Expected relative fitness and the adaptive topography of fluctuating selection

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, . The expected evolution of p or is a product of genetic variability and the gradient of the long-run growth rate of the population, , with respect to p or . This shows that the expected evolution maximizes , the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, as a function of p or represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of . Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.     

Lysosomal enzyme inactivation associated with defects in post-translational modification during development in Dictyostelium discoideum

The developmental accumulation of lysosomal alpha-mannosidase-1 activity in Dictyostelium discoideum is controlled at the level of de novo enzyme precursor biosynthesis. Aggregation-deficient mutants are defective with regard to the accumulation of alpha-mannosidase-1 activity beyond 8-16 h of development. We used enzyme-specific monoclonal antibodies to show that the activity defect in aggregation-deficient strains is not due to a lack of alpha-mannosidase-1-precursor synthesis or processing, or to preferential degradation of the mature enzyme protein. Instead, the defect is a result of enzyme inactivation: cells of aggregation-deficient strains contain significant amounts of inactive alpha-mannosidase-1 protein late in development. The alpha-mannosidase-1 inactivation phenotype is associated with a more general defect in lysosomal enzyme modification. A change in the post-translational modification system occurs during normal slime-mold development, as shown by differences in enzyme isoelectric point, antigenicity, and thermolability. We found that this change in modification does not occur in mutant strains blocked early in development. We propose a model in which pleiotropic mutations in early aggregation-essential genes can indirectly affect the accumulation of alpha-mannosidase-1 activity by preventing the expression of a developmentally controlled change in the post-translational modification system, a change which is required for the stability of several lysosomal enzymes late in development.     

Transformation of sib-pair values for the Haseman-Elston method

The squared sib-pair phenotype difference (SQD) has been used as a dependent variable in the Haseman-Elston (H-E) regression quantitative-trait locus (QTL) linkage method, but it has been shown that the SQD does not make full use of linkage information. In this study, we examine the efficiency of SQD in H-E regression compared to other proposed functions of the sib-pair phenotypes. A new function of sib-pair phenotypes, the product of pair values corrected with family mean (PCF), is shown to have desirable properties in many realistic situations. Consistent results were obtained using a combination of large-sample analytic approximations, simulation, and analyses of quantitative-trait data from Genetic Analysis Workshop 10. The advantages of PCF are further improved in the presence of family-specific effects arising from environmental factors or when additional QTLs influence the trait. All of the phenotype functions are incorporated in our new, freely available linkage-mapping program MULTIGENE 1.0 for the PC environment.     

When three traits make a line: evolution of phenotypic plasticity and genetic assimilation through linear reaction norms in stochastic environments

Genetic assimilation emerges from selection on phenotypic plasticity. Yet, commonly used quantitative genetics models of linear reaction norms considering intercept and slope as traits do not mimic the full process of genetic assimilation. We argue that intercept–slope reaction norm models are insufficient representations of genetic effects on linear reaction norms and that considering reaction norm intercept as a trait is unfortunate because the definition of this trait relates to a specific environmental value (zero) and confounds genetic effects on reaction norm elevation with genetic effects on environmental perception. Instead, we suggest a model with three traits representing genetic effects that, respectively, (i) are independent of the environment, (ii) alter the sensitivity of the phenotype to the environment and (iii) determine how the organism perceives the environment. The model predicts that, given sufficient additive genetic variation in environmental perception, the environmental value at which reaction norms tend to cross will respond rapidly to selection after an abrupt environmental change, and eventually becomes equal to the new mean environment. This readjustment of the zone of canalization becomes completed without changes in genetic correlations, genetic drift or imposing any fitness costs of maintaining plasticity. The asymptotic evolutionary outcome of this three‐trait linear reaction norm generally entails a lower degree of phenotypic plasticity than the two‐trait model, and maximum expected fitness does not occur at the mean trait values in the population.     

Plastic inducible morphologies are not always adaptive: The importance of time delays in a stochastic environment

Summary We present a mathematical model for predicting the expected fitness of phenotypically plastic organisms experiencing a variable environment. We assume that individuals experience two discrete environments probabilistically in time (as a Markov process) and that there are two different phenotypic states, each yielding the highest fitness in one of the two environments. We compare the expected fitness of a phenotypically fixed individual to that of an individual whose phenotype is induced to produce the better phenotype in each environment with a time lag between experiencing a new environment and realization of the new phenotype. Such time lags are common in organisms where phenotypically plastic, inducible traits have been documented. We find that although plasticity is generally adaptive when time lags are short (relative to the time scale of environmental variability), plasticity can be disadvantageous for longer lag times. Asymmetries in environmental change probabilities and/or the relative fitnesses of each phenotype strongly influence whether plasticity is favoured. In contrast to other models, our model does not require costs for plasticity to be disadvantageous; costs affect the results quantitatively, not qualitatively.     

Modeling of technical training of discus throwers in the period of significant changes of their mass-inertia characteristics

The use of artificial neural networks for simulation of the control of an anthropomorphic mechanism when its mass-inertia characteristics are changing is considered in this paper. It is shown in theory that the change in mass-inertia characteristics of the model does not have a linear relationship with the output parameter but a spurt-like change in the pattern of the output function after a certain threshold. The data of the model experiment served as a basis for a full-scale test with discus throwers who had different height-weight parameters during a year of study. Specific traits in the technique of standing discus throwing are shown, and their dependence on the changes of anthropometric characteristics of sportsmen.     

Existence of steady-state probability distributions in multilocus models for genotype evolution

It is shown that a representative Fisher-Wright model withn(≥3) diallelic loci admits a necessary condition for existence of a time-independent steady-state probability distribution. This necessary condition states that a global integral depending on the phenotype fitness functions of natural selection must be larger than a certain quantity depending on the parameters associated with genetic drift.     

Transition regime diffusion and the structure of the insect tracheolar system

A model is developed for the diffusion of oxygen along insect tracheoles. It is shown that reduction of the effective tracheolar diameter is advantageous until this quantity approaches the mean free path of diffusing oxygen molecules, and that, once this transition regime has been entered, further reduction of tracheolar diameter is disadvantageous. This finding offers a plausible explanation of Weis-Fogh's observation that the respiratory pathway in insects continues to branch until the smallest ‘twigs’ approach a mean free path in diameter.     

The relationships between the metabolic fluxes and 13C-labeled isotopomer distribution for the flux analysis of the main metabolic pathways

It has been known that ¹³C-labeling technique is quite useful in estimating the metabolic fluxes. Although the program-based flux analysis is powerful, it is not easy to be confident with the result obtained without experiences and exhaustive trial and errors based on statistical analysis for the confidence intervals in practice. It is, therefore, quite important to grasp the relationship between the fluxes and the ¹³C-labeled isotopomer distribution to get deeper insight into the metabolic flux analysis. In the present research, it was shown explicitly how the isotopomer distribution changes with respect to the fluxes in relation to the labeling patterns of the substrate, where either labeled glucose, acetate, or pyruvate was used as a carbon source. Some of the analytical expressions were derived based on the matrix representation, and they were utilized for analysis. It was shown that the isotopomer pattern does not necessarily change uniformly with respect to fluxes, but changes in a complicated way in particular for the case of using pyruvate as a carbon source where some isotopomers do not necessarily change monotonically. It was shown to be quite important to grasp how the isotopomer pattern changes with respect to fluxes and the labeling pattern of the substrate for flux determination and the experimental design. It was also shown that the mixture of [1-¹³C] acetate and [2-¹³C] acetate should not be used from the information index point of view. Some of the experimental data were evaluated from the present approach. It was also shown that the isotopomer distribution is less sensitive to the bidirectional fluxes in the reversible pathway.     

Effect of nonlocal electron kinetics on the characteristics of a dielectric barrier discharge in xenon

The established dynamics of a dielectric barrier discharge in xenon at a pressure of 400 Torr is simulated in the framework of a one-dimensional fluid model in the local and nonlocal field approximations. It is shown that taking into account the nonlocal character of the electric field does not qualitatively change physical processes in a dielectric barrier discharge, but significantly affects its quantitative characteristics. In particular, the sheath thickness decreases, plasma ionization intensifies, the spatiotemporal distribution of the mean electron energy changes, and the discharge radiation efficiency increases. Electron kinetics in a dielectric barrier discharge in xenon is analyzed using the nonlocal field approximation.     

Overexpression of the RADICAL-INDUCED CELL DEATH1 (RCD1) gene of Arabidopsis causes weak rcd1 phenotype with compromised oxidative-stress responses

rcd1 is a mutant of Arabidopsis thaliana that is more resistant to methyl viologen, but more sensitive to ozone than the wild type. rcd1-2 is caused by a single nucleotide substitution that results in a premature stop codon at Trp-332. The rcd1-2 mRNA level does not change significantly with the mutation. Since overexpression of rcd1-1 cDNA has been shown to bring about an rcd1-like phenotype, we created and examined the overexpression lines of RCD1 by the use of the cauliflower mosaic virus 35S promoter. The transgenic lines exhibited a weak rcd1-like phenotype, although no resistance to methyl viologen was observed. Further, they fully complemented the aberrant rcd1-2 phenotype. Subcellular localization of RCD1 was examined by transiently expressing green fluorescent protein (GFP) fused with RCD1 in onion epidermal cells. GFP signals are observed as aggregated foci in the inner nuclear matrix-like region.     

FeMo cofactor synthesis by a nifH mutant with altered MgATP reactivity.

We have characterized a Nif- mutant of Azotobacter vinelandii, designated UW91 (Shah, V. K., Davis, L. C., Gordon, J. K., Orme-Johnson, W. H., and Brill, W. J. (1973) Biochim. Biophys. Acta 292, 246-255). The specific Fe protein mutation giving rise to the Nif- phenotype was shown by DNA sequencing and site-directed mutagenesis to be the substitution of a conserved alanine at position 157 by a serine. The UW91 Fe protein was purified and shown to have a normal [4Fe-4S] cluster and normal MgATP binding activity. The substitution of alanine 157 by serine, however, prevents the MgATP-induced conformational change that occurs for the wild-type Fe protein, prevents MgATP hydrolysis, and prevents productive electron transfer to the MoFe protein. The UW91 Fe protein does bind to the MoFe protein to give a normal cross-linking pattern; however, it does not compete very successfully with wild-type Fe protein in an activity assay. The UW91 MoFe protein was also purified and characterized and shown to be indistinguishable from the wild-type protein. Thus, the substitution of Fe protein residue alanine 157 by serine does not change the Fe protein's ability to function in FeMo cofactor biosynthesis or insertion. This demonstrates that these events do not require the MgATP-induced conformational change, MgATP hydrolysis, or productive electron transfer to the MoFe protein.     

Maintenance of Genetic Variability under Strong Stabilizing Selection: A Two-Locus Model

We study a two locus model with additive contributions to the phenotype to explore the relationship between stabilizing selection and recombination. We show that if the double heterozygote has the optimum phenotype and the contributions of the loci to the trait are different, then any symmetric stabilizing selection fitness function can maintain genetic variability provided selection is sufficiently strong relative to linkage. We present results of a detailed analysis of the quadratic fitness function which show that selection need not be extremely strong relative to recombination for the polymorphic equilibria to be stable. At these polymorphic equilibria the mean value of the trait, in general, is not equal to the optimum phenotype, there exists a large level of negative linkage disequilibrium which ``hides' additive genetic variance, and different equilibria can be stable simultaneously. We analyze dependence of different characteristics of these equilibria on the location of optimum phenotype, on the difference in allelic effect, and on the strength of selection relative to recombination. Our overall result that stabilizing selection does not necessarily eliminate genetic variability is compatible with some experimental results where the lines subject to strong stabilizing selection did not have significant reductions in genetic variability.     

Stochastic Fluctuations Through Intrinsic Noise in Evolutionary Game Dynamics

A one-step (birth–death) process is used to investigate stochastic noise in an elementary two-phenotype evolutionary game model based on a payoff matrix. In this model, we assume that the population size is finite but not fixed and that all individuals have, in addition to the frequency-dependent fitness given by the evolutionary game, the same background fitness that decreases linearly in the total population size. Although this assumption guarantees population extinction is a globally attracting absorbing barrier of the Markov process, sample trajectories do not illustrate this result even for relatively small carrying capacities. Instead, the observed persistent transient behavior can be analyzed using the steady-state statistics (i.e., mean and variance) of a stochastic model for intrinsic noise that assumes the population does not go extinct. It is shown that there is good agreement between the theory of these statistics and the simulation results. Furthermore, the ESS of the evolutionary game can be used to predict the mean steady state.     

Characterization of an Acholeplasma laidlawii variant with a REP- phenotype.

An Acholeplasma laidlawii variant has been isolated that has a REP- phenotype. The properties of this variant, relative to parental cells, are: (i) it exhibits no change in cell growth kinetics; (ii) it does not propagate single-stranded deoxyribonucleic acid (DNA) mycoplasmaviruses but does propagate double-stranded DNA mycoplasmaviruses; (iii) it converts parental circular single-stranded mycoplasmavirus DNA to double-stranded replicative forms that are not replicated further; (iv) it exhibits no change in host modification and restriction; and (v) it has an increased ultraviolet light sensitivity. The REP- isolate is the first stable mycoplasma variant to which a physiological defect has been attributed.     

An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.     

Naturally occurring CD4+Foxp3+ regulatory T cells are an essential, IL-10-independent part of the immunoregulatory network in Schistosoma mansoni egg-induced inflammation

In acute and chronic schistosomiasis, survival of the host requires a carefully balanced immune response against highly immunogenic parasite eggs. We characterized the phenotype, distribution, and functional role of CD4(+)Foxp3(+) naturally occurring regulatory T cells (naTregs) in schistosome egg-induced inflammation. In adoptive transfer experiments and by intracellular staining for Foxp3, we demonstrate significant frequencies of naTregs in hepatic granulomas and draining lymphoid tissues of mice infected with the trematode Schistosoma mansoni. Strikingly, egg-induced inflammation does not change the normal ratio between naTregs and effector CD4(+) T cells at the inflammatory site or in lymphoid organs in acute or chronic disease. However, increasing frequencies of CD103-expressing cells in the naTreg compartment indicate a change in phenotype for naTregs with disease progression. Because CD103 was described recently as an activation marker for naTregs, we speculate that naTregs in chronic schistosomiasis are potentially more suppressive. Furthermore, we found that most naTregs do not contribute to egg-induced IL-4 and IL-10 production. Importantly, depletion of CD25(+) naTregs strongly enhances the frequency of IL-4-producing effector T cells in acute egg-induced inflammation. It does not change clonal expansion of activated CD4(+) T cells. This regulation of egg-induced cytokine production does not require the presence of IL-10. These data demonstrate that naTregs limit egg-induced effector-cytokine production in our model. Our results identify naTregs as an important, IL-10-independent part of the regulatory network in schistosome egg-induced inflammation.     

A new statistical method for identifying interconnections between neuronal network elements

A new method is proposed to analyse dependencies in point processes, which takes into account specific character of neuronal activity. Simulation modelling of neuronal network revealed that the estimated weight of connection depends monotonically on the value of the model synaptic strength. In contrast to the crosscorrelation, the method allows for nonlinear interconnections and does not require point processes to be stationary and samples to be large. Examples are presented of the method's application to neurophysiological data analysis.     

Bayesian Inference of the Evolution of a Phenotype Distribution on a Phylogenetic Tree

The distribution of a phenotype on a phylogenetic tree is often a quantity of interest. Many phenotypes have imperfect heritability, so that a measurement of the phenotype for an individual can be thought of as a single realization from the phenotype distribution of that individual. If all individuals in a phylogeny had the same phenotype distribution, measured phenotypes would be randomly distributed on the tree leaves. This is, however, often not the case, implying that the phenotype distribution evolves over time. Here we propose a new model based on this principle of evolving phenotype distribution on the branches of a phylogeny, which is different from ancestral state reconstruction where the phenotype itself is assumed to evolve. We develop an efficient Bayesian inference method to estimate the parameters of our model and to test the evidence for changes in the phenotype distribution. We use multiple simulated data sets to show that our algorithm has good sensitivity and specificity properties. Since our method identifies branches on the tree on which the phenotype distribution has changed, it is able to break down a tree into components for which this distribution is unique and constant. We present two applications of our method, one investigating the association between HIV genetic variation and human leukocyte antigen and the other studying host range distribution in a lineage of Salmonella enterica, and we discuss many other potential applications.