Reproductive variance can drive behavioral dynamics.

The concept of fitness is central to evolution, but it quantifies only the expected number of offspring an individual will produce. The actual number of offspring is also subject to demographic stochasticity-that is, randomness associated with birth and death processes. In nature, individuals who are more fecund tend to have greater variance in their offspring number. Here, we develop a model for the evolution of two types competing in a population of nonconstant size. The fitness of each type is determined by pairwise interactions in a prisoner's dilemma game, and the variance in offspring number depends upon its mean. Although defectors are preferred by natural selection in classical population models, since they always have greater fitness than cooperators, we show that sufficiently large offspring variance can reverse the direction of evolution and favor cooperation. Large offspring variance produces qualitatively new dynamics for other types of social interactions, as well, which cannot arise in populations with a fixed size or with a Poisson offspring distribution.

The role of plasticity and stochasticity in coexistence.

Species coexistence in ecological communities is a central feature of biodiversity. Different concepts, i.e., contemporary niche theory, modern coexistence theory, and the unified neutral theory, have identified many building blocks of such ecological assemblies. However, other factors, such as phenotypic plasticity and stochastic inter-individual variation, have received little attention, in particular in animals. For example, how resource polyphenisms resulting in predator-prey interactions affect coexistence is currently unknown. Here, we present an integrative theoretical-experimental framework using the nematode plasticity model Pristionchus pacificus with its well-studied mouth-form dimorphism resulting in cannibalism. We develop an individual-based model that relies upon synthetic data based on our empirical measurements of fecundity and polyphenism to preserve demographic heterogeneity. We demonstrate how the interplay between plasticity and individual stochasticity result in all-or-nothing outcomes at the local level. Coexistence is made possible when spatial structure is introduced.

High Juvenile Mortality Overwhelms Benefits of Mating Potential for Reproductive Fitness.

AbstractAn individual's access to mates (i.e., its "mating potential") can constrain its reproduction but may also influence its fitness through effects on offspring survival. For instance, mate proximity may correspond with relatedness and lead to inbreeding depression in offspring. While offspring production and survival might respond differently to mating potential, previous studies have not considered the simultaneous effects of mating potential on these fitness components. We investigated the relationship of mating potential with both production and survival of offspring in populations of a long-lived herbaceous perennial, Echinacea angustifolia. Across 7 years and 14 sites, we quantified the mating potential of maternal plants in 1,278 mating bouts and followed the offspring from these bouts over 8 years. We used aster models to evaluate the relationship of mating potential with the number of offspring that emerged and that were alive after 8 years. Seedling emergence increased with mating potential. Despite this, the number of offspring surviving after 8 years showed no relationship to mating potential. Our results support the broader conclusion that the effect of mating potential on fitness erodes over time because of demographic stochasticity at the maternal level.

Building pyramids against the evolutionary emergence of pathogens.

Mutations allowing pathogens to escape host immunity promote the spread of infectious diseases in heterogeneous host populations and can lead to major epidemics. Understanding the conditions that slow down this evolution is key for the development of durable control strategies against pathogens. Here, we use theory and experiments to compare the efficacy of three strategies for the deployment of resistance: (i) a mixing strategy where the host population contains two single-resistant genotypes, (ii) a pyramiding strategy where the host carries a double-resistant genotype, (iii) a combining strategy where the host population is a mix of a single-resistant genotype and a double-resistant genotype. First, we use evolutionary epidemiology theory to clarify the interplay between demographic stochasticity and evolutionary dynamics to show that the pyramiding strategy always yields lower probability of evolutionary emergence. Second, we test experimentally these predictions with the introduction of bacteriophages into bacterial populations where we manipulated the diversity and the depth of immunity using a Clustered Regularly Interspaced Short Palindromic Repeats-CRISPR associated (CRISPR-Cas) system. These biological assays confirm that pyramiding multiple defences into the same host genotype and avoiding combination with single-defence genotypes is a robust way to reduce pathogen evolutionary emergence. The experimental validation of these theoretical recommendations has practical implications in various areas, including for the optimal deployment of resistance varieties in agriculture and for the design of durable vaccination strategies.

Statistical Mobility of Multicellular Colonies of Flagellated Swimming Cells.

We study the stochastic hydrodynamics of colonies of flagellated swimming cells, typified by multicellular choanoflagellates, which can form both rosette and chainlike shapes. The objective is to link cell-scale dynamics to colony-scale dynamics for various colonial morphologies. Via autoregressive stochastic models for the cycle-averaged flagellar force dynamics and statistical models for demographic cell-to-cell variability in flagellar properties and placement, we derive effective transport properties of the colonies, including cell-to-cell variability. We provide the most quantitative detail on disclike geometries to model rosettes, but also present formulas for the dynamics of general planar colony morphologies, which includes planar chain-like configurations.

Adaption, neutrality and life-course diversity.

Heterogeneity among individuals in fitness components is what selection acts upon. Evolutionary theories predict that selection in constant environments acts against such heterogeneity. But observations reveal substantial non-genetic and also non-environmental variability in phenotypes. Here, we examine whether there is a relationship between selection pressure and phenotypic variability by analysing structured population models based on data from a large and diverse set of species. Our findings suggest that non-genetic, non-environmental variation is in general neither truly neutral, selected for, nor selected against. We find much variations among species and populations within species, with mean patterns suggesting nearly neutral evolution of life-course variability. Populations that show greater diversity of life courses do not show, in general, increased or decreased population growth rates. Our analysis suggests we are only at the beginning of understanding the evolution and maintenance of non-genetic non-environmental variation.

Quantifying stochastic establishment of mutants in microbial adaptation.

Studies of microbial evolution, especially in applied contexts, have focused on the role of selection in shaping predictable, adaptive responses to the environment. However, chance events - the appearance of novel genetic variants and their establishment, i.e. outgrowth from a single cell to a sizeable population - also play critical initiating roles in adaptation. Stochasticity in establishment has received little attention in microbiology, potentially due to lack of awareness as well as practical challenges in quantification. However, methods for high-replicate culturing, mutant labelling and detection, and statistical inference now make it feasible to experimentally quantify the establishment probability of specific adaptive genotypes. I review methods that have emerged over the past decade, including experimental design and mathematical formulas to estimate establishment probability from data. Quantifying establishment in further biological settings and comparing empirical estimates to theoretical predictions represent exciting future directions. More broadly, recognition that adaptive genotypes may be stochastically lost while rare is significant both for interpreting common lab assays and for designing interventions to promote or inhibit microbial evolution.

Evolutionary rescue under demographic and environmental stochasticity.

Populations suffer two types of stochasticity: demographic stochasticity, from sampling error in offspring number, and environmental stochasticity, from temporal variation in the growth rate. By modelling evolution through phenotypic selection following an abrupt environmental change, we investigate how genetic and demographic dynamics, as well as effects on population survival of the genetic variance and of the strength of stabilizing selection, differ under the two types of stochasticity. We show that population survival probability declines sharply with stronger stabilizing selection under demographic stochasticity, but declines more continuously when environmental stochasticity is strengthened. However, the genetic variance that confers the highest population survival probability differs little under demographic and environmental stochasticity. Since the influence of demographic stochasticity is stronger when population size is smaller, a slow initial decline of genetic variance, which allows quicker evolution, is important for population persistence. In contrast, the influence of environmental stochasticity is population-size-independent, so higher initial fitness becomes important for survival under strong environmental stochasticity. The two types of stochasticity interact in a more than multiplicative way in reducing the population survival probability. Our work suggests the importance of explicitly distinguishing and measuring the forms of stochasticity during evolutionary rescue.

Partitioning variance in population growth for models with environmental and demographic stochasticity.

How demographic factors lead to variation or change in growth rates can be investigated using life table response experiments (LTRE) based on structured population models. Traditionally, LTREs focused on decomposing the asymptotic growth rate, but more recently decompositions of annual 'realized' growth rates using 'transient' LTREs have gained in popularity. Transient LTREs have been used particularly to understand how variation in vital rates translate into variation in growth for populations under long-term study. For these, complete population models may be constructed to investigate how temporal variation in environmental drivers affect vital rates. Such investigations have usually come down to estimating covariate coefficients for the effects of environmental variables on vital rates, but formal ways of assessing how they lead to variation in growth rates have been lacking. We extend transient LTREs to further partition the contributions from vital rates into contributions from temporally varying factors that affect them. The decomposition allows one to compare the resultant effect on the growth rate of different environmental factors, as well as density dependence, which may each act via multiple vital rates. We also show how realized growth rates can be decomposed into separate components from environmental and demographic stochasticity. The latter is typically omitted in LTRE analyses. We illustrate these extensions with an integrated population model (IPM) for data from a 26 years study on northern wheatears (Oenanthe oenanthe), a migratory passerine bird breeding in an agricultural landscape. For this population, consisting of around 50-120 breeding pairs per year, we partition variation in realized growth rates into environmental contributions from temperature, rainfall, population density and unexplained random variation via multiple vital rates, and from demographic stochasticity. The case study suggests that variation in first year survival via the unexplained random component, and adult survival via temperature are two main factors behind environmental variation in growth rates. More than half of the variation in growth rates is suggested to come from demographic stochasticity, demonstrating the importance of this factor for populations of moderate size.

Quantifying invasibility.

Invasibility, the chance of a population to grow from rarity and become established, plays a fundamental role in population genetics, ecology, epidemiology and evolution. For many decades, the mean growth rate of a species when it is rare has been employed as an invasion criterion. Recent studies show that the mean growth rate fails as a quantitative metric for invasibility, with its magnitude sometimes even increasing while the invasibility decreases. Here we provide two novel formulae, based on the diffusion approximation and a large-deviations (Wentzel-Kramers-Brillouin) approach, for the chance of invasion given the mean growth and its variance. The first formula has the virtue of simplicity, while the second one holds over a wider parameter range. The efficacy of the formulae, including their accompanying data analysis technique, is demonstrated using synthetic time series generated from canonical models and parameterised with empirical data.

Stochasticity Leads to Coexistence of Generalists and Specialists in Assembling Mutualistic Communities.

AbstractSpecies interaction networks are subject to natural and anthropogenic disturbances that lead to their disassembly, while natural regeneration or restoration efforts facilitate their reassembly. Previous models for assembling ecological networks did not include stochasticity at the level of population dynamics (e.g., demographic noise, environmental noise) and focused mainly on food webs. Here, we present a model for the assembly of mutualistic bipartite networks, such as plant-pollinator networks, and examine the influence of demographic noise on the trajectory of species and strategy diversity, that is, the range of present strategies from specialism to generalism. We find that assembled communities show at intermediate assembly stages a maximum of species diversity and of average generalization. Our model thus provides a mechanism for nonlinear, hump-shaped diversity trajectories at intermediate succession, consistent with the intermediate disturbance hypothesis. Long-term coexistence of specialists and generalists emerges only in the presence of demographic noise and is due to a persistent species turnover. These findings highlight the importance of stochasticity for maintaining long-term diversity.

How temporal environmental stochasticity affects species richness: Destabilization, neutralization and the storage effect.

Temporal environmental stochasticity (TES), along with the variations of demographic rates associated with it, is ubiquitous in nature. Here we study the effect of TES on the species richness of diverse communities. In such communities the biodiversity at equilibrium reflects the balance between the rate at which new types are added (via migration, mutation or speciation) and the rate of extinction. We analyze a few generic models in which the speciation rate is fixed and TES affects the rate of extinction, and identify three different mechanisms. First, TES increases abundance variations and shortens extinction times, thus decreasing the species richness (destabilizing effect). Second, TES blurs the time-independent fitness differences between species, making the dynamics more symmetric and thereby increasing the diversity (neutralizing effect). Third, the storage effect allows TES to facilitate the invasion of inferior species, again contributing to the species richness. The stabilizing effect of storage declines significantly in diverse communities and it can overcome the destabilizing effect of TES only when environmental fluctuations are rapid enough.

A white noise approach to evolutionary ecology.

Although the evolutionary response to random genetic drift is classically modelled as a sampling process for populations with fixed abundance, the abundances of populations in the wild fluctuate over time. Furthermore, since wild populations exhibit demographic stochasticity and since random genetic drift is in part due to demographic stochasticity, theoretical approaches are needed to understand the role of demographic stochasticity in eco-evolutionary dynamics. Here we close this gap for quantitative characters evolving in continuously reproducing populations by providing a framework to track the stochastic dynamics of abundance density across phenotypic space using stochastic partial differential equations. In the process we develop a set of heuristics to operationalize the powerful, but abstract theory of white noise and diffusion-limits of individual-based models. Applying these heuristics, we obtain stochastic ordinary differential equations that generalize classical expressions of ecological quantitative genetics. In particular, by supplying growth rate and reproductive variance as functions of abundance densities and trait values, these equations track population size, mean trait and additive genetic variance responding to mutation, demographic stochasticity, random genetic drift, deterministic selection and noise-induced selection. We demonstrate the utility of our approach by formulating a model of diffuse coevolution mediated by exploitative competition for a continuum of resources. In addition to trait and abundance distributions, this model predicts interaction networks defined by niche-overlap, competition coefficients, or selection gradients. Using a high-richness approximation, we find linear selection gradients and competition coefficients are uncorrelated, but magnitudes of linear selection gradients and quadratic selection gradients are both positively correlated with competition coefficients. Hence, competing species that strongly affect each other's abundance tend to also impose selection on one another, but the directionality is not predicted. This approach contributes to the development of a synthetic theory of evolutionary ecology by formalizing first principle derivations of stochastic models tracking feedbacks of biological processes and the patterns of diversity they produce.

Assessing metacommunity processes through signatures in spatiotemporal turnover of community composition.

Although metacommunity ecology has been a major field of research in the last decades, with both conceptual and empirical outputs, the analysis of the temporal dynamics of metacommunities has only emerged recently and consists mostly of repeated static analyses. Here we propose a novel analytical framework to assess metacommunity processes using path analyses of spatial and temporal diversity turnovers. We detail the principles and practical aspects of this framework and apply it to simulated datasets to illustrate its ability to decipher the respective contributions of entangled drivers of metacommunity dynamics. We then apply it to four empirical datasets. Empirical results support the view that metacommunity dynamics may be generally shaped by multiple ecological processes acting in concert, with environmental filtering being variable across both space and time. These results reinforce our call to go beyond static analyses of metacommunities that are blind to the temporal part of environmental variability.

The inherent multidimensionality of temporal variability: how common and rare species shape stability patterns.

Empirical knowledge of diversity-stability relationships is mostly based on the analysis of temporal variability. Variability, however, often depends on external factors that act as disturbances, which makes comparisons across systems difficult to interpret. Here, we show how variability can reveal inherent stability properties of ecological communities. This requires that we abandon one-dimensional representations, in which a single variability measurement is taken as a proxy for how stable a system is, and instead consider the whole set of variability values generated by all possible stochastic perturbations. Despite this complexity, in species-rich systems, a generic pattern emerges from community assembly, relating variability to the abundance of perturbed species. Strikingly, the contrasting contributions of different species abundance classes to variability, driven by different types of perturbations, can lead to opposite diversity-stability patterns. We conclude that a multidimensional perspective on variability helps reveal the dynamical richness of ecological systems and the underlying meaning of their stability patterns.

Extinction vortex dynamics of top predators isolated by urbanization.

Extinction risk is elevated in small, isolated populations due to demographic and genetic interactions. Therefore, it is critical to model these processes realistically in population viability analyses (PVA) to inform local management and contribute to a greater understanding of mechanisms within the extinction vortex. We conducted PVA's for two small mountain lion populations isolated by urbanization in southern California to predict population growth, extinction probability, and loss of genetic diversity with empirical data. Specifically, we (1) provide the first PVA for isolated mountain lions in the Santa Ana Mountains (SAM) that considers both demographic and genetic risk factors and (2) test the hypothesis that variation in abundance and mortality between the SAM and Santa Monica Mountains (SMM) result in differences in population growth, loss of heterozygosity, and extinction probability. Our models predicted 16-21% probability of local extinction in the SAM due purely to demographic processes over 50 yr with current low levels or no immigration. Our models also predicted that genetic diversity will further erode in the SAM such that concern regarding inbreeding depression is warranted unless gene flow is increased, and that if inbreeding depression occurs, rapid local extinction will be highly likely. Dynamics of the two populations were broadly similar, but they also exhibited differences driven by larger population size and higher mortality in the SAM. Density-independent scenarios predicted a rapidly increasing population in the SMM, whereas growth potential did not differ from a stable trend in the SAM. Demographic extinction probability and loss of heterozygosity were greater in the SMM for density-dependent scenarios without immigration. However, higher levels of immigration had stronger, positive influences on both demographic viability and retention of genetic diversity in the SMM driven by lower abundance and higher adult survival. Our results elucidate demographic and genetic threats to small populations within the extinction vortex, and how these vary relative to demographic structure. Importantly, simulating seemingly attainable increases in connectivity was sufficient to greatly reduce extinction probability. Our work highlights that conservation of large carnivores is achievable within urbanized landscapes, but requires land protection, connectivity, and strategies to promote coexistence with humans.

Life-history traits and the fate of translocated populations.

Attempts to identify predictors and mechanisms of invasion success have been weakened by poor data quality, mostly because monitoring does not begin immediately after introduction events. To overcome this issue, we used data from conservation translocations of threatened bird species. We analyzed information on >1200 translocation events of >150 bird species to investigate how life-history traits affect population establishment measured based on rates of survival and reproduction. Species position along the slow-fast life-history continuum was a key predictor of translocation success. Species with fast-paced life histories were less likely to survive (over both short- and mid-term) and more likely to breed successfully than species with slow life histories. The temporal partitioning of reproductive effort (number of clutches per year) also affected the probability of successful reproduction. Our results illustrate how conservation-motivated reintroduction programs can provide proxies for the initial stages of the invasion process, enabling empirical tests of predictions from life-history theory and informing management.

Atributos de las Historias de Vida y el Destino de las Poblaciones Reubicadas Resumen Los intentos por identificar los pronosticadores y los mecanismos del éxito de invasión han sido debilitados por la poca calidad de los datos, principalmente porque el monitoreo no inicia inmediatamente después de los eventos de introducción. Para superar este tema, usamos datos a partir de las reubicaciones por conservación de especies amenazadas de aves. Analizamos la información de más de 1,200 eventos de reubicación para más de 150 especies de aves y así investigar cómo los atributos de las historias de vida afectan el establecimiento de la población medido con base en tasas de supervivencia y reproducción. La posición de las especies a lo largo del continuo de historias de vida lenta-rápida fue un pronosticador importante para el éxito de la reubicación. Las especies con historias de vida rápidas tuvieron una menor posibilidad de sobrevivir (tanto a corto como a mediano plazo) y una mayor probabilidad de reproducirse exitosamente que las especies con historias de vida lentas. La división temporal del esfuerzo reproductivo (número de puestas por año) también afectó la probabilidad del éxito de la reproducción. Nuestros resultados ilustran cómo los programas de reintroducción motivados por la conservación pueden proporcionar sustitutos para los estadios iniciales del proceso de invasión, permitiendo pruebas empíricas a partir de la teoría de la historia de vida e informando a los administradores.

Applications of WKB and Fokker-Planck Methods in Analyzing Population Extinction Driven by Weak Demographic Fluctuations.

In large but finite populations, weak demographic stochasticity due to random birth and death events can lead to population extinction. The process is analogous to the escaping problem of trapped particles under random forces. Methods widely used in studying such physical systems, for instance, Wentzel-Kramers-Brillouin (WKB) and Fokker-Planck methods, can be applied to solve similar biological problems. In this article, we comparatively analyse applications of WKB and Fokker-Planck methods to some typical stochastic population dynamical models, including the logistic growth, endemic SIR, predator-prey, and competitive Lotka-Volterra models. The mean extinction time strongly depends on the nature of the corresponding deterministic fixed point(s). For different types of fixed points, the extinction can be driven either by rare events or typical Gaussian fluctuations. In the former case, the large deviation function that governs the distribution of rare events can be well-approximated by the WKB method in the weak noise limit. In the later case, the simpler Fokker-Planck approximation approach is also appropriate.

Prediction and scale in savanna ecosystems.

Contents Summary 52 I. Introduction 52 II. Determinants of savanna vegetation structure 53 III. Are trees in savannas really more heterogeneous? 53 IV. Are trees in savannas a 'slow' variable? 54 V. Are trees in savannas spatially patterned? 55 VI. Conclusions 55 Acknowledgements 55 References 56 SUMMARY: Savannas are highly variable systems, and predicting variation, especially in the tree layer, represents a major unresolved challenge for forecasting biosphere responses to global change. Prediction to date has focused on disentangling interactions between resource limitation and chronic disturbances to identify what determines local savanna vegetation heterogeneity. By focusing at too fine a scale, this approach overlooks: sample size limitation arising from sparse tree distributions; stochasticity in demographic and environmental processes that is preserved as heterogeneity among tree populations with slow dynamics; and spatial self-organization. Renewed focus on large (1-50 ha) permanent plots and on spatial patterns of tree-layer variability at even larger landscape spatial scales (≥1000s of ha) promises to resolve these limitations, consistent with the goal of predicting large-scale biosphere responses to global change.

Experimental evidence that density dependence strongly influences plant invasions through fragmented landscapes.

Populations of range expanding species encounter patches of both favorable and unfavorable habitat as they spread across landscapes. Theory shows that increasing patchiness slows the spread of populations modeled with continuously varying population density when dispersal is not influence by the environment or individual behavior. However, as is found in uniformly favorable landscapes, spread remains driven by fecundity and dispersal from low density individuals at the invasion front. In contrast, when modeled populations are composed of discrete individuals, patchiness causes populations to build up to high density before dispersing past unsuitable habitat, introducing an important influence of density dependence on spread velocity. To test the hypothesized interaction between habitat patchiness and density dependence, we simultaneously manipulated these factors in a greenhouse system of annual plants spreading through replicated experimental landscapes. We found that increasing the size of gaps and amplifying the strength of density dependence both slowed spread velocity, but contrary to predictions, the effect of amplified density dependence was similar across all landscape types. Our results demonstrate that the discrete nature of individuals in spreading populations has a strong influence on how both landscape patchiness and density dependence influence spread through demographic and dispersal stochasticity. Both finiteness and landscape structure should be critical components to theoretical predictions of future spread for range expanding native species or invasive species colonizing new habitat.