A test of balanced fitness limitations theory: Pollen limitation in plants

When reproductive success is determined by the relative availabilities of a series of essential, non-substitutable resources, the theory of balanced fitness limitations predicts that the cost of harvesting a particular resource shapes the likelihood that a shortfall of that resource will constrain realized fitness. Plant reproduction through female function offers a special opportunity to test this theory; essential resources in this context include, first, the pollen received from pollinators or abiotic vectors that is used to fertilize ovules, and, second, the resources needed to provision the developing seeds and fruit. For many plants realized reproductive success through female function can be readily quantified in the field, and one key potential constraint on fitness, pollen limitation, can be assessed experimentally by manually supplementing pollen receipt. We assembled a comparative dataset of pollen limitation using only studies that supplement pollen to all flowers produced over the plant's reproductive lifespan. Pre- and post-pollination costs were estimated using the weight of flowers and fruits and estimates of fruit set. Consistent with expectations, we find self-incompatible plants make greater pre-pollination investments and experience greater pollen limitation. However, contrary to theoretical expectations, when variation due to self-compatibility is accounted for by including self-compatibility in the statistical model as a covariate, we find no support for the prediction that plants that invest more heavily in pre-pollination costs are subject to greater pollen limitation. Strong within-species, between-population variation in the expression of pollen limitation makes the quantification of mean pollen limitation difficult. We urge plant ecologists to conduct more studies of pollen limitation using whole-plant pollen supplementation to produce a richer comparative dataset that would support a more robust test of the balanced limitations hypothesis.

Granivore abundance shapes mutualism quality in plant-scatterhoarder interactions

Conditional mutualisms involve costs and benefits that vary with environmental factors, but mechanisms driving these dynamics remain poorly understood. Scatterhoarder-plant interactions are a prime example of this phenomenon, as scatterhoarders can either increase or reduce plant recruitment depending on the balance between seed dispersal and predation. We explored factors that drive the magnitude of net benefits for plants in this interaction using a mathematical model, with parameter values based on European beech (Fagus sylvatica) and yellow-necked mice (Apodemus flavicollis). We measured benefits as the percentage of germinating seeds, and examined how varying rodent survival (reflecting, e.g. changes in predation pressure), the rate of seed loss to other granivores, the abundance of alternative food resources, and changes in masting patterns affect the quality of mutualism. We found that increasing granivore abundance can degrade the quality of plant-scatterhoarder mutualism due to increased cache pilferage. Scatterhoarders are predicted to respond by increasing immediate consumption of gathered seeds, leading to higher costs and reduced benefits for plants. Thus, biotic changes that are detrimental to rodent populations can be beneficial for tree recruitment due to adaptive behavior of rodents. When scatterhoarder populations decline too drastically (< 5 individuals ha-1 ); however, tree recruitment may also suffer.

Building modern coexistence theory from the ground up: The role of community assembly

Modern coexistence theory (MCT) is one of the leading methods to understand species coexistence. It uses invasion growth rates-the average, per-capita growth rate of a rare species-to identify when and why species coexist. Despite significant advances in dissecting coexistence mechanisms when coexistence occurs, MCT relies on a 'mutual invasibility' condition designed for two-species communities but poorly defined for species-rich communities. Here, we review well-known issues with this component of MCT and propose a solution based on recent mathematical advances. We propose a clear framework for expanding MCT to species-rich communities and for understanding invasion resistance as well as coexistence, especially for communities that could not be analysed with MCT so far. Using two data-driven community models from the literature, we illustrate the utility of our framework and highlight the opportunities for bridging the fields of community assembly and species coexistence.

Stage-mediated priority effects and season lengths shape long-term competition dynamics

The relative arrival time of species can affect their interactions and thus determine which species persist in a community. Although this phenomenon, called priority effect, is widespread in natural communities, it is unclear how it depends on the length of growing season. Using a seasonal stage-structured model, we show that differences in stages of interacting species could generate priority effects by altering the strength of stabilizing and equalizing coexistence mechanisms, changing outcomes between exclusion, coexistence and positive frequency dependence. However, these priority effects are strongest in systems with just one or a few generations per season and diminish in systems where many overlapping generations per season dilute the importance of stage-specific interactions. Our model reveals a novel link between the number of generations in a season and the consequences of priority effects, suggesting that consequences of phenological shifts driven by climate change should depend on specific life histories of organisms.

Eco-evolutionary maintenance of diversity in fluctuating environments

Growing evidence suggests that temporally fluctuating environments are important in maintaining variation both within and between species. To date, however, studies of genetic variation within a population have been largely conducted by evolutionary biologists (particularly population geneticists), while population and community ecologists have concentrated more on diversity at the species level. Despite considerable conceptual overlap, the commonalities and differences of these two alternative paradigms have yet to come under close scrutiny. Here, we review theoretical and empirical studies in population genetics and community ecology focusing on the 'temporal storage effect' and synthesise theories of diversity maintenance across different levels of biological organisation. Drawing on Chesson's coexistence theory, we explain how temporally fluctuating environments promote the maintenance of genetic variation and species diversity. We propose a further synthesis of the two disciplines by comparing models employing traditional frequency-dependent dynamics and those adopting density-dependent dynamics. We then address how temporal fluctuations promote genetic and species diversity simultaneously via rapid evolution and eco-evolutionary dynamics. Comparing and synthesising ecological and evolutionary approaches will accelerate our understanding of diversity maintenance in nature.

Coevolution of Patch Selection in Stochastic Environments

AbstractSpecies interact in landscapes where environmental conditions vary in time and space. This variability impacts how species select habitat patches. Under equilibrium conditions, evolution of this patch selection can result in ideal free distributions where per capita growth rates are zero in occupied patches and negative in unoccupied patches. These ideal free distributions, however, do not explain why species occupy sink patches, why competitors have overlapping spatial ranges, or why predators avoid highly productive patches. To understand these patterns, we solve for coevolutionarily stable strategies (coESSs) of patch selection for multispecies stochastic Lotka-Volterra models accounting for spatial and temporal heterogeneity. In occupied patches at the coESS, we show that the differences between the local contributions to the mean and the variance of the long-term population growth rate are equalized. Applying this characterization to models of antagonistic interactions reveals that environmental stochasticity can partially exorcize the ghost of competition past, select for new forms of enemy-free and victimless space, and generate hydra effects over evolutionary timescales. Viewing our results through the economic lens of modern portfolio theory highlights why the coESS for patch selection is often a bet-hedging strategy coupling stochastic sink populations. Our results highlight how environmental stochasticity can reverse or amplify evolutionary outcomes as a result of species interactions or spatial heterogeneity.

Does deterministic coexistence theory matter in a finite world?

Contemporary studies of species coexistence are underpinned by deterministic models that assume that competing species have continuous (i.e., noninteger) densities, live in infinitely large landscapes, and coexist over infinite time horizons. By contrast, in nature, species are composed of discrete individuals subject to demographic stochasticity and occur in habitats of finite size where extinctions occur in finite time. One consequence of these discrepancies is that metrics of species' coexistence derived from deterministic theory may be unreliable predictors of the duration of species coexistence in nature. These coexistence metrics include invasion growth rates and niche and fitness differences, which are now commonly applied in theoretical and empirical studies of species coexistence. In this study, we tested the efficacy of deterministic coexistence metrics on the duration of species coexistence in a finite world. We introduce new theoretical and computational methods to estimate coexistence times in stochastic counterparts of classic deterministic models of competition. Importantly, we parameterized this model using experimental field data for 90 pairwise combinations of 18 species of annual plants, allowing us to derive biologically informed estimates of coexistence times for a natural system. Strikingly, we found that for species expected to deterministically coexist, community sizes containing only 10 individuals had predicted coexistence times of more than 1000 years. We also found that invasion growth rates explained 60% of the variation in intrinsic coexistence times, reinforcing their general usefulness in studies of coexistence. However, only by integrating information on both invasion growth rates and species' equilibrium population sizes could most (>99%) of the variation in species coexistence times be explained. This integration was achieved with demographically uncoupled single-species models solely determined by the invasion growth rates and equilibrium population sizes. Moreover, because of a complex relationship between niche overlap/fitness differences and equilibrium population sizes, increasing niche overlap and increasing fitness differences did not always result in decreasing coexistence times, as deterministic theory would predict. Nevertheless, our results tend to support the informed use of deterministic theory for understanding the duration of species' coexistence while highlighting the need to incorporate information on species' equilibrium population sizes in addition to invasion growth rates.

Evolutionary history mediates population response to rapid environmental change through within-generational and transgenerational plasticity

AbstractRapid environmental change is affecting many organisms; some are coping well, but many species are in decline. A key mechanism for facilitating success following environmental change is phenotypic plasticity. Organisms use cues to respond phenotypically to environmental conditions; many incorporate recent information (within-generation plasticity) and information from previous generations (transgenerational plasticity). We extend an existing evolutionary model where organisms utilize within-generational plasticity, transgenerational plasticity, and bet hedging to include changes in environmental regime. We show how when rapid evolution of plasticity is not possible, the effect of environmental change (altering the environment mean, variance, or autocorrelation or cue reliability) on population growth rate depends on the population's evolutionary history and past evolutionary responses to historical environmental conditions. We then evaluate the predictions that populations adapted to highly variable environments or with greater within-generational plasticity are more likely to successfully respond to environmental change. We identify when these predictions fail and show that environmental change is most detrimental when previously reliable cues become unreliable. When multiple cues become unreliable, environmental change can cause deleterious effects regardless of the population's evolutionary history. Overall, this work provides a general framework for understanding the role of plasticity in population responses to rapid environmental change.

Pathways to the density-dependent expression of cannibalism, and consequences for regulated population dynamics

Cannibalism, once viewed as a rare or aberrant behavior, is now recognized to be widespread and to contribute broadly to the self-regulation of many populations. Cannibalism can produce endogenous negative feedback on population growth because it is expressed as a conditional behavior, responding to the deteriorating ecological conditions that flow, directly or indirectly, from increasing densities of conspecifics. Thus, cannibalism emerges as a strongly density-dependent source of mortality. In this synthesis, we review recent research that has revealed a rich diversity of pathways through which rising density elicits increased cannibalism, including both factors that (a) elevate the rate of dangerous encounters between conspecifics and (b) enhance the likelihood that such encounters will lead to successful cannibalistic attacks. These pathways include both features of the autecology of cannibal populations and features of interactions with other species, including food resources and pathogens. Using mathematical models, we explore the consequences of including density-dependent cannibal attack rates on population dynamics. The conditional expression of cannibalism generally enhances stability and population regulation in single-species models but also may increase opportunities for alternative states and prey population escape from control by cannibalistic predators.

Temporally auto-correlated predator attacks structure ecological communities

For species primarily regulated by a common predator, the P* rule of Holt & Lawton (Holt & Lawton, 1993. Am. Nat.142, 623–645. (doi:10.1086/285561)) predicts that the prey species that supports the highest mean predator density (P*) excludes the other prey species. This prediction is re-examined in the presence of temporal fluctuations in the vital rates of the interacting species including predator attack rates. When the fluctuations in predator attack rates are temporally uncorrelated, the P* rule still holds even when the other vital rates are temporally auto-correlated. However, when temporal auto-correlations in attack rates are positive but not too strong, the prey species can coexist due to the emergence of a positive covariance between predator density and prey vulnerability. This coexistence mechanism is similar to the storage effect for species regulated by a common resource. Negative or strongly positive auto-correlations in attack rates generate a negative covariance between predator density and prey vulnerability and a stochastic priority effect can emerge: with non-zero probability either prey species is excluded. These results highlight how temporally auto-correlated species’ interaction rates impact the structure and dynamics of ecological communities.

Mast seeding promotes evolution of scatter-hoarding

Many plant species worldwide are dispersed by scatter-hoarding granivores: animals that hide seeds in numerous, small caches for future consumption. Yet, the evolution of scatter-hoarding is difficult to explain because undefended caches are at high risk of pilferage. Previous models have attempted to solve this problem by giving cache owners large advantages in cache recovery, by kin selection, or by introducing reciprocal pilferage of 'shared' seed resources. However, the role of environmental variability has been so far overlooked in this context. One important form of such variability is masting, which is displayed by many plant species dispersed by scatterhoarders. We use a mathematical model to investigate the influence of masting on the evolution of scatter-hoarding. The model accounts for periodically varying annual seed fall, caching and pilfering behaviour, and the demography of scatterhoarders. The parameter values are based mostly on research on European beech (Fagus sylvatica) and yellow-necked mice (Apodemus flavicollis). Starvation of scatterhoarders between mast years decreases the population density that enters masting events, which leads to reduced seed pilferage. Satiation of scatterhoarders during mast events lowers the reproductive cost of caching (i.e. the cost of caching for the future rather than using seeds for current reproduction). These reductions promote the evolution of scatter-hoarding behaviour especially when interannual variation in seed fall and the period between masting events are large. This article is part of the theme issue 'The ecology and evolution of synchronized seed production in plants'.

Sick of eating: Eco-evo-immuno dynamics of predators and their trophically acquired parasites

When predators consume prey, they risk becoming infected with their prey's parasites, which can then establish the predator as a secondary host. A predator population's diet therefore influences what parasites it is exposed to, as has been repeatedly shown in many species such as threespine stickleback (Gasterosteus aculeatus) (more benthic‐feeding individuals obtain nematodes from oligocheate prey, whereas limnetic‐feeding individuals catch cestodes from copepod prey). These differing parasite encounters, in turn, determine how natural selection acts on the predator's immune system. We might therefore expect that ecoevolutionary dynamics of a predator's diet (as determined by its ecomorphology) should drive correlated evolution of its immune traits. Conversely, the predator's immunity to certain parasites might alter the relative costs and benefits of different prey, driving evolution of its ecomorphology. To evaluate the potential for ecological morphology to drive evolution of immunity, and vice versa, we use a quantitative genetics framework coupled with an ecological model of a predator and two prey species (the diet options). Our analysis reveals fundamental asymmetries in the evolution of ecomorphology and immunity. When ecomorphology rapidly evolves, it determines how immunity evolves, but not vice versa. Weak trade‐offs in ecological morphology select for diet generalists despite strong immunological trade‐offs, but not vice versa. Only weak immunological trade‐offs can explain negative diet‐infection correlations across populations. The analysis also reveals that eco‐evo‐immuno feedbacks destabilize population dynamics when trade‐offs are sufficiently weak and heritability is sufficiently high. Collectively, these results highlight the delicate interplay between multivariate trait evolution and the dynamics of ecological communities.

Is Evolution in Response to Extreme Events Good for Population Persistence?

AbstractClimate change is predicted to increase the severity of environmental perturbations, including storms and droughts, which act as strong selective agents. These extreme events are often of finite duration (pulse disturbances). Hence, while evolution during an extreme event may be adaptive, the resulting phenotypic changes may become maladaptive when the event ends. Using individual-based models and analytic approximations that fuse quantitative genetics and demography, we explore how heritability and phenotypic variance affect population size and extinction risk in finite populations under an extreme event of fixed duration. Since more evolution leads to greater maladaptation and slower population recovery following an extreme event, greater heritability can increase extinction risk when the extreme event is short. Alternatively, when an extreme event is sufficiently long, heritability often helps a population persist. We also find that when events are severe, the buffering effect of phenotypic variance can outweigh the increased load it causes.

Effects of size selection versus density dependence on life histories: A first experimental probe

When prey experience size-based harvesting by predators, they are not only subject to selection due to larger individuals being preferentially harvested but also selection due to reductions in population density. Density-dependent selection represents one of the most basic interactions between ecology and evolution. Yet, the reduction in density associated with exploitation has not been tested as a possible driving force of observed evolutionary changes in populations harvested size-dependently. Using an artificial selection experiment with a mixture of Daphnia clones, we partition the evolutionary effects of size-based harvesting into the effects of removing large individuals and the effects of lowering the population density. We show that both size selection and density-dependent selection are significant drivers of life-history evolution. Importantly, these drivers affected different life-history traits with size-selective harvesting selecting for slower juvenile growth rates and a larger size at maturity, and low-density selecting for reduced reproductive output.

Positively and Negatively Autocorrelated Environmental Fluctuations Have Opposing Effects on Species Coexistence

AbstractEnvironmental fluctuations can mediate coexistence between competing species via the storage effect. This fluctuation-dependent coexistence mechanism requires three conditions: (i) there is a positive covariance between species responses to environmental conditions and the strength of competition, (ii) there are species-specific environmental responses, and (iii) species are less sensitive to competition in environmentally unfavorable years. In serially uncorrelated environments, condition (i) occurs only if favorable environmental conditions immediately and directly increase the strength of competition. For many demographic parameters, this direct link between favorable years and competition may not exist. Moreover, many environmental variables are temporal autocorrelated, but theory has largely focused on serially uncorrelated environments. To address this gap, a model of competing species in autocorrelated environments is analyzed. This analysis shows that positive autocorrelations in demographic rates that increase fitness (e.g., maximal fecundity or adult survival) produce the positive environment-competition covariance in condition (i). Hence, when these demographic rates contribute to buffered population growth, positive temporal autocorrelations generate a storage effect; otherwise, they destabilize competitive interactions. For negatively autocorrelated environments, this theory highlights an alternative stabilizing mechanism that requires three conditions: (i') there is a negative environment-competition covariance, (ii) there are species-specific environmental responses, and (iii') species are less sensitive to competition in more favorable years. When the conditions for either of these stabilizing mechanisms are violated, temporal autocorrelations can generate stochastic priority effects or hasten competitive exclusion. Collectively, these results highlight that temporal autocorrelations in environmental conditions can play a fundamental role in determining ecological outcomes of competing species.

Cross-scale dynamics and the evolutionary emergence of infectious diseases

When emerging pathogens encounter new host species for which they are poorly adapted, they must evolve to escape extinction. Pathogens experience selection on traits at multiple scales, including replication rates within host individuals and transmissibility between hosts. We analyze a stochastic model linking pathogen growth and competition within individuals to transmission between individuals. Our analysis reveals a new factor, the cross-scale reproductive number of a mutant virion, that quantifies how quickly mutant strains increase in frequency when they initially appear in the infected host population. This cross-scale reproductive number combines with viral mutation rates, single-strain reproductive numbers, and transmission bottleneck width to determine the likelihood of evolutionary emergence, and whether evolution occurs swiftly or gradually within chains of transmission. We find that wider transmission bottlenecks facilitate emergence of pathogens with short-term infections, but hinder emergence of pathogens exhibiting cross-scale selective conflict and long-term infections. Our results provide a framework to advance the integration of laboratory, clinical, and field data in the context of evolutionary theory, laying the foundation for a new generation of evidence-based risk assessment of emergence threats.

Technical Comment on Pande et al. (2020): Why invasion analysis is important for understanding coexistence

Pande et al. (2020) point out that persistence time can decrease even as invader growth rates (IGRs) increase, which potentially undermines modern coexistence theory. However, because persistence time increases rapidly with system size only when IGR > 0, to understand how any real community persists, we should first identify the mechanisms producing positive IGR.

Individual variation in dispersal and fecundity increases rates of spatial spread

Dispersal and fecundity are two fundamental traits underlying the spread of populations. Using integral difference equation models, we examine how individual variation in these fundamental traits and the heritability of these traits influence rates of spatial spread of populations along a one-dimensional transect. Using a mixture of analytic and numerical methods, we show that individual variation in dispersal rates increases spread rates and the more heritable this variation, the greater the increase. In contrast, individual variation in lifetime fecundity only increases spread rates when some of this variation is heritable. The highest increases in spread rates occur when variation in dispersal positively co-varies with fecundity. Our results highlight the importance of estimating individual variation in dispersal rates, dispersal syndromes in which fecundity and dispersal co-vary positively and heritability of these traits to predict population rates of spatial spread.

Destabilizing evolutionary and eco-evolutionary feedbacks drive empirical eco-evolutionary cycles

We develop a method to identify how ecological, evolutionary, and eco-evolutionary feedbacks influence system stability. We apply our method to nine empirically parametrized eco-evolutionary models of exploiter-victim systems from the literature and identify which particular feedbacks cause some systems to converge to a steady state or to exhibit sustained oscillations. We find that ecological feedbacks involving the interactions between all species and evolutionary and eco-evolutionary feedbacks involving only the interactions between exploiter species (predators or pathogens) are typically stabilizing. In contrast, evolutionary and eco-evolutionary feedbacks involving the interactions between victim species (prey or hosts) are destabilizing more often than not. We also find that while eco-evolutionary feedbacks rarely altered system stability from what would be predicted from just ecological and evolutionary feedbacks, eco-evolutionary feedbacks have the potential to alter system stability at faster or slower speeds of evolution. As the number of empirical studies demonstrating eco-evolutionary feedbacks increases, we can continue to apply these methods to determine whether the patterns we observe are common in other empirical communities.

Predicting evolutionarily stable strategies from functional responses of Sonoran Desert annuals to precipitation

For many decades, researchers have studied how plants use bet-hedging strategies to insure against unpredictable, unfavourable conditions. We improve upon earlier analyses by explicitly accounting for how variable precipitation affects annual plant species’ bet-hedging strategies. We consider how the survival rates of dormant seeds (in a ‘seed bank’) interact with precipitation responses to influence optimal germination strategies. Specifically, we incorporate how response to resource availability (i.e. the amount of offspring (seeds) generated per plant in response to variation in desert rainfall) influences the evolution of germination fractions. Using data from 10 Sonoran Desert annual plants, we develop models that explicitly include these responses to model fitness as a function of precipitation. For each of the species, we identify the predicted evolutionarily stable strategies (ESSs) for the fraction of seeds germinating each year and then compare our estimated ESS values to the observed germination fractions. We also explore the relative importance of seed survival and precipitation responses in shaping germination strategies by regressing ESS values and observed germination fractions against these traits. We find that germination fractions are lower for species with higher seed survival, with lower reproductive success in dry years, and with better yield responses in wet years. These results illuminate the evolution of bet-hedging strategies in an iconic system, and provide a framework for predicting how current and future environmental conditions may reshape those strategies.

Social information drives ecological outcomes among competing species

Through its behavior, an organism intentionally or unintentionally produces information. Use of this "social information" by surrounding conspecifics or heterospecifics is a ubiquitous phenomenon that can drive strong correlations in fitness-associated behaviors, such as predator avoidance, enhancing survival within and among competing species. By eliciting indirect positive interactions between competing individuals or species, social information might alter overall competitive outcomes. To test this potential, we present new theory that quantifies the effect of social information, modeled as predator avoidance signals/cues, on the outcomes from intraspecific and interspecific competition. Our analytical and numerical results reveal that social information can rescue populations from extinction and can shift the long-term outcome of competitive interactions from mutual exclusion to coexistence, or vice versa, depending on the relative strengths of intraspecific and interspecific social information and competition. Our findings highlight the importance of social information in determining ecological outcomes.

Consequences of intraspecific variation in seed dispersal for plant demography, communities, evolution and global change

As the single opportunity for plants to move, seed dispersal has an important impact on plant fitness, species distributions and patterns of biodiversity. However, models that predict dynamics such as risk of extinction, range shifts and biodiversity loss tend to rely on the mean value of parameters and rarely incorporate realistic dispersal mechanisms. By focusing on the mean population value, variation among individuals or variability caused by complex spatial and temporal dynamics is ignored. This calls for increased efforts to understand individual variation in dispersal and integrate it more explicitly into population and community models involving dispersal. However, the sources, magnitude and outcomes of intraspecific variation in dispersal are poorly characterized, limiting our understanding of the role of dispersal in mediating the dynamics of communities and their response to global change. In this manuscript, we synthesize recent research that examines the sources of individual variation in dispersal and emphasize its implications for plant fitness, populations and communities. We argue that this intraspecific variation in seed dispersal does not simply add noise to systems, but, in fact, alters dispersal processes and patterns with consequences for demography, communities, evolution and response to anthropogenic changes. We conclude with recommendations for moving this field of research forward.

Persistence and extinction for stochastic ecological models with internal and external variables

The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include abiotic factors or non-focal species. These internal or external variables may fluctuate due to stochastic fluctuations in environmental conditions. The interplay between these variables and species densities can determine whether a particular population persists or goes extinct. To understand this interplay, we prove theorems for stochastic persistence and exclusion for stochastic ecological difference equations accounting for internal and external variables. Specifically, we use a stochastic analog of average Lyapunov functions to develop sufficient and necessary conditions for (i) all population densities spending little time at low densities i.e. stochastic persistence, and (ii) population trajectories asymptotically approaching the extinction set with positive probability. For (i) and (ii), respectively, we provide quantitative estimates on the fraction of time that the system is near the extinction set, and the probability of asymptotic extinction as a function of the initial state of the system. Furthermore, in the case of persistence, we provide lower bounds for the expected time to escape neighborhoods of the extinction set. To illustrate the applicability of our results, we analyze stochastic models of evolutionary games, Lotka-Volterra dynamics, trait evolution, and spatially structured disease dynamics. Our analysis of these models demonstrates environmental stochasticity facilitates coexistence of strategies in the hawk-dove game, but inhibits coexistence in the rock-paper-scissors game and a Lotka-Volterra predator-prey model. Furthermore, environmental fluctuations with positive auto-correlations can promote persistence of evolving populations and persistence of diseases in patchy landscapes. While our results help close the gap between the persistence theories for deterministic and stochastic systems, we highlight several challenges for future research.

Restoration of eastern oyster populations with positive density dependence

Positive density dependence (i.e., Allee effects) can create a threshold of population states below which extinction of the population occurs. The existence of this threshold, which can often be a complex, multi-dimensional surface, rather than a single point, is of particular importance in degraded populations for which there is a desire for successful restoration. Here, we incorporated positive density dependence into a closed, size- and age-structured integral projection model parameterized with empirical data from an eastern oyster, Crassostrea virginica, population in Pamlico Sound, North Carolina, USA. To understand the properties of the threshold surface, and implications for restoration, we introduced a general method based on a linearization of the threshold surface at its unique, unstable equilibrium. We estimated the number of oysters of a particular age (i.e., stock enhancement), or the surface area of dead shell substrate required (i.e., habitat enhancement) to move a population from an extinction trajectory to a persistence trajectory. The location of the threshold surface was strongly affected by changes in the amount of local larval retention. Traditional stock enhancement with oysters <1 yr old (i.e., spat) required three times as many oysters relative to stock enhancement with oysters between ages 3 and 7 yr old, while the success of habitat enhancement depended upon the initial size distribution of the population. The methodology described here demonstrates the importance of considering positive density dependence in oyster populations, and also provides insights into effective management and restoration strategies when dealing with a high dimensional threshold separating extinction and persistence.

Doppler and Duplex Sonography for the Diagnosis of the Irreversible Cessation of Brain Function ("Brain Death"): Current Guidelines in Germany and Neighboring Countries

Extra- and transcranial sonography of brain-supplying arteries is accepted worldwide in brain death protocols as a valid "ancillary" method of proving brain circulatory arrest. Color-coded duplex sonography and CT angiography have been newly incorporated in the fourth update of the German Medical Association's guidelines for the determination of the irreversible cessation of brain function ("brain death"), effective July 2015. The updated guidelines address in more detail the diagnostic procedures and the required qualifications of the examiners. The present article summarizes the guidelines and the recommendations regarding the application and documentation of ultrasound findings for the diagnosis of brain circulatory arrest in children and adults, as valid in Germany. The method, limitations, and procedure in the case of inconclusive findings are described. Age-related minimum values of mean arterial pressure for the diagnosis of cerebral circulatory arrest in children are presented. A concise overview of the respective regulations for the use of sonography for diagnosing brain death in other countries, especially in the countries neighboring Germany, is given.

Evolution of natal dispersal in spatially heterogenous environments

Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results in an ideal free distribution, is evolutionary stable in spatially varying but temporally constant environments. Many species, however, primarily disperse prior to reproduction (natal dispersal) and less commonly between reproductive events (breeding dispersal). These species include territorial species such as birds and reef fish, and sessile species such as plants, and mollusks. As demographic and dispersal terms combine in a multiplicative way for models of natal dispersal, rather than the additive way for the previously studied models, we develop new mathematical methods to study the evolution of natal dispersal for continuous-time and discrete-time models. A fundamental ecological dichotomy is identified for the non-trivial equilibrium of these models: (i) the per-capita growth rates for individuals in all patches are equal to zero, or (ii) individuals in some patches experience negative per-capita growth rates, while individuals in other patches experience positive per-capita growth rates. The first possibility corresponds to an ideal-free distribution, while the second possibility corresponds to a "source-sink" spatial structure. We prove that populations with a dispersal strategy leading to an ideal-free distribution displace populations with dispersal strategy leading to a source-sink spatial structure. When there are patches which cannot sustain a population, ideal-free strategies can be achieved by sedentary populations, and we show that these populations can displace populations with any irreducible dispersal strategy. Collectively, these results support that evolution selects for natal or breeding dispersal strategies which lead to ideal-free distributions in spatially heterogenous, but temporally homogenous, environments.

The demographic consequences of growing older and bigger in oyster populations

Structured population models, particularly size- or age-structured, have a long history of informing conservation and natural resource management. While size is often easier to measure than age and is the focus of many management strategies, age-structure can have important effects on population dynamics that are not captured in size-only models. However, relatively few studies have included the simultaneous effects of both age- and size-structure. To better understand how population structure, particularly that of age and size, impacts restoration and management decisions, we developed and compared a size-structured integral projection model (IPM) and an age- and size-structured IPM, using a population of Crassostrea gigas oysters in the northeastern Pacific Ocean. We analyzed sensitivity of model results across values of local retention that give populations decreasing in size to populations increasing in size. We found that age- and size-structured models yielded the best fit to the demographic data and provided more reliable results about long-term demography. Elasticity analysis showed that population growth rate was most sensitive to changes in the survival of both large (>175 mm shell length) and small (<75 mm shell length) oysters, indicating that a maximum size limit, in addition to a minimum size limit, could be an effective strategy for maintaining a sustainable population. In contrast, the purely size-structured model did not detect the importance of large individuals. Finally, patterns in stable age and stable size distributions differed between populations decreasing in size due to limited local retention and populations increasing in size due to high local retention. These patterns can be used to determine population status and restoration success. The methodology described here provides general insight into the necessity of including both age- and size-structure into modeling frameworks when using population models to inform restoration and management decisions.

Does an 'oversupply' of ovules cause pollen limitation?

Lifetime seed production can be constrained by shortfalls of pollen receipt ('pollen limitation'). The ovule oversupply hypothesis states that, in response to unpredictable pollen availability, plants evolve to produce more ovules than they expect to be fertilized, and that this results in pollen limitation of seed production. Here, we present a cartoon model and a model of optimal plant reproductive allocations under stochastic pollen receipt to evaluate the hypothesis that an oversupply of ovules leads to increased pollen limitation. We show that an oversupply of ovules has two opposing influences on pollen limitation of whole-plant seed production. First, ovule oversupply increases the likelihood that pollen receipt limits the number of ovules that can be fertilized ('prezygotic pollen limitation'). Second, ovule oversupply increases the proportion of pollen grains received that are used to fertilize ovules ('pollen use efficiency'). As a result of these opposing influences, ovule oversupply has only a modest effect on the degree to which lifetime seed production is constrained by pollen receipt, producing a small decrease in the incidence of pollen limitation. Ovule oversupply is not the cause of the pollen limitation problem, but rather is part of the evolutionary solution to that problem.

Modest Pollen Limitation of Lifetime Seed Production Is in Good Agreement with Modest Uncertainty in Whole-Plant Pollen Receipt

We recently introduced a model that predicts the degree to which a plant's lifetime seed production may be constrained by unpredictable shortfalls of pollen receipt ("pollen limitation"). Burd's comment in this issue criticized our analysis, first by arguing that the empirical literature documents much higher levels of pollen limitation than our model predicts and then suggesting that the apparent discrepancy stemmed from our (1) underestimating the costs of securing a fertilized ovule and (2) assuming too little unpredictability in whole-plant pollen receipt. We reply as follows. First, the empirical literature must be consulted carefully. Burd relies on pollen supplementation experiments performed on parts of plants or on whole plants but during only one reproductive season for polycarpic perennials; in both cases, resource reallocation often leads to gross overestimates of pollen limitation. We comprehensively review pollen limitation estimates that are free of these estimation problems and find strong agreement with our model predictions. Second, although cost estimates for different components of seed production are imprecise, errors are likely to be small relative to the >1,000-fold differences observed across plant species, the primary focus of our article. Finally, contrary to Burd's argument, pollen receipt by entire plants is much more predictable than that by individual flowers because the flower-to-flower variation "averages out" when summed across many flowers. Our model uses parameter values that are in broad agreement with the empirical record of modest plant-to-plant variation in pollen receipt and thus predicts the generally modest pollen limitation that is observed in nature.

The Posterior Cerebral Artery and its Main Cortical Branches Identified with Noninvasive Transcranial Color-Coded Duplex Sonography

PURPOSE

To differentiate PCA segments and cortical branches by means of transcranial color-coded duplex sonography (TCCD) and to measure flow parameters at rest and during visual stimulation.

MATERIALS AND METHODS

60 healthy subjects with a good acoustic temporal bone window were examined. The main stem of the PCA (P1, P2 and P3) and 4 main cortical branches - the anterior temporal artery (ATA), the occipital temporal artery (OTA), the parietooccipital artery (POA) and the calcarine artery (CA) - were assessed using an axial transtemporal approach. Systolic and diastolic blood flow velocities (BFVs) were recorded at rest and during visual stimulation.

RESULTS

Identification of the P1 segment of the PCA was successful in 97.5% (117/120) of cases. The P2 and P3 segments were visualized in all cases. The 4 main cortical branches could be identified to varying degrees: ATA in 88%, OTA in 96%, POA in 69% and CA in 62%. There was an evoked flow response in the P2 main stem and in all cortical branches. The most pronounced increase in diastolic/systolic BFV after visual stimulation test was seen in the CA (42%/35%), followed by P2 (30%/24%), the POA (27%/27%), the OTA (16%/13%) and the ATA (9%/8%).

CONCLUSION

Insonation through the temporal bone window with TCCD confidently allows the assessment of the P1 to P3 segments of the PCA as well as the 2 proximal branches, the ATA and the OTA. An ultrasound-based classification of PCA anatomy and its cortical branches may be used as a noninvasive method for the evaluation of posterior circulation pathology.

Unifying Within- and Between-Generation Bet-Hedging Theories: An Ode to J. H. Gillespie

In the 1970s, John Gillespie introduced two principles in which evolution selects for genotypes with lower variation in offspring numbers. First, if the variation in offspring number primarily occurs within generations, the strength of this selective force is inversely proportional to population size. Second, if this variation primarily occurs between generations, the strength of this selective force is proportional to the variance and independent of population size. These principles lie at the core of bet-hedging theory. Using the common currency of fixation probabilities, I derive a general principle for which within-generation correlation of individual fitness acts as a dial between Gillespie's limiting cases. At low correlations, within-generation variation is the primary selective force. At high correlations, between-generation variation is the dominant selective force. As corollary of this general principle, selection for diversified bet-hedging strategies is shown to require higher within-generation environmental correlations in smaller populations.

Ocean acidification through the lens of ecological theory

Ocean acidification, chemical changes to the carbonate system of seawater, is emerging as a key environmental challenge accompanying global warming and other human-induced perturbations. Considerable research seeks to define the scope and character of potential outcomes from this phenomenon, but a crucial impediment persists. Ecological theory, despite its power and utility, has been only peripherally applied to the problem. Here we sketch in broad strokes several areas where fundamental principles of ecology have the capacity to generate insight into ocean acidification's consequences. We focus on conceptual models that, when considered in the context of acidification, yield explicit predictions regarding a spectrum of population- and community-level effects, from narrowing of species ranges and shifts in patterns of demographic connectivity, to modified consumer-resource relationships, to ascendance of weedy taxa and loss of species diversity. Although our coverage represents only a small fraction of the breadth of possible insights achievable from the application of theory, our hope is that this initial foray will spur expanded efforts to blend experiments with theoretical approaches. The result promises to be a deeper and more nuanced understanding of ocean acidification'and the ecological changes it portends.

Pushed beyond the brink: Allee effects, environmental stochasticity, and extinction

To understand the interplay between environmental stochasticity and Allee effects, we analyse persistence, asymptotic extinction, and conditional persistence for stochastic difference equations. Our analysis reveals that persistence requires that the geometric mean of fitness at low densities is greater than one. When this geometric mean is less than one, asymptotic extinction occurs with high probability for low initial population densities. Additionally, if the population only experiences positive density-dependent feedbacks, conditional persistence occurs provided the geometric mean of fitness at high population densities is greater than one. However, if the population experiences both positive and negative density-dependent feedbacks, conditional persistence only occurs if environmental fluctuations are sufficiently small. We illustrate counter-intuitively that environmental fluctuations can increase the probability of persistence when populations are initially at low densities, and can cause asymptotic extinction of populations experiencing intermediate predation rates despite conditional persistence occurring at higher predation rates.