Sebastian Schreiber | University of California, Davis (original) (raw)

Papers by Sebastian Schreiber

arXiv (Cornell University), Aug 23, 2018

The dynamics of species' densities depend both on internal and external variables. Internal varia... more 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.

arXiv (Cornell University), May 17, 2020

Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For ... more Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number R0 determines their global dynamics. If R0 ≤ 1, then the frequency of infected individuals asymptotically converges to zero. If R0 > 1, then the infectious class uniformly persists for all time; conditions for a globally stable, endemic equilibrium are given. In contrast, the infection goes extinct in finite time with probability one in the stochastic models for all R0 values. To understand the length of the transient prior to extinction as well as the behavior of the transients, the quasi-stationary distributions and the associated mean time to extinction are analyzed using large deviation methods. When R0 > 1, these mean times to extinction are shown to increase exponentially with the population size N. Moreover, as N approaches ∞, the quasi-stationary distributions are supported by a compact set bounded away from extinction; sufficient conditions for convergence to a Dirac measure at the endemic equilibrium of the deterministic model are also given. In contrast, when R0 < 1, the mean times to extinction are bounded above 1/(1 − α) where α < 1 is the geometric rate of decrease of the infection when rare; as N approaches ∞, the quasi-stationary distributions converge to a Dirac measure at the disease-free equilibrium for the deterministic model. For several special cases, explicit formulas for approximating the quasi-stationary distribution and the associated mean extinction are given. These formulas illustrate how for arbitrarily small R0 values, the mean time to extinction can be arbitrarily large, and how for arbitrarily large R0 values, the mean time to extinction can be arbitrarily large.

Ecology, Jul 21, 2022

Cannibalism, once viewed as a rare or aberrant behavior, is now recognized to be widespread and t... more 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.

arXiv (Cornell University), Aug 23, 2018

Species' densities experience both internal frequency-dependent feedbacks due spatial, age, or ge... more Species' densities experience both internal frequency-dependent feedbacks due spatial, age, or genetic structure, and external feedbacks with abiotic factors such as climatic conditions and nutrient availability. These feedbacks play an important role in determining whether populations persist or go extinct and may be subject to stochastic fluctuations. We develop theorems for stochastic persistence and exclusion for stochastic ecological difference equations accounting for these feedbacks. Specifically, we use the stochastic analog of average Lyapunov functions to develop sufficient and necessary conditions for (i) all population densities to spend little time at low densities, (ii) population trajectories asymptotically approaching the extinction set with positive probability, and (iii) under an additional accessibility condition, this asymptotic extinction occurring with probability one. 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. To illustrate our results, we analyze models of (a) trait evolution, (b) spatially structured disease dynamics, (c) competing species, and (d) evolutionary games. Our analysis of these models demonstrates that temporal autocorrelations can enhance persistence of evolving populations (a), and can facilitate or disrupt species coexistence (c). Also, we find that environmental stochasticity in the evolutionary game of rock-paper-scissors (d) disrupts the maintenance of genetic polymorphisms. In contrast, environmental fluctuations can promote disease persistence in patchy landscapes (b). While these results help close the gap between the persistence theories for deterministic and stochastic systems, we conclude by highlighting several challenges for future research.

Virus Evolution, 2021

When emerging pathogens encounter new host species for which they are poorly adapted, they must e... more 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.

Species interact in landscapes where environmental conditions vary in time and space. This variab... more Species interact in landscapes where environmental conditions vary in time and space. This variability impacts how species select habitat patches. Under equilibrium conditions, coevolution 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, don’t explain why species occupy sink patches, competitors have overlapping spatial ranges, or why predators avoid highly productive patches. To understand these patterns, we analyze multi-species Lotka-Volterra models accounting for spatial heterogeneity and environmental stochasticity. 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 gho...

ABSTRACTMany plant species worldwide are dispersed by scatterhoarding granivores: animals that hi... more ABSTRACTMany plant species worldwide are dispersed by scatterhoarding granivores: animals that hide seeds in numerous, small caches for future consumption. Yet, the evolution of scatterhoarding 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 behavior, and the demography of scatterhoarders. The parameter values are based mostly on research on European beech (Fagu...

AoB PLANTS, 2019

As the single opportunity for plants to move, seed dispersal has an important impact on plant fit... more 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 indi...

The American Naturalist, 2015

Recent studies investigating feedbacks between evolution and ecology suggest that microevolution ... more Recent studies investigating feedbacks between evolution and ecology suggest that microevolution may affect community structure. Motivated by this, we use a quantitative genetics and Lotka-Volterra framework to understand the impact of eco-evolutionary feedbacks on an intraguild predation community in which the intraguild predator evolves between a phenotype specialized for attacking its competitor (the intraguild prey) and a phenotype specialized for attacking a common resource. We show that evolution can drive both sudden and gradual shifts in community structure. Evolutionary rescue of the community, in which evolution prevents the loss of species, occurs in two ways: (i) selection to a particular phenotype that supports coexistence and (ii) continuous evolution between prey-and resource-specialist phenotypes that support communitylevel Red Queen dynamics in which the community fluctuates between prey-and predator-dominated states. Paradoxically, the predator can evolve to extirpate itself from the community provided that the ecological dynamics support bistability. Strong trade-offs between specialist phenotypes can lead to trait-based alternative states of the community resembling either a food chain or exploitative competition. Finally, we show that rapid evolution can stabilize equilibria that are unstable for the ecological dynamics, whereas slow evolution can stabilize equilibria that are unstable for the evolutionary dynamics. Our results demonstrate that eco-evolutionary feedbacks can drive shifts in community structure and that the overall dynamics depend on the trade-off strength and evolutionary rate.

Frontiers in Marine Science, 2015

Restoration strategies for native oyster populations rely on multiple sources of information, whi... more Restoration strategies for native oyster populations rely on multiple sources of information, which often conflict due to time-and space-varying patterns in abundance and distribution. For instance, strategies based on population connectivity and disease resistance can differ, and extant and historical records of abundance and distribution are often at odds, such that the optimal strategy is unclear and valuable restoration sites may be excluded from consideration. This was the case for the Lynnhaven River subestuary of lower Chesapeake Bay, which was deemed unsuitable for Eastern Oyster (Crassostrea virginica) restoration based on physical conditions, disease challenge, and extant oyster abundance. Consequently, we (i) evaluated previously unknown historical data from the 1800s, (ii) quantified extant oyster recruitment and abundance, physical conditions, and disease presence on constructed restoration reefs and alternative substrates, and (iii) assessed simulations from biophysical models to identify potential restoration sites in the metapopulation. The collective data distinguished numerous restoration sites (i) in the polyhaline zone (salinity 18.4-22.2) where disease resistance is evolving, (ii) where oysters were abundant in the late 1800s-early 1900s, (iii) of recent high recruitment, abundance and survival, despite consistent and elevated disease challenge, and (iv) interconnected as a metapopulation via larval dispersal. Moreover, a network of constructed restoration reefs met size structure, abundance and biomass standards of restoration success. These findings demonstrate that assumptions about the suitability of sites for oyster restoration based on individual processes can be severely flawed, and that in-depth examination of multiple processes and sources of information are required for oyster reef restoration plans to maximize success. We use these findings and previous information to recommend a strategy for successful restoration of subtidal oyster reefs throughout the range of the Eastern Oyster.

arXiv (Cornell University), Aug 23, 2018

When predators consume prey, they risk becoming infected with their prey’s parasites, which can t... more When predators consume prey, they risk becoming infected with their prey’s parasites, which can then establish the predator as a secondary host. For example, stickleback in northern temperate lakes consume benthic or limnetic prey, which are intermediate hosts for distinct species of parasites (e.g. Eustrongylides nematodes in benthic oligocheates and Schistocephalus solidus copepods in limnetic copepods). These worms then establish the stickleback as a secondary host and can cause behavioral changes linked to increased predation by birds. In this study, we use a quantitative genetics framework to consider the simultaneous eco-evolutionary dynamics of predator ecomorphology and predator immunity when alternative prey may confer different parasite exposures. When evolutionary tradeoffs are sufficiently weak, predator ecomorphology and immunity are correclated among populations, potentially generating a negative correlation between parasite intake and infection.

AoB PLANTS, 2019

Seed dispersal enables plants to reach hospitable germination sites and escape natural enemies. U... more Seed dispersal enables plants to reach hospitable germination sites and escape natural enemies. Understanding when and how much seed dispersal matters to plant fitness is critical for understanding plant population and community dynamics. At the same time, the complexity of factors that determine if a seed will be successfully dispersed and subsequently develop into a reproductive plant is daunting. Quantifying all factors that may influence seed dispersal effectiveness for any potential seed-vector relationship would require an unrealistically large amount of time, materials and financial resources. On the other hand, being able to make dispersal predictions is critical for predicting whether single species and entire ecosystems will be resilient to global change. Building on current frameworks, we here posit that seed dispersal ecology should adopt plant functional groups as analytical units to reduce this complexity to manageable levels. Functional groups can be used to distingui...

Proceedings of the Royal Society B: Biological Sciences, 2019

For many decades, researchers have studied how plants use bet-hedging strategies to insure agains... more 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 ...

F1000 - Post-publication peer review of the biomedical literature, 2011

F1000 - Post-publication peer review of the biomedical literature, 2010

F1000 - Post-publication peer review of the biomedical literature, 2012

Some reef-building corals have been shown to respond to environmental change by shifting the comp... more Some reef-building corals have been shown to respond to environmental change by shifting the composition of their algal symbiont (genus Symbiodinium) communities. These shifts have been proposed as a potential mechanism by which corals might survive climate stressors, such as increased temperatures. Conventional molecular methods suggest this adaptive capacity may not be widespread because few ($25%) coral species have been found to associate with multiple Symbiodinium clades. However, these methods can fail to detect low abundance symbionts (typically less than 10-20% of the total algal symbiont community). To determine whether additional Symbiodinium clades are present, but are not detected using conventional techniques, we applied a high-resolution, real-time PCR assay to survey Symbiodinium (in clades AD) from 39 species of phylogenetically and geographically diverse scleractinian corals. This survey included 26 coral species thought to be restricted to hosting a single Symbiodinium clade ('symbiotic specialists'). We detected at least two Symbiodinium clades (C and D) in at least one sample of all 39 coral species tested; all four Symbiodinium clades were detected in over half (54%) of the 26 symbiotic specialist coral species. Furthermore, on average, 68 per cent of all sampled colonies within a given coral species hosted two or more symbiont clades. We conclude that the ability to associate with multiple symbiont clades is common in scleractinian (stony) corals, and that, in coral-algal symbiosis, 'specificity' and 'flexibility' are relative terms: specificity is rarely absolute. The potential for reef corals to adapt or acclimatize to environmental change via symbiont community shifts may therefore be more phylogenetically widespread than has previously been assumed.

Rapid environmental change is affecting many organisms; some are coping well but many species are... more Rapid 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, rapid evolution, and bet-hedging. 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 selection for within-generation plasticity and transgenerational plasticity under historical environmental conditions. We then evaluate the predictions that populations adapted to highly variabl...

Journal of Mathematical Biology

To understand the mechanisms underlying species coexistence, ecologists often study invasion grow... more To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to average per-capita growth rates of one species with respect to an ergodic measure supporting other species. In the ecological literature, coexistence often is equated with the invasion growth rates being positive. Intuitively, positive invasion growth rates ensure that species recover from being rare. To provide a mathematically rigorous framework for this approach, we prove theorems that answer two questions: (i) When do the signs of the invasion growth rates determine coexistence? (ii) When signs are sufficient, which invasion growth rates need to be positive? We focus on deterministic models and equate coexistence with permanence, i.e., a global attractor bounded away from extinction. For models satisfying certain technical assumptions, we introduce invasion graphs where vertices correspond to proper subs...

For species primarily regulated by a common predator, the P* rule of Holt and Lawton [1993] predi... more For species primarily regulated by a common predator, the P* rule of Holt and Lawton [1993] 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 stocha...

arXiv (Cornell University), Aug 23, 2018

arXiv (Cornell University), May 17, 2020

Ecology, Jul 21, 2022

arXiv (Cornell University), Aug 23, 2018

Virus Evolution, 2021

AoB PLANTS, 2019

The American Naturalist, 2015

Frontiers in Marine Science, 2015

arXiv (Cornell University), Aug 23, 2018

AoB PLANTS, 2019

Proceedings of the Royal Society B: Biological Sciences, 2019

F1000 - Post-publication peer review of the biomedical literature, 2011

F1000 - Post-publication peer review of the biomedical literature, 2010

F1000 - Post-publication peer review of the biomedical literature, 2012

Journal of Mathematical Biology