Mutualism at the leading edge: insights into the eco-evolutionary dynamics of host-symbiont communities during range expansion.

The evolution of mutualism between host and symbiont communities plays an essential role in maintaining ecosystem function and should therefore have a profound effect on their range expansion dynamics. In particular, the presence of mutualistic symbionts at the leading edge of a host-symbiont community should enhance its propagation in space. We develop a theoretical framework that captures the eco-evolutionary dynamics of host-symbiont communities, to investigate how the evolution of resource exchange may shape community structure during range expansion. We consider a community with symbionts that are mutualistic or parasitic to various degrees, where parasitic symbionts receive the same amount of resource from the host as mutualistic symbionts, but at a lower cost. The selective advantage of parasitic symbionts over mutualistic ones is increased with resource availability (i.e. with host density), promoting mutualism at the range edges, where host density is low, and parasitism at the population core, where host density is higher. This spatial selection also influences the speed of spread. We find that the host growth rate (which depends on the average benefit provided by the symbionts) is maximal at the range edges, where symbionts are more mutualistic, and that host-symbiont communities with high symbiont density at their core (e.g. resulting from more mutualistic hosts) spread faster into new territories. These results indicate that the expansion of host-symbiont communities is pulled by the hosts but pushed by the symbionts, in a unique push-pull dynamic where both the host and symbionts are active and tightly-linked players.

metanetwork: A R package dedicated to handling and representing trophic metanetworks.

Trophic networks describe interactions between species at a given location and time. Due to environmental changes, anthropogenic perturbations or sampling effects, trophic networks may vary in space and time. The collection of network time series or networks in different sites thus constitutes a metanetwork. We present here the R package metanetwork, which will ease the representation, the exploration and analysis of trophic metanetwork data sets that are increasingly available. Our main methodological advance consists in suitable layout algorithm for trophic networks, which is based on trophic levels and dimension reduction in a graph diffusion kernel. In particular, it highlights relevant features of trophic networks (trophic levels, energetic channels). In addition, we developed tools to handle, compare visually and quantitatively and aggregate those networks. Static and dynamic visualisation functions have been developed to represent large networks. We apply our package workflow to several trophic network data sets.

Ancestral Lineages in Mutation Selection Equilibria with Moving Optimum.

Many populations can somehow adapt to rapid environmental changes. To understand this fast evolution, we investigate the genealogy of individuals inside those populations. More precisely, we use a deterministic model to describe the phenotypic density of a population under selection when the fitness optimum moves at constant speed. We study the inside dynamics of this population using the neutral fractions approach. We then define a Markov process characterizing the distribution of ancestral phenotypic lineages inside the equilibrium. This construction yields qualitative as well as quantitative properties on the phenotype of typical ancestors. In particular, we show that in asexual populations typical ancestors of present individuals carried traits much closer to the fitness optimum than most individuals alive at the same time. We also investigate more deeply the asymptotic regime of small mutation effects. In this regime, we obtain an explicit formula for the typical ancestral lineage using the description of the solutions of the Hamilton Jacobi equation as a minimizer of an optimization problem. In addition, we compare our deterministic results on lineages with the lineages of stochastic models.

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.

Co-inoculation with arbuscular mycorrhizal fungi differing in carbon sink strength induces a synergistic effect in plant growth.

Arbuscular mycorrhizal (AM) fungi play a key role in determining ecosystem functionality. Understanding how diversity in the fungal community affects plant productivity is therefore an important question in ecology. Current research has focused on understanding the role of functional complementarity in the fungal community when the host plant faces multiple stress factors. Fewer studies, however, have investigated how variation in traits affecting nutrient exchange can impact the plant growth dynamics, even in the absence of environmental stressors. Combining experimental data and a mathematical model based on ordinary differential equations, we investigate the role played by carbon sink strength on plant productivity. We simulate and measure plant growth over time when the plant is associated with two fungal isolates with different carbon sink strength, and when the plant is in pairwise association with each of the isolates alone. Overall, our theoretical as well as our experimental results show that co-inoculation with fungi with different carbon sink strength can induce positive non-additive effects (or synergistic effects) in plant productivity. Fungi with high carbon sink strength are able to quickly establish a fungal community and increase the nutrient supply to the plant, with a consequent positive impact on plant growth rate. On the other side, fungi with low carbon sink strength inflict lower carbon costs to the host plant, and support maximal plant productivity once plant biomass is large. As AM fungi are widely used as organic fertilizers worldwide, our findings have important implications for restoration ecology and agricultural management.

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.

Diversity within mutualist guilds promotes coexistence and reduces the risk of invasion from an alien mutualist.

Biodiversity is an important component of healthy ecosystems, and thus understanding the mechanisms behind species coexistence is critical in ecology and conservation biology. In particular, few studies have focused on the dynamics resulting from the co-occurrence of mutualistic and competitive interactions within a group of species. Here we build a mathematical model to study the dynamics of a guild of competitors who are also engaged in mutualistic interactions with a common partner. We show that coexistence as well as competitive exclusion can occur depending on the competition strength and on strength of the mutualistic interactions, and we formulate concrete criteria for predicting invasion success of an alien mutualist based on propagule pressure, alien traits (such as its resource exchange ability) and composition of the recipient community. We find that intra guild diversity promotes the coexistence of species that would otherwise competitively exclude each other, and makes a guild less vulnerable to invasion. Our results can serve as a useful framework to predict the consequences of species manipulation in mutualistic communities.

Inside dynamics for stage-structured integrodifference equations.

A stage-structured model of integrodifference equations is used to study the asymptotic neutral genetic structure of populations undergoing range expansion. That is, we study the inside dynamics of solutions to stage-structured integrodifference equations. To analyze the genetic consequences for long term population spread, we decompose the solution into neutral genetic components called neutral fractions. The inside dynamics are then given by the spatiotemporal evolution of these neutral fractions. We show that, under some mild assumptions on the dispersal kernels and population projection matrix, the spread is dominated by individuals at the leading edge of the expansion. This result is consistent with the founder effect. In the case where there are multiple neutral fractions at the leading edge we are able to explicitly calculate the asymptotic proportion of these fractions found in the long-term population spread. This formula is simple and depends only on the right and left eigenvectors of the population projection matrix evaluated at zero and the initial proportion of each neutral fraction at the leading edge of the range expansion. In the absence of a strong Allee effect, multiple neutral fractions can drive the long-term population spread, a situation not possible with the scalar model.

The Paris Agreement objectives will likely halt future declines of emperor penguins.

The Paris Agreement is a multinational initiative to combat climate change by keeping a global temperature increase in this century to 2°C above preindustrial levels while pursuing efforts to limit the increase to 1.5°C. Until recently, ensembles of coupled climate simulations producing temporal dynamics of climate en route to stable global mean temperature at 1.5 and 2°C above preindustrial levels were not available. Hence, the few studies that have assessed the ecological impact of the Paris Agreement used ad-hoc approaches. The development of new specific mitigation climate simulations now provides an unprecedented opportunity to inform ecological impact assessments. Here we project the dynamics of all known emperor penguin (Aptenodytes forsteri) colonies under new climate change scenarios meeting the Paris Agreement objectives using a climate-dependent-metapopulation model. Our model includes various dispersal behaviors so that penguins could modulate climate effects through movement and habitat selection. Under business-as-usual greenhouse gas emissions, we show that 80% of the colonies are projected to be quasiextinct by 2100, thus the total abundance of emperor penguins is projected to decline by at least 81% relative to its initial size, regardless of dispersal abilities. In contrast, if the Paris Agreement objectives are met, viable emperor penguin refuges will exist in Antarctica, and only 19% and 31% colonies are projected to be quasiextinct by 2100 under the Paris 1.5 and 2 climate scenarios respectively. As a result, the global population is projected to decline by at least by 31% under Paris 1.5 and 44% under Paris 2. However, population growth rates stabilize in 2060 such that the global population will be only declining at 0.07% under Paris 1.5 and 0.34% under Paris 2, thereby halting the global population decline. Hence, global climate policy has a larger capacity to safeguard the future of emperor penguins than their intrinsic dispersal abilities.

Beneficial mutation-selection dynamics in finite asexual populations: a free boundary approach.

Using a free boundary approach based on an analogy with ice melting models, we propose a deterministic PDE framework to describe the dynamics of fitness distributions in the presence of beneficial mutations with non-epistatic effects on fitness. Contrarily to most approaches based on deterministic models, our framework does not rely on an infinite population size assumption, and successfully captures the transient as well as the long time dynamics of fitness distributions. In particular, consistently with stochastic individual-based approaches or stochastic PDE approaches, it leads to a constant asymptotic rate of adaptation at large times, that most deterministic approaches failed to describe. We derive analytic formulas for the asymptotic rate of adaptation and the full asymptotic distribution of fitness. These formulas depend explicitly on the population size, and are shown to be accurate for a wide range of population sizes and mutation rates, compared to individual-based simulations. Although we were not able to derive an analytic description for the transient dynamics, numerical computations lead to accurate predictions and are computationally efficient compared to stochastic simulations. These computations show that the fitness distribution converges towards a travelling wave with constant speed, and whose profile can be computed analytically.

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.

Allee effect promotes diversity in traveling waves of colonization.

Most mathematical studies on expanding populations have focused on the rate of range expansion of a population. However, the genetic consequences of population expansion remain an understudied body of theory. Describing an expanding population as a traveling wave solution derived from a classical reaction-diffusion model, we analyze the spatio-temporal evolution of its genetic structure. We show that the presence of an Allee effect (i.e., a lower per capita growth rate at low densities) drastically modifies genetic diversity, both in the colonization front and behind it. With an Allee effect (i.e., pushed colonization waves), all of the genetic diversity of a population is conserved in the colonization front. In the absence of an Allee effect (i.e., pulled waves), only the furthest forward members of the initial population persist in the colonization front, indicating a strong erosion of the diversity in this population. These results counteract commonly held notions that the Allee effect generally has adverse consequences. Our study contributes new knowledge to the surfing phenomenon in continuous models without random genetic drift. It also provides insight into the dynamics of traveling wave solutions and leads to a new interpretation of the mathematical notions of pulled and pushed waves.

Success rate of a biological invasion in terms of the spatial distribution of the founding population.

We analyze the role of the spatial distribution of the initial condition in reaction-diffusion models of biological invasion. Our study shows that, in the presence of an Allee effect, the precise shape of the initial (or founding) population is of critical importance for successful invasion. Results are provided for one-dimensional and two-dimensional models. In the one-dimensional case, we consider initial conditions supported by two disjoint intervals of length L/2 and separated by a distance α. Analytical as well as numerical results indicate that the critical size L*(α) of the population, where the invasion is successful if and only if L > L*(α), is a continuous function of α and tends to increase with α, at least when α is not too small. This result emphasizes the detrimental effect of fragmentation. In the two-dimensional case, we consider more general, stochastically generated initial conditions u0, and we provide a new and rigorous definition of the rate of fragmentation of u0. We then conduct a statistical analysis of the probability of successful invasion depending on the size of the support of u0 and the fragmentation rate of u0. Our results show that the outcome of an invasion is almost completely determined by these two parameters. Moreover, we observe that the minimum abundance required for successful invasion tends to increase in a non-linear fashion with the fragmentation rate. This effect of fragmentation is enhanced as the strength of the Allee effect is increased.