The spatio-temporal dynamics of neutral genetic diversity

Pushed waves, trailing edges, and extreme events: Eco-evolutionary dynamics of a geographic range shift in the owl limpet, Lottia gigantea

As climatic variation re-shapes global biodiversity, understanding eco-evolutionary feedbacks during species range shifts is of increasing importance. Theory on range expansions distinguishes between two different forms: "pulled" and "pushed" waves. Pulled waves occur when the source of the expansion comes from low-density peripheral populations, while pushed waves occur when recruitment to the expanding edge is supplied by high-density populations closer to the species' core. How extreme events shape pushed/pulled wave expansion events, as well as trailing-edge declines/contractions, remains largely unexplored. We examined eco-evolutionary responses of a marine invertebrate (the owl limpet, Lottia gigantea) that increased in abundance during the 2014-2016 marine heatwaves near the poleward edge of its geographic range in the northeastern Pacific. We used whole-genome sequencing from 19 populations across >11 degrees of latitude to characterize genomic variation, gene flow, and demographic histories across the species' range. We estimated present-day dispersal potential and past climatic stability to identify how contemporary and historical seascape features shape genomic characteristics. Consistent with expectations of a pushed wave, we found little genomic differentiation between core and leading-edge populations, and higher genomic diversity at range edges. A large and well-mixed population in the northern edge of the species' range is likely a result of ocean current anomalies increasing larval settlement and high-dispersal potential across biogeographic boundaries. Trailing-edge populations have higher differentiation from core populations, possibly driven by local selection and limited gene flow, as well as high genomic diversity likely as a result of climatic stability during the Last Glacial Maximum. Our findings suggest that extreme events can drive poleward range expansions that carry the adaptive potential of core populations, while also cautioning that trailing-edge extirpations may threaten unique evolutionary variation. This work highlights the importance of understanding how both trailing and leading edges respond to global change and extreme events.

Seed predation-induced Allee effects, seed dispersal and masting jointly drive the diversity of seed sources during population expansion

The environmental factors affecting plant reproduction and effective dispersal, in particular biotic interactions, have a strong influence on plant expansion dynamics, but their demographic and genetic consequences remain an understudied body of theory. Here, we use a mathematical model in a one-dimensional space and on a single reproductive period to describe the joint effects of predispersal seed insect predators foraging strategy and plant reproduction strategy (masting) on the spatio-temporal dynamics of seed sources diversity in the colonisation front of expanding plant populations. We show that certain foraging strategies can result in a higher seed predation rate at the colonisation front compared to the core of the population, leading to an Allee effect. This effect promotes the contribution of seed sources from the core to the colonisation front, with long-distance dispersal further increasing this contribution. As a consequence, our study reveals a novel impact of the predispersal seed predation-induced Allee effect, which mitigates the erosion of diversity in expanding populations. We use rearrangement inequalities to show that masting has a buffering role: it mitigates this seed predation-induced Allee effect. This study shows that predispersal seed predation, plant reproductive strategies and seed dispersal patterns can be intermingled drivers of the diversity of seed sources in expanding plant populations, and opens new perspectives concerning the analysis of more complex models such as integro-difference or reaction-diffusion equations.

Life history traits and dispersal shape neutral genetic diversity in metapopulations

Genetic diversity at population scale, depends on species life-history traits, population dynamics and local and global environmental factors. We first investigate the effect of life-history traits on the neutral genetic diversity of a single population using a deterministic mathematical model. When the population is stable, we show that semelparous species with precocious maturation and iteroparous species with delayed maturation exhibit higher diversity because their life history traits tend to balance the lifetimes of non reproductive individuals (juveniles) and adults which reproduce. Then, we extend our model to a metapopulation to investigate the additional effect of dispersal on diversity. We show that dispersal may truly modify the local effect of life history on diversity. As a result, the diversity at the global scale of the metapopulation differ from the local diversity which is only described through local life history traits of the populations. In particular, dispersal usually promotes diversity at the global metapopulation scale.

Dispersal and Good Habitat Quality Promote Neutral Genetic Diversity in Metapopulations

Dispersal is a fundamental and crucial ecological process for a metapopulation to survive in heterogeneous or changing habitats. In this paper, we investigate the effect of the habitat quality and the dispersal on the neutral genetics diversity of a metapopulation. We model the metapopulation dynamics on heterogeneous habitats using a deterministic system of ordinary differential equations. We decompose the metapopulation into several neutral genetic fractions seeing as they could be located in different habitats. By using a mathematical model which describes their temporal dynamics inside the metapopulation, we provide the analytical results of their transient dynamics, as well as their asymptotic proportion in the different habitats. The diversity indices show how the genetic diversity at a global metapopulation scale is preserved by the correlation of two factors: the dispersal of the population, as well as the existence of adequate and sufficiently large habitats. The diversity indices show how the genetic diversity at a global metapopulation scale is preserved by the correlation of two factors: the dispersal of the population as well as the existence of adequate and sufficiently large habitats. Moreover, they ensure genetic diversity at the local habitat scale. In a source-sink metapopulation, we demonstrate that the diversity of the sink can be rescued if the condition of the sink is not too deteriorated and the migration from the source is larger than the migration from the sink. Furthermore, our study provides an analytical insight into the dynamics of the solutions of the systems of ordinary differential equations.

The impact of long-range dispersal on gene surfing

Range expansions lead to distinctive patterns of genetic variation in populations, even in the absence of selection. These patterns and their genetic consequences have been well studied for populations advancing through successive short-ranged migration events. However, most populations harbor some degree of long-range dispersal, experiencing rare yet consequential migration events over arbitrarily long distances. Although dispersal is known to strongly affect spatial genetic structure during range expansions, the resulting patterns and their impact on neutral diversity remain poorly understood. Here, we systematically study the consequences of long-range dispersal on patterns of neutral variation during range expansion in a class of dispersal models which spans the extremes of local (effectively short-ranged) and global (effectively well-mixed) migration. We find that sufficiently long-ranged dispersal leaves behind a mosaic of monoallelic patches, whose number and size are highly sensitive to the distribution of dispersal distances. We develop a coarse-grained model which connects statistical features of these spatial patterns to the evolution of neutral diversity during the range expansion. We show that growth mechanisms that appear qualitatively similar can engender vastly different outcomes for diversity: Depending on the tail of the dispersal distance distribution, diversity can be either preserved (i.e., many variants survive) or lost (i.e., one variant dominates) at long times. Our results highlight the impact of spatial and migratory structure on genetic variation during processes as varied as range expansions, species invasions, epidemics, and the spread of beneficial mutations in established populations.

Expansion Under Climate Change: The Genetic Consequences

Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction-diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure. Our analysis shows that range expansions and range shifts under slow climate change preserve genetic diversity. This is because slow climate change creates range boundaries that promote spatial mixing of genetic components. Mathematically, the mixing leads to so-called pushed travelling wave solutions. This mixing phenomenon is not seen in spatially homogeneous environments, where range expansion reduces genetic diversity through gene surfing arising from pulled travelling wave solutions. However, the preservation of diversity is diminished when climate change occurs too quickly. Using diversity indices, we show that fast expansions and range shifts erode genetic diversity more than slow range expansions and range shifts. Our study provides analytical insight into the dynamics of travelling wave solutions in heterogeneous environments.

Mathematical Modelling of Plankton-Oxygen Dynamics Under the Climate Change

Ocean dynamics is known to have a strong effect on the global climate change and on the composition of the atmosphere. In particular, it is estimated that about 70% of the atmospheric oxygen is produced in the oceans due to the photosynthetic activity of phytoplankton. However, the rate of oxygen production depends on water temperature and hence can be affected by the global warming. In this paper, we address this issue theoretically by considering a model of a coupled plankton-oxygen dynamics where the rate of oxygen production slowly changes with time to account for the ocean warming. We show that a sustainable oxygen production is only possible in an intermediate range of the production rate. If, in the course of time, the oxygen production rate becomes too low or too high, the system's dynamics changes abruptly, resulting in the oxygen depletion and plankton extinction. Our results indicate that the depletion of atmospheric oxygen on global scale (which, if happens, obviously can kill most of life on Earth) is another possible catastrophic consequence of the global warming, a global ecological disaster that has been overlooked.