The evolution of chemodiversity in plants-From verbal to quantitative models.

Plants harbour a great chemodiversity, that is diversity of specialised metabolites (SMs), at different scales. For instance, individuals can produce a large number of SMs, and populations can differ in their metabolite composition. Given the ecological and economic importance of plant chemodiversity, it is important to understand how it arises and is maintained over evolutionary time. For other dimensions of biodiversity, that is species diversity and genetic diversity, quantitative models play an important role in addressing such questions. Here, we provide a synthesis of existing hypotheses and quantitative models, that is mathematical models and computer simulations, for the evolution of plant chemodiversity. We describe each model's ingredients, that is the biological processes that shape chemodiversity, the scales it considers and whether it has been formalized as a quantitative model. Although we identify several quantitative models, not all are dynamic and many influential models have remained verbal. To fill these gaps, we outline our vision for the future of chemodiversity modelling. We identify quantitative models used for genetic variation that may be adapted for chemodiversity, and we present a flexible framework for the creation of individual-based models that address different scales of chemodiversity and combine different ingredients that bring this chemodiversity about.

Sexual Antagonism, Temporally Fluctuating Selection, and Variable Dominance Affect a Regulatory Polymorphism in Drosophila melanogaster.

Understanding how genetic variation is maintained within species is a major goal of evolutionary genetics that can shed light on the preservation of biodiversity. Here, we examined the maintenance of a regulatory single-nucleotide polymorphism (SNP) of the X-linked Drosophila melanogaster gene fezzik. The derived variant at this site is at intermediate frequency in many worldwide populations but absent in populations from the ancestral species range in sub-Saharan Africa. We collected and genotyped wild-caught individuals from a single European population biannually over a period of 5 years, which revealed an overall difference in allele frequency between the sexes and a consistent change in allele frequency across seasons in females but not in males. Modeling based on the observed allele and genotype frequencies suggested that both sexually antagonistic and temporally fluctuating selection may help maintain variation at this site. The derived variant is predicted to be female-beneficial and mostly recessive; however, there was uncertainty surrounding our dominance estimates and long-term modeling projections suggest that it is more likely to be dominant. By examining gene expression phenotypes, we found that phenotypic dominance was variable and dependent upon developmental stage and genetic background, suggesting that dominance may be variable at this locus. We further determined that fezzik expression and genotype are associated with starvation resistance in a sex-dependent manner, suggesting a potential phenotypic target of selection. By characterizing the mechanisms of selection acting on this SNP, our results improve our understanding of how selection maintains genetic and phenotypic variation in natural populations.

Modeling minimum viable population size with multiple genetic problems of small populations.

An important goal for conservation is to define minimum viable population (MVP) sizes for long-term persistence of a species. There is increasing evidence of the role of genetics in population extinction; thus, conservation practitioners are starting to consider the effects of deleterious mutations (DM), in particular the effects of inbreeding depression on fitness. We sought to develop methods to account for genetic problems other than inbreeding depression in MVP estimates, quantify the effect of the interaction of multiple genetic problems on MVP sizes, and find ways to reduce the arbitrariness of time and persistence probability thresholds in MVP analyses. To do so, we developed ecoevolutionary quantitative models to track population size and levels of genetic diversity. We assumed a biallelic multilocus genome with loci under single or multiple, interacting genetic forces. We included mutation-selection-drift balance (for loci with DM) and 3 forms of balancing selection for loci for which variation is lost through genetic drift. We defined MVP size as the lowest population size that avoids an ecoevolutionary extinction vortex. For populations affected by only balancing selection, MVP size decreased rapidly as mutation rates increased. For populations affected by mutation-selection-drift balance, the MVP size increased rapidly. In addition, MVP sizes increased rapidly as the number of loci increased under the same or different selection mechanisms until even arbitrarily large populations could not survive. In the case of fixed number of loci under selection, interaction of genetic problems did not always increase MVP sizes. To further enhance understanding about interaction of genetic problems, there is need for more empirical studies to reveal how different genetic processes interact in the genome.

Resumen Un objetivo importante de la conservación es definir los tamaños de una población mínima viable (PMV) para la persistencia a largo plazo de una especie. Cada vez hay más evidencia del papel que tiene la genética en la extinción poblacional; por lo tanto, quienes practican la conservación comienzan a considerar los efectos de las mutaciones deletéreas (MD) causadas por los cambios en la adaptabilidad ocasionados por la depresión endogámica. Buscamos desarrollar varios métodos que consideren otros problemas genéticos además de la depresión endogámica en las estimaciones de la PMV, cuantifiquen el efecto de la interacción entre múltiples problemas genéticos sobre los tamaños de la PMV y encuentren maneras para reducir la arbitrariedad de los umbrales de tiempo y de probabilidad de persistencia en los análisis de la PMV. Para realizar lo anterior, desarrollamos unos modelos cuantitativos ecoevolutivos para darle seguimiento al tamaño poblacional y a los niveles de diversidad genética. Partimos de un supuesto genoma bialélico multilocus con loci bajo una o varias fuerzas genéticas en interacción. Incluimos un equilibrio de mutación-selección-deriva (para los loci con MD) y tres formas de selección equilibradora para los loci cuya variación se pierde mediante la deriva génica. Definimos el tamaño de la PMV como el tamaño poblacional más reducido que evita un vórtice de extinción ecoevolutiva. Para las poblaciones afectadas solamente por la selección equilibradora, el tamaño de la PMV disminuyó rápidamente conforme incrementaron las tasas de mutación. Para las poblaciones afectadas por el equilibrio mutación-selección-deriva, el tamaño de la PMV incrementó rápidamente. Además, los tamaños de la PMV incrementaron rápidamente conforme el número de loci incrementó bajo el mismo mecanismo de selección o alguno distinto hasta que las poblaciones arbitrariamente grandes no podían sobrevivir más. En el caso de un número fijo de loci bajo selección, la interacción de los problemas genéticos no siempre incrementó el tamaño de la PMV. Para incrementar aún más el conocimiento sobre las interacciones de los problemas genéticos, se necesitan más estudios empíricos que revelen cómo los diferentes procesos genéticos interactúan en el genoma.

Models for Eco-Evolutionary Extinction Vortices under Balancing Selection.

AbstractThe smaller a population is, the faster it loses genetic diversity as a result of genetic drift. Loss of genetic diversity can reduce population growth rate, making populations even smaller and more vulnerable to loss of genetic diversity. Ultimately, the population can be driven to extinction by this "eco-evolutionary extinction vortex." While there are already quantitative models for extinction vortices resulting from inbreeding depression and mutation accumulation, to date extinction vortices resulting from loss of genetic diversity at loci under various forms of balancing selection have been mainly described verbally. To understand better when such extinction vortices arise and to develop methods for detecting them, we propose quantitative eco-evolutionary models, both stochastic individual-based simulations and deterministic approximations, linking loss of genetic diversity and population decline. Using mathematical analysis and simulations, we identify parameter combinations that exhibit strong interactions between population size and genetic diversity and match our definition of an eco-evolutionary vortex (i.e., per capita population decline rates and per-locus fixation rates increase with decreasing population size and number of polymorphic loci). We further highlight cues that may be exhibited by such populations but find that classical early-warning signals are of limited use in detecting populations undergoing an eco-evolutionary extinction vortex.

Density dependence on multiple spatial scales maintains spatial variation in both abundance and traits.

Population density affects fitness through various processes, such as mate finding and competition. The fitness of individuals in a population can in turn affect its density, making population density a key quantity linking ecological and evolutionary processes. Density effects are, however, rarely homogeneous. Different life-history processes can be affected by density over different spatial scales. In birds, for example, competition for food may depend on the number of birds nesting in the direct vicinity, while competition for nesting sites may occur over larger areas. Here we investigate how the effects of local density and of density in a nearby patch can jointly affect the emergence of spatial variation in abundance as well as phenotypic diversification. We study a two-patch model that is described by coupled ordinary differential equations. The patches have no intrinsic differences: they both have the same fitness function that describes how an individual's fitness depends on density in its own patch as well as the density in the other patch. We use a phase-space analysis, combined with a mathematical stability analysis to study the long-term behaviour of the system. Our results reveal that the mutual effect that the patches have on each other can lead to the emergence and long-term maintenance of a low and a high density patch. We then add traits and mutations to the model and show that different selection pressures in the high and low density patch can lead to diversification between these patches. Via eco-evolutionary feedbacks, this diversification can in turn lead to changes in the long-term population densities: under some parameter settings, both patches reach the same equilibrium density when mutations are absent, but different equilibrium densities when mutations are allowed. We thus show how, even in the absence of differences between patches, interactions between them can lead to differences in long-term population density, and potentially to trait diversification.

Seasonally fluctuating selection can maintain polymorphism at many loci via segregation lift.

Most natural populations are affected by seasonal changes in temperature, rainfall, or resource availability. Seasonally fluctuating selection could potentially make a large contribution to maintaining genetic polymorphism in populations. However, previous theory suggests that the conditions for multilocus polymorphism are restrictive. Here, we explore a more general class of models with multilocus seasonally fluctuating selection in diploids. In these models, the multilocus genotype is mapped to fitness in two steps. The first mapping is additive across loci and accounts for the relative contributions of heterozygous and homozygous loci-that is, dominance. The second step uses a nonlinear fitness function to account for the strength of selection and epistasis. Using mathematical analysis and individual-based simulations, we show that stable polymorphism at many loci is possible if currently favored alleles are sufficiently dominant. This general mechanism, which we call "segregation lift," requires seasonal changes in dominance, a phenomenon that may arise naturally in situations with antagonistic pleiotropy and seasonal changes in the relative importance of traits for fitness. Segregation lift works best under diminishing-returns epistasis, is not affected by problems of genetic load, and is robust to differences in parameters across loci and seasons. Under segregation lift, loci can exhibit conspicuous seasonal allele-frequency fluctuations, but often fluctuations may be small and hard to detect. An important direction for future work is to formally test for segregation lift in empirical data and to quantify its contribution to maintaining genetic variation in natural populations.

Eco-Evolutionary Buffering: Rapid Evolution Facilitates Regional Species Coexistence despite Local Priority Effects.

Inhibitory priority effects, in which early-arriving species exclude competing species from local communities, are thought to enhance regional species diversity via community divergence. Theory suggests, however, that these same priority effects make it difficult for species to coexist in the region unless individuals are continuously supplied from an external species pool, often an unrealistic assumption. Here we develop an eco-evolutionary hypothesis to solve this conundrum. We build a metacommunity model in which local priority effects occur between two species via interspecific interference. Within each species there are two genotypes: one is more resistant to interspecific interference than the other but pays a fitness cost for its resistance. Because of this trade-off, species evolve to become less resistant as they become regionally more common. Rare species can then invade some local patches and consequently recover in regional frequency. This "eco-evolutionary buffering" enables the regional coexistence of species despite local priority effects, even in the absence of immigration from an external species pool. Our model predicts that eco-evolutionary buffering is particularly effective when local communities are small and connected by infrequent dispersal.

Genetic Allee effects and their interaction with ecological Allee effects.

It is now widely accepted that genetic processes such as inbreeding depression and loss of genetic variation can increase the extinction risk of small populations. However, it is generally unclear whether extinction risk from genetic causes gradually increases with decreasing population size or whether there is a sharp transition around a specific threshold population size. In the ecological literature, such threshold phenomena are called 'strong Allee effects' and they can arise for example from mate limitation in small populations. In this study, we aim to (i) develop a meaningful notion of a 'strong genetic Allee effect', (ii) explore whether and under what conditions such an effect can arise from inbreeding depression due to recessive deleterious mutations, and (iii) quantify the interaction of potential genetic Allee effects with the well-known mate-finding Allee effect. We define a strong genetic Allee effect as a genetic process that causes a population's survival probability to be a sigmoid function of its initial size. The inflection point of this function defines the critical population size. To characterize survival-probability curves, we develop and analyse simple stochastic models for the ecology and genetics of small populations. Our results indicate that inbreeding depression can indeed cause a strong genetic Allee effect, but only if individuals carry sufficiently many deleterious mutations (lethal equivalents). Populations suffering from a genetic Allee effect often first grow, then decline as inbreeding depression sets in and then potentially recover as deleterious mutations are purged. Critical population sizes of ecological and genetic Allee effects appear to be often additive, but even superadditive interactions are possible. Many published estimates for the number of lethal equivalents in birds and mammals fall in the parameter range where strong genetic Allee effects are expected. Unfortunately, extinction risk due to genetic Allee effects can easily be underestimated as populations with genetic problems often grow initially, but then crash later. Also interactions between ecological and genetic Allee effects can be strong and should not be neglected when assessing the viability of endangered or introduced populations.

Using predator-prey theory to predict outcomes of broadscale experiments to reduce apparent competition.

Apparent competition is an important process influencing many ecological communities. We used predator-prey theory to predict outcomes of ecosystem experiments aimed at mitigating apparent competition by reducing primary prey. Simulations predicted declines in secondary prey following reductions in primary prey because predators consumed more secondary prey until predator numbers responded to reduced prey densities. Losses were exacerbated by a higher carrying capacity of primary prey and a longer lag time of the predator's numerical response, but a gradual reduction in primary prey was less detrimental to the secondary prey. We compared predictions against two field experiments where endangered woodland caribou (Rangifer tarandus caribou) were victims of apparent competition. First, when deer (Odocoileus sp.) declined suddenly following a severe winter, cougar (Puma concolor) declined with a 1-2-year lag, yet in the interim more caribou were killed by cougars, and caribou populations declined by 40%. Second, when moose (Alces alces) were gradually reduced using a management experiment, wolf (Canis lupus) populations declined but did not shift consumption to caribou, and the largest caribou subpopulation stabilized. The observed contrasting outcomes of sudden versus gradual declines in primary prey supported theoretical predictions. Combining theory with field studies clarified how to manage communities to mitigate endangerment caused by apparent competition that affects many taxa.

Multi-scale effects of habitat loss and the role of trait evolution.

Habitat loss (HL) is a major cause of species extinctions. Although the effects of HL beyond the directly impacted area have been previously observed, they have not been modelled explicitly, especially in an eco-evolutionary context. To start filling this gap, we study a two-patch deterministic consumer-resource model, with one of the patches experiencing loss of resources as a special case of HL. Our model allows foraging and mating within a patch as well as between patches. We then introduce heritable variation in consumer traits related to resource utilization and patch use to investigate eco-evolutionary dynamics and compare results with constant and no trait variation scenarios. Our results show that HL in one patch can indeed reduce consumer densities in the neighbouring patch but can also increase consumer densities in the neighbouring patch when the resources are overexploited. Yet at the landscape scale, the effect of HL on consumer densities is consistently negative. Patch isolation increases consumer density in the patch experiencing HL but has generally negative effects on the neighbouring patch, with context-dependent results at the landscape scale. With high cross-patch dependence and coupled foraging and mating preferences, local HL can sometimes even lead to landscape-level consumer extinction. Eco-evolutionary dynamics can rescue consumers from such extinction in some cases if their death rates are sufficiently small. More generally, trait evolution had positive or negative effects on equilibrium consumer densities after HL, depending on the evolving trait and the spatial scale considered. In summary, our findings show that HL at a local scale can affect the neighbouring patch and the landscape as a whole, where heritable trait variation can, in some cases, alleviate the impact of HL. We thus suggest joint consideration of multiple spatial scales and trait variation when assessing and predicting the impacts of HL.

Ecological and genetic effects of introduced species on their native competitors.

Species introductions to new habitats can cause a decline in the population size of competing native species and consequently also in their genetic diversity. We are interested in why these adverse effects are weak in some cases whereas in others the native species declines to the point of extinction. While the introduction rate and the growth rate of the introduced species in the new environment clearly have a positive relationship with invasion success and impact, the influence of competition is poorly understood. Here, we investigate how the intensity of interspecific competition influences the persistence time of a native species in the face of repeated and ongoing introductions of the nonnative species. We analyze two stochastic models: a model for the population dynamics of both species and a model that additionally includes the population genetics of the native species at a locus involved in its adaptation to a changing environment. Counterintuitively, both models predict that the persistence time of the native species is lowest for an intermediate intensity of competition. This phenomenon results from the opposing effects of competition at different stages of the invasion process: With increasing competition intensity more introduction events are needed until a new species can establish, but increasing competition also speeds up the exclusion of the native species by an established nonnative competitor. By comparing the ecological and the eco-genetic model, we detect and quantify a synergistic feedback between ecological and genetic effects.

Conceptual frameworks and methods for advancing invasion ecology.

Invasion ecology has much advanced since its early beginnings. Nevertheless, explanation, prediction, and management of biological invasions remain difficult. We argue that progress in invasion research can be accelerated by, first, pointing out difficulties this field is currently facing and, second, looking for measures to overcome them. We see basic and applied research in invasion ecology confronted with difficulties arising from (A) societal issues, e.g., disparate perceptions of invasive species; (B) the peculiarity of the invasion process, e.g., its complexity and context dependency; and (C) the scientific methodology, e.g., imprecise hypotheses. To overcome these difficulties, we propose three key measures: (1) a checklist for definitions to encourage explicit definitions; (2) implementation of a hierarchy of hypotheses (HoH), where general hypotheses branch into specific and precisely testable hypotheses; and (3) platforms for improved communication. These measures may significantly increase conceptual clarity and enhance communication, thus advancing invasion ecology.

Modeling the genetic footprint of fluctuating balancing selection: from the local to the genomic scale.

Natural selection not only affects the actual loci under selection but also leaves "footprints" in patterns of genetic variation in linked genetic regions. This offers exciting opportunities for inferring selection and for understanding the processes shaping levels of genetic variation in natural populations. Here, we develop analytical approximations based on coalescent theory to characterize the genetic footprint of a complex, but potentially common type of natural selection: balancing selection with seasonally fluctuating allele frequencies. As we show analytically and confirm with stochastic simulations, seasonal allele frequency fluctuations can have important (and partly unexpected) consequences for the genetic footprint of balancing selection. Fluctuating balancing selection generally leads to an increase in genetic diversity close to the selected site, the effect of balancing selection, but reduces diversity further away from the selected site, which is a consequence of the allele-frequency fluctuations effectively producing recurrent bottlenecks of allelic backgrounds. This medium- and long-range reduction usually outweighs the short-range increase when averaging diversity levels across the entire chromosome. Strong fluctuating balancing selection even induces a loss of genetic variation in unlinked regions, e.g. on different chromosomes. If many loci in the genome are simultaneously under fluctuating balancing selection this can lead to substantial genome-wide reductions in genetic diversity, even when allele-frequency fluctuations are small and local footprints are difficult to detect. Thus, together with genetic drift, selective sweeps and background selection, fluctuating selection could be a major force shaping levels of genetic diversity in natural populations.

Climate Change and Green Sea Turtle Sex Ratio-Preventing Possible Extinction.

Climate change poses a threat to species with temperature-dependent sex determination (TSD). A recent study on green sea turtles (Chelonia mydas) at the northern Great Barrier Reef (GBR) showed a highly female-skewed sex ratio with almost all juvenile turtles being female. This shortage of males might eventually cause population extinction, unless rapid evolutionary rescue, migration, range shifts, or conservation efforts ensure a sufficient number of males. We built a stochastic individual-based model inspired by C. mydas but potentially transferrable to other species with TSD. Pivotal temperature, nest depth, and shading were evolvable traits. Additionally, we considered the effect of crossbreeding between northern and southern GBR, nest site philopatry, and conservation efforts. Among the evolvable traits, nest depth was the most likely to rescue the population, but even here the warmer climate change scenarios led to extinction. We expected turtles to choose colder beaches under rising temperatures, but surprisingly, nest site philopatry did not improve persistence. Conservation efforts promoted population survival and did not preclude trait evolution. Although extra information is needed to make reliable predictions for the fate of green sea turtles, our results illustrate how evolution can shape the fate of long lived, vulnerable species in the face of climate change.

Genetic diversity in introduced populations with an Allee effect.

A phenomenon that strongly influences the demography of small introduced populations and thereby potentially their genetic diversity is the demographic Allee effect, a reduction in population growth rates at small population sizes. We take a stochastic modeling approach to investigate levels of genetic diversity in populations that successfully overcame either a strong Allee effect, in which populations smaller than a certain critical size are expected to decline, or a weak Allee effect, in which the population growth rate is reduced at small sizes but not negative. Our results indicate that compared to successful populations without an Allee effect, successful populations with a strong Allee effect tend to (1) derive from larger founder population sizes and thus have a higher initial amount of genetic variation, (2) spend fewer generations at small population sizes where genetic drift is particularly strong, and (3) spend more time around the critical population size and thus experience more genetic drift there. In the case of multiple introduction events, there is an additional increase in diversity because Allee-effect populations tend to derive from a larger number of introduction events than other populations. Altogether, a strong Allee effect can either increase or decrease genetic diversity, depending on the average founder population size. By contrast, a weak Allee effect tends to decrease genetic diversity across the entire range of founder population sizes. Finally, we show that it is possible in principle to infer critical population sizes from genetic data, although this would require information from many independently introduced populations.

Population genetic consequences of the Allee effect and the role of offspring-number variation.

A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. But many species are repeatedly introduced to the same location and eventually one population may overcome the Allee effect by chance. With the help of stochastic models, we investigate how much genetic diversity such successful populations harbor on average and how this depends on offspring-number variation, an important source of stochastic variability in population size. We find that with increasing variability, the Allee effect increasingly promotes genetic diversity in successful populations. Successful Allee-effect populations with highly variable population dynamics escape rapidly from the region of small population sizes and do not linger around the critical population size. Therefore, they are exposed to relatively little genetic drift. It is also conceivable, however, that an Allee effect itself leads to an increase in offspring-number variation. In this case, successful populations with an Allee effect can exhibit less genetic diversity despite growing faster at small population sizes. Unlike in many classical population genetics models, the role of offspring-number variation for the population genetic consequences of the Allee effect cannot be accounted for by an effective-population-size correction. Thus, our results highlight the importance of detailed biological knowledge, in this case on the probability distribution of family sizes, when predicting the evolutionary potential of newly founded populations or when using genetic data to reconstruct their demographic history.