Search for: All records

Abstract Matrix population models are frequently built and used by ecologists to analyse demography and elucidate the processes driving population growth or decline. Life Table Response Experiments (LTREs) are comparative analyses that decompose the realized difference or variance in population growth rate () into contributions from the differences or variances in the vital rates (i.e. the matrix elements). Since their introduction, LTREs have been based on approximations and have not included biologically relevant interaction terms.We used the functional analysis of variance framework to derive an exact LTRE method, which calculates the exact response of to the difference or variance in a given vital rate, for all interactions among vital rates—including higher‐order interactions neglected by the classical methods. We used the publicly available COMADRE and COMPADRE databases to perform a meta‐analysis comparing the results of exact and classical LTRE methods. We analysed 186 and 1487 LTREs for animal and plant matrix population models, respectively.We found that the classical methods often had small errors, but that very high errors were possible. Overall error was related to the difference or variance in the matrices being analysed, consistent with the Taylor series basis of the classical method. Neglected interaction terms accounted for most of the errors in fixed design LTRE, highlighting the importance of two‐way interaction terms. For random design LTRE, errors in the contribution terms present in both classical and exact methods were comparable to errors due to neglected interaction terms. In most examples we analysed, evaluating exact contributions up to three‐way interaction terms was sufficient for interpreting 90% or more of the difference or variance in .Relative error, previously used to evaluate the accuracy of classical LTREs, is not a reliable metric of how closely the classical and exact methods agree. Error compensation between estimated contribution terms and neglected contribution terms can lead to low relative error despite faulty biological interpretation. Trade‐offs or negative covariances among matrix elements can lead to high relative error despite accurate biological interpretation. Exact LTRE provides reliable and accurate biological interpretation, and the R packageexactLTREmakes the exact method accessible to ecologists. 

Abstract To cope with uncertainty and variability in their environment, plants evolve distinct life‐history strategies by allocating different fractions of energy to growth, survival and fecundity. These differences in life‐history strategies could potentially influence ecosystem‐level dynamics, such as the sensitivity of primary production to resource fluctuations. However, linkages between evolutionary and ecosystem dynamics are not well understood.We used an annual plant population model to ask, when might differences in plant life‐history strategies produce differences in the sensitivity of primary production to resource fluctuations?Consistent with existing theory, we found that a highly variable and unpredictable environment led to the evolution of a conservative strategy characterized by relatively low and invariant germination fractions, while a variable but predictable environment favoured a riskier strategy featuring more variable germination fractions. Unexpectedly, we found that the influence of life‐history strategy on the sensitivity of production to resource fluctuations depended on competitive interactions, specifically the rate at which production saturates with the number of competing individuals. Rapid saturation overwhelms the influence of life‐history strategy, but when production saturates more slowly, the risky strategy translated to high sensitivity, whereas the conservative strategy translated to low sensitivity.Empirical estimates from Sonoran Desert annual plant populations indicate that production saturates relatively rapidly with the number of individuals for most species, suggesting that life‐history differences are unlikely to alter sensitivity of production to resource fluctuations, at least in this community.Synthesis. Our modelling results imply that research to understand the sensitivity of primary production to resource fluctuations should focus more on the intraspecific competitive interactions shaping the density–yield relationship than on the life‐history strategies that determine temporal risk‐spreading. 

Abstract: One strand of modern coexistence theory (MCT) partitions invader growth rates (IGR) to quantify how different mechanisms contribute to species coexistence, highlighting fluctuation‐dependent mechanisms. A general conclusion from the classical analytic MCT theory is that coexistence mechanisms relying on temporal variation (such as the temporal storage effect) are generally less effective at promoting coexistence than mechanisms relying on spatial or spatiotemporal variation (primarily growth‐density covariance). However, the analytic theory assumes continuous population density, and IGRs are calculated for infinitesimally rare invaders that have infinite time to find their preferred habitat and regrow, without ever experiencing intraspecific competition. Here we ask if the disparity between spatial and temporal mechanisms persists when individuals are, instead, discrete and occupy finite amounts of space. We present a simulation‐based approach to quantifying IGRs in this situation, building on our previous approach for spatially non‐varying habitats. As expected, we found that spatial mechanisms are weakened; unexpectedly, the contribution to IGR from growth‐density covariance could even become negative, opposing coexistence. We also found shifts in which demographic parameters had the largest effect on the strength of spatial coexistence mechanisms. Our substantive conclusions are statements about one model, across parameter ranges that we subjectively considered realistic. Using the methods developed here, effects of individual discreteness should be explored theoretically across a broader range of conditions, and in models parameterized from empirical data on real communities. 

In 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. 

Abstract: 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. 

Over 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 luck peaks are potential targets for interventions to benefit a population of concern, different from those identified by eigenvalue elasticity analysis.