The effect of demographic population factors and individual biological parameters on the rate of the neutral molecular evolution

The dependence of the rate of neutral molecular evolution on both biological parameters and demographic population factors has been investigated. Real genetic data and an individual-based model of the population dynamics were used for the study. The first part of the study deals with tracing the neutral molecular evolution occurring in the model concurrently with adaptive speciation. The second part concerns the effect of individual biological parameters and demographic population factors of members of the Order Testudines (Turtles) on the relative rate of evolution of the mitochondrial CytB gene. It has been shown that demographic population factors and individual biological parameters affect the rate of the neutral molecular evolution.     

Rainbow trout: a population simulation based on individual responses to varying environmental and demographic parameters

Synopsis An age-structured simulation model of the growth and population dynamics of a migratory rainbow trout population is presented. The model includes all principal life-history intervals and incorporates the food density-temperature relationships of salmonid growth efficiency proposed by Brett et al. (1969) and Shelbourn et al. (1973). Population size, mean weight, and biomass are adjusted and output monthly over time in age, sex, and location categories; a simulation run may continue for as long as 100 years. A variety of environmental and and biological parameters are utilized in the simulation which can be altered as a user option. Simulation results compare favorably with field data. Sensitivity analyses illustrate the importance of age-sex specific maturation ratios, age-class strength fluctuations, and natural mortality rates in determining population size.     

Influence of spatial and temporal heterogeneities on the estimation of demographic parameters in a continuous population using individual microsatellite data

Drift and migration disequilibrium are very common in animal and plant populations. Yet their impact on methods of estimation of demographic parameters was rarely evaluated especially in complex realistic population models. The effect of such disequilibria on the estimation of demographic parameters depends on the population model, the statistics, and the genetic markers used. Here we considered the estimation of the product Dsigma2 from individual microsatellite data, where D is the density of adults and sigma2 the average squared axial parent-offspring distance in a continuous population evolving under isolation by distance. A coalescence-based simulation algorithm was used to study the effect on Dsigma2 estimation of temporal and spatial fluctuations of demographic parameters. Estimation of present-time Dsigma2 values was found to be robust to temporal changes in dispersal, to density reduction, and to spatial expansions with constant density, even for relatively recent changes (i.e., a few tens of generations ago). By contrast, density increase in the recent past gave Dsigma2 estimations biased largely toward past demographic parameters values. The method was also robust to spatial heterogeneity in density and estimated local demographic parameters when the density is homogenous around the sampling area (e.g., on a surface that equals four times the sampling area). Hence, in the limit of the situations studied in this article, and with the exception of the case of density increase, temporal and spatial fluctuations of demographic parameters appear to have a limited influence on the estimation of local and present-time demographic parameters with the method studied.     

The nearly neutral and selection theories of molecular evolution under the fisher geometrical framework: substitution rate, population size, and complexity

The general theories of molecular evolution depend on relatively arbitrary assumptions about the relative distribution and rate of advantageous, deleterious, neutral, and nearly neutral mutations. The Fisher geometrical model (FGM) has been used to make distributions of mutations biologically interpretable. We explored an FGM-based molecular model to represent molecular evolutionary processes typically studied by nearly neutral and selection models, but in which distributions and relative rates of mutations with different selection coefficients are a consequence of biologically interpretable parameters, such as the average size of the phenotypic effect of mutations and the number of traits (complexity) of organisms. A variant of the FGM-based model that we called the static regime (SR) represents evolution as a nearly neutral process in which substitution rates are determined by a dynamic substitution process in which the population's phenotype remains around a suboptimum equilibrium fitness produced by a balance between slightly deleterious and slightly advantageous compensatory substitutions. As in previous nearly neutral models, the SR predicts a negative relationship between molecular evolutionary rate and population size; however, SR does not have the unrealistic properties of previous nearly neutral models such as the narrow window of selection strengths in which they work. In addition, the SR suggests that compensatory mutations cannot explain the high rate of fixations driven by positive selection currently found in DNA sequences, contrary to what has been previously suggested. We also developed a generalization of SR in which the optimum phenotype can change stochastically due to environmental or physiological shifts, which we called the variable regime (VR). VR models evolution as an interplay between adaptive processes and nearly neutral steady-state processes. When strong environmental fluctuations are incorporated, the process becomes a selection model in which evolutionary rate does not depend on population size, but is critically dependent on the complexity of organisms and mutation size. For SR as well as VR we found that key parameters of molecular evolution are linked by biological factors, and we showed that they cannot be fixed independently by arbitrary criteria, as has usually been assumed in previous molecular evolutionary models.     

Estimating the rate of evolution of the rate of molecular evolution

A simple model for the evolution of the rate of molecular evolution is presented. With a Bayesian approach, this model can serve as the basis for estimating dates of important evolutionary events even in the absence of the assumption of constant rates among evolutionary lineages. The method can be used in conjunction with any of the widely used models for nucleotide substitution or amino acid replacement. It is illustrated by analyzing a data set of rbcL protein sequences.      

Sociality and the rate of molecular evolution

The molecular clock does not tick at a uniform rate in all taxa but may be influenced by species characteristics. Eusocial species (those with reproductive division of labor) have been predicted to have faster rates of molecular evolution than their nonsocial relatives because of greatly reduced effective population size; if most individuals in a population are nonreproductive and only one or few queens produce all the offspring, then eusocial animals could have much lower effective population sizes than their solitary relatives, which should increase the rate of substitution of "nearly neutral" mutations. An earlier study reported faster rates in eusocial honeybees and vespid wasps but failed to correct for phylogenetic nonindependence or to distinguish between potential causes of rate variation. Because sociality has evolved independently in many different lineages, it is possible to conduct a more wide-ranging study to test the generality of the relationship. We have conducted a comparative analysis of 25 phylogenetically independent pairs of social lineages and their nonsocial relatives, including bees, wasps, ants, termites, shrimps, and mole rats, using a range of available DNA sequences (mitochondrial and nuclear DNA coding for proteins and RNAs, and nontranslated sequences). By including a wide range of social taxa, we were able to test whether there is a general influence of sociality on rates of molecular evolution and to test specific predictions of the hypothesis: (1) that social species have faster rates because they have reduced effective population sizes; (2) that mitochondrial genes would show a greater effect of sociality than nuclear genes; and (3) that rates of molecular evolution should be correlated with the degree of sociality. We find no consistent pattern in rates of molecular evolution between social and nonsocial lineages and no evidence that mitochondrial genes show faster rates in social taxa. However, we show that the most highly eusocial Hymenoptera do have faster rates than their nonsocial relatives. We also find that social parasites (that utilize the workers from related species to produce their own offspring) have faster rates than their social relatives, which is consistent with an effect of lower effective population size on rate of molecular evolution. Our results illustrate the importance of allowing for phylogenetic nonindependence when conducting investigations of determinants of variation in rate of molecular evolution.     

On the rate of molecular evolution

Summary There are at least two outstanding features that characterize the rate of evolution at the molecular level as compared with that at the phenotypic level. They are; (1) remarkable uniformity for each molecule, and (2) very high overall rate when extrapolated to the whole DNA content.The population dynamics for the rate of mutant substitution was developed, and it was shown that if mutant substitutions in the population are carried out mainly by natural selection, the rate of substitution is given byk = 4 N _e s ₁ v, whereN _e is the effective population number,s ₁ is the selective advantage of the mutants, andv is the mutation rate per gamete for such advantageous mutants (assuming that 4N _e s ₁ 1). On the other hand, if the substitutions are mainly carried out by random fixation of selectively neutral or nearly neutral mutants, we havek = v, wherev is the mutation rate per gamete for such mutants.Reasons were presented for the view that evolutionary change of amino acids in proteins has been mainly caused by random fixation of neutral mutants rather than by natural selection.It was concluded that if this view is correct, we should expect that genes of living fossils have undergone almost as many DNA base replacements as the corresponding genes of more rapidly evolving species.Contribution No. 789 from the National Institute of Genetics, Mishima, Shizuokaken 411 Japan. Aided in part by a grant-in-aid from the Ministry of Education, Japan.     

Genetic demographic parameters of the marriage structure of the Yevpatoria population

Records on marriages contracted in the city of Yevpatoria, Ukraine in 1960/1961, 1985, 1993, and 1994/1995 were used to determine some parameters of the city population structure. The coefficients of correlation with respect to the age of marriage in reproductive-age couples contracting marriages in these years were 0.77, 0.81, and 0.80, respectively. Women that contracted marriages at reproductively unfavorable ages (under 20 and over 30 years) in the respective years constituted 28.3, 40.6, and 45.4% of the total sample. The proportions of interethnic marriages in these years were 39.4, 43.9, and 46.6%. The proportion of Slavs decreased from 94 to 91% during 35 years, but the proportion of Ukrainians increased from 23.1 to 26.5%. The proportion of other ethnic groups (Tatars, Armenians, Karaites, Poles, Germans, etc.) increased from 3 to 8.6%. The marriage contingency with respect to ethnicity (K = 0.26 in 1960/1961, K = 0.22 in 1985, and K = 0.28 in 1994/1995) was higher than with respect to education (K = 0.18 in 1985 and K = 0.23 in 1993) or occupation (K = 0.18 in 1960/1961, K = 0.17 in 1985, and K = 0.23 in 1994/1995). The marriage assortativeness with respect to ethnicity was the highest in ethnic minorities (A' = 55.1%); that with respect to education, in persons who had higher or primary education (A' = 40.1% and A'= 78.0%, respectively); and that with respect to occupation, in students, military personnel, and production workers (60.6, 58.7, and 30.9%).     

Genetic demographic parameters of the marriage structure of the Yevpatoria population

Records on marriages contracted in the city of Yevpatoria, Ukraine in 1960/1961, 1985, 1993, and 1994/1995 were used to determine some parameters of the city population structure. The coefficients of correlation with respect to the age of marriage in reproductive-age couples contracting marriages in these years were 0.77, 0.81, and 0.80, respectively. Women that contracted marriages at reproductively unfavorable ages (under 20 and over 30 years) in the respective years constituted 28.3, 40.6, and 45.4% of the total sample. The proportions of interethnic marriages in these years were 39.4, 43.9, and 46.6%. The proportion of Slavs decreased from 94 to 91% during 35 years, but the proportion of Ukrainians increased from 23.1 to 26.5%. The proportion of other ethnic groups (Tatars, Armenians, Karaites, Poles, Germans, etc.) increased from 3 to 8.6%. The marriage contingency with respect to ethnicity (K = 0.26 in 1960/1961, K = 0.22 in 1985, and K = 0.28 in 1994/1995) was higher than with respect to education (K = 0.18 in 1985 and K = 0.23 in 1993) or occupation (K = 0.18 in 1960/1961, K = 0.17 in 1985, and K = 0.23 in 1993). The marriage assortativeness with respect to ethnicity was the highest in ethnic minorities (A′ = 55.1%); that with respect to education, in persons who had higher or primary education (A′ = 40.1% and A′ = 78.0%, respectively); and that with respect to occupation, in students, military personnel, and production workers (60.6, 58.7, and 30.9%).     

The effect of population structure on the rate of evolution

Ecological factors exert a range of effects on the dynamics of the evolutionary process. A particularly marked effect comes from population structure, which can affect the probability that new mutations reach fixation. Our interest is in population structures, such as those depicted by ‘star graphs’, that amplify the effects of selection by further increasing the fixation probability of advantageous mutants and decreasing the fixation probability of disadvantageous mutants. The fact that star graphs increase the fixation probability of beneficial mutations has lead to the conclusion that evolution proceeds more rapidly in star-structured populations, compared with mixed (unstructured) populations. Here, we show that the effects of population structure on the rate of evolution are more complex and subtle than previously recognized and draw attention to the importance of fixation time. By comparing population structures that amplify selection with other population structures, both analytically and numerically, we show that evolution can slow down substantially even in populations where selection is amplified.     

Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance

In numerous species, individual dispersal is restricted in space so that "continuous" populations evolve under isolation by distance. A method based on individual genotypes assuming a lattice population model was recently developed to estimate the product Dsigma2, where D is the population density and sigma2 is the average squared parent-offspring distance. We evaluated the influence on this method of both mutation rate and mutation model, with a particular reference to microsatellite markers, as well as that of the spatial scale of sampling. Moreover, we developed and tested a nonparametric bootstrap procedure allowing the construction of confidence intervals for the estimation of Dsigma2. These two objectives prompted us to develop a computer simulation algorithm based on the coalescent theory giving individual genotypes for a continuous population under isolation by distance. Our results show that the characteristics of mutational processes at microsatellite loci, namely the allele size homoplasy generated by stepwise mutations, constraints on allele size, and change of slippage rate with repeat number, have little influence on the estimation of Dsigma2. In contrast, a high genetic diversity (approximately 0.7-0.8), as is commonly observed for microsatellite markers, substantially increases the precision of the estimation. However, very high levels of genetic diversity (>0.85) were found to bias the estimation. We also show that statistics taking into account allele size differences give unreliable estimations (i.e., high variance of Dsigma2 estimation) even under a strict stepwise mutation model. Finally, although we show that this method is reasonably robust with respect to the sampling scale, sampling individuals at a local geographical scale gives more precise estimations of Dsigma2.     

Biases in the estimation of the demographic parameters of a snowshoe hare population

1. Survival rates and natalities for a population of snowshoe hares in the Yukon were estimated independently of and simultaneously with estimates of population change during the increase phase of a hare cycle.
2. Simple demographic models are used to show that even though the estimated survival rates and natalities were high relative to previously published estimates, the observed demographic parameters are unable to explain the extent of population increase, and we conclude that some of these parameters must be underestimates.
3. A sensitivity analysis is used to examine the potential influence of changes in these demographic parameters on the population growth rate. During most years of the hare cycle the population growth rate is potentially most sensitive to changes in juvenile postweaning survival. Only during crash years is adult survivorship likely to be a more important determinant of the rate of population change.
4. Examination of previously published data sets on two full population cycles suggests that while survival rates are positively correlated with population growth rates, their incorporation into demographic models results in frequent underestimation of the rate of population increase.     

The influence of Nickel on population dynamics and on some demographic parameters of Daphnia magna

Daphnia magna was cultured with two different techniques at sublethal nickel concentrations from 0 up to 200 µg Ni l^-1. The results of the experiments run with cohorts of single individuals in static cultures were compared with the results obtained with populations held in flow through cultures. The most sensitive demographic parameters in cohorts were life span, the total number of progeny and the achievable maximum body length. The investigated nickel concentrations lowered the mean animal density in populations. Size class distribution was affected and the oscillation of the percentage of ovigorous adults increased with increasing nickel concentrations. In 200 µg Ni l^-1 one population extincted. Individuals in static cultures exposed to the same nickel concentration produced at least two neonates. Both employed techniques are discussed.     

The role of compensatory neutral mutations in molecular evolution

A pair of mutations at different loci (or sites) which are singly deleterious but restore normal fitness in combination may be called compensatory neutral mutations. Population dynamics concerning evolutionary substitutions of such mutants was developed by making use of the diffusion equation method. Based on this theory and, also, by the help of Monte Carlo simulation experiments, a remarkable phenomenon was disclosed that the double mutants can easily become fixed in the population by random drift under continued mutation pressure if the loci arc tightly linked, even when the single mutants are definitely deleterious. More specifically, I consider two loci with allelesA andA’ in the first locus, and allelesB andB’in the second locus, and assign relative fitnesses 1, 1-s’, 1-s’ and 1 respectively to the four gene combinationsAB, A’B, AB’ andA’B’, wheres’ is the selection coefficient against the single mutants (s’ > 0). Letv be the mutation rate per locus per generation and assume that mutation occurs irreversibly fromA toA’ at the first locus, and fromB toB’ at the second locus, whereA andB are wild type genes, andA’ andB’ are their mutant alleles. In a diploid population of effective size N _e (or a haploid population of 2N _e breeding individuals), it was shown that the average time (T) until joint fixation of the double mutant (A’B’) starting from the state in which the population consists exclusively of the wild type genes (AB) is not excessively long even for large 4N _e s’ values. In fact, assuming2N _e v = 1 we have -T = 54Ne for 4Nes’ = 400, and -T = 128Ne for 4N _e s’ = 1000. These values are not unrealistically long as compared with -T~ 5N _e obtained for 4N _e s’ = 0. The approximate analytical treatment has also been extended to estimate the effect of low rate crossing over in retarding fixation. The bearing of these findings on molecular evolution is discussed with special reference to coupled substitutions at interacting amino acid (or nucleotide) sites within a folded protein (orrna) molecule. It is concluded that compensatory neutral mutants may play an important role in molecular evolution.