A SIMULATION OF WRIGHT'S SHIFTING-BALANCE PROCESS: MIGRATION AND THE THREE PHASES

Wright partitioned the shifting-balance process into three phases. Phase one is the shift of a deme within a population to the domain of a higher adaptive peak from that of the historical peak. Phase two is mass selection within a deme towards that higher peak. Phase three is the conversion of additional demes to the higher peak. The migration rate between demes is critical for the existence of phases one and three. Phase one requires small effective population sizes, hence low migration rates. Phase three is optimal under high migration rates that spread the most-fit genotype from deme to deme. Thus, a population-wide peak shift requires intermediate levels of migration. By altering the rates of phases one and three, migration affects the predominant direction of mass selection within a population. This study examines the degree to which migration, through its effects on phases one and three, determines the probability of a simulated population arriving at its genotypic optimum after 12,000 generations. These simulations reveal that there is a range of migration rates for which an entire population might be expected to shift to a higher peak. Below m = 0.001 peak shifts occur frequently (phases I and II) but are not successfully exported out of subpopulations (phase III), and above 0.01 peak shifts within demes (phase I and II), required to initiate phase III, become increasingly uncommon. Because it is unlikely that real populations will have uniform migration rates from generation to generation, the probable effects of varying migration rates on broadening the range of conditions producing peak shifts are discussed.     

Evolution of altruism under group selection in large and small populations in fluctuating environments

A continuous, graded form of group selection which does not involve extinction of demes can effectively oppose selection on the individual level against an altruistic allele under fluctuating environments in infinitely large demes among which uniform mixing occurs every generation. Although group selection cannot alter the conditions necessary for the initial increase of altruistic alleles, group selection can significantly influence the stationary distribution of gene frequency which is attained once stochastic forces have allowed theirintroduction. Drift is a more effective source of variation than fluctuations in selection when the variance in selection is moderate to small. High numbers of demes promote polymorphism under both graded group selection and extinction group selection.     

Populational heritability: empirical studies of evolution in metapopulations

Using demes from experimental metapopulations of the flour beetle, Tribolium castaneum, we investigated phase 3 of Wright's shifting balance process. Using parent demes of high, intermediate, and low mean fitness, we experimentally modeled migration of varying amounts from demes of high mean fitness into demes of lower mean fitness (like phase 3) as well as the reciprocal (the opposite of phase 3). In natural populations, some migration among demes occurs independently of deme fitness. In this case, demes of high mean fitness are likely to receive migrants from demes of lower mean fitness; these effects might limit the effectiveness of phase 3 but have not been studied experimentally. We estimated the populational heritability of mean fitness by the regression of offspring deme means on the weighted parental means and found moderate levels of demic heritability one (0.641-0.690) and two (0.518-0.552) generations after migration. We discuss our findings in relation to the role of interdemic migration in "adaptive peak shifts" in metapopulations and the controversies over group selection and the units of inheritance.     

PHASE III OF WRIGHT'S SHIFTING BALANCE PROCESS AND THE VARIANCE AMONG DEMES IN MIGRATION RATE

Interdemic selection by the differential migration of individuals out from demes of high fitness and into demes of low fitness (Phase III) is one of the most controversial aspects of Wright's Shifting Balance Theory. I derive a relationship between Phase III migration and the interdemic selection differential, S, and show its potential effect on F_ST. The relationship reveals a diversifying effect of interdemic selection by Phase III migration on the genetic structure of a metapopulation. Using experimental metapopulations, I explored the effect of Phase III migration on F_ST by comparing the genetic variance among demes for two different patterns of migration: (1) island model migration and (2) Wright's Phase III migration. Although mean migration rates were the same, I found that the variance among demes in migration rate was significantly higher with Phase III than with island model migration. As a result, F_ST for the frequency of a neutral marker locus was higher with Phase III than it was with island model migration. By increasing F_ST, Phase III enhanced the genetic differentiation among demes for traits not subject to interdemic selection. This feature makes Wright's process different from individual selection which, by reducing effective population size, decreases the genetic variance within demes for all other traits. I discussed this finding in relation to the efficacy of Phase III and random migration for effecting peak shifts, and the contribution of genes with indirect effects to among‐deme variation.     

Metabolic network alignment in large scale by network compression

Metabolic network alignment is a system scale comparative analysis that discovers important similarities and differences across different metabolisms and organisms. Although the problem of aligning metabolic networks has been considered in the past, the computational complexity of the existing solutions has so far limited their use to moderately sized networks. In this paper, we address the problem of aligning two metabolic networks, particularly when both of them are too large to be dealt with using existing methods. We develop a generic framework that can significantly improve the scale of the networks that can be aligned in practical time. Our framework has three major phases, namely the compression phase, the alignment phase and the refinement phase. For the first phase, we develop an algorithm which transforms the given networks to a compressed domain where they are summarized using fewer nodes, termed supernodes, and interactions. In the second phase, we carry out the alignment in the compressed domain using an existing network alignment method as our base algorithm. This alignment results in supernode mappings in the compressed domain, each of which are smaller instances of network alignment problem. In the third phase, we solve each of the instances using the base alignment algorithm to refine the alignment results. We provide a user defined parameter to control the number of compression levels which generally determines the tradeoff between the quality of the alignment versus how fast the algorithm runs. Our experiments on the networks from KEGG pathway database demonstrate that the compression method we propose reduces the sizes of metabolic networks by almost half at each compression level which provides an expected speedup of more than an order of magnitude. We also observe that the alignments obtained by only one level of compression capture the original alignment results with high accuracy. Together, these suggest that our framework results in alignments that are comparable to existing algorithms and can do this with practical resource utilization for large scale networks that existing algorithms could not handle. As an example of our method's performance in practice, the alignment of organism-wide metabolic networks of human (1615 reactions) and mouse (1600 reactions) was performed under three minutes by only using a single level of compression.     

Spatial heterogeneity in the strength of selection against deleterious alleles and the mutation load

According to current estimates of genomic deleterious mutation rates (which are often of the order 0.1-1) the mutation load (defined as a reduction in the average fitness of a population due to the presence of deleterious alleles) may be important in many populations. In this paper, I use multilocus simulations to explore the effect of spatial heterogeneity in the strength of selection against deleterious alleles on the mutation load (for example, it has been suggested that stressful environments may increase the strength of selection). These simulations show contrasted results: in some situations, spatial heterogeneity may greatly reduce the mutation load, due to the fact that migrants coming from demes under stronger selection carry relatively few deleterious alleles, and benefit from a strong advantage within demes under weaker selection (where individuals carry many more deleterious alleles); in other situations, however, deleterious alleles accumulate within demes under stronger selection, due to migration pressure from demes under weaker selection, leading to fitness erosion within those demes. This second situation is more frequent when the productivity of the different demes is proportional to their mean fitness. The effect of spatial heterogeneity is greatly reduced, however, when the response to environmental differences is inconsistent across loci.     

Genotype-by-Environment Interactions for Seedling Establishment Across Native and Degraded-Forest Habitats in a Long-Lived Cycad

Habitat differences might promote adaptive differentiation among populations that can be evidenced by genotype-by-environment interactions (GxE). I examined GxE in seed germination and seedling survival in demes of a rainforest cycad across their native and degraded-forest habitats, and explored the role of maternal effects and resource availability on the observed GxE. A reciprocal-transplant experiment showed a home-site advantage in terms of establishmen of the demes. Germination in a manipulative greenhouse experiment mirrored the patterns in natural environments, with GxE in response to light and water availability. Overall germination was lower in the degraded-forest habitat and under high-light and low-water conditions in the greenhouse. Several analysis suggested that maternal effects related to size on germination are weak, but maternal effects are suggested by better survival of larger seedlings in the degraded-forest habitat. With weak maternal effects, GxE in establishment of individuals suggest some adaptive differentiation across demes in this cycad, which could have implications for population persistence in its habitats.     

PERSPECTIVE: A CRITIQUE OF SEWALL WRIGHT'S SHIFTING BALANCE THEORY OF EVOLUTION

We evaluate Sewall Wright's three-phase “shifting balance” theory of evolution, examining both the theoretical issues and the relevant data from nature and the laboratory. We conclude that while phases I and II of Wright's theory (the movement of populations from one “adaptive peak” to another via drift and selection) can occur under some conditions, genetic drift is often unnecessary for movement between peaks. Phase III of the shifting balance, in which adaptations spread from particular populations to the entire species, faces two major theoretical obstacles: (1) unlike adaptations favored by simple directional selection, adaptations whose fixation requires some genetic drift are often prevented from spreading by barriers to gene flow; and (2) it is difficult to assemble complex adaptations whose constituent parts arise via peak shifts in different demes. Our review of the data from nature shows that although there is some evidence for individual phases of the shifting balance process, there are few empirical observations explained better by Wright's three-phase mechanism than by simple mass selection. Similarly, artificial selection experiments fail to show that selection in subdivided populations produces greater response than does mass selection in large populations. The complexity of the shifting balance process and the difficulty of establishing that adaptive valleys have been crossed by genetic drift make it impossible to test Wright's claim that adaptations commonly originate by this process. In view of these problems, it seems unreasonable to consider the shifting balance process as an important explanation for the evolution of adaptations.     

Stochasticity, complex spatial structure, and the feasibility of the shifting balance theory

Sewall Wright's shifting balance theory of evolution posits a mechanism by which a structured population may escape local fitness optima and find a global optimum. We examine a one-locus, two-allele model of underdominance in populations with differing spatial arrangements of demes, both analytically and with Monte Carlo simulations. We find that inclusion of variance in interpatch connectivities can significantly reduce the number of generations required for fixation of the more favorable allele relative to island and stepping-stone models. Although time to fixation increases with migration rate in all cases, the presence of one or two relatively isolated demes may reduce the number of generations by 80% or more. These results suggest that the shifting balance process may operate under less restrictive conditions than those found with a simple spatial arrangement of demes.     

Peak shifts and extinction under sex-specific selection

A well-known property of sexual selection combined with a cross-sex genetic correlation (r_mf) is that it can facilitate a peak shift on the adaptive landscape. How do these diversifying effects of sexual selection + r_mf balance with the constraints imposed by such sexual antagonism, to affect the macroevolution of sexual dimorphism? Here, I extend existing quantitative genetic models of evolution on complex adaptive landscapes. Beyond recovering classical predictions for the conditions promoting a peak shift, I show that when r_mf is moderate to strong, relatively weak sexual selection is required to induce a peak shift in males only. Increasing the strength of sexual selection leads to a sexually concordant peak shift, suggesting that macroevolutionary rates of sexual dimorphism may be largely decoupled from the strength of within-population sexual selection. Accounting explicitly for demography further reveals that sex-specific peak shifts may be more likely to be successful than concordant shifts in the face of extinction, especially when natural selection is strong. An overarching conclusion is that macroevolutionary patterns of sexual dimorphism are unlikely to be readily explained by within-population estimates of selection or constraint alone.     

Small-world networks decrease the speed of Muller's ratchet

Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of non-recombining genomes, such as the mitochondria, the degeneration of the Y chromosome, and the evolution of sex and recombination. Here we study the speed of Muller's ratchet in a spatially structured population which is subdivided into many small populations (demes) connected by migration, and distributed on a graph. We studied different types of networks: regular networks (similar to the stepping-stone model), small-world networks and completely random graphs. We show that at the onset of the small-world network - which is characterized by high local connectivity among the demes but low average path length - the speed of the ratchet starts to decrease dramatically. This result is independent of the number of demes considered, but is more pronounced the larger the network and the stronger the deleterious effect of mutations. Furthermore, although the ratchet slows down with increasing migration between demes, the observed decrease in speed is smaller in the stepping-stone model than in small-world networks. As migration rate increases, the structured populations approach, but never reach, the result in the corresponding panmictic population with the same number of individuals. Since small-world networks have been shown to describe well the real contact networks among people, we discuss our results in the light of the evolution of microbes and disease epidemics.     

Rate of adaptive peak shifts with partial genetic robustness

How adaptive evolution occurs with individually deleterious but jointly beneficial mutations has been one of the major problems in population genetics theory. Adaptation in this case is commonly described as a population's escape from a local peak to a higher peak on Sewall Wright's fitness landscape. Recent molecular genetic and computational studies have suggested that genetic robustness can facilitate such peak shifts. If phenotypic expressions of new mutations are suppressed under genetic robustness, mutations that are otherwise deleterious can accumulate in the population as neutral variants. When the robustness is perturbed by an environmental change or a major mutation, these variants become exposed to natural selection. It is argued that this process promotes adaptation because allelic combinations enriched under genetic robustness can then be positively selected. Here, I propose simple two- and three-locus models of adaptation with partial genetic robustness as suggested by recent studies. The waiting time until the fixation of an adaptive haplotype was observed in stochastic simulations and compared to the expectation without robustness. It is shown that peak shifts can be delayed or accelerated depending on the conditions of genetic robustness. The evolutionary significance of these processes is discussed.     

The interactions of cartilage proteoglycans with collagens are determined by their structures.

In the present work, the interaction of aggrecan, decorin and biglycan isolated from pig laryngeal cartilage and of the three squid cartilage proteoglycans with collagen type I and II was studied. The interaction was examined under conditions allowing the formation of collagen fibrils. It was found that biglycan interacted strongly with collagen type II and not with type I and the interaction seemed to proceed exclusively through its core proteins. Decorin interacted with collagen type I but not with type II. Aggrecan interacted very poorly with both collagen types. The two squid proteoglycans of large size, D1D1A and D1D2, interacted only with collagen type I through both glycosaminoglycans and core proteins. The third squid proteoglycan of small size, D1D1B, interacted poorly only with collagen type I. The results suggested that the interactions of cartilage proteoglycans with collagen were mainly due to the primary structure of both molecules, and would contribute to the maintenance of the integrity of the tissue. The biochemical significance of these interactions might be more critical in aged vertebrate cartilage, where loss of aggrecan and increase of the small proteoglycans was observed, a large proportion of which is found in the extracellular matrix free of glycosaminoglycan chains.     

Invasion and fixation of sex-reversal genes

We simulated a meta-population with random dispersal among demes but local mating within demes to investigate conditions under which a dominant female-determining gene W, with no individual selection advantage, can invade and become fixed in females, changing the population from male to female heterogamety. Starting with one mutant W in a single deme, the interaction of sex ratio selection and random genetic drift causes W to be fixed among females more often than a comparable neutral mutation with no influence on sex determination, even when YY males have slightly reduced viability. Meta-population structure and interdeme selection can also favour the fixation of W. The reverse transition from female to male heterogamety can also occur with higher probability than for a comparable neutral mutation. These results help to explain the involvement of sex-determining genes in the evolution of sex chromosomes and in sexual selection and speciation.     

Population genetics in the American Tropics XVI. Data on partial dominance of recessives in Drosophila willistoni

Summary Through a series of genetic load studies made on 1) samples of Drosophila willistoni from two sites in Mesitas, Colombia, it was found that the relative contributions to the total, subvital and lethal loads reflect lethal equivalences (B/A) ratios which support more the balancing theory of population structure than the neutralist theory. Moreover, measurements of population size have revealed the existance of very small demes in local populations. Under such conditions we have calculated extremely small lethal equivalence ratios in demes where probably a great deal of consanguinity takes place. We are aware that under these conditions B/A ratios cannot be very good monitors of random load measurements and, therefore, suggest a change in the mathematical formulation that take into consideration the existance of small populations.Furthermore, it appears plausible that the degree of penetrance in the heterozygous condition changes as the population structure changes. We speculate that natural populations may have unknown selective mechanisms capable of guiding unknown dominance modifiers according to the intensity of selection.     

Effects of polymorphism for locally adapted genes on rates of neutral introgression in structured populations

Adaptation to local conditions within demes balanced by migration can maintain polymorphisms for variants that reduce fitness in certain ecological contexts. Here, we address the effects of such polymorphisms on the rate of introgression of neutral marker genes, possibly genetically linked to targets of selection. Barriers to neutral gene flow are expected to increase with linkage to targets of local selection and with differences between demes in the frequencies of locally adapted alleles. This expectation is borne out under purifying and disruptive selection, regimes that promote monomorphism within demes. In contrast, overdominance within demes induces minimal barriers to neutral introgression even in the face of very large differences between demes in the frequencies of locally adapted alleles. Further, segregation distortion, a phenomenon observed in a number of interspecific hybrids, can in fact promote transmission by migrants to future generations at rates exceeding those of residents.     

Bacterial Adaptation through Loss of Function

The metabolic capabilities and regulatory networks of bacteria have been optimized by evolution in response to selective pressures present in each species'' native ecological niche. In a new environment, however, the same bacteria may grow poorly due to regulatory constraints or biochemical deficiencies. Adaptation to such conditions can proceed through the acquisition of new cellular functionality due to gain of function mutations or via modulation of cellular networks. Using selection experiments on transposon-mutagenized libraries of bacteria, we illustrate that even under conditions of extreme nutrient limitation, substantial adaptation can be achieved solely through loss of function mutations, which rewire the metabolism of the cell without gain of enzymatic or sensory function. A systematic analysis of similar experiments under more than 100 conditions reveals that adaptive loss of function mutations exist for many environmental challenges. Drawing on a wealth of examples from published articles, we detail the range of mechanisms through which loss-of-function mutations can generate such beneficial regulatory changes, without the need for rare, specific mutations to fine-tune enzymatic activities or network connections. The high rate at which loss-of-function mutations occur suggests that null mutations play an underappreciated role in the early stages of adaption of bacterial populations to new environments.     

Population structure and evolutionary progress

Wright's shifting-balance theory is discussed as an example of a process that can cause species to evolve combinations of characters that could not evolve under natural selection alone. A review of the existing theory of peak shifts indicates that the conditions of extreme isolation that are necessary to permit genetic drift to alter the outcome of natural selection in local populations would make gene flow too weak to spread a new combination of genes to other populations in a reasonable time. Instead, it seems likely that major demographic changes must occur in a species for the shifting-balance process to work. A discussion of direct and indirect studies of gene flow in natural populations suggests that the current genetic structure of many species is likely to reflect past demographic events rather than ongoing gene flow. It is possible then that demographic processes could be responsible for spreading new traits in a species, but that would be true whether those new traits evolved only owing to natural selection or owing in addition to genetic drift and other forces.     

An approach for searching insertions in bacterial genes leading to the phase shift of triplet periodicity

The concept of the phase shift of triplet periodicity (TP) was used for searching potential DNA insertions in genes from 17 bacterial genomes. A mathematical algorithm for detection of these insertions has been developed. This approach can detect potential insertions and deletions with lengths that are not multiples of three bases, especially insertions of relatively large DNA fragments (>100 bases). New similarity measure between triplet matrixes was employed to improve the sensitivity for detecting the TP phase shift. Sequences of 17,220 bacterial genes with each consisting of more than 1,200 bases were analyzed, and the presence of a TP phase shift has been shown in ～16% of analysed genes (2,809 genes), which is about 4 times more than that detected in our previous work. We propose that shifts of the TP phase may indicate the shifts of reading frame in genes after insertions of the DNA fragments with lengths that are not multiples of three bases. A relationship between the phase shifts of TP and the frame shifts in genes is discussed.     

Further Evidence for the Presence of a Circadian Clock in the Prothoracic Glands of the Saturniid Moth Samia cynthia ricini: Decapitated Larvae Can Respond to Light-Dark Changes

A small peak of haemolymph ecdysteroid titre precedes the gut purge that characterizes larval-prepupal transition of the saturniid moth Samia cynthia ricini. This peak shifts its phase in parallel with the phase shifts of gut purge according to the changes in light-dark conditions preceding gut purge. Decapitated larvae responded to these light-dark changes as intact larvae did, as assessed by the phase shifts of the haemolymph ecdysteroid peak. This indicates that the brain-centred PTTH clock is not prerequisite for realization of the circadian-clock-controlled timing in the initiation of prepupal development, and supports indirectly our previous notion that the prothoracic glands of Samia possess a circadian clock dictating gut purge timing.