Maja Kajin

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. Yet most established demographic methods rely on linear assumptions that rank the importance of vital rates but are insensitive to whether the returns of the population growth rate are diminishing or accelerating. Here, we introduce the second‐order elasticities of mean individual fitness in the population, the S‐elasticity. The S‐elasticity is a proportional, element‐wise measure that can quantify the curvature of mean individual fitness with respect to single matrix population model (MPM) elements (self S‐elasticity) and to pairs of elements (mixed S‐elasticity). S‐elasticities (1) classify concavity versus convexity of local fitness surfaces, (2) provide a relative‐curvature diagnostic by scaling second‐order to first‐order effects, (3) sum to zero across elements—facilitating comparisons across populations and species—and (4) connect fitness curvature to biologically feasible trade‐offs via the elasticity ratio K . We provide a simple inequality based on the S‐elasticities and the K ‐ratio that detects local fitness peaks along constraint directions corresponding to each pair of matrix elements. We illustrate the framework with an average 4 × 4 MPM for Didelphis aurita (Marsupialia, Didelphidae) and compare our results to classical second‐order derivatives of population growth rate applied to the same dataset. First‐order elasticities identify survival of weaned and subadult survival as dominant linear levers of fitness; their negative self S‐elasticities reveal diminishing returns for increases and amplified losses for decreases relative to linear expectations. Mixed S‐elasticities expose a costly trade‐off between survival of weaned and aged females' fertility: The curvature‐only surface is concave near the baseline and the trade‐off direction is a local peak, whereas several other element pairs lie along flatter, more substitutable directions. Together, S‐elasticities provide a compact diagnostic for when linear rankings suffice, when nonlinearity dominates, and where feasible substitutions are most constrained. Because they are proportional, additive (sum‐to‐zero), and rooted in life cycle pathways, S‐elasticities complement classic elasticity and make second‐order demographic information directly comparable across systems—yielding actionable guidance for evolutionary inference and for prioritizing management actions under realistic trade‐offs.

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 have been largely disconnected. We present a matrix framework that links press and pulse perturbations within the same analytical approach, showing how transient nonlinearities and demography shape fitness. We find that transient responses to pulse perturbations 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 the 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 Cohen's cumulative distance measure for populations converging to stability. Our framework provides ecologists with a general tool to predict population responses to diverse environmental changes.

Natural populations may suffer negatively from increased environmental variability due to climate change; however, several mechanisms can mitigate those effects by changing the vital rates of a population ( e.g ., survival, reproduction). Despite important analytical and theoretical advances, we still do not know how and to what extent environmental regimes, life history traits, and evolutionary history determine the buffering capacity of natural populations. To address these questions, we parameterise a Bayesian generalised linear mixed model with high-resolution vital rate data from 121 natural populations across 78 plant species. We show that population responses to environmental variability vary four 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.

Extremotolerant fungi inhabit environments with multiple overlapping stressors, yet most studies examine stresses individually. We tested whether preconditioning with salt, cold, or both improves survival after desiccation and freezing, and whether combined salinity and temperature effects on growth are additive or synergistic. We studied Aureobasidium pullulans, Aureobasidium subglaciale, Aureobasidium melanogenum, and Hortaea werneckii (haploid and diploid). All preconditioning treatments significantly increased long-term desiccation survival in A. pullulans, reflecting its generalist capacity to activate cross-protective responses. H. werneckii displayed smaller improvements, consistent with a specialist strategy. Freezing survival without cryoprotectants remained ~100% in both species, indicating high intrinsic tolerance. Growth analyses revealed synergistic effects of salinity and temperature in Aureobasidium spp. Species differed in salinity sensitivity (A. melanogenum > A. pullulans > A. subglaciale) and thermal preferences. A. melanogenum and A. pullulans grew faster at higher temperatures, while A. subglaciale showed the opposite trend. In H. werneckii, salinity governed growth. Haploids slowed as salinity increased, while the diploid remained unaffected. This is the first confirmation of the long-standing suggestion that hybrid diploid genomes of many H. werneckii are an adaptation to osmotic stress. These findings illustrate two pathways to extremotolerance: inducible flexibility in Aureobasidium versus constitutive halotolerance in H. werneckii.

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 Pyne’s 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.

Sociality is hypothesised to buffer populations against environmental stochasticity by stabilising key vital rates, yet this has rarely been tested across diverse taxa. We compiled demographic time series from 87 populations for 66 animal species spanning 12 taxonomic classes to test whether sociality promotes demographic buffering and whether this relationship depends on environmental context. Using stochastic elasticities and phylogenetically comparative analyses, we find broad support for the social buffering hypothesis: more social species exhibit lower sensitivity of population growth to vital rate variance (lower stochastic elasticity to vital rate variances, | T _σ |), particularly in juvenile survival and reproduction. Contrary to expectations, juvenile vital rates, but not adult survival, showed the strongest buffering patterns in social taxa, suggesting life-stage-specific social mechanisms. Furthermore, we show that social species invest more in maximising the average performance of adult survival and reproduction (higher stochastic elasticity to vital rate means, T _μ ), consistent with adaptive strategies favouring canalisation of fitness-related traits. This buffering benefit is especially relevant in highly unpredictable environments: in climates with erratic precipitation, social species have greater demographic advantages, exhibiting even lower T _σ values. Together, these findings provide support for the social buffering hypothesis, especially in highly stochastic environments. Social traits confer some demographic stability under moderate climatic conditions, but may become more relevant under extreme stochasticity—an insight particularly important for understanding population resilience in a rapidly changing world.

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 the strategies being demographic buffering. Whilst various methods exist to quantify demographic buffering, we still do not know which environmental components and demographic mechanisms are most responsible for the demographic buffering observed in natural populations. Here, we introduce a framework to explore the relative impacts of environmental components (i.e., temporal autocorrelation and variance in demographic rates) on demographic buffering and the demographic mechanisms that underly these impacts (i.e., population structure and demographic rates). Using integral projection models, we show how demographic buffering is more sensitive to environmental variance relative to environmental autocorrelation. In addition, environmental autocorrelation and variance impact demographic buffering through distinct demographic mechanisms—i.e., population structure and demographic rates, respectively.

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 the strategies being demographic buffering. Whilst various methods exist to quantify demographic buffering, we still do not know which environmental components and demographic mechanisms are most responsible for the demographic buffering observed in natural populations. Here, we introduce a framework to explore the relative impacts of environmental components (i.e., temporal autocorrelation and variance in demographic rates) on demographic buffering and the demographic mechanisms that underly these impacts (i.e., population structure and demographic rates). Using integral projection models, we show how demographic buffering is more sensitive to environmental variance relative to environmental autocorrelation. In addition, environmental autocorrelation and variance impact demographic buffering through distinct demographic mechanisms—i.e., population structure and demographic rates, respectively.

Environmental stochasticity impacts population dynamics and their viability. As such, understanding how organisms cope with this variability is crucial. Here, we investigate demographic buffering, the ability of populations to maintain stable growth despite environmental fluctuations. We integrate well-established stochastic and deterministic approaches to investigate characteristics of demographic buffering, analysing stochastic elasticities and self-second derivatives of deterministic population growth rate. We test the hypothesis that buffered species exhibit low stochastic elasticity to temporal variability and signs of concave selection (i.e. negative second derivatives of population growth rate with respect to demographic processes), reducing variance in key demographic processes. Analysing 43 natural populations of 37 mammal species, we find limited support for this hypothesis. Indeed, while primates often show low stochastic elasticity, concave selection is less prevalent than expected. Our findings highlight the complex and dynamic relationship between demographic processes, environmental variability, and selection pressures in determining population persistence.

The Demographic Buffering Hypothesis (DBH) predicts that natural selection reduces the temporal fluctuations in demographic processes (such as survival, development, and reproduction), due to their negative impacts on population dynamics. However, a comprehensive approach that allows for the examination of demographic buffering patterns across multiple species is still lacking. Here, we propose a three-step framework aimed at quantifying demographic buffering. Firstly, we categorize species along a continuum of variance based on the sums of stochastic elasticities. Secondly, we examine the linear selection gradients, followed by the examination of nonlinear selection gradients as the third step. With these three steps, our framework overcomes existing limitations of conventional approaches to quantify demographic buffering, allows for multi-species comparisons, and offers insight into the evolutionary forces that shape demographic buffering. We apply this framework to mammal species and discuss both the advantages and potential of our framework.