Impact of small fitness costs on pest adaptation to crop varieties with multiple toxins: a heuristic model

A deterministic two-locus model was used to examine how small fitness costs to individuals carrying resistance alleles could impact the risk of panmictic insect pest populations adapting to crop varieties that produced two distinct toxins. Parameters examined were (1) level of toxicity of each toxin, (2) initial frequencies of alleles for adaptation to the toxins, (3) percentage of population feeding on nontoxic plants, and (4) level of fitness cost associated with adaptation to each of the two toxins. Resistance to each toxin was assumed to be biochemically independent, controlled by a resistance coding allele at a single locus, and inherited as a partially recessive trait in the field. When plants are extremely toxic to the pest, effective refuge size is 10%, and there is a fitness cost to resistance alleles only when in homozygous form (5%), the pest population is never predicted to adapt to either toxin as long as the initial frequencies of the resistance alleles are below 0.05. Even if the initial frequency of the allele for adapting to one toxin is 0.95 when a two-toxin cultivar completely replaces a one-toxin cultivar, the model predicts that a low equilibrium allelic frequency will develop for both resistance alleles, as long as the frequency of the allele for adapting to the second toxin is initially 0.001 or less. If cultivars with one and two toxins are planted, the model predicts that resistance will develop. Nonrandom mating and stochastic variation within subpopulations also could lead to evolution of resistance.     

The effect of linkage and population size on inbreeding depression due to mutational load.

Using a stochastic model of a finite population in which there is mutation to partially recessive detrimental alleles at many loci, we study the effects of population size and linkage between the loci on the population mean fitness and inbreeding depression values. Although linkage between the selected loci decreases the amount of inbreeding depression, neither population size nor recombination rate have strong effects on these quantities, unless extremely small values are assumed. We also investigate how partial linkage between the loci that determine fitness affects the invasion of populations by alleles at a modifier locus that controls the selfing rate. In most of the cases studied, the direction of selection on modifiers was consistent with that found in our previous deterministic calculations. However, there was some evidence that linkage between the modifier locus and the selected loci makes outcrossing less likely to evolve; more losses of alleles promoting outcrossing occurred in runs with linkage than in runs with free recombination. We also studied the fate of neutral alleles introduced into populations carrying detrimental mutations. The times to loss of neutral alleles introduced at low frequency were shorter than those predicted for alleles in the absence of selected loci, taking into account the reduction of the effective population size due to inbreeding. Previous studies have been confined to outbreeding populations, and to alleles at frequencies close to one-half, and have found an effect in the opposite direction. It therefore appears that associations between neutral and selected loci may produce effects that differ according to the initial frequencies of the neutral alleles.     

Allee effects, immigration, and the evolution of species' niches

Theoretical studies of adaptation to sink environments (with conditions outside the niche requirements of a species) have shown that immigration from source habitats can either facilitate or inhibit local adaptation. Here, we examine the influence of immigration on the evolution of local adaptation, given an Allee effect (i.e., at low densities, absolute fitness increases with population density). We consider a deterministic model for evolution at a haploid locus, and a stochastic individual-based model for evolution of a quantitative trait, and several kinds of Allee effects. We demonstrate that increased immigration can greatly facilitate adaptive evolution in the sink; with greater immigration, local population sizes rise, and because of the Allee effect, there is a positive indirect effect of immigration on local fitness. This makes it easier for alleles of modest effect to be captured by natural selection, transforming the sink into a locally adapted population that can persist without immigration.     

Continuous selective models with mutation and migration

The continuous selective model formulated previously for a single locus with multiple alleles in a monoecious population is extended to include mutation and migration. Somatic and germ line genotypic frequencies are distinguished, and the alternative hypotheses of constant mutation rates and age-independent mutation frequencies are analyzed in detail for arbitrary selection and mating schemes. With any mating pattern, if there is no selection, the equilibrium allelic frequencies are shown to be unaffected by the generalizations introduced in this paper. If, in addition, mating is at random, the equilibrium genotypic frequencies are proved to be in Hardy-Weinberg proportions. For both models, the nature of the approach to equilibrium is discussed. Migration is treated in the island model.     

A gene's eye view of epistasis,selection and speciation

In this mini‐review, I discuss the effects of gene interaction or epistasis from a `gene's eye view.' By a `gene's eye view' of epistasis, I mean that I will consider a single, bi‐allelic locus, A , whose effects on fitness result only from its interactions with alleles of another, unknown locus, X . I will show how changes in the frequencies of alleles at the background locus affect the relationship of alleles at the A ‐locus to fitness. Changing the genetic background changes the fundamental characteristics of the A ‐locus, such as the magnitude and sign of allelic effects on fitness, and, consequently, it changes the strength and pattern of selection. I consider each of the four kinds of pair–wise interactions between two loci and show that some kinds of epistasis are more sensitive than others to population genetic subdivision. Lastly, I show that some kinds of epistasis are more likely than others to affect the process of speciation and contribute to or be responsible for general genetic features of interspecific hybrids, such as Haldane's rule.     

Allele multiplicity in simple Mendelian disorders.

A model of selection involving two selectively equivalent classes of alleles at a locus is considered. One class consists of normal alleles A1, A2, A3,. . .; the other class consists of detrimental alleles a1, a2, a3, . . . . Mutation within and between allelic classes can occur without restriction, but selection operates in such a way as to maintain an approximately constant overall frequency of A-type and a-type alleles is derived, and it is shown that the distribution of allele frequencies in a sample of detrimental alleles depends on the forward (A to a) mutation rate but not on the selection coefficient, degree of dominance, or mutation rate among a-type alleles. Recurrent mutation therefore generates allelic multiplicity among detrimental alleles, and this is discussed in the context of clinical heterogeneity in simple Mendelian disorders.     

Frequency and fitness cost of resistance to Bacillus thuringiensis in Chrysomela tremulae (Coleoptera: Chrysomelidae)

The "high dose-refuge" (HDR) strategy is commonly recommended and currently used for delaying or preventing pest adaptation to transgenic plants producing Bacillus thuringiensis (Bt) toxins. The efficiency of this strategy depends, among other factors, on the initial frequency of Bt resistance alleles and on the fitness costs associated with these alleles. Two years ago, an allele conferring resistance to Bt poplar was detected in a French population of the poplar pest Chrysomela tremulae F. Although this pest had never been subjected to Bt selection pressure due to human activities, the frequency of this allele was estimated at 0.0037, with a 95% credible (CI) interval of 0.00045-0.0080. We investigated the frequency of this allele in a second sample of C. tremulae collected more than 500 km from the site of the initial population. The estimated frequency in this sample was 0.0113 (95% CI 0.0031-0.0247), reinforcing the conclusion that resistance to Bt plants may be present at detectable frequencies in pest populations before selection resulting from pest management by humans. The frequency of the Bt resistance allele over the two samples was 0.0049 (95% CI 0.0020-0.0091). We also followed five laboratory lines in which the frequency of this allele was initially fixed at 0.500. After five generations maintained on non-Bt poplar leaves, the frequency of this allele decreased in all lines, whereas allelic frequencies at a neutral locus were unaffected. Thus, the Bt resistance allele detected in French populations of C. tremulae is probably associated with a fitness cost.     

Insect oviposition behavior affects the evolution of adaptation to <Emphasis Type="Italic">Bt</Emphasis> crops: consequences for refuge policies

The major lepidopteran insect pests of cotton and maize harbor intra-specific variation for behavior determining the selection of host plants for oviposition. Yet, the consequences of behavioral adaptation for fitness have neither been modeled nor monitored for Bt cotton and maize crops, the most widely grown transgenic herbivore-resistant plants. Here, we present a general two-locus heuristic model to examine potential outcomes of natural selection when pest populations initially have low frequencies of alleles for both physiological and behavioral adaptation to Bt crops. We demonstrate that certain ecological conditions allow for the evolution of behavioral choices favoring alternative oviposition hosts that limit the increase in resistance alleles, even when they are phenotypically dominant. These results have implications for current refuge policies, which should be adapted to promote the evolution of certain behavioral choices for alternative oviposition hosts in addition to dilution of physiological resistance alleles. Collection of data on oviposition host preference as a component of monitoring schemes will provide important insights into mechanisms underlying the durability of Bt-transgenic host-plant resistance.     

The effect of selection on esterase allozymes in a barley population

Changes in gene and genotypic frequencies at four esterase loci were monitored over 25 generations in Composite Cross V, an experimental population of barley, to obtain experimental evidence concerning the balance of forces responsible for: (1) the marked differences in allelic frequencies among barleys from different ecogeographical regions of the world; and (2) the extensive allelic variation found within local populations of barley. Analyses of the highly significant changes in allelic frequencies which occurred in CCV showed they were due to directional selection favoring particular alleles and not to mutation, migration or genetic drift. The results show that intense balancing selection, featuring consistent excesses of heterozygotes, also occurred in CCV. It is concluded that among the factors of neo-Darwinian evolution, natural selection plays the predominant role in determining the observed patterns of allelic variation in the barley species as a whole.     

The diffusion model for migration and selection in a plant population

 The diffusion approximation is derived for migration and selection at a multiallelic locus in a partially selfing plant population subdivided into a lattice of colonies. Generations are discrete and nonoverlapping; both pollen and seeds disperse. In the diffusion limit, the genotypic frequencies at each point are those determined at equilibrium by the local rate of selfing and allelic frequencies. If the drift and diffusion coefficients are taken as the appropriate linear combination of the corresponding coefficients for pollen and seeds, then the migration terms in the partial differential equation for the allelic frequencies have the standard form for a monoecious animal population. The selection term describes selection on the local genotypic frequencies. The boundary conditions and the unidimensional transition conditions for a geographical barrier and for coincident discontinuities in the carrying capacity and migration rate have the standard form. In the diallelic case, reparametrization renders the entire theory of clines and of the wave of advance of favorable alleles directly applicable to plant populations. Received 30 August 1995; received in revised form 23 February 1996     

Exon 1 Polymorphisms in the Equine CSN3 Gene: SNPs Distribution Analysis in Murgese Horse Breed

The aim of this study was to assess genetic polymorphism at two loci in the exon 1 of the CSN3 gene in Murgese horse breed by PCR-RFLP analysis. The overall frequencies of alleles A and G at c.-66A > G locus were 0.80 and 0.20, respectively, and no GG animals were found in the population. At the c.-36C > A locus allelic frequencies were 0.74 and 0.26 for allele C and A, respectively, and no AA animals were detected. Population genetic indexes, namely gene heterozygosity, gene homozygosity, effective allele numbers, fixation index, and polymorphism information index were calculated. Combined genotypic frequencies and possible haplotypes frequencies were also reported. Only three out of nine possible genotypic combinations were found in the studied population. The most frequent genotype was AACC (0.49) while the frequency of AGCA was 0.40. Only five animals were genotyped as AACA (11%). Consequently, the most frequent haplotype in the population was AC (0.744), followed by GA (0.200) and AA (0.056).     

The Evolution of One- and Two-Locus Systems

Assuming age-independent fertilities and mortalities and random mating, continuous-time models for a monoecious population are investigated for weak selection. A single locus with multiple alleles and two alleles at each of two loci are considered. A slow-selection analysis of diallelic and multiallelic two-locus models with discrete nonoverlapping generations is also presented. The selective differences may be functions of genotypic frequencies, but their rate of change due to their explicit dependence on time (if any) must be at most of the second order in s, (i.e., O( s²)), where s is the intensity of natural selection. Then, after several generations have elapsed, in the continuous time models the time-derivative of the deviations from Hardy-Weinberg proportions is of O(s²), and in the two-locus models the rate of change of the linkage disequilibrium is of O(s²). It follows that, if the rate of change of the genotypic fitnesses is smaller than second order in s (i.e., o(s²)), then to O(s²) the rate of change of the mean fitness of the population is equal to the genic variance. For a fixed value of s, however, no matter how small, the genic variance may occasionally be smaller in absolute value than the (possibly negative) lower order terms in the change in fitness, and hence the mean fitness may decrease. This happens if the allelic frequencies are changing extremely slowly, and hence occurs often very close to equilibrium. Some new expressions are derived for the change in mean fitness. It is shown that, with an error of O( s), the genotypic frequencies evolve as if the population were in Hardy-Weinberg proportions and linkage equilibrium. Thus, at least for the deterministic behavior of one and two loci, deviations from random combination appear to have very little evolutionary significance.     

Between migration load and evolutionary rescue: dispersal,adaptation and the response of spatially structured populations to environmental change

The evolutionary potential of populations is mainly determined by population size and available genetic variance. However, the adaptability of spatially structured populations may also be affected by dispersal: positively by spreading beneficial mutations across sub-populations, but negatively by moving locally adapted alleles between demes. We develop an individual-based, two-patch, allelic model to investigate the balance between these opposing effects on a population''s evolutionary response to rapid climate change. Individual fitness is controlled by two polygenic traits coding for local adaptation either to the environment or to climate. Under conditions of selection that favour the evolution of a generalist phenotype (i.e. weak divergent selection between patches) dispersal has an overall positive effect on the persistence of the population. However, when selection favours locally adapted specialists, the beneficial effects of dispersal outweigh the associated increase in maladaptation for a narrow range of parameter space only (intermediate selection strength and low linkage among loci), where the spread of beneficial climate alleles is not strongly hampered by selection against non-specialists. Given that local selection across heterogeneous and fragmented landscapes is common, the complex effect of dispersal that we describe will play an important role in determining the evolutionary dynamics of many species under rapidly changing climate.     

Exon 1 polymorphisms in the equine CSN3 gene: SNPs distribution analysis in Murgese horse breed

The aim of this study was to assess genetic polymorphism at two loci in the exon 1 of the CSN3 gene in Murgese horse breed by PCR-RFLP analysis. The overall frequencies of alleles A and G at c.-66A?>?G locus were 0.80 and 0.20, respectively, and no GG animals were found in the population. At the c.-36C?>?A locus allelic frequencies were 0.74 and 0.26 for allele C and A, respectively, and no AA animals were detected. Population genetic indexes, namely gene heterozygosity, gene homozygosity, effective allele numbers, fixation index, and polymorphism information index were calculated. Combined genotypic frequencies and possible haplotypes frequencies were also reported. Only three out of nine possible genotypic combinations were found in the studied population. The most frequent genotype was AACC (0.49) while the frequency of AGCA was 0.40. Only five animals were genotyped as AACA (11%). Consequently, the most frequent haplotype in the population was AC (0.744), followed by GA (0.200) and AA (0.056).     

Evolutionary consequences of asymmetric dispersal rates

We study the consequences of asymmetric dispersal rates (e.g., due to wind or current) for adaptive evolution in a system of two habitat patches. Asymmetric dispersal rates can lead to overcrowding of the "downstream" habitat, resulting in a source-sink population structure in the absence of intrinsic quality differences between habitats or can even cause an intrinsically better habitat to function as a sink. Source-sink population structure due to asymmetric dispersal rates has similar consequences for adaptive evolution as a source-sink structure due to habitat quality differences: natural selection tends to be biased toward the source habitat. We demonstrate this for two models of adaptive evolution: invasion of a rare allele that improves fitness in one habitat but reduces it in the other and antagonistic selection on a quantitative trait determined by five additive loci. If a habitat can sustain a population without immigration, the conditions for adaptation to that habitat are most favorable if there is little or no immigration from the other habitat; the influence of emigration depends on the magnitude of the allelic effects involved and other parameters. If, however, the population is initially unable to persist in a given habitat without immigration, our model predicts that the population will be most likely to adapt to that habitat if the dispersal rates in both directions are high. Our results highlight the general message that the effect of gene flow upon local adaptation should depend profoundly on the demographic context of selection.     

Correlation of DNA fragment sizes within loci in the presence of non-detectable alleles

At present most forensic databases of DNA profiling of individuals consist of DNA fragment sizes measured from Southern blot restriction fragment length polymorphism (RFLP) analysis. Statistical studies of these databases have revealed that, when fragment sizes are measured from RFLP analysis, some of the single-band patterns of individuals may actually be due to heterozygosity of alleles in which fragment size resulting from one allele remains undetected. In this work, we evaluate the effect of such allelic non-detectability on correlation of fragment sizes within individuals at a locus, and its impact on the inference of independence of fragment sizes within loci. We show that when non-detectable alleles are present in a population at a locus, positive correlations of fragment sizes are expected, which increase with the proportion of non-detectable alleles at the locus. Therefore, a non-zero positive correlation is not a proof of allelic dependence within individuals. Applications of this theory to the current forensic RFLP databases within the US show that there is virtually no evidence of significant allelic dependence within any of the loci. Therefore, the assumption that DNA fragment sizes within loci are independent is valid, and hence, the population genetic principles of computing DNA profile frequencies by multiplying binned frequencies of fragment sizes are most likely to be appropriate for forensic applications of DNA typing data.Editor's commentsThe presence of non-detectable alleles for VNTR loci has plagued the use of these highly-discriminating systems in human identification. The authors take explicit account of these alleles, and are able to show independence of the frequencies of detectable alleles. They raise the troubling issue of how to account for occasional significant results when multiple tests are performed. By invoking Bonferroni corrections, they regard all tests, even those performed on different loci, as addressing the same hypothesis—the absence of dependence at any VNTR locus.     

The generation and maintenance of genetic variation by frequency-dependent selection: constructing polymorphisms under the pairwise interaction model

Frequency-dependent selection remains the most commonly invoked heuristic explanation for the maintenance of genetic variation. For polymorphism to exist, new alleles must be both generated and maintained in the population. Here we use a construction approach to model frequency-dependent selection with mutation under the pairwise interaction model. The pairwise interaction model is a general model of frequency-dependent selection at the genotypic level. We find that frequency-dependent selection is able to generate a large number of alleles at a single locus. The construction process generates multiallelic polymorphisms with a wide range of allele-frequency distributions and genotypic fitness relationships. Levels of polymorphism and mean fitness are uncoupled, so constructed polymorphisms remain permanently invasible to new mutants; thus the model never settles down to an equilibrium state. Analysis of constructed fitness sets reveals signatures of heterozygote advantage and positive frequency dependence.     

Unequal allelic frequencies at the self‐incompatibility locus within local populations of Prunus avium L.: an effect of population structure?

In this paper, we investigated the genetic structure and distribution of allelic frequencies at the gametophytic self-incompatibility locus in three populations of Prunus avium L. In line with theoretical predictions under balancing selection, genetic structure at the self-incompatibility locus was almost three times lower than at seven unlinked microsatellites. Furthermore, we found that S-allele frequencies in wild cherry populations departed significantly from the expected isoplethic distribution towards which balancing selection is expected to drive allelic frequencies (i.e. identical frequency equal to the inverse of the number of alleles in the population). To assess whether this departure could be caused either by drift alone or by population structure, we used numerical simulations to compare our observations with allelic frequency distributions expected : (1) within a single deme from a subdivided population with various levels of differentiation; and (2) within a finite panmictic population with identical allelic diversity. We also investigated the effects of sample size and degree of population structure on tests of departure from isoplethic equilibrium. Overall, our results showed that the observed allele frequency distributions were consistent with a model of subdivided population with demes linked by moderate migration rate.     

Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape

The emergence and persistence of polymorphism within populations generally requires specific regimes of natural or sexual selection. Here, we develop a unified theoretical framework to explore how polymorphism at targeted loci can be generated and maintained by either disassortative mating choice or balancing selection due to, for example, heterozygote advantage. To this aim, we model the dynamics of alleles at a single locus A in a population of haploid individuals, where reproductive success depends on the combination of alleles carried by the parents at locus A. Our theoretical study of the model confirms that the conditions for the persistence of a given level of allelic polymorphism depend on the relative reproductive advantages among pairs of individuals. Interestingly, equilibria with unbalanced allelic frequencies were shown to emerge from successive introduction of mutants. We then investigate the role of the function linking allelic divergence to reproductive advantage on the evolutionary fate of alleles within the population. Our results highlight the significance of the shape of this function for both the number of alleles maintained and their level of genetic divergence. Large number of alleles are maintained with substantial replacement of alleles, when disassortative advantage slowly increases with allelic differentiation . In contrast, few highly differentiated alleles are predicted to be maintained when genetic differentiation has a strong effect on disassortative advantage. These opposite effects predicted by our model explain how disassortative mate choice may lead to various levels of allelic differentiation and polymorphism, and shed light on the effect of mate preferences on the persistence of balanced and unbalanced polymorphism in natural population.