Biology subjects

Tuljapurkar, S. D.

Publications and source records attributed to Tuljapurkar, S. D..

15 recordsLinked to original sources

bioRxiv2026

Extinction in Random Environments

An important currency for individuals is their lifetime reproductive success (LRS), which is random simply due to demographic stochasticity. That randomness determines extinction probability. However, the distribution of LRS is also significantly affected by environmental variation. Previously we have shown (for a random environment that follows a Markov chain) how LRS is affected by an individual's birth environment. But our previous analysis severs the temporal linkage between a parent's birth environment and the environments into which its offspring are born. Here, we show how to compute the exact joint probability distribution of LRS for lineages spanning multiple environmental states (assuming a Markovian environment). From this joint distribution, we derive exact lineage extinction probabilities that fully incorporate demographic stochasticity, environmental frequency, and temporal autocorrelation. Applying our framework to Pacific Chinook salmon (semelparous with extreme early mortality) and European roe deer (iteroparous with delayed maturity), we demonstrate that initial birth states shape lineage fate. For salmon, the initial environment permanently separates trajectories; a poor birth state leads to near-certain extinction regardless of subsequent environmental shifts. For roe deer, we discover a counterintuitive dynamic where highly persistent poor conditions can rescue highly vulnerable individuals by expanding the right tail of reproduction. Furthermore, our exact calculations reveal that aggregated one-dimensional LRS distributions homogenize the reproductive landscape, overestimating extinction risks for lineages originating in poor environments and underestimating them for those in good environments. Accurately predicting evolutionary viability and the establishment of advantageous mutations requires preserving the environmental covariance. As global climate change amplifies environmental volatility, utilizing exact joint demographic models is critical for assessing true extinction risks.

evolutionary biology↗

bioRxiv2026

Life history traits predict the contribution of transient dynamics to variation in population growth

The performance of any natural population in variable environments depends on contemporaneous changes in its vital rates (e.g., survival, reproduction) as well as legacies carried by its population structure. Yet whether the relative contribution of these two pathways can be predicted from life history remains unknown. Here, we use stochastic simulations of 1,986 matrix population models from 137 species to quantify the contribution of transient dynamics to variation in population growth rate, and test its associations with key life history traits. Longer generation times were associated with reductions in transient contributions, contrary to theoretical expectations. Greater stage-specific survival heterogeneities were associated with increases in transient contributions, whereas greater iteroparity was associated with decreases in plants but increases in animals. These associations were robust to body size, phylogenetic relationships, and vital-rate variability. Life history traits therefore provide a strong predictor for when population structure shapes population responses to environmental variability.

ecology↗

bioRxiv2025

Second-order elasticities for Ecology and Evolution: Unravelling nonlinear fitness responses to perturbations

In ecology and evolutionary biology, understanding the relationship between vital rates (e.g., survival, development, reproduction) and population growth is essential to elucidate how life history strategies are shaped by natural selection. However, the established demographic methods to decipher the relationship between vital rates and population growth often analyse only the linear changes in population fitness as a result of changes in vital rates, thus simplifying the complexities of said relationships. To overcome the widespread linearity simplification, here we introduce the second-order elasticities of mean population fitness, the S-elasticity. The S-elasticity quantifies how changes in one or more vital rates can produce a second-order change in mean fitness. We provide a systematic mathematical framework behind the S-elasticity, revealing its ability to identify the convex and concave responses of mean fitness to perturbations of vital rates. Through structured population models, we demonstrate the distinct roles of linear and nonlinear mean fitness responses, and their combination, enabling to characterise local concavity/convexity of the mean population fitness function. We illustrate the application and the differences of S-elasticities and their biological meanings using matrix population models of the armadillo (Dasupys novemcinctus) and Pynes plum (Astragallus bibullatus). These two case studies showcase how the S-elasticity provides key insights into mean fitness responses to perturbations on demographic process and their correlations. We discuss the improvements that the S-elasticity provides for species management and our understanding of how natural populations cope with environmental change.

ecology↗

bioRxiv2024

Biocultural vulnerability of traditional crops in the Indian Trans Himalaya

Traditional agricultural landscapes are critical for conserving biocultural and ecological diversity. Despite their significance, traditional systems have often been overlooked, leading to genetic erosion of crop landraces. Using the fragile ecosystems of northwest Himalaya as case study, we examine the ecological and genetic resilience of an understudied and lesser-known traditional crop, black pea, and barley (Hordeum vulgare) and compare them to the introduced cash crop of green pea (Pisum sativum L.). We co-designed field experiments with local farmers to assess survival and reproductive traits for the crops. We performed whole-genome sequencing to investigate the genetic diversity of black pea and describe their nutritional profile. Our findings indicate that traditional crops are better adapted to local climatic conditions and hold considerable genetic diversity and nutritional potential. We emphasize the importance of integrating traditional knowledge with scientific research to promote sustainable food systems and socio-ecological stability in vulnerable mountain regions.

plant biology↗

bioRxiv2024

Human populations with low survival at advanced ages and postponed fertility reduce long-term growth in high inflation environments

Temporal variability in inflation can lead to important fluctuations in the long-term growth rate of human populations via their differential impacts on vital rates like survival and fertility. However, historically, demographic studies have overlooked this time-dependent relationship. Here, we test whether human populations have higher stochastic population growth rates when exposed to lower levels of inflation. We also examine if lower survival rates at older ages (>60 years) and fertility rates at the later reproductive years (>30 years) among populations exposed to higher inflation rates determine their expected lower long-term growth rate compared to those exposed to lower inflation rates. To explore the impact of variability in inflation on vital rates response, we develop a quantitative pipeline with four steps, and parameterise it with high-resolution economic and demographic data across 76 countries from 1971-2021. The four steps are (1) defining treatment groups based on levels of trend inflation (creeping inflation (0-3%), walking inflation (3-10%), galloping inflation (10-50%), and hyperinflation (>50%)) among which the stochastic population growth rates will be compared; (2) constructing matrix population models for each environmental state under every treatment. The environmental states for each treatment are defined on the basis of the duration of inflation (e.g., 0, 2, 4, six years or above); (3) estimating the stochastic population growth rate for each treatment by considering a Markovian environment dictated by the long-term frequency (f) and temporal autocorrelation (p) of the treatment; and (4) decomposing the differences in the population growth rate between treatments into contributions from environmental variability and vital rate differences between environments to test how vital rates impact on population growth under varying environmental scenarios. In agreement with our hypothesis, we find that the stochastic population growth rate at lower levels of inflation is systematically higher than that at a higher level of inflation at all stationary frequencies and temporal autocorrelation of the inflation environment. Moreover, the disadvantage in survival at older ages (>60 years) and fertility at ages >30 years led to the lower stochastic growth rate among populations exposed to higher level of inflation such as walking inflation compared to lower level of inflation, such as creeping inflation. Our framework explicitly links human population performance and inflation environment by describing nonlinear feedback between inflation, human survival, fertility, population growth, and its age structure. We discuss the potential of our approach to study the life-history strategies and population dynamics of a wide range of drivers of environmental variability.

animal behavior and cognition↗

bioRxiv2024

Population responses to environmental stochasticity are primarily driven by survival-reproduction trade-offs and mediated by aridity

Forecasting responses of natural populations to increasingly stochastic environments is a major challenge in Ecology and Conservation Biology. We now know that populations can modulate how their vital rates (e.g., survival, reproduction) change through time to minimise the negative impacts of environmental stochasticity. However, despite the important analytical and theoretical advances that have led to this knowledge, we still do not know (1) how much this ability of natural populations to buffer against environmental stochasticity can vary in nature, nor (2) the drivers of these strategies, with likely candidates including the environmental regimes themselves, as well as the life history traits and phylogenetic ancestry of the species of interest. To address these questions, we parameterised a Bayesian generalised linear mixed model with high-resolution vital rate data from 134 natural populations across 89 species of plants and animals. We show that population responses to environmental stochasticity vary three orders of magnitude along a demographic buffering continuum. Furthermore, the position of a given population along said continuum is predicted by a survival-reproduction trade-off and by the degree of aridity the population experiences. Our findings open a promising avenue of research to improve ecological forecasts and management of natural populations in the Anthropocene.

ecology↗

bioRxiv2024

Density dependence shapes life-history trade-offs in a food limited ungulate population

Quantifying trade-offs within populations is an important goal in life-history and evolutionary theory. However, most studies focusing on life-history variation assume trade-offs to be static. In this paper, we provide a framework for understanding life-history variation at different densities while enabling us to reveal trade-offs that are often masked due to individual heterogeneity. We use published individual-based data from a population of Soay sheep and find density dependence strongly shapes life-history trade-offs and the distribution of lifetime reproductive success. We find trade-offs between juvenile survival and growth structures life-history variation for Soay sheep at all densities, but the intensity of the trade-offs increases with population density. At carrying capacity (K), a new trade-off appears between reproduction and juvenile survival. In addition, we find the distribution of LRS to be highly constrained at K, with mothers of prime adult sizes ([~] 25kg) contributing the most to reproduction. We also find the effects of density-dependence on demographic measures such as net reproductive rate, stable size distribution, and average vital rate functions. Our results suggest high density limits the diversity of individual life history strategies and has implications for better understanding the evolution of reproductive tactics via density-dependent selection and management of ungulates in food limited environments.

ecology↗

bioRxiv2023

From disturbances to nonlinear fitness and back.

Disturbances can occur as short-lived pulses (e.g., storms) or sustained presses (e.g., chronic drought). Much work in ecology has developed methods to help predict how natural populations respond to disturbances, but analyses of pulse and press disturbances has been largely disconnected. We present a unified matrix framework that links presses and pulses within the same analytical approach, showing how transient nonlinearities and demography shape fitness. We find that transient responses to pulse disturbances accumulate to determine the long-term response to press disturbances. For structured-population models, this cumulative change is given by a new Transient Response Matrix (TRM). Strikingly, the TRM also yields the second derivatives of population growth rate with respect to matrix elements. Thus, there is an intimate but unexpected relationship between nonlinear selection pressures on demographic rates, and the transient dynamics of populations. This relationship yields a strong correlation between TRM and generation time across 439 unique plant and animal species (2690 population models). We also show that the TRM is directly related to Cohens cumulative distance measure for populations converging to stability. Our framework provides ecologists with a general tool to predict population responses to diverse environmental changes.

ecology↗

bioRxiv2023

Structured demographic buffering: A framework to explore the environment drivers and demographic mechanisms underlying demographic buffering

Environmental stochasticity is a key determinant of population viability. Decades of work exploring how environmental stochasticity influences population dynamics have highlighted the ability of some natural populations to limit the negative effects of environmental stochasticity, one of these strategies being demographic buffering. Whilst various methods exist to quantify demographic buffering, we still do not know which environment factors and demographic characteristics are most responsible for the demographic buffering observed in natural populations. Here, we introduce a framework to quantify the relative effects of three key drivers of demographic buffering: environment components (e.g., temporal autocorrelation and variance), population structure, and demographic rates (e.g., progression and fertility). Using Integral Projection Models, we explore how these drivers impact the demographic buffering abilities of three plant species with different life histories and demonstrate how our approach successfully characterises a populations capacity to demographically buffer against environmental stochasticity in a changing world.

ecology↗

bioRxiv2023

Sensitivity and uncertainty in the Lee-Carter mortality model

BACKGROUNDThe Lee-Carter model (LC) is widely used in research and applications for forecasting age specific mortality, and typically performs well regardless of the uncertainty and often the limited quality of mortality data. OBJECTIVEWhy dose LC perform well regardless of the uncertainty and the limited data quality? METHODSWe analyze the robustness of LC using sensitivity analyses based on matrix perturbation theory, coupled with simulations that examine the effect of unavoidable randomness in mortality data. The combined effects of sensitivity and uncertainty determine the robustness of LC. RESULTSWe find that the sensitivity of LC and the uncertainty of death rates both have nonuniform patterns across ages and years. The sensitivities are small in general, with largest sensitivities at both ends of the period. The uncertainty of death rates are high in young ages (5-19) and old ages (90+) with rising in young ages but dropping in old ages. CONCLUSIONSThe sensitivity and uncertainty analyses indicate that the randomness hardly interrupts the prediction of LC. The divergence of long term prediction in LC is likely due to structural changes in the age-year specific mortality, which is associated with the development of public health policy, medical innovations and chronic disasters. CONTRIBUTIONOur results reveal that LC is robust against random perturbation and sudden short term changes.

ecology↗

bioRxiv2022

Adaptive and neutral processes that select on life course diversification

Heterogeneity among individuals in fitness components is what selection acts upon. One of the fundamental questions in evolution is how such heterogeneity arises and is maintained. Fundamental evolutionary theories predict that selection acts against such heterogeneity but contrasting these predictions substantial non-genetic and non-environmental driven variability in phenotypes can be observed; not only under highly controlled lab conditions, but also in less controlled settings. Here we ask, by analysing structured population models across a large range of biological taxa, how selective forces act on the processes that generate variation among life courses. Our findings suggest that non-genetic, non-environmental driven variation is in general neither truly neutral, selected for, or selected against. Much variation exists among species and populations within species, with mean patterns suggesting close to neutral evolution of life course variability. Populations that show greater diversity of life courses do not show, in general, increased or decreased population growth rates, and selective forces acting on the processes of diversification seem not to generally increase or decrease life course variability. Approaches in quantitative genetics that identified similar lack of understanding of maintenance of variability might be extended to include non-genetic and non-environmental driven variability. We believe to be only at the beginning in understanding the evolution and maintenance of non-genetic non environmental variation.

evolutionary biology↗

bioRxiv2022

Density dependent environments can select for extremes of body size

Body size variation is an enigma. We do not understand why species achieve the sizes they do, and this means we also do not understand the circumstances under which gigantism or dwarfism is selected. We develop size-structured integral projection models to explore evolution of body size and life history speed. We make few assumptions and keep models simple: all functions remain constant across models except for the one that describes development of body size with age. We set sexual maturity to occur when size attains 80% of the asymptotic size, which is typical of a large mammal, and allow negative density dependence to only affect either reproduction or juvenile survival. Fitness - the quantity that is maximized by adaptive evolution - is carrying capacity in our models, and we are consequently interested in how it changes with size at sexual maturity, and how this association varies with development rate. The simple models generate complex dynamics while providing insight into the circumstances when extremes of body size evolve. The direction of selection leading to either gigantism or dwarfism crucially depends on the proportion of the population that is sexually mature, which in turn depends on how the development function determines the survivorship schedule. The developmental trajectories consequently interact with size-specific survival or reproductive rates to determine the best life history and the optimal body size emerges from that interaction. These dynamics result in trade-offs between different components of the life history, with the form of the trade-off that emerges depending upon where in the life history density dependence operates most strongly. Empirical application of the approach we develop has potential to help explain the enigma of body size variation across the tree of life.

evolutionary biology↗

bioRxiv2020

Life-history dynamics: damping time, demographic dispersion and generation time

Transient dynamics are crucial for understanding ecological and life-history dynamics. In this study, we analyze damping time, the time taken by a population to converge to a stable (st)age structure following a perturbation, for over 600 species of animals and plants. We expected damping time to be associated with both generation time Tc and demographic dispersion{sigma} based on previous theoretical work. Surprisingly, we find that damping time (calculated from the population projection matrix) is approximately proportional to Tc across taxa on the log-log scale, regardless of{sigma} . The result suggests that species at the slow end of fast-slow continuum (characterized with long generation time, late maturity, low fecundity) are more vulnerable to external disturbances as they take more time to recover compared to species with fast life-histories. The finding on damping time led us to next examine the relationship between generation time and demographic dispersion. Our result reveals that the two life-history variables are positively correlated on a log-log scale across taxa, implying long generation time promotes demographic dispersion in reproductive events. Finally, we discuss our results in the context of metabolic theory and contribute to existing allometric scaling relationships.

ecology↗

bioRxiv2020

Distributions of LRS in varying environments

Studies of lifetime reproductive success (LRS) have shown that important random events can be in ecology and evolution. Randomness should be amplified in stochastic environments, and here we show here we show this to be the case by computing the complete distribution of LRS when vital rates are Markovian can be readily computed by building on our recent paper (Tuljapurkar et al. 2020). These results complement the work of van Daalen and Caswell (2020) on moments of LRS. We use empirical studies of Roe deer, Capreolus capreolus, to show that environments at birth have strong effects on future performance, and that analyses of the LRS in stochastic environments are a valuable element of studies of the consequences of climate change.

ecology↗

bioRxiv2018

Age Distribution, Trends, and Forecasts of Under-5 Mortality in Sub-Saharan Africa

BackgroundDespite the sharp decline in global under-5 deaths since 1990, uneven progress has been achieved across and within countries. In Sub-Saharan Africa, the Millennium Development Goals targets for child mortality were met only by a few countries, and recently new targets were set in goals for Sustainable Development that include the eradication of preventable deaths by reducing neonatal and under-5 mortality rates to at least as low 12 and 25 per 1000 live births by 2030, respectively. As the reduction of preventable deaths has a direct impact on their age distribution, the foci of this study are assessing age patterns, trends over time, and forecasts of mortality rates in Sub-Saharan Africa.\n\nMethods and findingsData came from 104 nationally-representative Demographic and Health Surveys with full birth histories from 31 Sub-Saharan African countries from 1990 to 2016 (a total of 448 country-years of data). We assessed the distribution of age at death through the following demographic model. First, we used a direct method for the estimation of death rates with full-birth histories from survey data to construct age profiles of under-5 mortality on a monthly basis. Second, a two-dimensional P-spline approach was used to smooth out raw estimates of death rates by age and time. Third, a variant of the Lee-Carter model, designed for populations with limited data, was used to fit and forecast age profiles of mortality. We used mortality estimates from the United Nations Inter-agency group for Child Mortality Estimation to adjust, validate and minimize the risk of bias in survival, truncation, and recall in mortality estimation.\n\nOur study has three salient findings. First, we observe a monotonous decline of death rates at every age in most countries, but with notable differences in the age-patterns over time. Second, our projections of continued decline of child mortality differ from existing estimates from the United Nations Inter-agency group for Child Mortality Estimation in 5 countries for both neonatal and under-5 mortality. Finally, we predict that only 5 countries (Guinea, Liberia, Rwanda, Tanzania, and Uganda) are on track to achieve the sustainable development goal targets on child mortality by 2030. Poor data quality issues that include bias in the report of births and deaths, or age heaping, remain a limitation of this study.\n\nConclusionsThis study is the first to combine full birth history data and mortality estimates from external reliable sources to model age patterns of under-5 mortality across time in Sub-Saharan Africa. We demonstrate that countries with a rapid pace of mortality reduction across ages would be more likely to achieve the sustainable development goal targets of child mortality reduction. Our mortality model predicts that if neonatal and under-5 deaths decline at the rates observed during the last 25 years, only 5 countries would reach those targets by 2030, 15 would achieve them between 2030 and 2050, and 11 afterwards.

epidemiology↗