Stochastic Growth Rate Research Articles

Temporal variability can promote migration between habitats

Understanding the conditions that promote the evolution of migration is important in ecology and evolution. When environments are fixed and there is one most favorable site, migration to other sites lowers overall growth rate and is not favored. Here we ask, can environmental variability favor migration when there is one best site on average? Previous work suggests that the answer is yes, but a general and precise answer remained elusive. Here we establish new, rigorous inequalities to show (and use simulations to illustrate) how stochastic growth rate can increase with migration when fitness (dis)advantages fluctuate over time across sites. The effect of migration between sites on the overall stochastic growth rate depends on the difference in expected growth rates and the variance of the fluctuating difference in growth rates. When fluctuations (variance) are large, a population can benefit from bursts of higher growth in sites that are worse on average. Such bursts become more probable as the between-site variance increases. Our results apply to many (≥ 2) sites, and reveal an interplay between the length of paths between sites, the average differences in site-specific growth rates, and the size of fluctuations. Our findings have implications for evolutionary biology as they provide conditions for departure from the reduction principle, and for ecological dynamics: even when there are superior sites in a sea of poor habitats, variability and habitat quality across space determine the importance of migration.

Life history costs drive the evolution of mycoheterotrophs: Increased sprouting and flowering in a strongly mycoheterotrophic Pyrola species

Abstract Land plants are typically photosynthetic, but some species have lost the ability to photosynthesize, instead relying on mycorrhizal fungi to obtain carbon. Increasing levels of partial mycoheterotrophy, in which seemingly autotrophic plants receive fungal carbon from their fungal partners, and reduced sprouting in concert with greater reproduction when sprouting, may be intermediate steps in the evolution of this trait. We studied the microevolutionary demography of Pyrola japonica and the closely related species P. subaphylla, which are currently considered sister species. While these species are both partially mycoheterotrophic, P. subaphylla is more strongly so, indicating that it may be closer to evolving full mycoheterotrophy. We tracked individuals in two nearby populations in Fukushima, Japan from 2015 to 2020. We analysed vital rates, population trends and long‐run population structure with historical function‐based matrix projection models. We assessed how shifts in P. subaphylla demography relate to fitness using a stochastic life table response experiment (SLTRE). P. subaphylla exhibited strong costs of growth to survival and of reproduction to sprouting, size and fecundity. It sprouted more than P. japonica but to smaller stages. P. subaphylla's flowering frequency was approximately four times that of P. japonica, but after flowering it was smaller and more likely to die. These life history costs appeared to drive differences in fitness, measured as stochastic population growth rate. Relative to P. japonica, shifts in fitness in P. subaphylla were due more to shifts in means than standard deviations of matrix elements. Shifts in growth transitions had the strongest negative impacts on fitness but also had the strongest positive impacts. Increased shifts to small non‐flowering stages were associated with increased fitness, while transitions involving dormancy were associated more strongly with drops in fitness. Synthesis. As far as we are aware, we found the first evidence that costs of growth and reproduction drive the evolution of increased sprouting and smaller size as a species becomes more intensely mycoheterotrophic. Surprisingly, vegetative dormancy did not evolve with mycoheterotrophy. We suggest further studies assessing whether these seemingly maladaptive trends result from genetic drift, genetic linkage or another mechanism.

Thirteen Years of Monitoring a Local Population of Eritrichium caucasicum: Stochastic Growth Rate under Reproductive Uncertainty

Thirteen Years of Monitoring a Local Population of Eritrichium caucasicum: Stochastic Growth Rate under Reproductive Uncertainty

Contrasting demographic responses under future climate for two populations of a montane amphibian

For species with complex life histories, climate change can have contrasting effects for different life stages within locally adapted populations and may result in responses counter to general climate change predictions. Using data from two, 14-year demographic studies for a North American montane amphibian, Cascades frog (Rana cascadae), we quantified how aspects of current climate influenced annual survival of larvae and adult stages and modeled the stochastic population growth rate (λs) of each population for current (1980–2006) and future periods (2080s). Climate drivers of survival for the populations were similar for larvae (i.e., decreases in precipitation lead to pond drying and mortality), but diverged for terrestrial stages where decreases in winter length and summer precipitation had opposite effects. By the 2080s, we predict one population will be in sharp decline (λs = 0.90), while the other population will remain nearly stable (λs = 0.99) in the absence of other stressors, such as mortality due to disease. Our case study demonstrates a result counter to many climate envelope predictions in that stage-specific responses to local climate and hydrology result in a higher extinction risk for the more northern population.

Survival induced by short-scale autocorrelations in birth-death-diffusion models with negative growth.

In a birth, death, and diffusion process, the extinction-survival transition occurs when the average net growth rate is zero. For instance, in the presence of normally distributed time-varying stochastic growth rates with no autocorrelation, the transition indeed occurs at zero net growth rates. In contrast, if the growth rates are constant in time, a large enough variance in the growth rate will systematically ensure the survival of the global population even in a small system and, more importantly, even with a negative net growth rate. We here show that, surprisingly, for any intermediate temporal autocorrelation, any length of correlation, and any negative average growth rate, the same result holds. We test this argument on exponential and power law autocorrelation models and propose a simple condition for the growth rate variance at the transition.

Consequences of cross-season demographic correlations for population viability.

Demographic correlations are pervasive in wildlife populations and can represent important secondary drivers of population growth. Empirical evidence suggests that correlations are in general positive for long-lived species, but little is known about the degree of variation among spatially segregated populations of the same species in relation to environmental conditions. We assessed the relative importance of two cross-season correlations in survival and productivity, for three Atlantic puffin (Fratercula arctica) populations with contrasting population trajectories and non-overlapping year-round distributions. The two correlations reflected either a relationship between adult survival prior to breeding on productivity, or a relationship between productivity and adult survival the subsequent year. Demographic rates and their correlations were estimated with an integrated population model, and their respective contributions to variation in population growth were calculated using a transient-life table response experiment. For all three populations, demographic correlations were positive at both time lags, although their strength differed. Given the different year-round distributions of these populations, this variation in the strength population-level demographic correlations points to environmental conditions as an important driver of demographic variation through life-history constraints. Consequently, the contributions of variances and correlations in demographic rates to population growth rates differed among puffin populations, which has implications for-particularly small-populations' viability under environmental change as positive correlations tend to reduce the stochastic population growth rate.

Transient population dynamics drive the spread of invasive wild pigs and reveal impacts of management in North America

Invasion of nonindigenous species is considered one of the most urgent problems affecting native ecosystems and agricultural systems. Mechanistic models that account for short-term population dynamics can improve prediction because they incorporate differing demographic processes that link the environmental conditions of a spatial location explicitly with the invasion process. Yet short-term population dynamics are rarely accounted for in spatial models of invasive species spread.Accounting for transient (short-term) population dynamics that arise from the interaction of age structure and vital rates, we predict the stochastic population growth rate and establishment probability of wild pigs following introduction into any location in North America. Established ecological theory suggests that the rate of spatial spread is proportional to population growth rate. Using observed geographic distribution data for wild pigs we calculated geographic spread rates (watersheds/year) from 1982 to 2021. We investigated if observed spread rates increased in watersheds with higher stochastic population growth rates. Stochastic population growth rate and establishment probability of wild pigs increased with increasing initial population (propagule) size and length of establishment time. Areas along the Mississippi, Ohio, and lower portions of the Missouri river drainages had the highest probability of wild pig establishment with many regions having probabilities close to 1. Spread rates demonstrated strong spatial heterogeneity with the greatest rates of spread (5.8 watersheds/year) occurring from 2008 to 2013 prior to the establishment of a National wild pig control program in 2013. Spread rates declined 82% (0.57 watersheds/year) in the period from 2013 to 2021 compared to the period from 1982 to 2013. We found significant positive associations among stochastic population growth rate and observed geographic rates of spread. Stochastic population growth rate explained a large amount of variation (79.3–92.1%) in annual rate of watershed spread of wild pigs. Our predicted probabilities of establishment and population growth can be used to inform surveillance and control efforts to reduce the potential for establishment and spread of wild pigs.

Anther smut pathogens as important drivers of population dynamics of long-lived perennial plants: A case study of Dianthus carthusianorum

Pollinator-transmitted pathogens typically hinder sexual reproduction of their hosts and affect pollen flow among remaining healthy individuals in a population. The extent to which a pathogen also influences host’s population growth depends on the importance of sexual reproduction for the host’s life cycle. Such pathogen impact cannot be traced by measuring only the vital rates directly affected by the pathogen, and thus a study of the host’s entire life cycle is necessary. In this study, we aimed to quantify the effects of the pollinator-transmitted anther smut pathogen Microbotryum carthusianorum on population growth rate in three populations of the long-lived perennial Dianthus carthusianorum. We followed plant individuals over three years and measured their size, disease state, and reproduction. We then constructed an Integral Projection Model (IPM). To evaluate the pathogen impact, we performed a stochastic analysis of the IPM for real diseased populations as well as for simulated populations without the pathogen. As the populations also hosted predispersal seed predators, the same approach was used to evaluate their impact. Stochastic population growth rates indicated two of the real populations to be increasing, and one to be declining. Comparison with the simulated healthy populations showed that the pathogen impact on the growth rate was negative and relatively strong, because the growth rate was highly sensitive to changes in sexual reproduction. However, the pathogen did not appear to cause the decline in the one decreasing population, since the growth rate there was impaired more substantially by high rates of predispersal seed predation and low germination rates than by the castration of diseased flowers. Overall, our study suggests that D. carthusianorum is highly vulnerable to biotic interactions affecting sexual reproduction pathway. Additionally, our study illustrated several complexities in disease dynamics (e.g., occurrence of partially or fully asymptomatic plants) that need to be incorporated into the assessment of the impact of pollinator-transmitted pathogens on long-lived perennials.

Learning increases growth and reduces inequality in shared noisy environments.

Stochastic multiplicative dynamics characterize many complex natural phenomena such as selection and mutation in evolving populations, and the generation and distribution of wealth within social systems. Population heterogeneity in stochastic growth rates has been shown to be the critical driver of wealth inequality over long time scales. However, we still lack a general statistical theory that systematically explains the origins of these heterogeneities resulting from the dynamical adaptation of agents to their environment. In this paper, we derive population growth parameters resulting from the general interaction between agents and their environment, conditional on subjective signals each agent perceives. We show that average wealth-growth rates converge, under specific conditions, to their maximal value as the mutual information between the agent's signal and the environment, and that sequential Bayesian inference is the optimal strategy for reaching this maximum. It follows that when all agents access the same statistical environment, the learning process attenuates growth rate disparities, reducing the long-term effects of heterogeneity on inequality. Our approach shows how the formal properties of information underlie general growth dynamics across social and biological phenomena, including cooperation and the effects of education and learning on life history choices.

Is It Feasible to Preserve a Self-Sustaining Population of Yangtze Finless Porpoise in the Highest Density Section of Yangtze River?

Using the VORTEX v. 10. 5.0.0, population viability analysis (PVA) was performed for Yangtze finless porpoise (YFP, Neophocaena asiaeorientalis) in the highest density section between Hukou and Meilong section (HMS) of the Yangtze River. Baseline model showed that this population was in a relatively vulnerability state; the deterministic growth rate (Det-r) was −0.0230; the stochastic growth rate (Stoch-r) was −0.0385; the probability of extinction (PE) was 0.5690; the mean population size of extant populations (N-extant) was 22; the genetic diversity (GD) was 0.7698. Under the general protection model, the Det-r was 0.0015, and the Stoch-r was −0.0092; Under the medium protection model, the Det-r was 0.0219, and the Stoch-r was 0.0144; Under the optimal protection model, the Det-r was 0.0383, and the Stoch-r was 0.0357. Sensitivity analysis found that adult females breeding rate, sex ratio at birth, and mortality rate of juvenile YFP were sensitive to maintaining population stability. The PVA showed that the conservation of YFP population in HMS depends on: neutralization of all threats affecting YFP population in the HMS; maintenance and, whenever possible, enhancement of the functional connectivity of the waterbody, increasing the food resources of YFP and reducing the risk of injury to YFP caused by human.

Thirteen years of monitoring a coenopopulation of <i>Eritrichium caucasicum</i>: Stochastic growth rate under reproductive uncertainty

Eritrichium caucasicum is an alpine short-lived perennial species endemic for the Caucasus. The stage structure of a local population has been observed on permanent plots in the alpine belt of the Northwestern Caucasus annually for 13 years (2009–2021), accumulating data of the “identified individuals from unknown parents” type. The latter circumstance has predetermined what is called reproductive uncertainty in the terminology of matrix models for discrete-structured population dynamics and means that the annual recruitment rates inherent in the groups of generative plants and final flowering generative plants cannot be calibrated in a uniquely way. As a result, instead of the annual values of the asymptotic growth rate, the model gives only certain ranges of their values that vary from year to year, corresponding to the data. This introduces both technical difficulties and uncertainty in the viability forecast based on the asymptotic growth rates. A well-known alternative approach is to estimate the stochastic growth rate λS, but only artificial modes of randomness involved in the calculation of λS have been proposed in the literature. Our realistic model of randomness is related to variations in weather and microclimatic conditions of the habitat. It is reconstructed from a fairly long (60 years) time series of the weather indicator. Using this realistic model in Monte Carlo calculations of λS, we have obtained a more reliable and accurate estimate of the stochastic growth rate.

On two conjectures about perturbations of the stochastic growth rate

SummaryThe stochastic growth rate describes long‐run growth of a population that lives in a fluctuating environment. Perturbation analysis of the stochastic growth rate provides crucial information for population managers, ecologists and evolutionary biologists. This analysis quantifies the response of the stochastic growth rate to changes in demographic parameters. A form of this analysis deals with changes that only occur in some environmental states. Caswell put forth two conjectures about environment‐specific perturbations of the stochastic growth rate. The conjectures link the stationary distribution of the stochastic environmental process with the magnitude of some environment‐specific perturbations. This note disproves one conjecture and proves the other.

Demographic consequences of changes in environmental periodicity.

The fate of natural populations is mediated by complex interactions among vital rates, which can vary within and among years. Although the effects of random, among-year variation in vital rates have been studied extensively, relatively little is known about how periodic, nonrandom variation in vital rates affects populations. This knowledge gap is potentially alarming as global environmental change is projected to alter common periodic variations, such as seasonality. We investigated the effects of changes in vital-rate periodicity on populations of three species representing different forms of adaptation to periodic environments: the yellow-bellied marmot (Marmota flaviventer), adapted to strong seasonality in snowfall; the meerkat (Suricata suricatta), adapted to inter-annual stochasticity as well as seasonal patterns in rainfall; and the dewy pine (Drosophyllum lusitanicum), adapted to fire regimes and periodic post-fire habitat succession. To assess how changes in periodicity affect population growth, we parameterized periodic matrix population models and projected population dynamics under different scenarios of perturbations in the strength of vital-rate periodicity. We assessed the effects of such perturbations on various metrics describing population dynamics, including the stochastic growth rate, log λS . Overall, perturbing the strength of periodicity had strong effects on population dynamics in all three study species. For the marmots, log λS decreased with increased seasonal differences in adult survival. For the meerkats, density dependence buffered the effects of perturbations of periodicity on log λS . Finally, dewy pines were negatively affected by changes in natural post-fire succession under stochastic or periodic fire regimes with fires occurring every 30years, but were buffered by density dependence from such changes under presumed more frequent fires or large-scale disturbances. We show that changes in the strength of vital-rate periodicity can have diverse but strong effects on population dynamics across different life histories. Populations buffered from inter-annual vital-rate variation can be affected substantially by changes in environmentally driven vital-rate periodic patterns; however, the effects of such changes can be masked in analyses focusing on inter-annual variation. As most ecosystems are affected by periodic variations in the environment such as seasonality, assessing their contributions to population viability for future global-change research is crucial.

Generation Time in Stage-Structured Populations under Fluctuating Environments.

AbstractA common measure of generation time is the average distance between two recruitment events along a genetic lineage. In populations with stage structure that live in a constant environment, this generation time can be computed from the elasticities of stable population growth to fecundities, and it is equivalent to another common measure of generation time: the average parental age of reproductive-value-weighted offspring. Here, we show three things. First, when the environment fluctuates, the average distance between two recruitment events along a genetic lineage is computed from the elasticities of the stochastic growth rate to fecundities. Second, under environmental stochasticity, this measure of generation time remains equivalent to the average parental age of reproductive-value-weighted offspring. Third, the generation time of a population in a fluctuating environment may deviate from the generation time the population would have in the average environment.

Demographic consequences of management actions for the successful reintroduction of the White Stork Ciconia ciconia to the UK

Summary Species reintroductions can be used in conservation management to increase biodiversity and aid in restoring ecosystem function. For reintroductions to be successful, it is important to identify the conditions required to establish a viable population. We developed a demographic model using Vortex10, an individual-based simulation software, to assess the long-term consequences of different management interventions on the success of the recent reintroduction of the white stork, Ciconia ciconia, to the UK. Demographic data obtained from this reintroduced population were supplemented with information from western European populations to build the models. The impact of incorporating different management actions (e.g. supplementing with captive-bred juveniles, provision of nesting platforms, and habitat improvement/supplementary feeding) on the stochastic population growth rate was assessed. Survival rates also differ depending on an individual’s migratory strategy, hence we tested the impact of having different proportions of the population as residents or migrants. Our models showed that if the British stork population adopts a fully migratory strategy, with its associated higher mortality rates, i.e. all individuals migrating to southern Europe or northern Africa, increasing the supplementation rate would not lead to a positive population growth rate. However, management actions which increased the number of fledglings per nest generated a slight positive growth rate that led to a 54.3% increase in population size after 50 years and, when combining all three management options, the population grew by 378.3%. Alternatively, if a minimum of 9% of individuals overwintered in Britain, which is likely based on field observations and tracking data, a positive growth rate can be achieved without additional management due to this behaviour’s lower mortality rates. We conclude that the British white stork population will likely be viable in the long term, but these models and projections should be updated as more demographic data on this novel population become available.

Flexible demographic strategies promote the population persistence of a pioneer conifer tree (Pinus massoniana) in ecological restoration

Understanding how plant species are able to persist in temporally variable environments is a fundamental goal in ecology. According to the demographic buffering hypothesis (DBH), organisms persist by minimizing variation over time in those vital rates (survival, growth, and/or reproduction) which affect the population growth rate the most. Alternatively, the demographic lability hypothesis (DLH) posits that a population could instead track and benefit from environmental fluctuations, by adjusting one or more of its vital rates accordingly, to maximize fitness. Empirical evidence has been found for and against each hypothesis, yet rarely are both tested in tandem for pioneer tree species, which may be the most responsive or vulnerable to environmental stochasticity in the course of forest restoration. Here we evaluated the stochastic population growth rate (λs) of Pinus massoniana, a pioneer conifer tree, using integral projection models (IPMs) applied to five plots spanning distinctive stages along early ecological restoration in Southeast China. We assessed the demographic strategy operating in each plot through an elasticity analysis and uncovered the sources of variability in these demographic strategies across plots. We found that the ca. 40-year stand populations of P. massoniana were stable or growing (i.e., λs ≥ 1) in most plots, but strategies shifted between demographically labile and buffer across plots, which was predominately driven by among-plot variation in reproduction. Our findings suggest that diverging demographic strategies may promote the persistence of pioneer tree species of P. massoniana and others similar to it during the ecological restoration of subtropical forests.

Age-specific sensitivity analysis of stable, stochastic and transient growth for stage-classified populations.

Sensitivity analysis in ecology and evolution is a valuable guide to rank demographic parameters depending on their relevance to population growth. Here, we propose a method to make the sensitivity analysis of population growth for matrix models solely classified by stage more fine-grained by considering the effect of age-specific parameters. The method applies to stable population growth, the stochastic growth rate, and transient growth. The method yields expressions for the sensitivity of stable population growth to age-specific survival and fecundity from which general properties are derived about the pattern of age-specific selective forces molding senescence in stage-classified populations.

Amplified Cyclicality in Mast Seeding Dynamics Positively Influences the Dynamics of a Seed Consumer Species.

AbstractTemporal autocorrelation in environmental conditions influences population dynamics through its effects on vital rates. However, a comprehensive understanding of how and to what extent temporal autocorrelation shapes population dynamics is still lacking because most empirical studies have unrealistically assumed that environmental conditions are temporally independent. Mast seeding is a biological event characterized by highly fluctuating and synchronized seed production at the tree population scale as well as a marked negative temporal autocorrelation. In the current context of global change, mast seeding events are expected to become more frequent, leading to strengthened negative temporal autocorrelations and thereby amplified cyclicality in mast seeding dynamics. Theory predicts that population growth rates are maximized when the environmental cyclicality of consumer resources and their generation times are closely matched. To test this prediction, we took advantage of the long-term monitoring of a wild boar population, a widespread seed consumer species characterized by a short generation time (∼2 years). As expected, simulations indicated that its stochastic population growth rate increased as mast seeding dynamics became more negatively autocorrelated. Our findings demonstrate that accounting for temporal autocorrelations in environmental conditions relative to the generation time of the focal population is required, especially under conditions of global warming, where the cyclicality in resource dynamics is likely to change.

Are genetic variation and demographic performance linked?

Quantifying relationships between genetic variation and population viability is important from both basic biological and applied conservation perspectives, yet few populations have been monitored with both long-term demographic and population genetics approaches. To empirically test whether and how genetic variation and population dynamics are related, we present one such paired approach. First, we use eight years of historical demographic data from five populations of Boechera fecunda (Brassicaceae), a rare, self-compatible perennial plant endemic to Montana, USA, and use integral projection models to estimate the stochastic population growth rate (λ S) and extinction risk of each population. We then combine these demographic estimates with previously published metrics of genetic variation in the same populations to test whether genetic diversity within populations is linked to demographic performance. Our results show that in this predominantly inbred species, standing genetic variation and demography are weakly positively correlated. However, the inbreeding coefficient was not strongly correlated with demographic performance, suggesting that more inbred populations are not necessarily less viable or at higher extinction risk than less inbred populations. A contemporary re-census of these populations revealed that neither genetic nor demographic parameters were consistently strong predictors of current population density, although populations showing lower probabilities of extinction in demographic models had larger population sizes at present. In the absence of evidence for inbreeding depression decreasing population viability in this species, we recommend conservation of distinct, potentially locally adapted populations of B. fecunda rather than alternatives such as translocations or reintroductions.

Stochastic line integrals and stream functions as metrics of irreversibility and heat transfer

Stochastic line integrals are presented as a useful metric for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled electrical circuits. Here we provide a general framework for understanding properties of stochastic line integrals and clarify their implementation for experiments and simulations. For two-dimensional systems, stochastic line integrals can be expressed in terms of a stream function, the sign of which determines the orientation of nonequilibrium steady-state probability currents. Theoretical results are supported by numerical studies of an overdamped two-dimensional mass-spring system driven out of equilibrium. Additionally, the stream function permits analytical understanding of the scaling dependence of stochastic area growth rate on key parameters such as the noise strength for both linear and nonlinear springs.