Inferring number of populations and changes in connectivity under the n-island model.

Inferring the demographic history of species is one of the greatest challenges in populations genetics. This history is often represented as a history of size changes, ignoring population structure. Alternatively, when structure is assumed, it is defined a priori as a population tree and not inferred. Here we propose a framework based on the IICR (Inverse Instantaneous Coalescence Rate). The IICR can be estimated for a single diploid individual using the PSMC method of Li and Durbin (2011). For an isolated panmictic population, the IICR matches the population size history, and this is how the PSMC outputs are generally interpreted. However, it is increasingly acknowledged that the IICR is a function of the demographic model and sampling scheme with limited connection to population size changes. Our method fits observed IICR curves of diploid individuals with IICR curves obtained under piecewise stationary symmetrical island models. In our models we assume a fixed number of time periods during which gene flow is constant, but gene flow is allowed to change between time periods. We infer the number of islands, their sizes, the periods at which connectivity changes and the corresponding rates of connectivity. Validation with simulated data showed that the method can accurately recover most of the scenario parameters. Our application to a set of five human PSMCs yielded demographic histories that are in agreement with previous studies using similar methods and with recent research suggesting ancient human structure. They are in contrast with the view of human evolution consisting of one ancestral population branching into three large continental and panmictic populations with varying degrees of connectivity and no population structure within each continent.

Coalescence times for three genes provide sufficient information to distinguish population structure from population size changes.

The increasing amount of genomic data currently available is expanding the horizons of population genetics inference. A wide range of methods have been published allowing to detect and date major changes in population size during the history of species. At the same time, there has been an increasing recognition that population structure can generate genetic data similar to those generated under models of population size change. Recently, Mazet et al. (Heredity 116(4):362-371, 2016) introduced the idea that, for any model of population structure, it is always possible to find a panmictic model with a particular function of population size-change having an identical distribution of [Formula: see text] (the time of the first coalescence for a sample of size two). This implies that there is an identifiability problem between a panmictic and a structured model when we base our analysis only on [Formula: see text]. In this paper, based on an analytical study of the rate matrix of the ancestral lineage process, we obtain new theoretical results about the joint distribution of the coalescence times [Formula: see text] for a sample of three haploid genes in a n-island model with constant size. Even if, for any [Formula: see text], it is always possible to find a size-change scenario for a panmictic population such that the marginal distribution of [Formula: see text] is exactly the same as in a n-island model with constant population size, we show that the joint distribution of the coalescence times [Formula: see text] for a sample of three genes contains enough information to distinguish between a panmictic population and a n-island model of constant size.

The IICR and the non-stationary structured coalescent: towards demographic inference with arbitrary changes in population structure.

In the last years, a wide range of methods allowing to reconstruct past population size changes from genome-wide data have been developed. At the same time, there has been an increasing recognition that population structure can generate genetic data similar to those produced under models of population size change. Recently, Mazet et al. (Heredity 116:362-371, 2016) showed that, for any model of population structure, it is always possible to find a panmictic model with a particular function of population size changes, having exactly the same distribution of T2 (the coalescence time for a sample of size two) as that of the structured model. They called this function IICR (Inverse Instantaneous Coalescence Rate) and showed that it does not necessarily correspond to population size changes under non-panmictic models. Besides, most of the methods used to analyse data under models of population structure tend to arbitrarily fix that structure and to minimise or neglect population size changes. Here, we extend the seminal work of Herbots (PhD thesis, University of London, 1994) on the structured coalescent and propose a new framework, the Non-Stationary Structured Coalescent (NSSC) that incorporates demographic events (changes in gene flow and/or deme sizes) to models of nearly any complexity. We show how to compute the IICR under a wide family of stationary and non-stationary models. As an example we address the question of human and Neanderthal evolution and discuss how the NSSC framework allows to interpret genomic data under this new perspective.

The IICR (inverse instantaneous coalescence rate) as a summary of genomic diversity: insights into demographic inference and model choice.

Several inferential methods using genomic data have been proposed to quantify and date population size changes in the history of species. At the same time an increasing number of studies have shown that population structure can generate spurious signals of population size change. Recently, Mazet et al. (2016) introduced, for a sample size of two, a time-dependent parameter, which they called the IICR (inverse instantaneous coalescence rate). The IICR is equivalent to a population size in panmictic models, but not necessarily in structured models. It is characterised by a temporal trajectory that suggests population size changes, as a function of the sampling scheme, even when the total population size was constant. Here, we extend the work of Mazet et al. (2016) by (i) showing how the IICR can be computed for any demographic model of interest, under the coalescent, (ii) applying this approach to models of population structure (1D and 2D stepping stone, split models, two- and three-island asymmetric gene flow, continent-island models), (iii) stressing the importance of the sampling strategy in generating different histories, (iv) arguing that IICR plots can be seen as summaries of genomic information that can thus be used for model choice or model exclusion (v) applying this approach to the question of admixture between humans and Neanderthals. Altogether these results are potentially important given that the widely used PSMC (pairwise sequentially Markovian coalescent) method of Li and Durbin (2011) estimates the IICR of the sample, not necessarily the history of the populations.

Demographic inference using genetic data from a single individual: Separating population size variation from population structure.

The rapid development of sequencing technologies represents new opportunities for population genetics research. It is expected that genomic data will increase our ability to reconstruct the history of populations. While this increase in genetic information will likely help biologists and anthropologists to reconstruct the demographic history of populations, it also represents new challenges. Recent work has shown that structured populations generate signals of population size change. As a consequence it is often difficult to determine whether demographic events such as expansions or contractions (bottlenecks) inferred from genetic data are real or due to the fact that populations are structured in nature. Given that few inferential methods allow us to account for that structure, and that genomic data will necessarily increase the precision of parameter estimates, it is important to develop new approaches. In the present study we analyze two demographic models. The first is a model of instantaneous population size change whereas the second is the classical symmetric island model. We (i) re-derive the distribution of coalescence times under the two models for a sample of size two, (ii) use a maximum likelihood approach to estimate the parameters of these models (iii) validate this estimation procedure under a wide array of parameter combinations, (iv) implement and validate a model rejection procedure by using a Kolmogorov-Smirnov test, and a model choice procedure based on the AIC, and (v) derive the explicit distribution for the number of differences between two non-recombining sequences. Altogether we show that it is possible to estimate parameters under several models and perform efficient model choice using genetic data from a single diploid individual.

Heterogeneity in effective size across the genome: effects on the inverse instantaneous coalescence rate (IICR) and implications for demographic inference under linked selection.

The relative contribution of selection and neutrality in shaping species genetic diversity is one of the most central and controversial questions in evolutionary theory. Genomic data provide growing evidence that linked selection, i.e. the modification of genetic diversity at neutral sites through linkage with selected sites, might be pervasive over the genome. Several studies proposed that linked selection could be modeled as first approximation by a local reduction (e.g. purifying selection, selective sweeps) or increase (e.g. balancing selection) of effective population size (Ne). At the genome-wide scale, this leads to variations of Ne from one region to another, reflecting the heterogeneity of selective constraints and recombination rates between regions. We investigate here the consequences of such genomic variations of Ne on the genome-wide distribution of coalescence times. The underlying motivation concerns the impact of linked selection on demographic inference, because the distribution of coalescence times is at the heart of several important demographic inference approaches. Using the concept of inverse instantaneous coalescence rate, we demonstrate that in a panmictic population, linked selection always results in a spurious apparent decrease of Ne along time. Balancing selection has a particularly large effect, even when it concerns a very small part of the genome. We also study more general models including genuine population size changes, population structure or transient selection and find that the effect of linked selection can be significantly reduced by that of population structure. The models and conclusions presented here are also relevant to the study of other biological processes generating apparent variations of Ne along the genome.

Impact of model assumptions on demographic inferences: the case study of two sympatric mouse lemurs in northwestern Madagascar.

BACKGROUND: Quaternary climate fluctuations have been acknowledged as major drivers of the geographical distribution of the extraordinary biodiversity observed in tropical biomes, including Madagascar. The main existing framework for Pleistocene Malagasy diversification assumes that forest cover was strongly shaped by warmer Interglacials (leading to forest expansion) and by cooler and arid glacials (leading to forest contraction), but predictions derived from this scenario for forest-dwelling animals have rarely been tested with genomic datasets. RESULTS: We generated genomic data and applied three complementary demographic approaches (Stairway Plot, PSMC and IICR-simulations) to infer population size and connectivity changes for two forest-dependent primate species (Microcebus murinus and M. ravelobensis) in northwestern Madagascar. The analyses suggested major demographic changes in both species that could be interpreted in two ways, depending on underlying model assumptions (i.e., panmixia or population structure). Under panmixia, the two species exhibited larger population sizes across the Last Glacial Maximum (LGM) and towards the African Humid Period (AHP). This peak was followed by a population decline in M. ravelobensis until the present, while M. murinus may have experienced a second population expansion that was followed by a sharp decline starting 3000 years ago. In contrast, simulations under population structure suggested decreasing population connectivity between the Last Interglacial and the LGM for both species, but increased connectivity during the AHP exclusively for M. murinus. CONCLUSION: Our study shows that closely related species may differ in their responses to climatic events. Assuming that Pleistocene climatic conditions in the lowlands were similar to those in the Malagasy highlands, some demographic dynamics would be better explained by changes in population connectivity than in population size. However, changes in connectivity alone cannot be easily reconciled with a founder effect that was shown for M. murinus during its colonization of the northwestern Madagascar in the late Pleistocene. To decide between the two alternative models, more knowledge about historic forest dynamics in lowland habitats is necessary. Altogether, our study stresses that demographic inferences strongly depend on the underlying model assumptions. Final conclusions should therefore be based on a comparative evaluation of multiple approaches.

A long-term evolutionary pressure on the amount of noncoding DNA.

A significant part of eukaryotic noncoding DNA is viewed as the passive result of mutational processes, such as the proliferation of mobile elements. However, sequences lacking an immediate utility can nonetheless play a major role in the long-term evolvability of a lineage, for instance by promoting genomic rearrangements. They could thus be subject to an indirect selection. Yet, such a long-term effect is difficult to isolate either in vivo or in vitro. Here, by performing in silico experimental evolution, we demonstrate that, under low mutation rates, the indirect selection of variability promotes the accumulation of noncoding sequences: Even in the absence of self-replicating elements and mutational bias, noncoding sequences constituted an important fraction of the evolved genome because the indirectly selected genomes were those that were variable enough to discover beneficial mutations. On the other hand, high mutation rates lead to compact genomes, much like the viral ones, although no selective cost of genome size was applied: The indirectly selected genomes were those that were small enough for the genetic information to be reliably transmitted. Thus, the spontaneous evolution of the amount of noncoding DNA strongly depends on the mutation rate. Our results suggest the existence of an additional pressure on the amount of noncoding DNA, namely the indirect selection of an appropriate trade-off between the fidelity of the transmission of the genetic information and the exploration of the mutational neighborhood. Interestingly, this trade-off resulted robustly in the accumulation of noncoding DNA so that the best individual leaves one offspring without mutation (or only neutral ones) per generation.

Evolutionary coupling between the deleteriousness of gene mutations and the amount of non-coding sequences.

The phenotypic effects of random mutations depend on both the architecture of the genome and the gene-trait relationships. Both levels thus play a key role in the mutational variability of the phenotype, and hence in the long-term evolutionary success of the lineage. Here, by simulating the evolution of organisms with flexible genomes, we show that the need for an appropriate phenotypic variability induces a relationship between the deleteriousness of gene mutations and the quantity of non-coding sequences maintained in the genome. The more deleterious the gene mutations, the shorter the intergenic sequences. Indeed, in a shorter genome, fewer genes are affected by rearrangements (duplications, deletions, inversions, translocations) at each replication, which compensates for the higher impact of each gene mutation. This spontaneous adjustment of genome structure allows the organisms to retain the same average fitness loss per replication, despite the higher impact of single gene mutations. These results show how evolution can generate unexpected couplings between distinct organization levels.

Spontaneous dynamics of asymmetric random recurrent spiking neural networks.

In this letter, we study the effect of a unique initial stimulation on random recurrent networks of leaky integrate-and-fire neurons. Indeed, given a stochastic connectivity, this so-called spontaneous mode exhibits various nontrivial dynamics. This study is based on a mathematical formalism that allows us to examine the variability of the afterward dynamics according to the parameters of the weight distribution. Under the independence hypothesis (e.g., in the case of very large networks), we are able to compute the average number of neurons that fire at a given time-the spiking activity. In accordance with numerical simulations, we prove that this spiking activity reaches a steady state. We characterize this steady state and explore the transients.