The Effect of Bacterial Recombination on Adaptation on Fitness Landscapes with Limited Peak Accessibility

There is ample empirical evidence revealing that fitness landscapes are often complex: the fitness effect of a newly arisen mutation can depend strongly on the allelic state at other loci. However, little is known about the effects of recombination on adaptation on such fitness landscapes. Here, we investigate how recombination influences the rate of adaptation on a special type of complex fitness landscapes. On these landscapes, the mutational trajectories from the least to the most fit genotype are interrupted by genotypes with low relative fitness. We study the dynamics of adapting populations on landscapes with different compositions and numbers of low fitness genotypes, with and without recombination. Our results of the deterministic model (assuming an infinite population size) show that recombination generally decelerates adaptation on these landscapes. However, in finite populations, this deceleration is outweighed by the accelerating Fisher-Muller effect under certain conditions. We conclude that recombination has complex effects on adaptation that are highly dependent on the particular fitness landscape, population size and recombination rate.     

Frequent recombination shapes the epidemic population structure of Planktothrix (Cyanoprokaryota) in Italian subalpine lakes

The planktonic genus Planktothrix, as other cyanobacteria, shows signals of both homologous and nonhomologous recombination. However, the frequency of recombination and its effect on Planktothrix population structuring is unknown. We isolated 290 Planktothrix strains from seven neighboring lakes in the subalpine Italian region and analyzed these using multilocus sequence typing. Four of six loci analyzed were polymorphic, resulting in 20 distinct multilocus genotypes. Association indices among alleles at different loci were suggestive of an “epidemic population structure,” resulting from an explosive (and temporary) dominance of one genotype against a panmictic background. ClonalFrame analyses supported this view by detecting: (i) three major clades affected by three distinct recombination events, (ii) a recombination rate about equal to the mutation rate, and (iii) the fact that recombination had an impact on introducing molecular diversity more than double the mutation rate. Furthermore, analysis of molecular variance over an annual cycle in three of seven lakes revealed that both local clonal expansion and recombination processes affected among‐lake diversity. Our observations suggest that recombination affects microevolution of Planktothrix and that an epidemic structure can emerge in populations of this genus.     

A population genetics model for multiple quantitative traits exhibiting pleiotropy and epistasis

We study a population genetics model of an organism with a genome of L(tot)loci that determine the values of T quantitative traits. Each trait is controlled by a subset of L loci assigned randomly from the genome. There is an optimum value for each trait, and stabilizing selection acts on the phenotype as a whole to maintain actual trait values close to their optima. The model contains pleiotropic effects (loci can affect more than one trait) and epistasis in fitness. We use adaptive walk simulations to find high-fitness genotypes and to study the way these genotypes are distributed in sequence space. We then simulate the evolution of haploid and diploid populations on these fitness landscapes and show that the genotypes of populations are able to drift through sequence space despite stabilizing selection on the phenotype. We study the way the rate of drift and the extent of the accessible region of sequence space is affected by mutation rate, selection strength, population size, recombination rate, and the parameters L and T that control the landscape shape. There are three regimes of the model. If LTL(tot), there are many small peaks that can be spread over a wide region of sequence space. Compensatory neutral mutations are important in the population dynamics in this case.     

Demographic stochasticity and resource autocorrelation control biological invasions in heterogeneous landscapes

Mounting theoretical evidence suggests that demographic stochasticity, environmental heterogeneity and biased movement of organisms individually affect the dynamics of biological invasions and range expansions. Studies of species spread in heterogeneous landscapes have traditionally characterized invasion velocities as functions of the mean resource density throughout the landscape, thus neglecting higher‐order moments of the spatial resource distribution. Here, we show theoretically that different spatial arrangements of resources lead to different spread velocities even if the mean resource density throughout the landscape is kept constant. Specifically, we find that increasing the resource autocorrelation length causes a reduction in the speed of species spread. The model shows that demographic stochasticity plays a key role in the slowdown, which is strengthened when individuals can actively move towards resources. We then experimentally corroborated the theoretically predicted reduction in propagation speed in microcosm experiments with the protist Euglena gracilis by comparing spread in landscapes with different resource autocorrelation lengths. Our work identifies the resource autocorrelation length as a key modulator and a simple measure of landscape susceptibility to biological invasions, which needs to be considered for predicting invasion dynamics within naturally heterogeneous environmental corridors.     

Evolutionary accessibility of mutational pathways

Functional effects of different mutations are known to combine to the total effect in highly nontrivial ways. For the trait under evolutionary selection ('fitness'), measured values over all possible combinations of a set of mutations yield a fitness landscape that determines which mutational states can be reached from a given initial genotype. Understanding the accessibility properties of fitness landscapes is conceptually important in answering questions about the predictability and repeatability of evolutionary adaptation. Here we theoretically investigate accessibility of the globally optimal state on a wide variety of model landscapes, including landscapes with tunable ruggedness as well as neutral 'holey' landscapes. We define a mutational pathway to be accessible if it contains the minimal number of mutations required to reach the target genotype, and if fitness increases in each mutational step. Under this definition accessibility is high, in the sense that at least one accessible pathway exists with a substantial probability that approaches unity as the dimensionality of the fitness landscape (set by the number of mutational loci) becomes large. At the same time the number of alternative accessible pathways grows without bounds. We test the model predictions against an empirical 8-locus fitness landscape obtained for the filamentous fungus Aspergillus niger. By analyzing subgraphs of the full landscape containing different subsets of mutations, we are able to probe the mutational distance scale in the empirical data. The predicted effect of high accessibility is supported by the empirical data and is very robust, which we argue reflects the generic topology of sequence spaces. Together with the restrictive assumptions that lie in our definition of accessibility, this implies that the globally optimal configuration should be accessible to genome wide evolution, but the repeatability of evolutionary trajectories is limited owing to the presence of a large number of alternative mutational pathways.     

Visualizing fitness landscapes

Fitness landscapes are a classical concept for thinking about the relationship between genotype and fitness. However, because the space of genotypes is typically high-dimensional, the structure of fitness landscapes can be difficult to understand and the heuristic approach of thinking about fitness landscapes as low-dimensional, continuous surfaces may be misleading. Here, I present a rigorous method for creating low-dimensional representations of fitness landscapes. The basic idea is to plot the genotypes in a manner that reflects the ease or difficulty of evolving from one genotype to another. Such a layout can be constructed using the eigenvectors of the transition matrix describing the evolution of a population on the fitness landscape when mutation is weak. In addition, the eigendecomposition of this transition matrix provides a new, high-level view of evolution on a fitness landscape. I demonstrate these techniques by visualizing the fitness landscape for selection for the amino acid serine and by visualizing a neutral network derived from the RNA secondary structure genotype-phenotype map.     

Genetic diversity and multilocus genetic structure in the relictual endemic herb<Emphasis Type="Italic"> Japonolirion osense</Emphasis> (Petrosaviaceae)

Plant clonality may greatly reduce effective population size and influence management strategies of rare and endangered species. We examined genetic diversity and the extent of clonality in four populations of the monotypic herbaceous perennial Japonolirion osense, which is one of the most rare flowering plants in Japan. Allozyme analysis revealed moderate levels of genetic variation, and the proportion of polymorphic loci (P=66.7%) was higher than the value for species with similar life-history traits. With four polymorphic loci, 19 multilocus genotypes were observed among 433 aerial shoot samples and 10 (52%) were found only in single populations. The proportion of distinguishable genotypes (PD=0.10) and Simpson's index of diversity (D=0.52) also exhibited moderate levels of genotypic diversity compared to other clonal plants, with genotype frequencies at Hardy-Weinberg equilibrium. The distributions of genotypes were often localized and they were mostly found within a radius of 5 m. Spatial autocorrelation analysis showed that shoot samples located 4 m apart were expected to be genetically independent. The results suggest that the spatial extent of genets was relatively narrow and thus the clonality was not extensive.     

Dynamics of a transferrin polymorphism in a population of Sylvilagus nuttallii

Summary Frequencies of three codominant alleles at the transferrin (Tf) locus and four of the six possible genotypes in a population of Nuttall's cottontails Sylvilagus nuttallii on an 87-ha study area in central Oregon were determined for parental stocks, trappable offspring, and over-winter survivors in 1974 and 1975. One rare allele disappeared during winter 1974–75 and did not reappear during the study. The Tf genotype frequency shifted in favor of Tf-BB between parents and offspring in 1974, remained stable over winter, shifted in favor of Tf-BC (to near the original frequency) between parents and offspring in 1975 and remained stable over winter. Allele and genotype frequencies were significantly different between 1974 and 1975 offspring; differences in frequencies between other samples were not significant because of the small number of cottontails that survived to spring each year. We were unable to discount the possibility of non-random breeding being responsible for observed differences, but, because survival of juveniles was related to moisture available for plant growth (and presumably to the moisture content in forage) during the cottontail breeding season and because frequencies of Tf genotypes of the four litters produced each year seemed related to available moisture, we postulated that precipitation was the selective force responsible for shifts in allele and genotype frequencies. Although we were unable to ascertain the probability that the polymorphism was balanced, the stochastic precipitation pattern seemed adequate to prevent fixation of an allele by selection if the selective mechanism was as postulated.     

Two-locus,fourth-order gene frequency moments: Implications for the variance of squared linkage disequilibrium and the variance of homozygosity

Identity coefficients are used to construct a sufficient set of equations to determine the fourth-order moments of gene frequencies for two linked loci. This allows the variance of the expected squared linkage disequilibrium to be found. It is shown that the coefficient of variation is generally greater than one and if the mutation rate is small, the standard deviation is more than four times the size of the mean. This demonstrates that squared linkage disequilibrium is a highly variable quantity. The variance of homozygosity for a gene which consists of two sites can also be obtained. Recombination between these sites increases the variance of homozygosity, suggesting that intragenic recombination significantly changes all the expected moments of gene frequencies if 4Nμ > 1.0 and r > μ (where N is the population size, μ is the mutation rate of the gene to neutral alleles, and r is the recombination rate between two sites within the gene).     

Genomic instability in mammalian cell hybrids. IV. Is mutation frequency elevated in hybrid cells?

In this study, we set out to determine whether the mutation frequency in cell hybrids is increased over the frequencies in the two parental lines, and whether this increase is related to the evolutionary divergence of the cell parents. Two test loci were chosen: forward mutation at the HPRT locus and mutation to resistance to the drug emetine. We conclude that while some cell combinations do seem to produce hybrids with higher mutation frequencies, this is not consistently so, and, indeed, mutation rates in hybrids may be higher, lower or very similar to rates in the parental lines. Further, evolutionary divergence between the parental lines does not appear to correlate to mutation frequency in the hybrids.     

Simon-Ando decomposability and fitness landscapes

In this paper, we investigate fitness landscapes (under point mutation and recombination) from the standpoint of whether the induced evolutionary dynamics have a “fast-slow” time scale associated with the differences in relaxation time between local quasi-equilibria and the global equilibrium. This dynamical hevavior has been formally described in the econometrics literature in terms of the spectral properties of the appropriate operator matrices by Simon and Ando (Econometrica 29 (1961) 111), and we use the relations they derive to ask which fitness functions and mutation/recombination operators satisfy these properties. It turns out that quite a wide range of landscapes satisfy the condition (at least trivially) under point mutation given a sufficiently low mutation rate, while the property appears to be difficult to satisfy under genetic recombination. In spite of the fact that Simon-Ando decomposability can be realized over fairly wide range of parameters, it imposes a number of restriction on which landscape partitionings are possible. For these reasons, the Simon-Ando formalism does not appear to be applicable to other forms of decomposition and aggregation of variables that are important in evolutionary systems.     

SNP genotyping for detecting the ‘rare allele phenomenon’ in hybrid zones

Hybrid zones are regions where genetically distinct populations meet, mate and produce offspring. In such zones, genetically less compatible gene combinations are usually generated, resulting in reduced fitness, and hybrid zones are often maintained because of continuous removal of unfit genotypes, balanced by gene flow into the zone from the parental populations (and are then referred to as ‘tension zones’). Tension zones often display unexpectedly high frequencies of gene variants that are rare outside the zone. Previous work has shown that this ‘rare allele phenomenon’ is not the result of intragenic recombination or increased mutation rates. Further understanding of the population genetics of the phenomenon requires an approach in which both the numbers of individuals and the numbers of loci is increased. Here, we report an approach using a combination of Illumina next‐generation sequencing and mass spectrophotometer genotyping to identify markers that may be used for genome‐wide investigations of the rare allele phenomenon. We test this approach on a hybrid zone in the land snail Albinaria hippolyti from Greece.     

Rapid evolutionary escape by large populations from local fitness peaks is likely in nature

Fitness interactions between loci in the genome, or epistasis, can result in mutations that are individually deleterious but jointly beneficial. Such epistasis gives rise to multiple peaks on the genotypic fitness landscape. The problem of evolutionary escape from such local peaks has been a central problem of evolutionary genetics for at least 75 years. Much attention has focused on models of small populations, in which the sequential fixation of valley genotypes carrying individually deleterious mutations operates most quickly owing to genetic drift. However, valley genotypes can also be subject to mutation while transiently segregating, giving rise to copies of the high fitness escape genotype carrying the jointly beneficial mutations. In the absence of genetic recombination, these mutations may then fix simultaneously. The time for this process declines sharply with increasing population size, and it eventually comes to dominate evolutionary behavior. Here we develop an analytic expression for N(crit), the critical population size that defines the boundary between these regimes, which shows that both are likely to operate in nature. Frequent recombination may disrupt high-fitness escape genotypes produced in populations larger than N(crit) before they reach fixation, defining a third regime whose rate again slows with increasing population size. We develop a novel expression for this critical recombination rate, which shows that in large populations the simultaneous fixation of mutations that are beneficial only jointly is unlikely to be disrupted by genetic recombination if their map distance is on the order of the size of single genes. Thus, counterintuitively, mass selection alone offers a biologically realistic resolution to the problem of evolutionary escape from local fitness peaks in natural populations.     

Negative frequency-dependent selection and asymmetrical transformation stabilise multi-strain bacterial population structures

Streptococcus pneumoniae can be divided into many strains, each a distinct set of isolates sharing similar core and accessory genomes, which co-circulate within the same hosts. Previous analyses suggested the short-term vaccine-associated dynamics of S. pneumoniae strains may be mediated through multi-locus negative frequency-dependent selection (NFDS), which maintains accessory loci at equilibrium frequencies. Long-term simulations demonstrated NFDS stabilised clonally-evolving multi-strain populations through preventing the loss of variation through drift, based on polymorphism frequencies, pairwise genetic distances and phylogenies. However, allowing symmetrical recombination between isolates evolving under multi-locus NFDS generated unstructured populations of diverse genotypes. Replication of the observed data improved when multi-locus NFDS was combined with recombination that was instead asymmetrical, favouring deletion of accessory loci over insertion. This combination separated populations into strains through outbreeding depression, resulting from recombinants with reduced accessory genomes having lower fitness than their parental genotypes. Although simplistic modelling of recombination likely limited these simulations’ ability to maintain some properties of genomic data as accurately as those lacking recombination, the combination of asymmetrical recombination and multi-locus NFDS could restore multi-strain population structures from randomised initial populations. As many bacteria inhibit insertions into their chromosomes, this combination may commonly underlie the co-existence of strains within a niche.Subject terms: Population genetics, Microbial ecology, Microbial genetics, Bacterial genetics, Phylogenetics     

Microsatellite DNA markers: evaluating their potential for estimating the proportion of hatchery-reared offspring in a stock enhancement programme

We describe a statistical method for estimating the effectiveness of a stock enhancement programme using nuclear DNA loci. It is based on knowing the population allele frequencies and the genotypes of the hatchery parents (mother only, or mother and father), and on determining the probability that a wild-born animal will by chance have a genotype consistent with hatchery origin. We show how to estimate the proportion of released animals in the wild population, and its standard error. The method is applied to a data set of eight microsatellite loci in brown tiger prawns (Penaeus esculentus), prior to the start of a possible enhancement programme. We conclude that, for this particular data set, the effectiveness of such an enhancement programme could be quantified accurately if both maternal and paternal genotypes are known, but not if maternal genotypes only are known. Full paternal genotyping would require offspring genotyping and thus would be expensive, but a partly typed paternal genotype from a mass homogenate of offspring would be almost as effective and much cheaper. The experiment would become feasible based on maternal genotypes alone, if a further three typical microsatellite loci could be found to add to the existing panel of eight. The methods detailed should be of interest to any enhancement project that relies on nuclear DNA markers to provide tags.     

Why sampling scheme matters: the effect of sampling scheme on landscape genetic results

There has been a recent trend in genetic studies of wild populations where researchers have changed their sampling schemes from sampling pre-defined populations to sampling individuals uniformly across landscapes. This reflects the fact that many species under study are continuously distributed rather than clumped into obvious “populations”. Once individual samples are collected, many landscape genetic studies use clustering algorithms and multilocus genetic data to group samples into subpopulations. After clusters are derived, landscape features that may be acting as barriers are examined and described. In theory, if populations were evenly sampled, this course of action should reliably identify population structure. However, genetic gradients and irregularly collected samples may impact the composition and location of clusters. We built genetic models where individual genotypes were either randomly distributed across a landscape or contained gradients created by neighbor mating for multiple generations. We investigated the influence of six different sampling protocols on population clustering using program STRUCTURE, the most commonly used model-based clustering method for multilocus genotype data. For models where individuals (and their alleles) were randomly distributed across a landscape, STRUCTURE correctly predicted that only one population was being sampled. However, when gradients created by neighbor mating existed, STRUCTURE detected multiple, but different numbers of clusters, depending on sampling protocols. We recommend testing for fine scale autocorrelation patterns prior to sample clustering, as the scale of the autocorrelation appears to influence the results. Further, we recommend that researchers pay attention to the impacts that sampling may have on subsequent population and landscape genetic results. The U.S. Government's right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Natural selection of UDP genotypes in an experimental population of Lolium perenne (Poaceae)

The mating system determines the range of genotypes on which selection will act. Ultimately, the population will contain only those genotypes that can survive in the current environment. This study was conducted to determine the extent to which selection affects genotype at four enzyme loci in Lolium perenne. Starch gel electrophoresis was used to determine genotype at the phosphoglucomutase, 6-phosphogluconate dehydrogenase, phosphoglucose isomerase, and UDP-glucose pyrophosphorylase loci. Genotypes of progeny arrays were used to infer maternal genotype in a field-grown population of plants. A mating system analysis was performed on maternal and progeny plants of the field population and also on a population of plants, from the same seed stock, grown in a greenhouse environment. Allelic frequencies differed among populations at the Udp locus. Results indicate that high mortality in the field strongly favored one allele. Assumptions of the mating system model are examined and used to interpret the observed differentiation among populations.     

Genetic and morphological variation over space and time in the invasive fire ant <Emphasis Type="Italic">Solenopsis invicta</Emphasis>

Social insects are among the most successful and damaging of invasive taxa. We studied spatial and temporal variation in two traits, colony genetic structure and worker mass, associated with social insect success in the introduced fire ant Solenopsis invicta. Our aim was to determine if changes in social structure occurred over time and if variation in worker size was related to worker genotype. We sampled 1139 workers from five multiple-queen S. invicta nests on six dates over a one-year period. The genotypes of workers were determined at ten microsatellite loci and at the selected locus general protein-9 (Gp-9). We found little evidence for genetic differentiation of workers sampled from distinct nests or from different dates at the microsatellite loci. However, worker Gp-9 genotype frequencies varied among nests and over time. In addition, worker mass was affected by nest-of-origin, sampling date, ploidy level, and Gp-9 genotype. Our results suggest that large numbers of queens contribute to the production of workers in introduced S. invicta nests throughout the year. Colony boundaries are semi-permeable, although the among-nest variation in Gp-9 genotype frequencies and worker mass does suggest that boundaries are present. In addition, selection operating on Gp-9 genotype depends on nest environment. Finally, worker mass is affected by both endogenous and exogenous factors in S. invicta. Overall, our data suggests that the key traits of colony social structure and worker size reflect the effects of variable selection in invasive social insects.     

Is the between-population variance negligible in the total variance of heterozygosity? Case of a finite number of loci subject to the infinite-allele model in finite monoecious populations

The decomposition of the variance of the average heterozygosity into variances between and within populations is studied in the general case of a finite number of loci. These loci are assumed randomly distributed over chromosome pairs having a non-interference recombination scheme, and independently subject to mutation according to the infinite-allele model. The equilibrium behavior of that decomposition is discussed in the monoecious mating case with regard to each parameter of the model: mutation rate per gene per generation (u), population size (N), number of loci (n), map length of chomosome pairs (L). It is shown that the proportion Q of the between-population variability in the total variance of the average heterozygosity is decreasing as either the mean heterozygosity (θ = 4Nu/(1 + 4Nu)) or the mean number of mutations per gamete per generation (v = nu) is increasing. Moreover, even if Q is always smaller than for this model, it is not negligible unless θ is close to one or v is much larger than one for L long enough.