Rare sex or out of reach equilibrium? The dynamics of F IS in partially clonal organisms.

BACKGROUND: Partially clonal organisms are very common in nature, yet the influence of partial asexuality on the temporal dynamics of genetic diversity remains poorly understood. Mathematical models accounting for clonality predict deviations only for extremely rare sex and only towards mean inbreeding coefficient [Formula: see text]. Yet in partially clonal species, both F IS < 0 and F IS > 0 are frequently observed also in populations where there is evidence for a significant amount of sexual reproduction. Here, we studied the joint effects of partial clonality, mutation and genetic drift with a state-and-time discrete Markov chain model to describe the dynamics of F IS over time under increasing rates of clonality. RESULTS: Results of the mathematical model and simulations show that partial clonality slows down the asymptotic convergence to F IS = 0. Thus, although clonality alone does not lead to departures from Hardy-Weinberg expectations once reached the final equilibrium state, both negative and positive F IS values can arise transiently even at intermediate rates of clonality. More importantly, such "transient" departures from Hardy Weinberg proportions may last long as clonality tunes up the temporal variation of F IS and reduces its rate of change over time, leading to a hyperbolic increase of the maximal time needed to reach the final mean [Formula: see text] value expected at equilibrium. CONCLUSION: Our results argue for a dynamical interpretation of F IS in clonal populations. Negative values cannot be interpreted as unequivocal evidence for extremely scarce sex but also as intermediate rates of clonality in finite populations. Complementary observations (e.g. frequency distribution of multiloci genotypes, population history) or time series data may help to discriminate between different possible conclusions on the extent of clonality when mean [Formula: see text] values deviating from zero and/or a large variation of F IS over loci are observed.

Patch leaving rules: a stochastic version of a well-known deterministic motivational model.

A famous motivational model proposed for insect parasitoids by Waage (1979) provides a candidate mechanism for patch-leaving decision rules in foragers. In this model, the animal is supposed to enter a patch of resources with an initial tendency to stay in it, which then regularly decreases. Every encounter with a resource item increases or decreases this tendency, and the forager is supposed to leave the patch when this tendency or motivation falls below a given threshold. Evidence of such increases and drops in this tendency to stay were often obtained by analyzing experimental data with a Cox (1972) proportional hazards model. The Waage (1979) model is purely deterministic and predicts a fixed departure time for a fixed set of encounters with foraging items. On the other hand, empirical data show a large variability of departure times under fixed conditions. We present a fully stochastic version which overcomes this problem and gives a quasi close form expression for the distribution of patch residence times as well as a statistical procedure to estimate its parameters. Two examples of the model fitting on experimental data sets are provided. This novel model, although more complicated than Waage (1979) model, improves its realism and provides a stochastic interpretation of motivation as a proximal mechanism leading foragers to optimality.

ClonEstiMate, a Bayesian method for quantifying rates of clonality of populations genotyped at two-time steps.

Partial clonality is commonly used in eukaryotes and has large consequences for their evolution and ecology. Assessing accurately the relative importance of clonal vs. sexual reproduction matters for studying and managing such species. Here, we proposed a Bayesian approach, ClonEstiMate, to infer rates of clonality c from populations sampled twice over a short time interval, ideally one generation time. The method relies on the likelihood of the transitions between genotype frequencies of ancestral and descendent populations, using an extended Wright-Fisher model explicitly integrating reproductive modes. Our model provides posterior probability distribution of inferred c, given the assumed rates of mutation, as well as inbreeding and selfing when occurring. Tested under various conditions, this model provided accurate inferences of c, especially when the amount of information was modest, that is low sample sizes, few loci, low polymorphism and strong linkage disequilibrium. Inferences remained robust when mutation models and rates were misinformed. However, the method was sensitive to moderate frequencies of null alleles and when the time interval between required samplings exceeding two generations. Misinformed rates on mating modes (inbreeding and selfing) also resulted in biased inferences. Our method was tested on eleven data sets covering five partially clonal species, for which the extent of clonality was formerly deciphered. It delivered highly consistent results with previous information on the biology of those species. ClonEstiMate represents a powerful tool for detecting and inferring clonality in finite populations, genotyped with SNPs or microsatellites. It is freely available at https://www6.rennes.inra.fr/igepp_eng/Productions/Software.

Interpretation and approximation tools for big, dense Markov chain transition matrices in population genetics.

BACKGROUND: Markov chains are a common framework for individual-based state and time discrete models in evolution. Though they played an important role in the development of basic population genetic theory, the analysis of more complex evolutionary scenarios typically involves approximation with other types of models. As the number of states increases, the big, dense transition matrices involved become increasingly unwieldy. However, advances in computational technology continue to reduce the challenges of "big data", thus giving new potential to state-rich Markov chains in theoretical population genetics. RESULTS: Using a population genetic model based on genotype frequencies as an example, we propose a set of methods to assist in the computation and interpretation of big, dense Markov chain transition matrices. With the help of network analysis, we demonstrate how they can be transformed into clear and easily interpretable graphs, providing a new perspective even on the classic case of a randomly mating, finite population with mutation. Moreover, we describe an algorithm to save computer memory by substituting the original matrix with a sparse approximate while preserving its mathematically important properties, including a closely corresponding dominant (normalized) eigenvector. A global sensitivity analysis of the approximation results in our example shows that size reduction of more than 90 % is possible without significantly affecting the basic model results. Sample implementations of our methods are collected in the Python module mamoth. CONCLUSION: Our methods help to make stochastic population genetic models involving big, dense transition matrices computationally feasible. Our visualization techniques provide new ways to explore such models and concisely present the results. Thus, our methods will contribute to establish state-rich Markov chains as a valuable supplement to the diversity of population genetic models currently employed, providing interesting new details about evolution e.g. under non-standard reproductive systems such as partial clonality.

The exact distributions of F(IS) under partial asexuality in small finite populations with mutation.

Reproductive systems like partial asexuality participate to shape the evolution of genetic diversity within populations, which is often quantified by the inbreeding coefficient F IS. Understanding how those mating systems impact the possible distributions of F IS values in theoretical populations helps to unravel forces shaping the evolution of real populations. We proposed a population genetics model based on genotypic states in a finite population with mutation. For populations with less than 400 individuals, we assessed the impact of the rates of asexuality on the full exact distributions of F IS, the probabilities of positive and negative F IS, the probabilities of fixation and the probabilities to observe changes in the sign of F IS over one generation. After an infinite number of generations, we distinguished three main patterns of effects of the rates of asexuality on genetic diversity that also varied according to the interactions of mutation and genetic drift. Even rare asexual events in mainly sexual populations impacted the balance between negative and positive F IS and the occurrence of extreme values. It also drastically modified the probability to change the sign of F IS value at one locus over one generation. When mutation prevailed over genetic drift, increasing rates of asexuality continuously increased the variance of F IS that reached its highest value in fully asexual populations. In consequence, even ancient asexual populations showed the entire F IS spectrum, including strong positive F IS. The prevalence of heterozygous loci only occurred in full asexual populations when genetic drift dominated.

"Supramolecular circuitry": three chemiluminescent, Cucurbit[7]uril-controlled on/off switches.

Three Cucurbit[7]uril-controlled chemiluminescent on/off switches based on the lucigenin motif have been synthesized. Light emission is triggered upon addition of sodium peroxide, interrupted or dimmed in the presence of Cucurbit[7]uril, and restored upon injection of a competitive guest. The process, which can be mimicked by a simple resistor-capacitor circuit, is rationalized by examining the role of the macrocyclic host on the network of equilibria involved in the chemiluminescent process.