Genetic variation for total fitness in Drosophila melanogaster: complex yet replicable patterns

The extent of genetic variation in fitness is a crucial issue in evolutionary biology and yet remains largely unresolved. In Drosophila melanogaster, we have devised a method that allows the net effects on fitness of heterozygous wild-type chromosomes to be measured, by competing them against two different "balancer" chromosomes. We have applied the method to a large sample of 40 wild-type third chromosomes and have measured fitnesses of nonlethal chromosomes as well as chromosomes bearing recessive lethals. The measurements were made in the environment to which the population was adapted and did not involve inbreeding. The results show an extraordinary similarity in the behavior of replicates of the same chromosome, indicating consistent genetic effects on total fitness. Some invading chromosomes increased rapidly and some slowly, and some rose to appreciable frequency after several months, but then declined again: in every case, the same pattern was seen in each replicate. We estimated relative fitnesses, rates of change of fitness, and relative viabilities, for each chromosome. There were significant fluctuations around the fitted model, which were also highly replicable. Wild-type chromosomes varied substantially in their effects on heterozygous fitness, and these effects vary through time, most likely as a result of genotype x environment interactions.     

Genetic variation for total fitness in Drosophila melanogaster.

We measured the heterozygous effects on net fitness of a sample of 12 wild-type third chromosomes in D. melanogaster. Effects on fitness were assessed by competing the wild-type chromosomes against balancer chromosomes, to prevent the production of recombinants. The measurements were carried out in the population cage environment in which the life history had been evolving, in an undisturbed population with overlapping generations, and replicated measurements were made on each chromosome to control for confounding effects such as mutation accumulation. We found significant variation among the wild type chromosomes in their additive genetic effect on net fitness. The system provides an opportunity to obtain an accurate estimate of the distribution of heterozygous effects on net fitness, the contribution of different fitness components including male mating success, and the role of intra-chromosomal epistasis in fitness variation.     

Pleiotropic Effects on Fitness of Mutations Affecting Viability in DROSOPHILA MELANOGASTER

The relative viabilities and fitnesses of wild-type second chromosomes in heterozygous condition were determined. Joint analysis of these permitted an estimation of a parameter that relates the viability effect of a mutation to its effect on fitness as a whole. For newly arisen mutations, the estimate was slightly greater than one, indicating that the reductions in viability caused by these mutations are associated with reductions in other components of fitness. For mutations from an equilibrium population, the estimate of the parameter was near zero, implying that the deleterious viability effects of these mutations are compensated by improvements in other aspects of fitness.     

Viabilities of Third Chromosomes of DROSOPHILA PSEUDOOBSCURA Differing in Relative Competitive Fitness

Arrowhead (AR) third chromosome arrangements of Drosophila pseudoobscura, whose competitive fitnesses had been determined in population cages, were tested for their genetic loads in homozygous, heterozygous (homokaryotypic), and heterokaryotypic (AR/CH) combinations. The results showed that their competitive population cage performances were correlated to their viabilities as homozygotes but were not correlated to their viabilities as heterozygotes or as heterokaryotypes. However, the results do not fit in too simply with the mutational model of population structure, since the improvement of homozygous viability with increased competitive fitness was not accompanied by a significant degree of dominance as measured by the regression of viabilities of heterozygotes on homozygotes. Only the AR chromosomes derived from the population with poorest competitive fitness showed marked partial dominance (h=.35). The viabilities of heterokaryotypes were markedly uniform for all chromosomes tested and produced significantly greater numbers of flies per culture than the homokaryotypes. In general, the results show that the ranking of relative competitive fitnesses of these chromosomes is not a simple extrapolation of their viabilities, although marked changes in the populations tested have occurred. It is proposed that the differences in competitive fitness, homozygous viability, and degree of dominance observed among these chromosomes, arise from differences in genetic variability which enable different linkage relationships to be established for genes affecting these attributes.     

Rates of movement of transposable elements on the second chromosome of Drosophila melanogaster

The rates of movement of 11 families of transposable elements of Drosophila melanogaster were studied by means of in situ hybridization of probes to polytene chromosomes of larvae from a long-term mutation accumulation experiment. Replicate mutation-accumulation lines carrying second chromosomes derived from a single common ancestral chromosome were maintained by backcrosses of single males heterozygous for a balancer chromosome and a wild-type chromosome, and were scored after 116 generations. Twenty-seven transpositions and 1 excision were detected using homozygous viable and fertile second chromosomes, for a total of 235,056 potential sources of transposition events and a potential 252,880 excision events. The overall transposition rate per element per generation was 1.15 x 10(-4) and the excision rate was 3.95 x 10(-6). The single excision (of a roo element) was due to recombination between the element's long terminal repeats. A survey of the five most active elements among nine homozygous lethal lines revealed no significant difference in the estimates of transposition and excision rates from those from viable lines. The excess of transposition over excision events is in agreement with the results of other in situ hybridization experiments, and supports the conclusion that replicative increase in transposable element copy number is opposed by selection. These conclusions are compared with those from other studies, and with the conclusions from population surveys of element frequencies.     

Nature of Deleterious Mutation Load in Drosophila

Much population genetics and evolution theory depends on knowledge of genomic mutation rates and distributions of mutation effects for fitness, but most information comes from a few mutation accumulation experiments in Drosophila in which replicated chromosomes are sheltered from natural selection by a balancer chromosome. I show here that data from these experiments imply the existence of a large class of minor viability mutations with approximately equivalent effects. However, analysis of the distribution of viabilities of chromosomes exposed to EMS mutagenesis reveals a qualitatively different distribution of effects lacking such a minor effects class. A possible explanation for this difference is that transposable element insertions, a common class of spontaneous mutation event in Drosophila, frequently generate minor viability effects. This explanation would imply that current estimates of deleterious mutation rates are not generally applicable in evolutionary models, as transposition rates vary widely. Alternatively, much of the apparent decline in viability under spontaneous mutation accumulation could have been nonmutational, perhaps due to selective improvement of balancer chromosomes. This explanation accords well with the data and implies a spontaneous mutation rate for viability two orders of magnitude lower than previously assumed, with most mutation load attributable to major effects.     

The Evolution of Multilocus Systems under Weak Selection

The evolution of multilocus systems under weak selection is investigated. Generations are discrete and nonoverlapping; the monoecious population mates at random. The number of multiallelic loci, the linkage map, dominance, and epistasis are arbitrary. The genotypic fitnesses may depend on the gametic frequencies and time. The results hold for s << c(min), where s and c(min) denote the selection intensity and the smallest two-locus recombination frequency, respectively. After an evolutionarily short time of t(1) ~ (ln s)/ln(1 - c(min)) generations, all the multilocus linkage disequilibria are of the order of s [i.e., O(s) as s -> 0], and then the population evolves approximately as if it were in linkage equilibrium, the error in the gametic frequencies being O(s). Suppose the explicit time dependence (if any) of the genotypic fitnesses is O(s(2)). Then after a time t(2) ~ 2t(1), the linkage disequilibria are nearly constant, their rate of change being O(s(2)). Furthermore, with an error of O(s(2)), each linkage disequilibrium is proportional to the corresponding epistatic deviation for the interaction of additive effects on fitness. If the genotypic fitnesses change no faster than at the rate O(s(3)), then the single-generation change in the mean fitness is ΔW = W(-1)V(g) + O(s(3)), where V(g) designates the genic (or additive genetic) variance in fitness. The mean of a character with genotypic values whose single-generation change does not exceed O(s(2)) evolves at the rate ΔZ = W(-1)C(g) + O(s(2)), where C(g) represents the genic covariance of the character and fitness (i.e., the covariance of the average effect on the character and the average excess for fitness of every allele that affects the character). Thus, after a short time t(2), the absolute error in the fundamental and secondary theorems of natural selection is small, though the relative error may be large.     

Genetic variation for rate of development in natural populations of Drosophila melanogaster

We have sampled wild chromosomes from two natural populations of Drosophila melanogaster and obtained flies fully homozygous for the second chromosome, the third chromosome, or both, as well as flies heterozygous for one or both wild chromosomes and balancer chromosomes. Rate of embryogenesis (egg laying to larval hatching) and rate of development from egg to adult are measured, by classifying the individuals into fast, intermediate, and slow developmental classes. The experiments indicate that variation for rate of embryogenesis and for rate of egg-to-adult development is plentiful in the natural populations. Various hypotheses are enunciated to account for the small range of phenotypic variation observed in wild-type individuals with respect to the two parameters (embryogenesis and egg-to-adult development) and for the difficulty in changing the mean rates by artificial selection. Appropriate experiments may decide among the hypotheses, helping us to understand the genetic control of rate of ontogenesis, which is an important fitness component.     

Chromosome Interactions in DROSOPHILA MELANOGASTER. II. Total Fitness

In a large experiment, using nearly 200 population cages, we have measured the fitness of Drosophila melanogaster homozygous (1) for the second chromosome, (2) for the third chromosome, and (3) for both chromosomes. Twentyfour second chromosomes and 24 third chromosomes sampled from a natural population were tested. The mean fitness of the homozygous flies is 0.081 ± 0.014 for the second chromosome, 0.080 ± 0.017 for the third chromosome, and 0.079 ± 0.024 for both chromosomes simultaneously. Assuming that fitnesses are multiplicative (the additive fitness model makes no sense in the present case because of the large selection coefficients involved), the expected mean fitness of the homozygotes for both chromosomes is 0.0066; their observed fitness is more than ten times greater. Thus, it appears that synergistic interactions between loci are considerable; and that, consequently, the fitness function substantially departs from linearity. Two models are tentatively suggested for the fitness function: a "threshold" model and a "synergistic" model.—The experiments reported here confirm previous results showing that the concealed genetic load present in natural populations of Drosophila is sufficient to account for the selective maintenance of numerous polymorphisms (of the order of 1000).     

Stable Equilibria at Two Loci in Populations with Large Selfing Rates

The equilibrium structure of two-locus, two-allele models with very large selfing rates is found using perturbation techniques. For free recombination, r = 1/2, the following results hold. If the heterozygotes do not have at least an approximate 30% advantage in fitness relative to homozygotes, a stable equilibrium with all alleles present is possible only if all of the homozygote fitnesses differ at most by approximately the outcrossing rate, t, and all stable polymorphic equilibria have disequilibrium values, D, that are at most on the order of the outcrossing rate. Once the heterozygote fitnesses are above the threshold, there are stable equilibria possible with D near its maximum possible value. The results show that the observed disequilibria in highly selfed plant populations are not likely to result from selection leading to an equilibrium.     

A method to infer positive selection from marker dynamics in an asexual population

MOTIVATION: The observation of positive selection acting on a mutant indicates that the corresponding mutation has some form of functional relevance. Determining the fitness effects of mutations thus has relevance to many interesting biological questions. One means of identifying beneficial mutations in an asexual population is to observe changes in the frequency of marked subsets of the population. We here describe a method to estimate the establishment times and fitnesses of beneficial mutations from neutral marker frequency data. RESULTS: The method accurately reproduces complex marker frequency trajectories. In simulations for which positive selection is close to 5% per generation, we obtain correlations upwards of 0.91 between correct and inferred haplotype establishment times. Where mutation selection coefficients are exponentially distributed, the inferred distribution of haplotype fitnesses is close to being correct. Applied to data from a bacterial evolution experiment, our method reproduces an observed correlation between evolvability and initial fitness defect.     

Phenogenetic drift and the evolution of genotype-phenotype relationships

Maintenance of a stable two-locus polymorphism is analyzed statistically by fitting a logistic regression with a quadratic function of genotypic fitnesses to the probability for a fitness set to maintain a polymorphism. The regression is fitted using a data set containing information on stable equilibria maintained by 32,00 randomly generated fitness sets with three recombination values (0. 005, 0.05, 0.5). Fitted logistic regressions discriminate with 88 to 90% accuracy between fitness sets maintaining and not maintaining a stable internal equilibrium, which implies the existence of a fitness structure (balance of fitnesses) maintaining a two-locus polymorphism. Aspects of the balance of fitnesses revealed by logistic regressions are discussed. It is demonstrated that logistic regression also discriminates between types of a stable polymorphism: globally stable polymorphism, several simultaneously stable polymorphisms, and stable equilibria in addition to a polymorphic one, which implies that different balances of fitnesses are responsible for the maintenance of different types of polymorphism.     

Multiple adaptive substitutions during evolution in novel environments

We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to be high, here we start the adaptation process with a low fitness corresponding to a population in a stressful novel environment. For generic fitness distributions, using an analytic argument we find that the average number of steps to a local optimum varies logarithmically with the genotype sequence length and increases as the correlations among genotypic fitnesses increase. When the fitnesses are exponentially or uniformly distributed, using an evolution equation for the distribution of population fitness, we analytically calculate the fitness distribution of fixed beneficial mutations and the walk length distribution.     

Evolution of total net fitness in thermal lines: Drosophila subobscura likes it 'warm'

Fisher's fundamental theorem states that heritable variation for net fitness sets a limit to the rate of response to natural selection. How will temperate (i.e. cold‐tolerant) species cope with contemporary rapid global warming? Using three‐fold replicated lines of Drosophila subobscura that had been allowed to evolve for 4 years (between 32 and 59 generations) at 13 °C (cold), 18 °C (the supposed optimum temperature), and 22 °C (warm) I assess here how net fitness changes according to thermal environments. Net fitness was estimated following the classical approach in population genetics of competing over a number of generation in outbred experimental populations multiple wild‐type O chromosomes (homologous to arm 3R in D. melanogaster) independently derived from each base thermal stock in an otherwise homogeneous genetic background against a balancer chromosome. Warm‐adapted populations (‘warm‐adapted O chromosomes’) performed comparatively well at all tested temperatures. However, net fitness was severely reduced in cold‐adapted populations when transferred to warmer conditions. It seems, therefore, that thermal fitness breath for D. subobscura flies is positively associated to temperature. These findings are discussed in relation to the fast world‐wide clinal shifts in the frequency of genetic markers correlated with current climate change.     

Male-female interactions in Drosophila melanogaster: model with one-locus and three-alleles

We develop a fertility model of fitness that is general in that it does not assume that the fitnesses of the mating combinations are symmetrical or that they are additive or multilicative (i. e., that they can be inferred from fitnesses of the two genotypes involved in a mating). %he model considers one locus with three alleles. An experimental test with Drosophila rnelanogaster confirms that the fitnesses of the mating types depart from both additivity (or multiplicativity) and symmetry although this last property is of no consequence for the development of analytical models). urnerical simulations yield the same, or very nearly the same, equilibrium freuencies as the analytical model, independently of whether or not Hardy-Weinberg equilibrium Trequencies are assumed at the beginning of each selection cycle.     

Selection components in background replacement lines of Drosophila

Selection components analysis was performed in lines of Drosophila melanogaster at three times during substitution backcrossing. The initial two lines were inbred isofemale lines from natural populations in California, and one had the spread wing mutation eagle. The selection components analysis revealed aspects of the genetic structure of the determinants of fitness by demonstrating changes in the marginal fitnesses of the eagle locus. Differences among backgrounds essentially disappeared by the 20th generation of backcrossing, suggesting that the previously observed differences were attributable to linkage disequilibrium. The method of bootstrapping was used as a novel means of determining statistical confidence in selection components.     

Two new mouse chromosome 11 balancers

Segmental inversions causing recombination suppression are an essential feature of balancer chromosomes. Meiotic crossing over between homologous chromosomes within an inversion interval will lead to nonviable gametes, while gametes generated from recombination events elsewhere on the chromosome will be unaffected. This apparent recombination suppression has been widely exploited in genetic studies in Drosophila to maintain and analyze stocks carrying recessive lethal mutations. Balancers are particularly useful in mutagenesis screens since they help to establish the approximate genomic location of alleles of genes causing phenotypes. Using the Cre-loxP recombination system, we have constructed two mouse balancer chromosomes carrying 8- and 30-cM inversions between Wnt3 and D11Mit69 and between Trp53 and EgfR loci, respectively. The Wnt3-D11Mit69 inversion mutates the Wnt3 locus and is therefore homozygous lethal. The Trp53-EgfR inversion is homozygous viable, since the EgfR locus is intact and mutations in p53 are homozygous viable. A dominantly acting K14-agouti minigene tags both rearrangements, which enables these balancer chromosomes to be visibly tracked in mouse stocks. With the addition of these balancers to the previously reported Trp53-Wnt3 balancer, most of mouse chromosome 11 is now available in balancer stocks.     

The Genetic Structure of Natural Populations of Drosophila melanogaster. Xx. Comparison of Genotype-Environment Interaction in Viability between a Northern and a Southern Population

In order to examine the operation of diversifying selection as the maintenance mechanism of excessive additive genetic variance for viability in southern populations in comparison with northern populations of Drosophila melanogaster, two sets of experiments were conducted using second chromosomes extracted from the Ogasawara population (a southern population in Japan) and from the Aomori population (a northern population in Japan). Chromosomal homozygote and heterozygote viabilities were estimated in eight kinds of artificially produced breeding environments. The main findings in the present investigation are as follows: (1) Significant genotype-environment interaction was observed using chromosomes extracted from the Ogasawara population. Indeed, the estimate of the genotype-environment interaction variance for heterozygotes was significantly larger than that of the genotypic variance. On the other hand, when chromosomes sampled from the Aomori population were examined, that interaction variance was significant only for homozygotes and its value was no more than one quarter of that for the chromosomes from the Ogasawara population. (2) The average genetic correlation between any two viabilities of the same lines estimated in the eight kinds of breeding environments for the chromosomes sampled from the Ogasawara population was smaller than that for the chromosomes from the Aomori population both in homozygotes and in heterozygotes, especially in the latter. (3) The stability of heterozygotes over homozygotes against fluctuations of environmental conditions was seen in the chromosomes from the Ogasawara population, but not from the Aomori population. (4) From the excessive genotype-environment interaction variance compared with the genotypic variance in heterozygotes, it was suggested for the chromosomes from the Ogasawara population that the reversal of viability order between homozygotes took place in some environments at the locus level. On the basis of these findings, it is strongly suggested that diversifying selection is operating in a southern population of D. melanogaster on some of the viability polygenes which are probably located outside the structural loci, and the excessive additive genetic variance of viability in southern populations is maintained by this type of selection.     

Evolutionary dynamics in frequency-dependent two-phenotype models

General frequency-dependent selection models based on two phenotypic classes are analyzed with underlying one-locus multiallele phenotypic determination systems in diploid populations. It is proved that the mean phenotypic fitnesses tend to equality over discrete generations and genetic mutations if a phenotypic polymorphism is to be maintained. The exact conditions are examined. The present results are valid for a wide class of models whenever random groupings or assortative patterns based on phenotype and affecting fitness, linearly or not, are independent of sex, mating preferences, or kinship. They can also be applied to two-sex haploid models.     

Density dependent selection 1: A stable feasible equilibrium may not be attainable

The joint evolution of gene frequency p, and population size N is studied. It is shown that when the genotypic fitnesses are logistic functions of the population size, sets of initial states exist which lead to bizarre behavior. Even though equilibria may be locally stable, these sets of initial conditions eventually produce negative fitnesses. Alternative models are discussed as are some general properties of the mean fitness.