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- Muller’s ratchet and the pattern of variation at a neutral locusPublication . Gordo, I.; Navarro, A.; Charlesworth, B.The levels and patterns of variation at a neutral locus are analyzed in a haploid asexual population Undergoing accumulation of deleterious mutations due to Muller's ratchet. We find that the movement Of Muller's ratchet can be associated with a considerable reduction in genetic diversity below classical neutral expectation. The extent to which variability is reduced is a function Of the deleterious initiation rate, the fitness effects of the Imitations, and the population size. Approximate analytical expressions for the expected genetic diversity are compared with simulation results under two different models of deleterious imitations: a model where all deleterious imitations have equal effects and a model where there are two classes of deleterious imitations. We also find that Muller's ratchet can produce a considerable distortion in the neutral frequency spectrum toward an excess of rare variants.
- Adaptation of asexual populations under Muller’s ratchetPublication . Bachtrog, D.; Gordo, I.We study the population genetics of adaptation in nonequilibrium haploid asexual populations. We find that the accumulation of deleterious mutations, due to the operation of Muller’s ratchet, can considerably reduce the rate of fixation of advantageous alleles. Such reduction can be approximated reasonably well by a reduction in the effective population size. In the absence of Muller’s ratchet, a beneficial mutation can only become fixed if it creates the best possible genotype; if Muller’s ratchet operates, however, mutations initially arising in a nonoptimal genotype can also become fixed in the population, since the loss of the least-loaded class implies that an initially nonoptimal background can become optimal. We show that, while the rate at which adaptive mutations become fixed is reduced, the rate of fixation of deleterious mutations due to the ratchet is not changed by the presence of beneficial mutations as long as the rate of their occurrence is low and the deleterious effects of mutations (sd) are higher than the beneficial effects (sa). When sa . sd, the advantage of a beneficial mutation can outweigh the deleterious effects of associated mutations. Under these conditions, a beneficial allele can drag to fixation deleterious mutations initially associated with it at a higher rate than in the absence of advantageous alleles. We propose analytical approximations for the rates of accumulation of deleterious and beneficial mutations. Furthermore, when allowing for the possible occurrence of interference between beneficial alleles, we find that the presence of deleterious mutations of either very weak or very strong effect can marginally increase the rate of accumulation of beneficial mutations over that observed in the absence of such deleterious mutations.
- Nonequilibrium model for estimating parameters of deleterious mutationsPublication . Gordo, I.; Dionisio, F.Deleterious mutations are of extreme evolutionary importance because, even though they are eliminated by natural selection, their continuous pressure creates a pool of variability in natural populations. They are of potential relevance for the existence of several features in evolution, such as sexual reproduction, and pose a risk to small asexual populations. Despite their extreme importance, the deleterious mutation rate and the effects of each mutation on fitness are poorly known quantities. Here we analyze a simple model that can be applied to simple experiments, in microorganisms, aiming at the quantification of these values.
- The evolution of a conjugative plasmid and its ability to increase bacterial fitness.Publication . Dionisio, F.; Conceição, I.C.; Marques, A.C.R.; Fernandes, L.; Gordo, I.Conjugative plasmids are extra-chromosomal DNA elements that are capable of horizontal transmission and are found in many natural isolated bacteria. Although plasmids may carry beneficial genes to their bacterial host, they may also cause a fitness cost. In this work, we studied the evolution of the R1 plasmid and we found that, in spite of the R1 plasmid conferring an initial cost to its host, after 420 generations the cost disappeared in all five independent evolution experiments. In fact, in two of these five experiments evolved conjugative plasmids actually conferred a fitness advantage to their hosts. Furthermore, the relative fitness of the ancestral clone bearing one of the evolved plasmids is significantly higher than both the plasmid-free ancestral cells and the evolved cells carrying the evolved plasmid. Given that the R1 plasmid may spread among different species of enterobacteria, we wondered what the effect of the evolved plasmid would be inside Salmonella enterica cells. We found that the evolved plasmid is also able to dramatically increase the relative fitness of these cells. Our results suggest that even if general usage of antibiotics is halted, conjugative plasmids that have been selected with antibiotics in previous years can still persist among bacterial populations or even invade new strains.
- Scaling, genetic drift and clonal interference in the extinction pattern of asexual populationsPublication . Rosas, A.; Gordo, I.; Campos, P.R.A.We investigate the dynamics of loss of favorable mutations in an asexual haploid population. In the current work, we consider homogeneous as well as spatially structured population models. We focus our analysis on statistical measurements of the probability distribution of the maximum population size N(sb) achieved by those mutations that have not reached fixation. Our results show a crossover behavior which demonstrates the occurrence of two evolutionary regimes. In the first regime, which takes place for small N(sb) , the probability distribution is described by a power law with characteristic exponent theta(d) =1.8 +/- 0.01. This power law is not influenced by the rate of beneficial mutations. The second regime, which occurs for intermediate to large values of N(sb), has a characteristic exponent theta(c) which increases as the rate of beneficial mutations grows. These results establish where genetic drift and clonal interference become the main underlying mechanism in the extinction of advantageous mutations.
- The tragedy of the commons, the public goods dilemma, and the meaning of rivalry and excludability in evolutionary biologyPublication . Dionisio, F.; Gordo, I.Problem: In the study of conflicts, both economists and evolutionary biologists use the concepts ‘tragedy of the commons’ and ‘public goods dilemma’. What is the relationship between the economist and evolutionist views of these concepts? Model features: The economics literature defines the tragedy of the commons and the public goods dilemma in terms of rivalry and excludability of the good. In contrast, evolutionists define these conflicts based on fitness functions with two components: individual and group components of fitness. Mathematical method: Evolutionary game theory and the calculation of evolutionarily stable strategy trait values by standard optimization techniques and by replacing slopes of group phenotype on individual genotype by coefficients of relatedness. Conclusion: There is a direct relationship between rivalry and the individual component of fitness and between excludability and the group component of fitness. Moreover, although the prisoner’s dilemma constitutes a suitable metaphor to analyse both the public goods dilemma and the tragedy of the commons, it gives the false idea that the two conflicts are symmetric since they refer to situations in which individuals consume a common resource – tragedy of the commons – or contribute to a collective action or common good – public goods dilemma. However, the two situations are clearly not symmetric: from the economical point of view they differ by rivalry, and from the evolutionary biology point of view the two conflicts differ by the significance of the within-group competition in the fitness function.
- The effect of spatial structure in adaptive evolutionPublication . Perfeito, L.; Gordo, I.; Campos, P.R.A.We study the dynamics of adaptation in a spatially structured population. The model assumes local competition for replication, where each organism interacts only with its nearest neighbors and is inspired by experimental methods that can be used to study the process of adaptive evolution in microbes. In such experiments microbial populations are grown on petri dishes and allowed to adapt by serial passage. We compare the rate of adaptation in a structured population where the structure is maintained intact to those where movement of individuals can occur. We observe that the rate of adaptive evolution is higher and the mean effect of fixed beneficial mutations is lower in intact structures than in structures with mixing.
- Adaptive evolution in a spatially structured asexual populationPublication . Gordo, I.; Campos, P.R.A.We study the process of adaptation in a spatially structured asexual haploid population. The model assumes a local competition for replication, where each organism interacts only with its nearest neighbors. We observe that the substitution rate of beneficial mutations is smaller for a spatially structured population than that seen for populations without structure. The difference between structured and unstructured populations increases as the adaptive mutation rate increases. Furthermore, the substitution rate decreases as the number of neighbors for local competition is reduced. We have also studied the impact of structure on the distribution of adaptive mutations that fix during adaptation.
- Muller's ratchet in random graphs and scale free networksPublication . Campos, P.R.A.; Combadão, J.; Dionísio, F.; Gordo, I.Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of mitochondria, the degeneration of the Y chromosome, the evolution of sex and recombination and the evolution of microbes. Here we study the speed of Muller's ratchet in a population subdivided into many small subpopulations connected by migration, and distributed on a network. We compare the speed of the ratchet in two distinct types of topologies: scale free networks and random graphs. The difference between the topologies is noticeable when the average connectivity of the network and the migration rate is large. In this situation we observe that the ratchet clicks faster in scale free networks than in random graphs. So contrary to intuition, scale free networks are more prone to loss of genetic information than random graphs. On the other hand, we show that scale free networks are more robust to the random extinction than random graphs. Since these complex networks have been shown to describe well real-life systems, our results open a framework for studying the evolution of microbes and disease epidemics.
- Controlling excludability in the evolution of cooperationPublication . Dionisio, F.; Gordo, I.Background: A tragedy of the commons arises if individuals cannot protect their future use of a depletable resource, and individual fitness increases if individuals exploit the resource at rates beyond sustainability. Natural selection then forces the individuals to diminish, perhaps even to destroy, their resource. One way to protect future use is privatization - that is, locally excluding rivals from the resource. Another is to reduce rivalry among individuals by restricting exploitation rates.