework theory published earlier.     

Equilibrium selection in evolutionary games with random matching of players

We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant one, where players are averse to risks. We assume that individuals play with randomly chosen opponents (they do not play against average strategies as in the standard replicator dynamics). We show that the long-run behavior of a population depends on its size and the mutation level.     

The biennial life strategy in a random environment

In a previous paper (J. Math. Biol. 26, 199–215 (1988)) we calculated the mean and variance of the long-run geometric growth rate of a discrete-time population model with two age classes in a random environment. The formula which was used in that paper as the starting point for the computation of the variance represents only the contribution of the one-period variances. Here we supplement these results by a calculation of the exact variance. All qualitative conclusions reached before are unaffected.     

The biennial life strategy in a random environment

A discrete-time population model with two age classes is studied which describes the growth of biennial plants in a randomly varying environment. A fraction of the oldest age class delays its flowering each year. The solution of the model involves products of random matrices. We calculate the exact mean and variance of the long-run geometric growth rate assuming a gamma distribution for the random number of offspring per flowering plant after one year. It is shown, both by analytical calculation and numerical examples, that it is profitable for the population to delay its flowering, in the sense that the average growth rate increases and the extinction probability decreases. The optimal values of the flowering fraction depend upon the environmental and model parameters.     

随机Lotka-Volterra系统的稳定性

利用Lyapunov方法与K．lto公式及鞅的理论,研究了随机Lotka-Volterra系统正平衡点的全局渐近稳定性．得到了随机全局渐近稳定的主要定理,并以确定性系统的全局稳定性作为定理的推论．     

Multivariate parametric random effect regression models for fecundability studies

Delay until conception is generally described by a mixture of geometric distributions. Weinberg and Gladen (1986, Biometrics 42, 547-560) proposed a regression generalization of the beta-geometric mixture model where covariates effects were expressed in terms of contrasts of marginal hazards. Scheike and Jensen (1997, Biometrics 53, 318-329) developed a frailty model for discrete event times data based on discrete-time analogues of Hougaard's results (1984, Biometrika 71, 75-83). This paper is on a generalization to a three-parameter family distribution and an extension to multivariate cases. The model allows the introduction of explanatory variables, including time-dependent variables at the subject-specific level, together with a choice from a flexible family of random effect distributions. This makes it possible, in the context of medically assisted conception, to include data sources with multiple pregnancies (or attempts at pregnancy) per couple.     

The evolution of dispersal in random environment

In this paper we introduce a stochastic model for a population living and migrating between s sites without distinction in the states between residents and immigrants. The evolutionary stable strategies (ESS) is characterized by the maximization of a stochastic growth rate. We obtain that the expectation of reproductive values, normalized by some random quantity, are constant on all sites and that the expectation of the normalized vector population structure is proportional to eigenvector of the dispersion matrix associated to eigenvalue one, which are, in some way, analogous to the results obtained in the deterministic case.     

The probability of HIV infection in a new host and its reduction with microbicides

We use a simple mathematical model to estimate the probability and its time dependence that one or more HIV virions successfully infect target cells. For the transfer of a given number of virions to target cells we derive expressions for the probability P(inf), of infection. Thus, in the case of needlestick transfer we determine P(inf) and an approximate time window for post-exposure prophylaxis (PEP). For heterosexual transmission, where the transfer process is more complicated, a parameter gamma is employed which measures the strength of the infection process. For the smaller value of gamma, P(inf) is from 6x10(-5) to 0.93 or from 7.82x10(-6) to 0.29, where the lower figures are for the transfer of 100 virions and the upper figures are for the transfer of 4.4 million virions. We estimate the reductions in P(inf) which occur with a microbicide of a given efficacy. It is found that reductions may be approximately as stated when the number of virions transferred is less than about 10(5), but declines to zero for viral loads above that number. It is concluded that PEP should always be applied immediately after a needlestick incident. Further, manufacturers of microbicides should be encouraged to investigate and report their effectiveness at various transferred viral burdens.     

On stochastic compartmental models

The statistical averaging of compartmental models with parameters being random processes is derived for the case of vanishing input and uniformly bounded input. The difference of resulting models is discussed.     

Numerical simulation of a stochastic model for cancerous cells submitted to chemotherapy

A stochastic model is proposed to study the problem of inherent resistance by cell populations when chemotherapeutic agents are used to control tumor growth. Stochastic differential equations are introduced and numerically integrated to simulate expected response to the chemotherapeutic strategies as a function of different parameters. Satisfactory demonstration runs of the model indicate that it could represent a useful tool in verifying the results of experimental and clinical chemotherapy courses and planning treatment strategies. Some types of behaviour are illustrated graphically.Work supported by the C.N.R. Grants: 85.02652.01; 86.02116.01     

Species co-occurrence, nestedness and guild–environment relationships in stream macroinvertebrates

1. Describing species distribution patterns and the underlying mechanisms is at the heart of ecological research. A number of recent studies have used null model approaches to explore mechanisms behind spatial variation in community structure.
2. However, unexplored questions are the degree to which single guilds of potentially competing stream macroinvertebrate species show: (i) interspecific segregation among-stream sites (i.e. occur together less often than expected by chance), suggesting competitive interactions; (ii) interspecific aggregation (i.e. occur together more often than expected by chance), suggesting similar responses to the environment; (iii) comply with nestedness, suggesting the existence of selective extinctions or colonisations and (iv) show similar environmental relationships.
3. The present analyses showed that guilds of stream macroinvertebrates exhibit non-random co-occurrence patterns that were generally contingent on the weighting of sites by stream size. Despite significant segregation of species, each guild also showed significantly nested patterns. Species richness was correlated with different environmental factors between the guilds, although these correlations were relatively low. By contrast, correlations between the major ordination axes and key environmental variables were slightly stronger in canonical correspondence analysis, and generally the same factors were most strongly correlated with variation in the species composition of each guild.
4. The present findings are the first to show that species within each stream macroinvertebrate guild show significant negative co-occurrence at the among-stream riffle scale. These findings present challenges for future studies that aim to disentangle whether these patterns comply with the habitat checkerboard or the competitive checkerboard explanations.     

Competition between two microbial populations in a nonmixed environment: effect of cell random motility

In a nonmixed environment, bacterial population growth can be influenced significantly by cell motility properties as well as by growth kinetic properties. Therefore, in a situation of competition between two bacterial populations for a single chemical nutrient in a nonmixed environment, the outcome may depend upon the respective cell motility properties. In this article, the authors have presented a simple mathematical model for competitive growth of two randomly motile (i.e., possessing no chemotactic behavior) populations in a finite nonmixed region. An understanding of the behavior of this model should provide insight into the behavior of a number of common microbial competition problems. Analysis of this model yields the following results: (1) There may be as many as three possible non-trivial steady-state (or long-time) configurations: when species 1 survives, species 2 dies out; when species 2 survives, species 1 dies out; and species 1 and species 2 coexist. (2) The coexistence state can exist even though one species possesses a smaller intrinsic growth rate constant at all nutrient concentrations, if that same species is sufficiently less motile than the other species. (3) In fact, the species with the smaller maximum specific growth rate may grow to a larger population than the other. (4) The possibility of coexistence can be decided essentially from the results for single population growth.     

Scleraldehyde as a stabilizing agent for collagen scaffold preparation

Schizophyllan is a natural polysaccharide, produced by fungi of the genus Schizophyllum. Periodate oxidation specifically cleaves the vicinal glycols in schizophyllan to form their dialdehyde derivatives. The present study investigates the interaction of scleraldehyde with Type I collagen membrane. The formation of the inter and intra interaction between scleraldehyde and the collagen fibres results in significant increase in viscosity of collagen. Crosslinking efficiency of scleraldehyde was found to increase with concentration of scleraldehyde. Scleraldehyde interacted collagen membrane exhibited an increase in thermal stability by 29 °C at pH 8. The gelling time of collagen fibrils was found to decrease with increase in concentration of scleraldehyde due to shift in nucleation centre. Swelling degree of collagen membrane was also found to decrease with increase in concentration of scleraldehyde. Scleraldehyde treated collagen membrane exhibited 93% resistance to collagenase. The modified collagen membrane exhibited non-toxicity towards the fibroblasts cells. The modified collagen membrane by scleraldehyde finds application as a stabilizing agent in scaffold preparation.     

The dynamics of sperm cooperation in a competitive environment

Sperm cooperation has evolved in a variety of taxa and is often considered a response to sperm competition, yet the benefit of this form of collective movement remains unclear. Here, we use fine-scale imaging and a minimal mathematical model to study sperm aggregation in the rodent genus Peromyscus. We demonstrate that as the number of sperm cells in an aggregate increase, the group moves with more persistent linearity but without increasing speed. This benefit, however, is offset in larger aggregates as the geometry of the group forces sperm to swim against one another. The result is a non-monotonic relationship between aggregate size and average velocity with both a theoretically predicted and empirically observed optimum of six to seven sperm per aggregate. To understand the role of sexual selection in driving these sperm group dynamics, we compared two sister-species with divergent mating systems. We find that sperm of Peromyscus maniculatus (highly promiscuous), which have evolved under intense competition, form optimal-sized aggregates more often than sperm of Peromyscus polionotus (strictly monogamous), which lack competition. Our combined mathematical and experimental study of coordinated sperm movement reveals the importance of geometry, motion and group size on sperm velocity and suggests how these physical variables interact with evolutionary selective pressures to regulate cooperation in competitive environments.     

The stabilizing effect of soluble macromolecules on enzyme performance

A new enzyme stabilization method is proposed which is associated with dynamical immobilization within an unstirred ultrafiltration membrane reactor. Upon injection of suitable amounts of macromolecular solutions, the very polarization phenomena that yield the immobilization produce high macromolecular concentration levels in the reactor region immediately upstream from the ultrafiltration membrane where the enzymes operate. This procedure results in considerable improvements in enzyme stability that seem to be quite independent of the nature of the stabilizing macromolecule adopted. Stabilization effects of the same order of magnitude have been obtained for different enzymatic systems.