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.     

Social behavior in a genetic model of dopamine dysfunction at different neurodevelopmental time points

Impairments in social behavior characterize many neurodevelopmental psychiatric disorders. In fact, the temporal emergence and trajectory of these deficits can define the disorder, specify their treatment and signal their prognosis. The sophistication of mouse models with neurobiological endophenotypes of many aspects of psychiatric diseases has increased in recent years, with the necessity to evaluate social behavior in these models. We adapted an assay for the multimodal characterization of social behavior at different development time points (juvenile, adolescent and adult) in control mice in different social contexts (specifically, different sex pairings). Although social context did not affect social behavior in juvenile mice, it did have an effect on the quantity and type of social interaction as well as ultrasonic vocalizations in both adolescence and adulthood. We compared social development in control mice to a transgenic mouse model of the increase in postsynaptic striatal D2R activity observed in patients with schizophrenia (D2R‐OE mice). Genotypic differences in social interactions emerged in adolescence and appeared to become more pronounced in adulthood. That vocalizations emitted from dyads with a D2R‐OE subject were negatively correlated with active social behavior while vocalizations from control dyads were positively correlated with both active and passive social behavior also suggest social deficits. These data show that striatal dopamine dysfunction plays an important role in the development of social behavior and mouse models such as the one studied here provide an opportunity for screening potential therapeutics at different developmental time points.     

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.     

Behavioral phenotypes of genetic mouse models of autism

More than a hundred de novo single gene mutations and copy‐number variants have been implicated in autism, each occurring in a small subset of cases. Mutant mouse models with syntenic mutations offer research tools to gain an understanding of the role of each gene in modulating biological and behavioral phenotypes relevant to autism. Knockout, knockin and transgenic mice incorporating risk gene mutations detected in autism spectrum disorder and comorbid neurodevelopmental disorders are now widely available. At present, autism spectrum disorder is diagnosed solely by behavioral criteria. We developed a constellation of mouse behavioral assays designed to maximize face validity to the types of social deficits and repetitive behaviors that are central to an autism diagnosis. Mouse behavioral assays for associated symptoms of autism, which include cognitive inflexibility, anxiety, hyperactivity, and unusual reactivity to sensory stimuli, are frequently included in the phenotypic analyses. Over the past 10 years, we and many other laboratories around the world have employed these and additional behavioral tests to phenotype a large number of mutant mouse models of autism. In this review, we highlight mouse models with mutations in genes that have been identified as risk genes for autism, which work through synaptic mechanisms and through the mTOR signaling pathway. Robust, replicated autism‐relevant behavioral outcomes in a genetic mouse model lend credence to a causal role for specific gene contributions and downstream biological mechanisms in the etiology of autism.     

The influence of variation in female fecundity on effective population size

Understanding the relationship between effective population size (N_e) and the number of adults in a population (N) is important for predicting genetic change in small populations. In general, N_e is expected to be close to N/2, i.e. in the range N/4-3N/4, provided that the powerful effect of population bottlenecks on reducing N_e is factored out (using the harmonic mean of N). However, some very low published estimates of N_e/N(< 0.1) raise the possibility that other factors acting to reduce N_e have been underestimated. Here one such factor, variation in female fecundity, is investigated. Its effect on N_e depends on the standardized variance in fecundity (per breeding season), a measure that is generally independent of mean fecundity. Empirical estimates of this standardized variance from 16 animal studies yielded an average value of 0.44, and a maximum value less than 1.5. To investigate the effect of such values, three kinds of fecundity variation were modelled: random (seasonal): individual; and age-related. Fixed individual differences among females reduce N_e the most. However, to reduce N_e to N/10, the resulting standardized variance must usually be 10 or more. Random differences need to be even larger to achieve the same reduction. One possible mechanism, the random loss of whole families, requires very high family mortality (90% or more). The third model, fecundity that increases linearly with age, is ineffective at causing a marked decrease in N_e. Given the finding that very unusual conditions are required to reduce N_e below N_e/10, low estimates of N_e/N need to be examined critically: the lowest published ratio, for a natural population of oysters, was found to be questionable because of possible immigration into the population by cultivated oysters.     

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.     

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     

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.     

Assessment of the genetic diversity and genetic relationships of Lilium in China using ISSR markers

China is a center of natural distribution and diversity of genus Lilium around the world. In the study, the genetic diversity and genetic relationships of Lilium in China were analyzed by inter-simple sequence Repeat (ISSR) markers. The 6 highly polymorphic ISSR primers were selected to amplify the 20 Lilium species. The results showed that a total of 114 DNA bands were amplified, all of which were polymorphic loci (P = 100%), the effective number of alleles (Ne) was 1.2753, and the difference value between observed number of alleles (Na) and effective number of alleles (Ne) was 0.7247, and the Nei's genetic diversity (H) was 0.2048, and the Shannon's information index (I) was 0.3503. These results indicated that there is significant genetic difference among Lilium species in China. Taking the average genetic similarity coefficient (Gs) 0.5313 as the threshold, the 20 tested Lilium species were clustered into 5 groups, which was not entirely consistent with traditional clustering by morphological traits. The results obtained from this study can provide a reference for the molecular study of Lilium germplasm resources.     

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.     

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

This article is part of a Special Issue Energy Balance.