Nonlinear life table response experiment analysis: Decomposing nonlinear and nonadditive population growth responses to changes in environmental drivers.

Life table response experiments (LTREs) decompose differences in population growth rate between environments into separate contributions from each underlying demographic rate. However, most LTRE analyses make the unrealistic assumption that the relationships between demographic rates and environmental drivers are linear and independent, which may result in diminished accuracy when these assumptions are violated. We extend regression LTREs to incorporate nonlinear (second-order) terms and compare the accuracy of both approaches for three previously published demographic datasets. We show that the second-order approach equals or outperforms the linear approach for all three case studies, even when all of the underlying vital rate functions are linear. Nonlinear vital rate responses to driver changes contributed most to population growth rate responses, but life history changes also made substantial contributions. Our results suggest that moving from linear to second-order LTRE analyses could improve our understanding of population responses to changing environments.

Distributions of LRS in varying environments.

The lifetime reproductive success (LRS) of individuals is affected by random events such as death, realized growth or realized reproduction, and the outcomes of these events can differ even when individuals have identical probabilities. Another source of randomness arises when these probabilities also change over time in variable environments. For structured populations in stochastic environments, we extend our recent method to determine how birth environment and birth stage determine the random distribution of the LRS. Our results provide a null model that quantifies effects on LRS of just the birth size or stage. Using Roe deer Capreolus capreolus as a case study, we show that the effect of an individual's birth environment on LRS varies with the frequency of environments and their temporal autocorrelation, and that lifetime performance is affected by changes in the pattern of environmental states expected as a result of climate change.

Skewed distributions of lifetime reproductive success: beyond mean and variance.

Lifetime reproductive performance is quantified here by the LRS (lifetime reproductive success), the random number of offspring an individual produces over its lifetime. Many field studies find that distributions of LRS among individuals are non-normal, zero-inflated and highly skewed. These results beg the question, what is the distribution of LRS predicted by demographic models when the only source of randomness is demographic stochasticity? Here we present the first exact analysis of the probability distribution of LRS for species described by age + stage models; our analysis starts with estimated vital rates. We illustrate with three examples: the Hadza, human hunter-foragers (age-only), the evergreen tree Tsuga canadensis (stage-only) and Roe deer, Capreolus capreolus (age + stage). For each we obtain the exact distribution of LRS, but also calculate and discuss the first three moments. Our results point to important questions about how such LRS distributions affect natural selection, and life history evolution.

Photosynthetic rates influence the population dynamics of understory herbs in stochastic light environments.

Temporal variability in light from gaps in the tree canopy strongly influences the vital rates of understory plants. From 2012 to 2015, we estimated the size-specific vital rates of two herbs, Calathea crotalifera and Heliconia tortuosa, over a range of light environments. We estimated maximum photosynthetic capacity (Amax ) for a subset of individuals each year during three annual censuses, and modelled future size as a linear function of current size (a plant trait that changes ontogenetically), canopy openness (an environmental variable), and Amax (a potentially plastic physiological trait). We estimated what the demographic success would be of a population comprised of individuals with a particular fixed Amax for each of several levels of canopy openness if the environment remained constant, by evaluating corresponding Integral Projection Models and their deterministic growth rates (λ). We then estimated their demographic success in the stochastic light environment (λS ) and its elasticities. As light increased, deterministic λ increased for Calathea by 33% but decreased for Heliconia by 52%, and increasing Amax had no effect on λ for Calathea but increased λ for Heliconia in low light. As Amax increased, λS increased for Heliconia, but not Calathea. We also investigated whether photosynthetic rates would influence the elasticities of λS, including its response to perturbation of vital rates in each environment (ESß ), vital rates over all environments (ES ), and variability of vital rates among environments (ESσ ). ES , ESσ , and ESß were influenced by Amax for Heliconia but not Calathea. Events that affect some vital rates in high light have a greater impact on overall fitness than events that affect the same vital rates in shady environments, and there is greater potential for selection on traits of large individuals in high light than in low light for Heliconia, while the reverse was true for Calathea. Photosynthetic rates, through their effects on growth, can strongly influence the population dynamics of plants in random light environments, but the magnitude of this effect varies between species. In the species for which fitness was independent of Amax , Calathea, there would be little opportunity for selection on photosynthetic rates.

Experimental assemblage of novel plant-herbivore interactions: ecological host shifts after 40 million years of isolation.

Geographic isolation is the first step in insect herbivore diet specialization. Such specialization is postulated to increase insect fitness, but may simultaneously reduce insect ability to colonize novel hosts. During the Paleocene-Eocene, plants from the order Zingiberales became isolated either in the Paleotropics or in the Neotropics. During the Cretaceous, rolled-leaf beetles diversified in the Neotropics concurrently with Neotropical Zingiberales. Using a community of Costa Rican rolled-leaf beetles and their Zingiberales host plants as study system, we explored if previous geographic isolation precludes insects to expand their diets to exotic hosts. We recorded interactions between rolled-leaf beetles and native Zingiberales by combining DNA barcodes and field records for 7450 beetles feeding on 3202 host plants. To determine phylogenetic patterns of diet expansions, we set 20 field plots including five exotic Zingiberales, recording beetles feeding on these exotic hosts. In the laboratory, using both native and exotic host plants, we reared a subset of insect species that had expanded their diets to the exotic plants. The original plant-herbivore community comprised 24 beetle species feeding on 35 native hosts, representing 103 plant-herbivore interactions. After exotic host plant introduction, 20% of the beetle species expanded their diets to exotic Zingiberales. Insects only established on exotic hosts that belong to the same plant family as their native hosts. Laboratory experiments show that beetles are able to complete development on these novel hosts. In conclusion, rolled-leaf beetles are pre-adapted to expand their diets to novel host plants even after millions of years of geographic isolation.

In a long-term experimental demography study, excluding ungulates reversed invader's explosive population growth rate and restored natives.

A major goal in ecology is to understand mechanisms that increase invasion success of exotic species. A recent hypothesis implicates altered species interactions resulting from ungulate herbivore overabundance as a key cause of exotic plant domination. To test this hypothesis, we maintained an experimental demography deer exclusion study for 6 y in a forest where the native ungulate Odocoileus virginianus (white-tailed deer) is overabundant and Alliaria petiolata (garlic mustard) is aggressively invading. Because population growth is multiplicative across time, we introduce metrics that correctly integrate experimental effects across treatment years, the cumulative population growth rate, λc, and its geometric mean, λper-year, the time-averaged annual population growth rate. We determined λc and λper-year of the invader and of a common native, Trillium erectum. Our results conclusively demonstrate that deer are required for the success of Alliaria; its projected population trajectory shifted from explosive growth in the presence of deer (λper-year = 1.33) to decline toward extinction where deer are excluded (λper-year = 0.88). In contrast, Trillium's λper-year was suppressed in the presence of deer relative to deer exclusion (λper-year = 1.04 vs. 1.20, respectively). Retrospective sensitivity analyses revealed that the largest negative effect of deer exclusion on Alliaria came from rosette transitions, whereas the largest positive effect on Trillium came from reproductive transitions. Deer exclusion lowered Alliaria density while increasing Trillium density. Our results provide definitive experimental support that interactions with overabundant ungulates enhance demographic success of invaders and depress natives' success, with broad implications for biodiversity and ecosystem function worldwide.

Interactions between plant size and canopy openness influence vital rates and life-history tradeoffs in two neotropical understory herbs.

UNLABELLED: • PREMISE OF THE STUDY: For tropical forest understory plants, the ability to grow, survive, and reproduce is limited by the availability of light. The extent to which reproduction incurs a survival or growth cost may change with light availability, plant size, and adaptation to shade, and may vary among similar species.• METHODS: We estimated size-specific rates of growth, survival, and reproduction (vital rates), for two neotropical understory herbs (order Zingiberales) in a premontane tropical rainforest in Costa Rica. During three annual censuses we monitored 1278 plants, measuring leaf area, number of inflorescences, and canopy openness. We fit regression models of all vital rates and evaluated them over a range of light levels. The best fitting models were selected using Akaike's Information Criterion.• KEY RESULTS: All vital rates were significantly influenced by size in both species, but not always by light. Increasing light resulted in higher growth and a higher probability of reproduction in both species, but lower survival in one species. Both species grew at small sizes but shrank at larger sizes. The size at which shrinkage began differed among species and light environments. Vital rates of large individuals were more sensitive to changes in light than small individuals.• CONCLUSIONS: Increasing light does not always positively influence vital rates; the extent to which light affects vital rates depends on plant size. Differences among species in their abilities to thrive under different light conditions and thus occupy distinct niches may contribute to the maintenance of species diversity.

Large size and high light do not lower the cost of reproduction for the Neotropical herb Goeppertia marantifolia.

UNLABELLED: • PREMISE OF THE STUDY: Sexual reproduction is often associated with a cost in terms of reduced survival, growth, or future reproduction. It has been proposed that plant size and the environment (availability of key resources) can sometimes lower or even nullify the cost of reproduction.• METHODS: We address this issue experimentally with the Neotropical herb Goeppertia marantifolia, by manipulating sexual reproductive effort and measuring the demographic performance of plants and of their clonal offspring, in the context of natural variation in light availability.• KEY RESULTS: Plants in the high-reproductive-effort treatment grew less between seasons but did not differ in their probability of flowering the second season or in inflorescence size compared with plants in the low-effort treatment. Reproductive effort of parent plants influenced the leaf area of their clonal offspring. Plants that invested less in sexual reproduction produced clonal offspring that were initially larger than those produced by plants that invested more in reproduction. The magnitude of this effect was greater in parent plants that received two seasons of the manipulated reproductive effort than in those that received a single season. The trade-off between reproductive modes dampened with time, leading to smaller differences in clonal offspring leaf area between treatments over time.• CONCLUSIONS: We found evidence of a cost of reproduction and trade-offs between reproductive modes, although the magnitude of these costs was small. However, we found no evidence of lower costs of reproduction for larger plants or for plants in higher-light environments over our 2-yr study period.

Derivatives of the stochastic growth rate.

We consider stochastic matrix models for population driven by random environments which form a Markov chain. The top Lyapunov exponent a, which describes the long-term growth rate, depends smoothly on the demographic parameters (represented as matrix entries) and on the parameters that define the stochastic matrix of the driving Markov chain. The derivatives of a-the "stochastic elasticities"-with respect to changes in the demographic parameters were derived by Tuljapurkar (1990). These results are here extended to a formula for the derivatives with respect to changes in the Markov chain driving the environments. We supplement these formulas with rigorous bounds on computational estimation errors, and with rigorous derivations of both the new and old formulas.

Non-timber forest product harvest in variable environments: modeling the effect of harvesting as a stochastic sequence.

With increasing reports of overexploitation of wild plants for timber and non-timber forest products, there has been an increase in the number of studies investigating the effect of harvest on the dynamics of harvested populations. However, most studies have failed to account for temporal and spatial variability in the ecological conditions in which these species occur, as well as variability in the patterns of harvest intensity. In reality, local harvesters harvest at variable rather than fixed intensity over time. Here we used Markov chains to investigate how different patterns of harvesting intensity (summarized as return time to high harvest) affected the stochastic population growth rate (lambda(s)) and its elasticity to perturbation of means and variances of vital rates. We studied the effect of bark and foliage harvest from African mahogany Khaya senegalensis in two contrasting ecological regions in Benin. Khaya populations declined regardless of time between harvests of high intensity. Moreover, lambda(s) increased with decreasing harvesting pressure in the dry region but, surprisingly, declined in the moist region toward lambda(s) = 0.956. The stochastic elasticity was dominated by the stasis of juveniles and adults. The declining growth rate with decreasing harvest pressure in the moist region was mainly driven by the declining mean survival rates of juveniles and adults. Our results suggest that modeling the temporal variability of harvest intensity as a Markov chain better mimics local practices and provides insights that are missed when temporal variability in harvest intensity is modeled as independent over time and drawn from a fixed distribution.

Experimental demography and the vital rates of generalist and specialist insect herbivores on native and novel host plants.

1. Colonization success of species when confronted with novel environments is of interest in ecological, evolutionary and conservation contexts. Such events may represent the first step for ecological diversification. They also play an important role in adaptive divergence and speciation. 2. A species that is able to do well across a range of environments has a higher plasticity than one whose success is restricted to a single or few environments. The breadth of environments in which a species can succeed is ultimately determined by the full pattern of its vital rates in each environment. 3. Examples of organisms colonizing novel environments are insect herbivores expanding their diets to novel host plants. One expectation for insect herbivores is that species with specialized diets may display less plasticity when faced with novel hosts than generalist species. 4. We examine this hypothesis for two generalist and two specialist neotropical beetles (genus Cephaloleia: Chrysomelidae) currently expanding their diets from native to novel plants of the order Zingiberales. Using an experimental approach, we estimated changes in vital rates, life-history traits and lifetime fitness for each beetle species when feeding on native or novel host plants. 5. We did not find evidence supporting more plasticity for generalists than for specialists. Instead, we found similar patterns of survival and fecundity for all herbivores. Larvae survived worse on novel hosts; adults survived at least as well or better, but reproduced less on the novel host than on natives. 6. Some of the novel host plants represent challenging environments where population growth was negative. However, in four novel plant-herbivore interactions, instantaneous population growth rates were positive. 7. Positive instantaneous population growth rates during initial colonization of novel host plants suggest that both generalist and specialist Cephaloleia beetles may be pre-adapted to feed on some novel hosts. This plasticity in host use is a key factor for successful colonization of novel hosts. Future success or failure in the colonization of these novel hosts will depend on the demographic rates described in this research, natural selection and the evolutionary responses of life-history traits in novel environments.

A time to grow and a time to die: a new way to analyze the dynamics of size, light, age, and death of tropical trees.

In tropical rain forests, rates of forest turnover and tree species' life-history differences are shaped by the life expectancy of trees and the time taken by seedlings to reach the canopy. These measures are therefore of both theoretical and applied interest. However, the relationship between size, age, and life expectancy is poorly understood. In this paper, we show how to obtain, in a dynamic environment, age-related population parameters from data on size and light transitions and survival of individuals over single time steps. We accomplish this goal by combining two types of analysis (integral projection modeling and age-from-stage analysis for variable environments) in a new way. The method uses an index of crown illumination (CI) to capture the key tree life-history axis of movement through the light environment. We use this method to analyze data on nine tropical tree species, chosen to sample two main gradients, juvenile recruitment niche (gap/nongap) and adult crown position niche (subcanopy, canopy-emergent). We validate the method using independent estimates of age and size from growth rings and 14C from some of the same species at the same site and use our results to examine correlations among age-related population parameters. Finally, we discuss the implications of these new results for life histories of tropical trees.

How climate affects extreme events and hence ecological population models.

Extreme events significantly impact ecosystems and are predicted to increase in frequency and/or magnitude with climate change. Generalized extreme value (GEV) distributions describe most ecologically relevant extreme events, including hurricanes, wildfires, and disease spread. In climate science, the GEV is widely used as an accurate and flexible tool over large spatial scales (>105  km2 ) to study how changes in climate shift extreme events. However, ecologists rarely use the GEV to study how climate change affects populations. Here we show how to estimate a GEV for hurricanes at an ecologically relevant (<103  km2 ) spatial scale, and use the results in a stochastic, empirically based, matrix population model. As a case study, we use an understory shrub in southeast Florida, USA with hurricane-driven dynamics and measure the effects of change using the stochastic population growth rate. We use sensitivities to analyze how population growth rate is affected by changes in hurricane frequency and intensity, canopy damage levels, and canopy recovery rates. Our results emphasize the importance of accurately estimating location-specific storm frequency. In a rapidly changing world, our methods show how to combine realistic extreme event and population models to assess ecological impacts and to prioritize conservation actions for at-risk populations.

Stage dynamics, period survival, and mortality plateaus.

Mortality plateaus at advanced ages have been found in many species, but their biological causes remain unclear. Here, we exploit age-from-stage methods for organisms with stage-structured demography to study cohort dynamics, obtaining age patterns of mortality by weighting one-period stage-specific survivals by expected age-specific stage structure. Cohort dynamics behave as a killed Markov process. Using as examples two African grasses, one pine tree, a temperate forest perennial herb, and a subtropical shrub in a hurricane-driven forest, we illustrate diverse patterns that may emerge. Age-specific mortality always reaches a plateau at advanced ages, but the plateau may be reached rapidly or slowly, and the trajectory may follow positive or negative senescence along the way. In variable environments, birth state influences mortality at early but not late ages, although its effect on the level of survivorship persists. A new parameter micro omega summarizes the risk of mortality averaged over the entire lifetime in a variable environment. Recent aging models for humans that employ nonobservable abstract states of "vitality" are also known to produce diverse trajectories and similar asymptotic behavior. We discuss connections, contrasts, and implications of our results to these models for the study of aging.

Longevity can buffer plant and animal populations against changing climatic variability.

Both means and year-to-year variances of climate variables such as temperature and precipitation are predicted to change. However, the potential impact of changing climatic variability on the fate of populations has been largely unexamined. We analyzed multiyear demographic data for 36 plant and animal species with a broad range of life histories and types of environment to ask how sensitive their long-term stochastic population growth rates are likely to be to changes in the means and standard deviations of vital rates (survival, reproduction, growth) in response to changing climate. We quantified responsiveness using elasticities of the long-term population growth rate predicted by stochastic projection matrix models. Short-lived species (insects and annual plants and algae) are predicted to be more strongly (and negatively) affected by increasing vital rate variability relative to longer-lived species (perennial plants, birds, ungulates). Taxonomic affiliation has little power to explain sensitivity to increasing variability once longevity has been taken into account. Our results highlight the potential vulnerability of short-lived species to an increasingly variable climate, but also suggest that problems associated with short-lived undesirable species (agricultural pests, disease vectors, invasive weedy plants) may be exacerbated in regions where climate variability decreases.

Poverty dynamics, poverty thresholds and mortality: An age-stage Markovian model.

Recent studies have examined the risk of poverty throughout the life course, but few have considered how transitioning in and out of poverty shape the dynamic heterogeneity and mortality disparities of a cohort at each age. Here we use state-by-age modeling to capture individual heterogeneity in crossing one of three different poverty thresholds (defined as 1×, 2× or 3× the "official" poverty threshold) at each age. We examine age-specific state structure, the remaining life expectancy, its variance, and cohort simulations for those above and below each threshold. Survival and transitioning probabilities are statistically estimated by regression analyses of data from the Health and Retirement Survey RAND data-set, and the National Longitudinal Survey of Youth. Using the results of these regression analyses, we parameterize discrete state, discrete age matrix models. We found that individuals above all three thresholds have higher annual survival than those in poverty, especially for mid-ages to about age 80. The advantage is greatest when we classify individuals based on 1× the "official" poverty threshold. The greatest discrepancy in average remaining life expectancy and its variance between those above and in poverty occurs at mid-ages for all three thresholds. And fewer individuals are in poverty between ages 40-60 for all three thresholds. Our findings are consistent with results based on other data sets, but also suggest that dynamic heterogeneity in poverty and the transience of the poverty state is associated with income-related mortality disparities (less transience, especially of those above poverty, more disparities). This paper applies the approach of age-by-stage matrix models to human demography and individual poverty dynamics. In so doing we extend the literature on individual poverty dynamics across the life course.

From stage to age in variable environments: life expectancy and survivorship.

Stage-based demographic data are now available on many species of plants and some animals, and they often display temporal and spatial variability. We provide exact formulas to compute age-specific life expectancy and survivorship from stage-based data for three models of temporal variability: cycles, serially independent random variation, and a Markov chain. These models provide a comprehensive description of patterns of temporal variation. Our formulas describe the effects of cohort (birth) environmental condition on mortality at all ages, and of the effects on survivorship of environmental variability experienced over the course of life. This paper complements existing methods for time-invariant stage-based data, and adds to the information on population growth and dynamics available from stochastic demography.

Ant-nest soil and seedling growth in a neotropical ant-dispersed herb.

A major hypothesis concerning the benefits of myrmecochory, seed dispersal by ants, to plants is that ant nests are nutrient-enriched microsites that are beneficial to seedling growth. We experimentally test this hypothesis for a neotropical myrmecochore, Calathea ovandensis, asking two questions: 1) is soil of nests of a seed-dispersing ant chemically or structurally distinct from surrounding soils, and 2) do seedlings grow better in soil collected from ant nests than in randomly collected soil? We found that although ant-nest soil was significantly enriched in nitrate-nitrogen, magnesium, iron, manganese, cadmium and percent organic matter compared to randomly collected soil, seedling growth was not significantly improved by ant-nest soil.

Parent-offspring conflicts, "optimal bad motherhood" and the "mother knows best" principles in insect herbivores colonizing novel host plants.

SPECIALIZATION OF INSECT HERBIVORES TO ONE OR A FEW HOST PLANTS STIMULATED THE DEVELOPMENT OF TWO HYPOTHESES ON HOW NATURAL SELECTION SHOULD SHAPE OVIPOSITION PREFERENCES: The "mother knows best" principle suggests that females prefer to oviposit on hosts that increase offspring survival. The "optimal bad motherhood" principle predicts that females prefer to oviposit on hosts that increase their own longevity. In insects colonizing novel host plants, current theory predicts that initial preferences of insect herbivores should be maladaptive, leading to ecological traps. Ecological trap theory does not take into account the fact that insect lineages frequently switch hosts at both ecological and evolutionary time scales. Therefore, the behavior of insect herbivores facing novel hosts is also shaped by natural selection. Using a study system in which four Cephaloleia beetles are currently expanding their diets from native to exotic plants in the order Zingiberales, we determined if initial oviposition preferences are conservative, maladaptive, or follow the patterns predicted by the "mother knows best" or the "optimal bad motherhood" principles. Interactions with novel hosts generated parent-offspring conflicts. Larval survival was higher on native hosts. However, adult generally lived longer on novel hosts. In Cephaloleia beetles, oviposition preferences are usually associated with hosts that increase larval survival, female fecundity, and population growth. In most cases, Cephaloleia oviposition preferences follow the expectations of the "mothers knows best" principle.

Trading stages: life expectancies in structured populations.

Interest in stage-and age structured models has recently increased because they can describe quantitative traits such as size that are left out of age-only demography. Available methods for the analysis of effects of vital rates on lifespan in stage-structured models have not been widely applied because they are hard to use and interpret, and tools for age and stage structured populations are missing. We present easily interpretable expressions for the sensitivities and elasticities of life expectancy to vital rates in age-stage models, and illustrate their application with two biological examples. Much of our approach relies on trading of time and mortality risk in one stage for time and risk in others. Our approach contributes to the new framework of the study of age- and stage-structured biodemography.