On continuous time models in genetic and Bernstein algebras

We discuss the long-time behavior of Andreoli's differential equation for genetic algebras and for Bernstein algebras and show convergence to an equilibrium in both cases. For a class of Bernstein algebras this equilibrium is determined explicitly.     

Methods for minimizing the loss of genetic diversity in conserved populations with overlapping generations

Minimization of the average coancestry in a population has been theoretically proven to be the most efficient method to preserve genetic diversity. In the present study, based on a population genetic model, two methods to minimize the average coancestry in populations with overlapping generations were developed. For a given parental coancestry structure, the first method (OG) minimizes the average coancestry in the next generation, and the second method (LT) is designed to minimize the long-term accumulation of coancestry. The efficiencies of the two methods were examined by stochastic simulation. Compared to random choice of parents, the annual effective population sizes under the two proposed methods increased 2–3 folds. The difference among the two methods was small in a population with short generation interval. For populations with long generation intervals, the OG method showed a slightly larger annual effective size in an initial few years. However, in the subsequent years, the LT method gave a 5–15% larger annual effective size than the OG method. From these results, it is suggested that the LT method would be preferred to the OG method in most practical situations.     

Deterministic genetic models in varying environments

Summary J. B. S. Haldane and S. D. Jayakar [J. Genet. 58, 237–242 (1963)] argue that, when genotype fitnesses fluctuate from generation to generation, if the geometric and arithmetic means of the fitnesses satisfy certain inequalities, there will be a protected polymorphism. Their assertions are biologically interesting, but their mathematical analysis is not sufficient to support their conclusions. We present a firm mathematical analysis and several examples that demonstrate the need for stronger hypotheses and, in some cases, weaker conclusions.Journal Paper No. J-10136 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project 1669. Partial support by National Institutes of Health, Grant GM 13827     

Allele frequency covariance among cohorts and its use in estimating effective size of age-structured populations

A general expression for the covariance of allele frequencies among cohorts in age-structured populations is derived. The expression is used to extend the so-called temporal method for estimating effective population size from allele frequency shifts among samples from cohorts born any number of years apart. Computer simulations are used to check on the accuracy and precision of the method, and an application to coastal Atlantic cod is presented.     

Dispersion population models discrete in time and continuous in space

We analyze a discrete-time model of populations that grow and disperse in separate phases. The growth phase is a nonlinear process that allows for the effects of local crowding. The dispersion phase is a linear process that distributes the population throughout its spatial habitat. Our study quantifies the issues of survival and extinction, the existence and stability of nontrivial steady states, and the comparison of various dispersion strategies. Our results show that all of these issues are tied to the global nature of various model parameters. The extreme strategies of staying-in place and going-everywhere-uniformly are compared numerically to diffusion strategies in various contexts. We approach the mathematical analysis of our model from a functional analysis and an operator theory point of view. We use recent results from the theory of positive operators in Banach lattices.     

Evolution of dispersal in a stepping-stone population with overlapping generations

We use Hamilton's inclusive fitness method to calculate the evolutionarily stable dispersal rate in 1- and 2-dimensional stepping-stone populations. This extends previous results by introducing a positive probability for adults to survive into the next generation and breed again. Relatedness between nearby individuals generally decreases with increasing survival, decreasing competition with kin and favouring greater dispersal rates.     

An equivalence between models of restricted selection and genetic groups

Summary An equivalence between a model of restricted selection and a model of genetic groups is presented. This correspondence leads to a realization of how genetic groups account for selection. Specifically, genetic groups act to remove the covariance between predictions of sire merit and functions of the true selection differentials. Further results illustrate a correspondence between models of selection on random effects and models of selection on residuals. Application of the results is useful, not in establishing concrete definitions for the structure of genetic groups, but in the analysis of how groups account for selection.     

Role of genetic variants in ADIPOQ in human eating behavior

The beneficial effects of adiponectin and its negative correlation with BMI are well described. Adiponectin serum levels are altered in eating disorders such as anorexia nervosa, bulimia nervosa or binge eating. Here, we tested the hypothesis that (1) adiponectin serum levels correlate with human eating behavior factors and (2) that genetic variants of the ADIPOQ locus influence both serum levels and eating behavior. We analyzed 11 SNPs within ADIPOQ and in the 5′ UTR and measured serum adiponectin levels in 1,036 individuals from the German Sorbs population. The German version of the three-factor eating questionnaire (FEV) was completed by 548 Sorbs. For replication purposes, we included an independent replication cohort from Germany (N = 350). In the Sorbs, we observed positive correlations of restraint with adiponectin serum levels (P = 0.001; r = 0.148) which, however, did not withstand adjustment for covariates (P = 0.083; r = 0.077). In addition, four SNPs were nominally associated with serum adiponectin levels (all P < 0.05). Of these, two variants (rs3774261; rs1501229, all P < 0.05) were also related to disinhibition. Furthermore, three variants were exclusively associated with hunger (rs2036373, P = 0.049) and disinhibition (rs822396; rs864265, all P < 0.05). However, none of these associations withstood Bonferroni corrections for multiple testing (all P > 9.3 × 10⁻⁴). In our replication cohort, we observed similar effect directions at rs1501229 for disinhibition and hunger. A meta-analysis resulted in nominal statistical significance P = 0.036 (Z score 2.086) and P = 0.017 (Z score 2.366), respectively. Given the observed relationship of the SNPs with adiponectin levels and eating behavior, our data support a potential role of adiponectin in human eating behavior. Whether the relationship with eating behavior is mediated by the effects of circulating adiponectin warrants further investigations.     

Adaptive diversity in genetic control of egg-laying behavior in Drosophila melanogaster

Summary

In the absence of insemination or of a suitable oviposition site, Drosophila melanogaster females react with egg retention patterns which differ as to the position in the genital tract at which the mechanism operates (ovarioles for initial retention; uterus for oviposition blocking) and to physiological basis. A study of the first laboratory generation of isofemale lines, founded by using three different samples of wild flies collected the same year from a natural population, showed a significant genetic variability in initial egg retention by virgin females and in the capacity for oviposition blocking by mated flies reacting to an unfavorable oviposition site. Comparison of isofemale lines showed that these two adaptive behavior patterns also differ in their genetic determination. They are controlled, and therefore can react, independently to selection pressures resulting from seasonal variation in the natural environment.     

A graph-theoretic method for the basic reproduction number in continuous time epidemiological models

In epidemiological models of infectious diseases the basic reproduction number is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for can be obtained from the digraphs in the reduction process.     

Interaction of spatial diffusion and delays in models of genetic control by repression

A class of models based on the Jacob and Monod theory of genetic repression for control of biosynthetic pathways in cells is considered. Both spatial diffusion and time delays are taken into account. A method is developed for representing the effects of spatial diffusion as distributed delay terms. This method is applied to two specific models and the interaction between the diffusion and the delays is treated in detail. The destabilization of the steadystate and the bifurcation of oscillatory solutions are studied as functions of the diffusivities and the delays. The limits of very small and very large diffusivities are analyzed and comparisons with well-mixed compartment models are made.On leave from North Carolina State University     

Discrete and continuous mathematical models of intraspecific behavior in the pharmacoethology of the mouse

An algorithm and software library were compiled in order to interpret the intraspecies agonistic animal behaviour in terms of discrete or continuous mathematical model. Applied aspects of the use of mathematical models in pharmacoethology were shown on concrete examples. The ways of construction of standard prototypes, and the integrative criteria of psychotropic drugs action were developed. The possibility was shown of identification of unknown substances by comparing with standard drugs by calculating the norm of standardized matrices.     

Existence of a globally asymptotically stable equilibrium in Volterra models with continuous time delay

A sufficient condition for the existence of a globally asymptotically stable equilibrium in Volterra models with continuous time delay is obtained, and some properties of the stable equilibrium are proven. Furthermore, some applications in which asymptotic stability only depends on the sign of the coefficients are considered.     

Minireview: Metabolic control of the reproductive physiology: Insights from genetic mouse models

This article is part of a Special Issue Energy Balance.     

The neuropeptide SIFamide modulates sexual behavior in Drosophila

The expression of Drosophila neuropeptide AYRKPPFNGSIFamide (SIFamide) was shown by both immunohistology and in situ hybridization to be restricted to only four neurons of the pars intercerebralis. The role of SIFamide in adult courtship behavior in both sexes was studied using two different approaches to perturb the function of SIFamide; targeted cell ablation and RNA interference (RNAi). Elimination of SIFamide by either of these methods results in promiscuous flies; males perform vigorous and indiscriminant courtship directed at either sex, while females appear sexually hyper-receptive. These results demonstrate that SIFamide is responsible for these behavioral effects and that the four SIFamidergic neurons and arborizations play an important function in the neuronal circuitry controlling Drosophila sexual behavior.     

Detection of putative quantitative trait loci in line crosses under infinitesimal genetic models

Quantitative trait locus (QTL) mapping studies often employ segregating generations derived from a cross between genetically divergent inbred lines. In the analysis of such data it is customary to fit a single QTL and use a null hypothesis which assumes that the genomic region under study contributes no genetic variance. To explore the situation in which multiple linked genes contribute to the genetic variance, we simulated an F₂-mapping experiment in which the genetic difference between the two original inbred strains was caused by a large number of loci, each having equal effect on the quantitative trait. QTLs were either in coupling, dispersion or repulsion phase in the base population of inbred lines, with the expected F₂ genetic variance explained by the QTLs being equivalent in the three models. Where QTLs were in coupling phase, one inbred line was fixed for all plus alleles, and the other line was fixed for minus alleles. Where QTLs were in dispersion phase, they were assumed to be randomly fixed for one or other allele (as if the inbred lines had evolved from a common ancestor by random drift). Where QTLs were in repulsion phase alleles within an inbred line were alternating plus and minus at adjacent loci, and alternative alleles were fixed in the two inbred lines. In all these genetic models a standard interval mapping test statistic used to determine whether there is a QTL of large effect segregating in the population was inflated on average. Furthermore, the use of a threshold for QTL detection derived under the assumption that no QTLs were segregating would often lead to spurious conclusions regards the presence of genes of large effects (i.e. type I errors). The employment of an alternative model for the analysis, including linked markers as cofactors in the analysis of a single interval, reduced the problem of type I error rate, although test statistics were still inflated relative to the case of no QTLs. It is argued that in practice one should take into account the difference between the strains or the genetic variance in the F₂ population when setting significance thresholds. In addition, tests designed to probe the adequacy of a single-QTL model or of an alternative infinitesimal coupling model are described. Such tests should be applied in QTL mapping studies to help dissect the true nature of genetic variation.     

Modeling time series of animal behavior by means of a latent-state model with feedback

Summary .   We describe a family of models developed for time series of animal feeding behavior. The models incorporate both an unobserved state, which can be interpreted as the motivational state of the animal, and a mechanism for feedback to this state from the observed behavior. We discuss methods for evaluating and maximizing the likelihood of an observed series of behaviors, and thereby estimating parameters, and for inferring the most likely sequence of underlying states. We indicate several extensions of the models, including the incorporation of random effects. We apply these methods in an analysis of the feeding behavior of the caterpillar Helicoverpa armigera , and thereby demonstrate the potential of this family of models as a tool in the investigation of behavior.