Evolution in heterogeneous populations: from migration models to fixation probabilities.

Although dispersal is recognized as a key issue in several fields of population biology (such as behavioral ecology, population genetics, metapopulation dynamics or evolutionary modeling), these disciplines focus on different aspects of the concept and often make different implicit assumptions regarding migration models. Using simulations, we investigate how such assumptions translate into effective gene flow and fixation probability of selected alleles. Assumptions regarding migration type (e.g. source-sink, resident pre-emption, or balanced dispersal) and patterns (e.g. stepping-stone versus island dispersal) have large impacts when demes differ in sizes or selective pressures. The effects of fragmentation, as well as the spatial localization of newly arising mutations, also strongly depend on migration type and patterns. Migration rate also matters: depending on the migration type, fixation probabilities at an intermediate migration rate may lie outside the range defined by the low- and high-migration limits when demes differ in sizes. Given the extreme sensitivity of fixation probability to characteristics of dispersal, we underline the importance of making explicit (and documenting empirically) the crucial ecological/ behavioral assumptions underlying migration models.

The fixation of locally beneficial alleles in a metapopulation.

Extinction, recolonization, and local adaptation are common in natural spatially structured populations. Understanding their effect upon genetic variation is important for systems such as genetically modified organism management or avoidance of drug resistance. Theoretical studies on the effect of extinction and recolonization upon genetic variance started appearing in the 1970s, but the role of local adaptation still has no good theoretical basis. Here we develop a model of a haploid species in a metapopulation in which a locally adapted beneficial allele is introduced. We study the effect of different spatial patterns of local adaptation, and different metapopulation dynamics, upon the fixation probability of the beneficial allele. Controlling for the average selection pressure, we find that a small area of positive selection can significantly increase the global probability of fixation. However, local adaptation becomes less important as extinction rate increases. Deme extinction and recolonization have a spatial smoothing effect that effectively reduces spatial variation in fitness.

A metapopulation model for the introgression from genetically modified plants into their wild relatives

Most models on introgression from genetically modified (GM) plants have focused on small spatial scales, modelling gene flow from a field containing GM plants into a single adjacent population of a wild relative. Here, we present a model to study the effect of introgression from multiple plantations into the whole metapopulation of the wild relative. The most important result of the model is that even very low levels of introgression and selection can lead to a high probability that the transgene goes to fixation in the metapopulation. Furthermore, the overall frequency of the transgene in the metapopulation, after a certain number of generations of introgression, depends on the population dynamics. If there is a high rate of migration or a high rate of population turnover, the overall transgene frequency is much higher than with lower rates. However, under an island model of population structure, this increased frequency has only a very small effect on the probability of fixation of the transgene. Considering these results, studies on the potential ecological risks of introgression from GM plants should look not only at the rate of introgression and selection acting on the transgene, but also at the metapopulation dynamics of the wild relative.

Rates of cultural change and patterns of cultural accumulation in stochastic models of social transmission.

Cultural variation in a population is affected by the rate of occurrence of cultural innovations, whether such innovations are preferred or eschewed, how they are transmitted between individuals in the population, and the size of the population. An innovation, such as a modification in an attribute of a handaxe, may be lost or may become a property of all handaxes, which we call "fixation of the innovation." Alternatively, several innovations may attain appreciable frequencies, in which case properties of the frequency distribution-for example, of handaxe measurements-is important. Here we apply the Moran model from the stochastic theory of population genetics to study the evolution of cultural innovations. We obtain the probability that an initially rare innovation becomes fixed, and the expected time this takes. When variation in cultural traits is due to recurrent innovation, copy error, and sampling from generation to generation, we describe properties of this variation, such as the level of heterogeneity expected in the population. For all of these, we determine the effect of the mode of social transmission: conformist, where there is a tendency for each naïve newborn to copy the most popular variant; pro-novelty bias, where the newborn prefers a specific variant if it exists among those it samples; one-to-many transmission, where the variant one individual carries is copied by all newborns while that individual remains alive. We compare our findings with those predicted by prevailing theories for rates of cultural change and the distribution of cultural variation.

Étude de quelques populations structurées : processus de coalescence et abondance d’une stratégie

Le fichiers qui accompagnent mon document ont été réalisés avec le logiciel Mathematica

Étude de quelques populations structurées : processus de coalescence et abondance d’une stratégie

Le fichiers qui accompagnent mon document ont été réalisés avec le logiciel Mathematica

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.

Perturbation expansions of multilocus fixation probabilities for frequency-dependent selection with applications to the Hill-Robertson effect and to the joint evolution of helping and punishment.

Natural populations are of finite size and organisms carry multilocus genotypes. There are, nevertheless, few results on multilocus models when both random genetic drift and natural selection affect the evolutionary dynamics. In this paper we describe a formalism to calculate systematic perturbation expansions of moments of allelic states around neutrality in populations of constant size. This allows us to evaluate multilocus fixation probabilities (long-term limits of the moments) under arbitrary strength of selection and gene action. We show that such fixation probabilities can be expressed in terms of selection coefficients weighted by mean first passages times of ancestral gene lineages within a single ancestor. These passage times extend the coalescence times that weight selection coefficients in one-locus perturbation formulas for fixation probabilities. We then apply these results to investigate the Hill-Robertson effect and the coevolution of helping and punishment. Finally, we discuss limitations and strengths of the perturbation approach. In particular, it provides accurate approximations for fixation probabilities for weak selection regimes only (Ns < or = 1), but it provides generally good prediction for the direction of selection under frequency-dependent selection.

Probabilité de fixation dans des modèles génétiques de populations à plusieurs allèles

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Probabilité et temps de fixation à l’aide de processus ancestraux

Ce mémoire analyse l’espérance du temps de fixation conditionnellement à ce qu’elle se produise et la probabilité de fixation d’un nouvel allèle mutant dans des populations soumises à différents phénomènes biologiques en uti- lisant l’approche des processus ancestraux. Tout d’abord, l’article de Tajima (1990) est analysé et les différentes preuves y étant manquantes ou incomplètes sont détaillées, dans le but de se familiariser avec les calculs du temps de fixa- tion. L’étude de cet article permet aussi de démontrer l’importance du temps de fixation sur certains phénomènes biologiques. Par la suite, l’effet de la sé- lection naturelle est introduit au modèle. L’article de Mano (2009) cite un ré- sultat intéressant quant à l’espérance du temps de fixation conditionnellement à ce que celle-ci survienne qui utilise une approximation par un processus de diffusion. Une nouvelle méthode utilisant le processus ancestral est présentée afin d’arriver à une bonne approximation de ce résultat. Des simulations sont faites afin de vérifier l’exactitude de la nouvelle approche. Finalement, un mo- dèle soumis à la conversion génique est analysé, puisque ce phénomène, en présence de biais, a un effet similaire à celui de la sélection. Nous obtenons finalement un résultat analytique pour la probabilité de fixation d’un nouveau mutant dans la population. Enfin, des simulations sont faites afin de détermi- nerlaprobabilitédefixationainsiqueletempsdefixationconditionnellorsque les taux sont trop grands pour pouvoir les calculer analytiquement.

Population-based design of mandibular fixation plates with bone quality and morphology considerations

In this paper we present a new population-based implant design methodology, which advances the state-of-the-art approaches by combining shape and bone quality information into the design strategy. The method may enhance the mechanical stability of the fixation and reduces the intra-operative in-plane bending which might impede the functionality of the locking mechanism. The computational method is presented for the case of mandibular locking fixation plates, where the mandibular angle and the bone quality at screw locations are taken into account. The method automatically derives the mandibular angle and the bone thickness and intensity values at the path of every screw from a set of computed tomography images. An optimization strategy is then used to optimize the two parameters of plate angle and screw position. The method was applied to two populations of different genders. Results for the new design are presented along with a comparison with a commercially available mandibular locking fixation plate (MODUS(®) TriLock(®) 2.0/2.3/2.5, Medartis AG, Basel, Switzerland). The proposed designs resulted in a statistically significant improvement in the available bone thickness when compared to the standard plate. There is a higher probability that the proposed implants cover areas of thicker cortical bone without compromising the bone mineral density around the screws. The obtained results allowed us to conclude that an angle and screw separation of 129° and 9 mm for females and 121° and 10 mm for males are more suitable designs than the commercially available 120° and 9 mm.

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.

Competition and fixation of cohorts of adaptive mutations under Fisher geometrical model

One of the simplest models of adaptation to a new environment is Fisher's Geometric Model (FGM), in which populations move on a multidimensional landscape defined by the traits under selection. The predictions of this model have been found to be consistent with current observations of patterns of fitness increase in experimentally evolved populations. Recent studies investigated the dynamics of allele frequency change along adaptation of microbes to simple laboratory conditions and unveiled a dramatic pattern of competition between cohorts of mutations, i.e., multiple mutations simultaneously segregating and ultimately reaching fixation. Here, using simulations, we study the dynamics of phenotypic and genetic change as asexual populations under clonal interference climb a Fisherian landscape, and ask about the conditions under which FGM can display the simultaneous increase and fixation of multiple mutations-mutation cohorts-along the adaptive walk. We find that FGM under clonal interference, and with varying levels of pleiotropy, can reproduce the experimentally observed competition between different cohorts of mutations, some of which have a high probability of fixation along the adaptive walk. Overall, our results show that the surprising dynamics of mutation cohorts recently observed during experimental adaptation of microbial populations can be expected under one of the oldest and simplest theoretical models of adaptation-FGM.

One Step Forward: Contrasting The Effects Of Toe Clipping And Pit Tagging On Frog Survival And Recapture Probability.

Amphibians have been declining worldwide and the comprehension of the threats that they face could be improved by using mark-recapture models to estimate vital rates of natural populations. Recently, the consequences of marking amphibians have been under discussion and the effects of toe clipping on survival are debatable, although it is still the most common technique for individually identifying amphibians. The passive integrated transponder (PIT tag) is an alternative technique, but comparisons among marking techniques in free-ranging populations are still lacking. We compared these two marking techniques using mark-recapture models to estimate apparent survival and recapture probability of a neotropical population of the blacksmith tree frog, Hypsiboas faber. We tested the effects of marking technique and number of toe pads removed while controlling for sex. Survival was similar among groups, although slightly decreased from individuals with one toe pad removed, to individuals with two and three toe pads removed, and finally to PIT-tagged individuals. No sex differences were detected. Recapture probability slightly increased with the number of toe pads removed and was the lowest for PIT-tagged individuals. Sex was an important predictor for recapture probability, with males being nearly five times more likely to be recaptured. Potential negative effects of both techniques may include reduced locomotion and high stress levels. We recommend the use of covariates in models to better understand the effects of marking techniques on frogs. Accounting for the effect of the technique on the results should be considered, because most techniques may reduce survival. Based on our results, but also on logistical and cost issues associated with PIT tagging, we suggest the use of toe clipping with anurans like the blacksmith tree frog.

Comparison Of Postoperative Stability Of Three Rigid Internal Fixation Techniques After Sagittal Split Ramus Osteotomy For Mandibular Advancement.

The aim of this investigation was to compare the skeletal stability of three different rigid fixation methods after mandibular advancement. Fifty-five class II malocclusion patients treated with the use of bilateral sagittal split ramus osteotomy and mandibular advancement were selected for this retrospective study. Group 1 (n = 17) had miniplates with monocortical screws, Group 2 (n = 16) had bicortical screws and Group 3 (n = 22) had the osteotomy fixed by means of the hybrid technique. Cephalograms were taken preoperatively, 1 week within the postoperative care period, and 6 months after the orthognathic surgery. Linear and angular changes of the cephalometric landmarks of the chin region were measured at each period, and the changes at each cephalometric landmark were determined for the time gaps. Postoperative changes in the mandibular shape were analyzed to determine the stability of fixation methods. There was minimum difference in the relapse of the mandibular advancement among the three groups. Statistical analysis showed no significant difference in postoperative stability. However, a positive correlation between the amount of advancement and the amount of postoperative relapse was demonstrated by the linear multiple regression test (p < 0.05). It can be concluded that all techniques can be used to obtain stable postoperative results in mandibular advancement after 6 months.