Diffusion approximations in population genetics and the rate of Muller's ratchet

Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook derivation of diffusion equations as scaling limits requires evolutionary parameters (selection coefficients, mutation rates) to scale like the inverse population size---a severe restriction that does not always reflect biological reality. Here we note that the Wright-Fisher model can be approximated by diffusion equations under more general conditions, including in regimes where selection and/or mutation are strong compared to genetic drift. As an illustration, we use a diffusion approximation of the Wright-Fisher model to improve estimates for the expected time to fixation of a strongly deleterious allele, i.e. the rate of Muller's ratchet.

Fixation probabilities in network structured meta-populations

The effect of population structure on evolutionary dynamics is a long-lasting research topic in evolutionary ecology and population genetics. Evolutionary graph theory is a popular approach to this problem, where individuals are located on the nodes of a network and can replace each other via the links. We study the effect of complex network structure on the fixation probability, but instead of networks of individuals, we model a network of sub-populations with a probability of migration between them. We ask how the structure of such a meta-population and the rate of migration affect the fixation probability. Many of the known results for networks of individuals carry over to meta-populations, in particular for regular networks or low symmetric migration probabilities. However, when patch sizes differ we find interesting deviations between structured meta-populations and networks of individuals. For example, a two patch structure with unequal population size suppresses selection for low migration probabilities.

The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis

Adaptation dynamics on fitness landscapes is often studied theoretically in the strong-selection, weak-mutation (SSWM) regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and how it affects the form of long-term fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitness-parameterized landscapes, we find that the change in the form of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the functional form of the fitness trajectory, while an enhancement of the beneficial mutation rate does the opposite of slowing down the form of the dynamics. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs. change in fraction of beneficial mutations).

Fixation probabilities in network structured meta-populations

The effect of population structure on evolutionary dynamics is a long-lasting research topic in evolutionary ecology and population genetics. Evolutionary graph theory is a popular approach to this problem, where individuals are located on the nodes of a network and can replace each other via the links. We study the effect of complex network structure on the fixation probability, but instead of networks of individuals, we model a network of sub-populations with a probability of migration between them. We ask how the structure of such a meta-population and the rate of migration affect the fixation probability. Many of the known results for networks of individuals carry over to meta-populations, in particular for regular networks or low symmetric migration probabilities. However, when patch sizes differ we find interesting deviations between structured meta-populations and networks of individuals. For example, a two-patch structure with unequal population size suppresses selection for low migration probabilities.

Population genetics of polymorphism and divergence in rapidly evolving populations

In rapidly evolving populations, numerous beneficial and deleterious mutations can arise and segregate within a population at the same time. In this regime, evolutionary dynamics cannot be analyzed using traditional population genetic approaches that assume that sites evolve independently. Instead, the dynamics of many loci must be analyzed simultaneously. Recent work has made progress by first analyzing the fitness variation within a population, and then studying how individual lineages interact with this traveling fitness wave. However, these "traveling wave" models have previously been restricted to extreme cases where selection on individual mutations is either much faster or much slower than the typical coalescent timescale T_c. In this work, we show how the traveling wave framework can be extended to intermediate regimes in which the scaled fitness effects of mutations (T_c s) are neither large nor small compared to one. This enables us to describe the dynamics of populations subject to a wide range of fitness effects, and in particular, in cases where it is not immediately clear which mutations are most important in shaping the dynamics and statistics of genetic diversity. We use this approach to derive new expressions for the fixation probabilities and site frequency spectra of mutations as a function of their scaled fitness effects, along with related results for the coalescent timescale T_c and the rate of adaptation or Muller's ratchet. We find that competition between linked mutations can have a dramatic impact on the proportions of neutral and selected polymorphisms, which is not simply summarized by the scaled selection coefficient T_c s. We conclude by discussing the implications of these results for population genetic inferences.

Migration pulsedness alters patterns of allele fixation and local adaptation in a mainland-island model

Gene flow, through allele migration and spread, is critical in determining patterns of population genetic structure, divergence and local adaptation. While evolutionary theory has typically envisioned gene flow as a continuous connection among populations, many processes can render it fluctuating and intermittent. We analyze mathematically a stochastic mainland-island model in continuous time, in which migration occur as recurrent ''pulses''. We derive simple analytical approximations regarding how migration pulsedness affects the effective migration rates across a range of selection and dominance scenarios. Predictions are validated with stochastic simulations and summarized with graphical interpretations in terms of fixation probabilities. We show that migration pulsedness can decrease or increase gene flow, respectively above or below a selection threshold that is s~-1/N for additive alleles and lower for recessive deleterious alleles. We propose that pulsedness may leave a genomic detectable signature, by differentially affecting the fixation rates of loci subjected to different selection regimes. The additional migration created by pulsedness is called a ''pulsedness'' load. Our results indicate that migration pulsedness, and more broadly temporally variable migration, is important to consider for evolutionary and population genetics predictions. Specifically, it would overall be detrimental to the local adaptation and persistence of small peripheral populations.

Revisiting the Notion of Deleterious Sweeps

It has previously been shown that, conditional on its fixation, the time to fixation of a semi-dominant deleterious autosomal mutation in a randomly mating population is the same as that of an advantageous mutation. This result implies that deleterious mutations could generate selective sweep-like effects. Although their fixation probabilities greatly differ, the much larger input of deleterious relative to beneficial mutations suggests that this phenomenon could be important. We here examine how the fixation of mildly deleterious mutations affects levels and patterns of polymorphism at linked sites - both in the presence and absence of interference amongst deleterious mutations - and how this class of sites may contribute to divergence between-populations and species. We find that, while deleterious fixations are unlikely to represent a significant proportion of outliers in polymorphism-based genomic scans within populations, minor shifts in the frequencies of deleterious mutations can influence the proportions of private variants and the value of FST after a recent population split. As sites subject to deleterious mutations are necessarily found in functional genomic regions, interpretations in terms of recurrent positive selection may require reconsideration.

Attentional processing of pain faces and other emotional faces in chronic pain–an eye-tracking study

Altered attentional processing of pain-associated stimuli–which might take the form of either avoidance or enhanced vigilance–is thought to be implicated in the development and maintenance of chronic pain. In contrast to reaction time tasks like the dot probe, eye tracking allows for tracking the time course of visual attention and thus differentiating early and late attentional processes. Our study aimed at investigating visual attention to emotional faces in patients with chronic musculoskeletal pain (N = 20) and matched pain-free controls (N = 20). Emotional faces (pain, angry, happy) were presented in pairs with a neutral face for 2000 ms each. Three parameters were determined: First fixation probabilities, fixation durations (overall and divided in four 500 ms intervals) and a fixation bias score as the relative fixation duration of emotional faces compared to neutral faces. There were no group differences in any of the parameters. First fixation probabilities were lower for pain faces than for angry faces. Overall, we found longer fixation duration on emotional compared to neutral faces (‘emotionality bias’), which is in accord with previous research. However, significant longer fixation duration compared to the neutral face was detected only for happy and angry but not for pain faces. In addition, fixation durations as well as bias scores yielded evidence for vigilant-avoidant processing of pain faces in both groups. These results suggest that attentional bias towards pain-associated stimuli might not generally differentiate between healthy individuals and chronic pain patients. Exaggerated attentional bias in patients might occur only under specific circumstances, e.g., towards stimulus material specifically relating to the specific pain of the patients under study or under high emotional distress.

Eye movements reflect expertise development in hybrid search

Domain-specific expertise changes the way people perceive, process, and remember information from that domain. This is often observed in visual domains involving skilled searches, such as athletics referees, or professional visual searchers (e.g., security and medical screeners). Although existing research has compared expert to novice performance in visual search, little work has directly documented how accumulating experiences change behavior. A longitudinal approach to studying visual search performance may permit a finer-grained understanding of experience-dependent changes in visual scanning, and the extent to which various cognitive processes are affected by experience. In this study, participants acquired experience by taking part in many experimental sessions over the course of an academic semester. Searchers looked for 20 categories of targets simultaneously (which appeared with unequal frequency), in displays with 0–3 targets present, while having their eye movements recorded. With experience, accuracy increased and response times decreased. Fixation probabilities and durations decreased with increasing experience, but saccade amplitudes and visual span increased. These findings suggest that the behavioral benefits endowed by expertise emerge from oculomotor behaviors that reflect enhanced reliance on memory to guide attention and the ability to process more of the visual field within individual fixations.

Fixation probabilities in graph-structured populations under weak selection

A population’s spatial structure affects the rate of genetic change and the outcome of natural selection. These effects can be modeled mathematically using the Birth-death process on graphs. Individuals occupy the vertices of a weighted graph, and reproduce into neighboring vertices based on fitness. A key quantity is the probability that a mutant type will sweep to fixation, as a function of the mutant’s fitness. Graphs that increase the fixation probability of beneficial mutations, and decrease that of deleterious mutations, are said to amplify selection. However, fixation probabilities are difficult to compute for an arbitrary graph. Here we derive an expression for the fixation probability, of a weakly-selected mutation, in terms of the time for two lineages to coalesce. This expression enables weak-selection fixation probabilities to be computed, for an arbitrary weighted graph, in polynomial time. Applying this method, we explore the range of possible effects of graph structure on natural selection, genetic drift, and the balance between the two. Using exhaustive analysis of small graphs and a genetic search algorithm, we identify families of graphs with striking effects on fixation probability, and we analyze these families mathematically. Our work reveals the nuanced effects of graph structure on natural selection and neutral drift. In particular, we show how these notions depend critically on the process by which mutations arise.