The natural history of luck: A synthesis study of structured population models.

Chance pervades life. In turn, life histories are described by probabilities (e.g. survival and breeding) and averages across individuals (e.g. mean growth rate and age at maturity). In this study, we explored patterns of luck in lifetime outcomes by analysing structured population models for a wide array of plant and animal species. We calculated four response variables: variance and skewness in both lifespan and lifetime reproductive output (LRO), and partitioned them into contributions from different forms of luck. We examined relationships among response variables and a variety of life history traits. We found that variance in lifespan and variance in LRO were positively correlated across taxa, but that variance and skewness were negatively correlated for both lifespan and LRO. The most important life history trait was longevity, which shaped variance and skew in LRO through its effects on variance in lifespan. We found that luck in survival, growth, and fecundity all contributed to variance in LRO, but skew in LRO was overwhelmingly due to survival luck. Rapidly growing populations have larger variances in LRO and lifespan than shrinking populations. Our results indicate that luck-induced genetic drift may be most severe in recovering populations of species with long mature lifespan and high iteroparity.

To Prosper, Live Long: Understanding the Sources of Reproductive Skew and Extreme Reproductive Success in Structured Populations.

AbstractIn many species, a few individuals produce most of the next generation. How much of this reproductive skew is driven by variation among individuals in fixed traits, how much by external factors, and how much by random chance? And what does it take to have truly exceptional lifetime reproductive output (LRO)? In the past, we and others have partitioned the variance of LRO as a proxy for reproductive skew. Here we explain how to partition LRO skewness itself into contributions from fixed trait variation, four forms of "demographic luck" (birth state, fecundity luck, survival trajectory luck, and growth trajectory luck), and two kinds of "environmental luck" (birth environment and environment trajectory). Each of these is further partitioned into contributions at different ages. We also determine what we can infer about individuals with exceptional LRO. We find that reproductive skew is largely driven by random variation in lifespan, and exceptional LRO generally results from exceptional lifespan. Other kinds of luck frequently bring skewness down rather than increasing it. In populations where fecundity varies greatly with environmental conditions, getting a good year at the right time can be an alternate route to exceptional LRO, so that LRO is less predictive of lifespan.

Beyond simple adaptation: Incorporating other evolutionary processes and concepts into eco-evolutionary dynamics.

Studies of eco-evolutionary dynamics have integrated evolution with ecological processes at multiple scales (populations, communities and ecosystems) and with multiple interspecific interactions (antagonistic, mutualistic and competitive). However, evolution has often been conceptualised as a simple process: short-term directional adaptation that increases population growth. Here we argue that diverse other evolutionary processes, well studied in population genetics and evolutionary ecology, should also be considered to explore the full spectrum of feedback between ecological and evolutionary processes. Relevant but underappreciated processes include (1) drift and mutation, (2) disruptive selection causing lineage diversification or speciation reversal and (3) evolution driven by relative fitness differences that may decrease population growth. Because eco-evolutionary dynamics have often been studied by population and community ecologists, it will be important to incorporate a variety of concepts in population genetics and evolutionary ecology to better understand and predict eco-evolutionary dynamics in nature.

Mechanistic Models of Trophic Interactions: Opportunities for Species Richness and Challenges for Modern Coexistence Theory.

AbstractMany potential mechanisms promote species coexistence, but we know little about their relative importance. To compare multiple mechanisms, we modeled a two-trophic planktonic food web based on mechanistic species interactions and empirically measured species traits. We simulated thousands of possible communities under realistic and altered interaction strengths to assess the relative importance of three potential drivers of phytoplankton and zooplankton species richness: resource-mediated coexistence mechanisms, predator-prey interactions, and trait trade-offs. Next, we computed niche and fitness differences of competing zooplankton to obtain a deeper understanding of how these mechanisms determine species richness. We found that predator-prey interactions were the most important driver of phytoplankton and zooplankton species richness and that large zooplankton fitness differences were associated with low species richness, but zooplankton niche differences were not associated with species richness. However, for many communities we could not apply modern coexistence theory to compute niche and fitness differences of zooplankton because of conceptual issues with the invasion growth rates arising from trophic interactions. We therefore need to expand modern coexistence theory to fully investigate multitrophic-level communities.

Predicting and Controlling Spillover in Multispecies Disease Transmission Networks: Steady-State Analysis.

AbstractIn multispecies disease systems, pathogen spillover from a "reservoir community" can maintain disease in a "sink community" where it would otherwise die out. We develop and analyze models for spillover and disease spread in sink communities, focusing on questions of control: which species or transmission links are the most important to target to reduce the disease impact on a species of concern? Our analysis focuses on steady-state disease prevalence, assuming that the timescale of interest is long compared with that of disease introduction and establishment in the sink community. We identify three regimes as the sink community R0 scales from 0 to 1. Up to R0≈0.3, overall infection patterns are dominated by direct exogenous infections and one-step subsequent transmission. For R0≈1, infection patterns are characterized by dominant eigenvectors of a force-of-infection matrix. In between, additional network details can be important; we derive and apply general sensitivity formulas that identify particularly important links and species.

A Time for Every Purpose: Using Time-Dependent Sensitivity Analysis to Help Understand and Manage Dynamic Ecological Systems.

AbstractSensitivity analysis is often used to help understand and manage ecological systems by assessing how a constant change in vital rates or other model parameters might affect the management outcome. This allows the manager to identify the most favorable course of action. However, realistic changes are often localized in time-for example, a short period of culling leads to a temporary increase in the mortality rate over the period. Hence, knowing when to act may be just as important as knowing what to act on. In this article, we introduce the method of time-dependent sensitivity analysis (TDSA) that simultaneously addresses both questions. We illustrate TDSA using three case studies: transient dynamics in static disease transmission networks, disease dynamics in a reservoir species with seasonal life history events, and endogenously driven population cycles in herbivorous invertebrate forest pests. We demonstrate how TDSA often provides useful biological insights, which are understandable on hindsight but would not have been easily discovered without the help of TDSA. However, as a caution, we also show how TDSA can produce results that mainly reflect uncertain modeling choices and are therefore potentially misleading. We provide guidelines to help users maximize the utility of TDSA while avoiding pitfalls.

Pathogen transport amplifies or dilutes disease transmission depending on the host dose-response relationship.

Pathogen transport by biotic or abiotic processes (e.g. mechanical vectors, wind, rain) can increase disease transmission by creating more opportunities for host exposure. But transport without replication has an inherent trade-off, that creating new venues for exposure decreases the average pathogen abundance at each venue. The host dose-response relationship is therefore required to correctly assess infection risk. We model and analyse two examples-biotic mechanical vectors in plant-pollinator networks, and abiotic-facilitated long-distance pathogen dispersal-to illustrate how oversimplifying the dose-response relationship can lead to incorrect epidemiological predictions. When the minimum infective dose is high, mechanical vectors amplify disease transmission less than suggested by simple compartment models, and may even dilute transmission. When long-distance dispersal leads to infrequent large exposures, models that assume a linear force of infection can substantially under-predict the speed of epidemic spread. Our work highlights an important general interplay between dose-response relationships and pathogen transport.

Snared in an Evil Time: How Age-Dependent Environmental and Demographic Variability Contribute to Variance in Lifetime Outcomes.

AbstractTo what degree is lifetime success determined by innate individual quality versus external events and random chance, whether success is measured by lifetime reproductive output, life span, years that a tree spends in the canopy, or some other measure? And how do external events and chance interact with development (survival and growth) to drive success? To answer these questions, we extend our earlier age partitioning of luck in lifetime outcomes in two ways: we incorporate effects of external environmental variation, and we subdivide demographic luck into contributions from survival and growth. Applying our methods to four case studies, we find that luck in survival, in growth, or in environmental variation can all be the dominant driver of success, depending on life history, but variation in individual quality remains a lesser driver. Luck in its various forms is most important at very early ages and again close to the time when individuals typically first begin to be successful (e.g., entering the canopy, reaching reproductive maturity), but different forms of luck peak at different times. For example, a favorable year can boost a tree into the canopy, while luck in survival is required to take full advantage of that fortunate event.

Time and Chance: Using Age Partitioning to Understand How Luck Drives Variation in Reproductive Success.

AbstractOver the course of individual lifetimes, luck usually explains a large fraction of the between-individual variation in life span or lifetime reproductive output (LRO) within a population, while variation in individual traits or "quality" explains much less. To understand how, where in the life cycle, and through which demographic processes luck trumps trait variation, we show how to partition by age the contributions of luck and trait variation to LRO variance and how to quantify three distinct components of luck. We apply these tools to several empirical case studies. We find that luck swamps effects of trait variation at all ages, primarily because of randomness in individual state dynamics ("state trajectory luck"). Luck early in life is most important. Very early state trajectory luck generally determines whether an individual ever breeds, likely by ensuring that they are not dead or doomed quickly. Less early luck drives variation in success among those breeding at least once. Consequently, the importance of luck often has a sharp peak early in life or it has two peaks. We suggest that ages or stages where the importance of luck peaks are potential targets for interventions to benefit a population of concern, different from those identified by eigenvalue elasticity analysis.

Host-pathogen immune feedbacks can explain widely divergent outcomes from similar infections.

A long-standing question in infection biology is why two very similar individuals, with very similar pathogen exposures, may have very different outcomes. Recent experiments have found that even isogenic Drosophila melanogaster hosts, given identical inoculations of some bacterial pathogens at suitable doses, can experience very similar initial bacteria proliferation but then diverge to either a lethal infection or a sustained chronic infection with much lower pathogen load. We hypothesized that divergent infection outcomes are a natural result of mutual negative feedbacks between pathogens and the host immune response. Here, we test this hypothesis in silico by constructing process-based dynamic models for bacterial population growth, host immune induction and the feedbacks between them, based on common mechanisms of immune system response. Mathematical analysis of a minimal conceptual model confirms our qualitative hypothesis that mutual negative feedbacks can magnify small differences among hosts into life-or-death differences in outcome. However, explaining observed features of chronic infections requires an extension of the model to include induced pathogen modifications that shield themselves from host immune responses at the cost of reduced proliferation rate. Our analysis thus generates new, testable predictions about the mechanisms underlying bimodal infection outcomes.

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 Specialization and Multihost Epidemics: Disease Spread in Plant-Pollinator Networks.

Many parasites infect multiple species and persist through a combination of within- and between-species transmission. Multispecies transmission networks are typically constructed at the species level, linking two species if any individuals of those species interact. However, generalist species often consist of specialized individuals that prefer different subsets of available resources, so individual- and species-level contact networks can differ systematically. To explore the epidemiological impacts of host specialization, we build and study a model for pollinator pathogens on plant-pollinator networks, in which individual pollinators have dynamic preferences for different flower species. We find that modeling and analysis that ignore individual host specialization can predict die-off of a disease that is actually strongly persistent and can badly over- or underpredict steady-state disease prevalence. Effects of individual preferences remain substantial whenever mean preference duration exceeds half of the mean time from infection to recovery or death. Similar results hold in a model where hosts foraging in different habitats have different frequencies of contact with an environmental reservoir for the pathogen. Thus, even if all hosts have the same long-run average behavior, dynamic individual differences can profoundly affect disease persistence and prevalence.

An expanded modern coexistence theory for empirical applications.

Understanding long-term coexistence of numerous competing species is a longstanding challenge in ecology. Progress requires determining which processes and species differences are most important for coexistence when multiple processes operate and species differ in many ways. Modern coexistence theory (MCT), formalised by Chesson, holds out the promise of doing that, but empirical applications remain scarce. We argue that MCT's mathematical complexity and subtlety have obscured the simplicity and power of its underlying ideas and hindered applications. We present a general computational approach that extends our previous solution for the storage effect to all of standard MCT's spatial and temporal coexistence mechanisms, and also process-defined mechanisms amenable to direct study such as resource partitioning, indirect competition, and life history trade-offs. The main components are a method to partition population growth rates into contributions from different mechanisms and their interactions, and numerical calculations in which some mechanisms are removed and others retained. We illustrate how our approach handles features that have not been analysed in the standard framework through several case studies: competing diatom species under fluctuating temperature, plant-soil feedbacks in grasslands, facilitation in a beach grass community, and niche differences with independent effects on recruitment, survival and growth in sagebrush steppe.

Can Population Genetics Adapt to Rapid Evolution?

Population genetics largely rests on a 'standard model' in which random genetic drift is the dominant force, selective sweeps occur infrequently, and deleterious mutations are purged from the population by purifying selection. Studies of phenotypic evolution in nature reveal a very different picture, with strong selection and rapid heritable trait changes being common. The time-rate scaling of phenotypic evolution suggests that selection on phenotypes is often fluctuating in direction, allowing phenotypes to respond rapidly to environmental fluctuations while remaining within relatively constant bounds over longer periods. Whether such rapid phenotypic evolution undermines the standard model will depend on how many genomic loci typically contribute to strongly selected traits and how phenotypic evolution impacts the dynamics of genetic variation in a population. Population-level sequencing will allow us to dissect the genetic basis of phenotypic evolution and study the evolutionary dynamics of genetic variation through direct measurement of polymorphism trajectories over time.

Why So Variable: Can Genetic Variance in Flowering Thresholds Be Maintained by Fluctuating Selection?

We use integral projection models (IPMs) and individual-based simulations to study the evolution of genetic variance in two monocarpic plant systems. Previous approaches combining IPMs with an adaptive dynamics-style invasion analysis predicted that genetic variability in the size threshold for flowering will not be maintained, which conflicts with empirical evidence. We ask whether this discrepancy can be resolved by making more realistic assumptions about the underlying genetic architecture, assuming a multilocus quantitative trait in an outcrossing diploid species. To do this, we embed the infinitesimal model of quantitative genetics into an IPM for a size-structured cosexual plant species. The resulting IPM describes the joint dynamics of individual size and breeding value of the evolving trait. We apply this general framework to the monocarpic perennials Oenothera glazioviana and Carlina vulgaris. The evolution of heritable variation in threshold size is explored in both individual-based models (IBMs) and IPMs, using a mutation rate modifier approach. In the Oenothera model, where the environment is constant, there is selection against producing genetically variable offspring. In the Carlina model, where the environment varies between years, genetically variable offspring provide a selective advantage, allowing the maintenance of genetic variability. The contrasting predictions of adaptive dynamics and quantitative genetics models for the same system suggest that fluctuating selection may be more effective at maintaining genetic variation than previously thought.

Trait-Based Modeling of Multihost Pathogen Transmission: Plant-Pollinator Networks.

Epidemiological models for multihost pathogen systems often classify individuals taxonomically and use species-specific parameter values, but in species-rich communities that approach may require intractably many parameters. Trait-based epidemiological models offer a potential solution but have not accounted for within-species trait variation or between-species trait overlap. Here we propose and study trait-based models with host and vector communities represented as trait distributions without regard to species identity. To illustrate this approach, we develop susceptible-infectious-susceptible models for disease spread in plant-pollinator networks with continuous trait distributions. We model trait-dependent contact rates in two common scenarios: nested networks and specialized plant-pollinator interactions based on trait matching. We find that disease spread in plant-pollinator networks is impacted the most by selective pollinators, universally attractive flowers, and cospecialized plant-pollinator pairs. When extreme pollinator traits are rare, pollinators with common traits are most important for disease spread, whereas when extreme flower traits are rare, flowers with uncommon traits impact disease spread the most. Greater nestedness and specialization both typically promote disease persistence. Given recent pollinator declines caused in part by pathogens, we discuss how trait-based models could inform conservation strategies for wild and managed pollinators. Furthermore, while we have applied our model to pollinators and pathogens, its framework is general and can be transferred to any kind of species interactions in any community.

Size-by-environment interactions: a neglected dimension of species' responses to environmental variation.

In both plant and animal systems, size can determine whether an individual survives and grows under different environmental conditions. However, it is unclear whether and when size-dependent responses to exogenous environmental fluctuations affect population dynamics. Size-by-environment interactions create pathways for environmental fluctuations to influence population dynamics by allowing for negative covariation between sizes within vital rates (e.g. small and large individuals have negatively covarying survival rates) and/or size-dependent variability in a vital rate (e.g. survival of large individuals varies less than small individuals through time). Whether these phenomena affect population dynamics depends on how they are mediated by elasticities (they must affect the sizes and vital rates that matter) and their projected impacts will depend on model functional form (the impact of reduced variance depends on the relationship between the environment and vital rate). We demonstrate these ideas with an analysis of fifteen species from five semiarid plant communities. We find that size-by-environment interactions are common but do not impact long-term population dynamics. Size-by-environment interactions may yet be important for other species. Our approach can be applied to species in other ecosystems to determine if and how size-by-environment interactions allow them to cope with, or exploit, fluctuating environments.

Generation Time in Structured Populations.

Generation time is an intuitively simple concept, but for structured populations there are multiple definitions and no general understanding of how they relate to each other. François Bienvenu and Stéphane Legendre, in their note "A New Approach to the Generation Time in Matrix Population Models," appearing in the June 2015 issue of The American Naturalist, introduced a new measure of generation time Ta, the average time between birth events in an ancestral lineage, and derived the remarkably simple formula [Formula: see text] for any matrix model, where F is the fecundity matrix, v is reproductive value, and w is stable population structure. Here I generalize their formula and interpretations of Ta to a continuous or continuous-discrete population structure and derive similar formulas for three other established generation time measures: average parent age across all births at one time ([Formula: see text]) and mean parent age at birth events for a cohort (µ1) or generation (Tc). The new formulas reveal that these differently defined measures are unexpectedly often identical in value and clarify when they differ.

Pluck or Luck: Does Trait Variation or Chance Drive Variation in Lifetime Reproductive Success?

While there has been extensive interest in how intraspecific trait variation affects ecological processes, outcomes are highly variable even when individuals are identical: some are lucky, while others are not. Trait variation is therefore important only if it adds substantially to the variability produced by luck. We ask when trait variation has a substantial effect on variability in lifetime reproductive success (LRS), using two approaches: (1) we partition the variation in LRS into contributions from luck and trait variation and (2) we ask what can be inferred about an individual's traits and with what certainty, given their observed LRS. In theoretical stage- and size-structured models and two empirical case studies, we find that luck usually dominates the variance of LRS. Even when individuals differ substantially in ways that affect expected LRS, unless the effects of luck are substantially reduced (e.g., low variability in reproductive life span or annual fecundity), most variance in lifetime outcomes is due to luck, implying that departures from "null" models omitting trait variation will be hard to detect. Luck also obscures the relationship between realized LRS and individual traits. While trait variation may influence the fate of populations, luck often governs the lives of individuals.

Weak interspecific interactions in a sagebrush steppe? Conflicting evidence from observations and experiments.

Stable coexistence requires intraspecific limitations to be stronger than interspecific limitations. The greater the difference between intra- and interspecific limitations, the more stable the coexistence, and the weaker the competitive release any species should experience following removal of competitors. We conducted a removal experiment to test whether a previously estimated model, showing surprisingly weak interspecific competition for four dominant species in a sagebrush steppe, accurately predicts competitive release. Our treatments were (1) removal of all perennial grasses and (2) removal of the dominant shrub, Artemisia tripartita. We regressed survival, growth, and recruitment on the locations, sizes, and species identities of neighboring plants, along with an indicator variable for removal treatment. If our "baseline" regression model, which accounts for local plant-plant interactions, accurately explains the observed responses to removals, then the removal coefficient should be non-significant. For survival, the removal coefficients were never significantly different from zero, and only A. tripartita showed a (negative) response to removals at the recruitment stage. For growth, the removal treatment effect was significant and positive for two species, Poa secunda and Pseudoroegneria spicata, indicating that the baseline model underestimated interspecific competition. For all three grass species, population models based on the vital rate regressions that included removal effects projected 1.4- to 3-fold increases in equilibrium population size relative to the baseline model (no removal effects). However, we found no evidence of higher response to removal in quadrats with higher pretreatment cover of A. tripartita, or by plants experiencing higher pre-treatment crowding by A. tripartita, raising questions about the mechanisms driving the positive response to removal. While our results show the value of combining observations with a simple removal experiment, more tightly controlled experiments focused on underlying mechanisms may be required to conclusively validate or reject predictions from phenomenological models.