Mutational Load and the Functional Fraction of the Human Genome

The fraction of the human genome that is functional is a question of both evolutionary and practical importance. Studies of sequence divergence have suggested that the functional fraction of the human genome is likely to be no more than ∼15%. In contrast, the ENCODE project, a systematic effort to map regions of transcription, transcription factor association, chromatin structure, and histone modification, assigned function to 80% of the human genome. In this article, we examine whether and how an analysis based on mutational load might set a limit on the functional fraction. In order to do so, we characterize the distribution of fitness of a large, finite, diploid population at mutation-selection equilibrium. In particular, if mean fitness is ∼1, the fitness of the fittest individual likely to occur cannot be unreasonably high. We find that at equilibrium, the distribution of log fitness has variance nus, where u is the per-base deleterious mutation rate, n is the number of functional sites (and hence incorporates the functional fraction f), and s is the selection coefficient of deleterious mutations. In a large (N=109) reproducing population, the fitness of the fittest individual likely to exist is ∼e5nus. These results apply to both additive and recessive fitness schemes. Our approach is different from previous work that compared mean fitness at mutation-selection equilibrium with the fitness of an individual who has no deleterious mutations; we show that such an individual is exceedingly unlikely to exist. We find that the functional fraction is not very likely to be limited substantially by mutational load, and that any such limit, if it exists, depends strongly on the selection coefficients of new deleterious mutations.

Mutational load and the functional fraction of the human genome

The fraction of the human genome that is functional is a question of both evolutionary and practical importance. Studies of sequence divergence have suggested that the functional fraction of the human genome is likely to be no more than ∼15%. In contrast, the ENCODE project, a systematic effort to map regions of transcription, transcription factor association, chromatin structure, and histone modification, assigned function to 80% of the human genome. In this paper we examine whether and how an analysis based on mutational load might set a limit on the functional fraction. In order to do so, we characterize the distribution of fitness of a large, finite, diploid population at mutation-selection equilibrium. In particular, if mean fitness is ∼1, the fitness of the fittest individual likely to occur cannot be unreasonably high. We find that at equilibrium, the distribution of log fitness has variance nus, where u is the per-base deleterious mutation rate, n is the number of functional sites (and hence incorporates the functional fraction f), and s is the selection coefficient of deleterious mutations. In a large (N = 109) reproducing population, the fitness of the fittest individual likely to exist is . These results apply to both additive and recessive fitness schemes. Our approach is different from previous work that compared mean fitness at mutation-selection equilibrium to the fitness of an individual who has no deleterious mutations; we show that such an individual is exceedingly unlikely to exist. We find that the functional fraction is not very likely to be limited substantially by mutational load, and that any such limit, if it exists, depends strongly on the selection coefficients of new deleterious mutations.

The Fisher-Wright model with deterministic seed bank and selection

Seed banks are a common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with selection coupled with a deterministic seed bank assuming the length of the seed bank is kept constant and the number of seeds is large. To assess the combined impact of seed banks and selection on genetic diversity, we derive a general diffusion model. We compute the equilibrium solution of the site-frequency spectrum and derive the times to fixation of an allele with and without selection. Finally, it is demonstrated that seed banks enhance the effect of selection onto the site-frequency spectrum while slowing down the time until the mutation-selection equilibrium is reached.

Convergent Evolution During Local Adaptation to Patchy Landscapes

Species often encounter, and adapt to, many patches of locally similar environmental conditions across their range. Such adaptation can occur through convergent evolution if different alleles arise and spread in different patches, or through the spread of shared alleles by migration acting to synchronize adaptation across the species. The tension between the two reflects the degree of constraint imposed on evolution by the underlying genetic architecture versus how effectively selection and geographic isolation act to inhibit the geographic spread of locally adapted alleles. This paper studies a model of the balance between these two routes to adaptation in continuous environments with patchy selection pressures. We address the following questions: How long does it take for a novel, locally adapted allele to appear in a patch of habitat where it is favored through mutation? Or, through migration from another, already adapted patch? Which is more likely to occur, as a function of distance between the patches? How can we tell which has occurred, i.e., what population genetic signal is left by the spread of migrant alleles? To answer these questions we examine the family structure underlying migration–selection equilibrium surrounding an already adapted patch, in particular treating those rare families that reach new patches as spatial branching processes. This provides a way to understand the role of geographic separation between patches in promoting convergent adaptation and the genomic signals it leaves behind. We illustrate these ideas using the convergent evolution of cryptic coloration in the rock pocket mouse, Chaetodipus intermedius, as an empirical example.Author SummaryOften, a large species range will include patches where the species differs because it has adapted to locally differing conditions. For instance, rock pocket mice are often found with a coat color that matches the rocks they live in, these color differences are controlled genetically, and mice that don’t match the local rock color are more likely to be eaten by predators. Sometimes, similar genetic changes have occurred independently in different patches, suggesting that there were few accessible ways to evolve the locally adaptive form. However, the genetic basis could also be shared if migrants carry the locally beneficial genotypes between nearby patches, despite being at a disadvantage between the patches. We use a mathematical model of random migration to determine how quickly adaptation is expected to occur through new mutation and through migration from other patches, and study in more detail what we would expect successful migrations between patches to look like. The results are useful for determining whether similar adaptations in different locations are likely to have the same genetic basis or not, and more generally in understanding how species adapt to patchy, heterogeneous landscapes.

A NOTE ON CREDIT MARKET DEVELOPMENT AND HUMAN CAPITAL ACCUMULATION

This paper explores the interplay between credit market development and human capital accumulation in a two-period overlapping-generations economy with asymmetric information under the assumption that young lenders channel credits to young borrowers and acquire education. We find that, at the self-selection equilibrium, lenders will allocate more time to acquire education if the cost of screening borrowers falls. Furthermore, a longer duration of lenders' schooling time suppresses borrowers' incentive to cheat thereby enabling lenders to screen less frequently. Our preliminary cross-country empirical analysis appears to support these findings.

Selection equilibrium for hatchery and wild spawning fitness in integrated breeding programs

Some salmon hatchery programs intentionally integrate the wild and hatchery population by taking naturally spawned fish as some fraction of the broodstock and allowing hatchery progeny to constitute some fraction of the adults spawning in the wild. This circumvents some ecological concerns about the effects of hatchery fish on the "wild" population while still reaping some of the benefits of increased potential for harvest, but it increases some genetic concerns. Here, we model phenotypic evolution in the integrated population to investigate the effects on natural spawning fitness at the joint selection and demographic equilibrium. We find a potential, but not a certainty, depending on quantitative aspects of the management interacting with biological characteristics of the stock, for substantial erosion of natural spawning fitness, compared with the original wild population, including the possibility of runaway selection driving natural spawning fitness effectively to zero. The vulnerability to such evolutionary deterioration increases with the magnitude of the contribution of hatchery breeding to the total production and increases with harvest. The response of the selection equilibrium to increasing contribution of hatchery progeny to the broodstock can exhibit a catastrophic discontinuity.