How demographic factors lead to variation or change in growth rates can be investigated using life table response experiments (LTRE) based on structured population models. Traditionally, LTREs focused on decomposing the asymptotic growth rate, but more recently decompositions of annual ‘realized’ growth rates have gained in popularity. Realized LTREs have been used particularly to understand how variation in vital rates translates into variation in growth for populations under long-term study. For these, complete population models may be constructed by combining data in an integrated population model (IPM). IPMs are also used to investigate how temporal variation in environmental drivers affect vital rates. Such investigations have usually come down to estimating covariate coefficients for the effects of environmental variables on vital rates, but formal ways of assessing how they lead to variation in growth rates have been lacking. We extend realized LTREs in two ways. First, we furt..., , The data are in the form of .Rdata files that can be opened with the R software.

Reliable estimates of effective population size Ne are of central importance in population genetics and evolutionary biology. For populations that fluctuate in size, harmonic mean population size is commonly used as a proxy for (multi-) generational effective size. This assumes no effects of density dependence on the ratio between effective and actual population size, which limits its potential application. Here we introduce density dependence on vital rates in a demographic model of variance effective size. We derive an expression for the ratio Ne/N in a density regulated population in a fluctuating environment. We show by simulations that yearly genetic drift is accurately predicted by our model, and not proportional to 1/(2N) as assumed by the harmonic mean model, where N is the total population size of mature individuals. We find a negative relationship between Ne/N and N. For a given N, the ratio depends on variance in reproductive success and the degree of resource limitation acting on the population growth rate. Finally, our model indicate that environmental stochasticity may affect Ne/N not only through fluctuations in N, but also for a given N at a given time. Our results show that estimates of effective population size must include effects of density dependence and environmental stochasticity.

Theory has shown that the effects of demographic stochasticity on communities may depend on the magnitude of fitness differences between species. In particular, it has been suggested that demographic stochasticity has the potential to significantly alter competitive outcomes when fitness differences are small (nearly neutral), but that it has minimal effects when fitness differences are large (highly non-neutral). Here we test such theory experimentally and extend it to examine how demographic stochasticity affects exclusion frequency and mean densities of consumers in simple, but non-neutral, consumer-resource communities. We used experimental microcosms of protists and rotifers feeding on a bacterial resource to test how varying absolute population sizes (a driver of demographic stochasticity) affected the probability of competitive exclusion of the weakest competitor. To explore whether demographic stochasticity could explain our experimental results, and to generalize beyond our experiment, we paired the experiment with a continuous-time stochastic model of resource competition, which we simulated for 11 different fitness inequalities between competiting consumers. Consistent with theory, in both our experiments and our simulations we found that demographic stochasticity altered competitive outcomes in communities where fitness differences were small. However, we also found that demographic stochasticity alone could affect communities in other ways, even when fitness differences between competitors were large. Specifically, demographic stochasticity altered mean densities of both weak and strong competitors in experimental and simulated communities. These findings highlight how demographic stochasticity can change both competitive outcomes in non-neutral communities and the processes underlying overall community dynamics.

DemStochZip file containing main.cpp (main script for simulating diffusion approximations from equations 1a and 1b), an example parameter input file param.txt and the README file.

Life history traits are used to predict asymptotic odds of extinction from dynamic conditions. Less is known about how life history traits interact with stochasticity and population structure of finite populations to predict near-term odds of extinction. Through empirically parameterized matrix population models, we study the impact of life history (reproduction, pace), stochasticity (environmental, demographic), and population history (existing, novel) on the transient population dynamics of finite populations of plant species. Among fast and slow pace and either uniform or increasing reproductive intensity or short or long reproductive lifespan, slow, semelparous species are at the greatest risk of extinction. Long reproductive lifespans buffer existing populations from extinction while the odds of extinction of novel populations decreases when reproductive effort is uniformly spread across the reproductive lifespan. Our study highlights the importance of population structure, pace, a..., We gathered empirically derived stage-based population models from the COMPADRE Plant Matrix Database v6.22.5.0 (created 2022-05-11; Salguero-Gomez et al. 2015) that (1) were ergodic and irreducible, (2) were modelled on an annual time step (Iles et al. 2016), and (3) did not explicitly parse clonal growth into a separate matrix. This subset resulted in 1,606 matrices representing multiple years and/or populations of 317 plant species., , # Data from: Pace and parity predict short-term persistence of small plant populations

Access these datasets on Dryad https://doi.org/10.5061/dryad.2547d7wzv

Empirically derived stage-based population models were collected from the COMPADRE Plant Matrix Database v6.22.5.0 (created 2022-05-11; Salguero-Gomez et al. 2015) that (1) were ergodic and irreducible, (2) were modelled on an annual time step, and (3) did not explicitly parse clonal growth into a separate matrix. This subset resulted in 1,606 matrices representing multiple years and/or populations of 317 plant species.

Life history traits were estimated from the matrix population models using the R package Rage (Jones et al. 2022).

Plant matrix population models were used to simulate asymptotic growth, demographic and environmental stochasticity and test the impact of initial population size, population structure, stochasticity, and life history on the odds of extinction. The impa...

UPDATED VERSION 2024-12-15 (models were updated)

This zip file contains the codes demonstrating how I analyzed and selected publicly available and globally extensive data on fish composition and environmental variables to test the hypothesis that random fluctuations caused by demographic stochasticity in small populations might extend to communities and metacommunities, potentially affecting stability propagation across biological levels and spatial scales. The READ_ME file contains additional details about the steps I took to develop this analysis.

This study was financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brasil (CAPES) - Finance Code 001.

Code to reproduce simulation analyses from > Dallas, TA, and L Santini. 2020. "The influence of stochasticity, landscape structure, and species traits on abundant-centre relationships"

Understanding the influence of environmental variability on population dynamics is a fundamental goal of ecology. Theory suggests that, for populations in variable environments, temporal correlations between demographic vital rates (e.g., growth, survival, reproduction) can increase (if positive) or decrease (if negative) the variability of year-to-year population growth. Because this variability generally decreases long-term population viability, vital rate correlations may importantly affect population dynamics in stochastic environments. Despite long-standing theoretical interest, it is unclear whether vital rate correlations are common in nature, whether their directions are predominantly negative or positive, and whether they are of sufficient magnitude to warrant broad consideration in studies of stochastic population dynamics. We used long-term demographic data for three perennial plant species, hierarchical Bayesian parameterization of population projection models, and stochasti...

1.A population's effective size (Ne) is a key parameter that shapes rates of inbreeding and loss of genetic diversity, thereby influencing evolutionary processes and population viability. However estimating Ne, and identifying key demographic mechanisms that underlie the Ne to census population size (N) ratio, remains challenging, especially for small populations with overlapping generations and substantial environmental and demographic stochasticity and hence dynamic age-structure.

2.A sophisticated demographic method of estimating Ne/N, which uses Fisher's reproductive value to account for dynamic age-structure, has been formulated. However this method requires detailed individual- and population-level data on sex- and age-specific reproduction and survival, and has rarely been implemented.

3.Here we use the reproductive value method and detailed demographic data to estimate Ne/N for a small and apparently isolated red-billed chough (Pyrrhocorax pyrrhocorax) population of high conse...

Index Files

Mounting theoretical evidence suggests that demographic stochasticity, environmental heterogeneity and biased movement of organisms individually affect the dynamics of biological invasions and range expansions. Studies of species spread in heterogeneous landscapes have traditionally characterized invasion velocities as functions of the mean resource density throughout the landscape, thus neglecting higher-order moments of the spatial resource distribution. Here, we show theoretically that different spatial arrangements of resources lead to different spread velocities even if the mean resource density throughout the landscape is kept constant. Specifically, we find that increasing the resource autocorrelation length causes a reduction in the speed of species spread. The model shows that demographic stochasticity plays a key role in the slowdown, which is strengthened when individuals can actively move towards resources. We then experimentally corroborated the theoretically predicted redu...

In nature, individual reproductive success is seldom independent from year to year, due to factors such as reproductive costs and individual heterogeneity. However, population projection models that incorporate temporal autocorrelations in individual reproduction can be difficult to parameterize, particularly when data are sparse. We therefore examine whether such models are necessary to avoid biased estimates of stochastic population growth and extinction risk, by comparing output from a matrix population model that incorporates reproductive autocorrelations to output from a standard age-structured matrix model that does not. We use a range of parameterizations, including a case study using moose data, treating probabilities of switching reproductive class as either fixed or fluctuating. Expected time to extinction from the two models is found to differ by only small amounts (under 10%) for most parameterizations, indicating that explicitly accounting for individual reproductive autocorrelations is in most cases not necessary to avoid bias in extinction estimates.

Despite growing concerns regarding increasing frequency of extreme climate events and declining population sizes, the influence of environmental stochasticity on the relationship between population carrying capacity and time-to-extinction has received little empirical attention. While time-to-extinction increases exponentially with carrying capacity in constant environments, theoretical models suggest increasing environmental stochasticity causes asymptotic scaling, thus making minimum viable carrying capacity vastly uncertain in variable environments. Using empirical estimates of environmental stochasticity in fish metapopulations, we showed that increasing environmental stochasticity resulting from extreme droughts was insufficient to create asymptotic scaling of time-to-extinction with carrying capacity in local populations as predicted by theory. Local time-to-extinction increased with carrying capacity due to declining sensitivity to demographic stochasticity, and the slope of this...

Demographic stochasticity can have large effects on the dynamics of small populations as well as on the persistence of rare genotypes and lineages. Survival is sensibly modeled as a binomial process, but annual reproductive success (ARS) is more complex and general models for demographic stochasticity do not exist. Here we introduce a stochastic model framework for ARS and illustrate some of its properties. We model a sequence of stochastic events: nest completion, the number of eggs or neonates produced, nest predation, and the survival of individual offspring to independence. We also allow multiple nesting attempts within a breeding season. Most of these components can be described by Bernoulli or binomial processes; the exception is the distribution of offspring number. Using clutch and litter size distributions from 53 vertebrate species, we demonstrate that among‐individual variability in offspring number can usually be described by the generalized Poisson distribution. Our model framework allows the demographic variance to be calculated from underlying biological processes and can easily be linked to models of environmental stochasticity or selection because of its parametric structure. In addition, it reveals that the distributions of ARS are often multimodal and skewed, with implications for extinction risk and evolution in small populations.

The extinction vortex is a theoretical model describing the process by which extinction risk is elevated in small, isolated populations owing to interactions between environmental, demographic, and genetic factors. However, empirical demonstrations of these interactions have been elusive. We modelled the dynamics of a small mountain lion population isolated by anthropogenic barriers in greater Los Angeles, California, to evaluate the influence of demographic, genetic, and landscape factors on extinction probability. The population exhibited strong survival and reproduction, and the model predicted stable median population growth and a 15% probability of extinction over 50 years in the absence of inbreeding depression. However, our model also predicted the population will lose 40–57% of its heterozygosity in 50 years. When we reduced demographic parameters proportional to reductions documented in another wild population of mountain lions that experienced inbreeding depression, extinction probability rose to 99.7%. Simulating greater landscape connectivity by increasing immigration to greater than or equal to one migrant per generation appears sufficient to largely maintain genetic diversity and reduce extinction probability. We provide empirical support for the central tenet of the extinction vortex as interactions between genetics and demography greatly increased extinction probability relative to the risk from demographic and environmental stochasticity alone. Our modelling approach realistically integrates demographic and genetic data to provide a comprehensive assessment of factors threatening small populations.

This is a Mathematica .nb file containing functions defined for the individual based simulation

The current extinction and climate change crises pressure us to predict population dynamics with ever-greater accuracy. Although predictions rest on the well-advanced theory of age-structured populations, two key issues remain poorly-explored. Specifically, how the age-dependency in demographic rates and the year-to-year interactions between survival and fecundity affect stochastic population growth rates. We use inference, simulations, and mathematical derivations to explore how environmental perturbations determine population growth rates for populations with different age-specific demographic rates and when ages are reduced to stages. We find that stage- vs. age-based models can produce markedly divergent stochastic population growth rates. The differences are most pronounced when there are survival-fecundity-trade-offs, which reduce the variance in the population growth rate. Finally, the expected value and variance of the stochastic growth rates of populations with different age-specific demographic rates can diverge to the extent that, while some populations may thrive, others will inevitably go extinct.

A discrete mathematical model was developed to study the population dynamics after a time-varying environmental disaster (R4.x261.000:0008). A 5-stage-structure matrix includes parameters for stage-specific survival and transition rates, as well as annual fecundity. This model can be used to examine the sensitivity and elasticity of the model, as well as demographic and environmental stochasticity, and many others.

Synergistic and antagonistic interactions in multi-species populations - such as resource sharing and competition - result in remarkably diverse behaviors in populations of interacting cells, such as in soil or human microbiomes, or clonal competition in cancer. The degree of inter- and intra-specific interaction can often be quantified through the notion of an ecological "niche". Typically, weakly interacting species that occupy largely distinct niches result in stable mixed populations, while strong interactions and competition for the same niche results in rapid extinctions of some species and fixations of others. We investigate the transition of a deterministically stable mixed population to a stochasticity-induced fixation as a function of the niche overlap between the two species. We also investigate the effect of the niche overlap on the population stability with respect to external invasions. Our results have important implications for a number of experimental systems.

Example of how to use the R-package to run the simulations