Discretising Keyfitz' entropy for studies of actuarial senescence and comparative demography

Keyfitz' entropy is a widely used metric to quantify the shape of the survivorship curve of populations, from plants to animals and microbes. Keyfitz' entropy values &lt;1 correspond to life histories with an increasing mortality rate with age (i.e. actuarial senescence), whereas values &gt;1 correspond to species with a decreasing mortality rate with age (negative senescence), and a Keyfitz entropy of exactly 1 corresponds to a constant mortality rate with age. Keyfitz' entropy was originally defined using a continuous-time model, and has since been discretised to facilitate its calculation from discrete-time demographic data. Here, we show that the previously used discretisation of the continuous-time metric does not preserve the relationship with increasing, decreasing or constant mortality rates. To resolve this discrepancy, we propose a new discrete-time formula for Keyfitz' entropy for age-classified life histories. We show that this new method of discretisation preserves the relationship with increasing, decreasing, or constant mortality rates. We analyse the relationship between the original and the new discretisation, and we find that the existing metric tends to underestimate Keyfitz' entropy for both short-lived species and long-lived species, thereby introducing a consistent bias. To conclude, to avoid biases when classifying life histories as (non-)senescent, we suggest researchers use either the new metric proposed here, or one of the many previously suggested survivorship shape metrics applicable to discrete-time demographic data such as Gini coefficient or Hayley's median.</p

Extrapolating demography with climate, proximity and phylogeny: approach with caution

Plant population responses are key to understanding the effects of threats such as climate change and invasions. However, we lack demographic data for most species, and the data we have are often geographically aggregated. We determined to what extent existing data can be extrapolated to predict population performance across larger sets of species and spatial areas. We used 550 matrix models, across 210 species, sourced from the COMPADRE Plant Matrix Database, to model how climate, geographic proximity and phylogeny predicted population performance. Models including only geographic proximity and phylogeny explained 5-40% of the variation in four key metrics of population performance. However, there was poor extrapolation between species and extrapolation was limited to geographic scales smaller than those at which landscape scale threats typically occur. Thus, demographic information should only be extrapolated with caution. Capturing demography at scales relevant to landscape level threats will require more geographically extensive sampling

Plant demographic knowledge is biased towards short-term studies of temperate-region herbaceous perennials

Plant demography has a long history resulting in a large knowledge base. Comparative analysis of this information allows exploration of the drivers of demographic patterns globally and the study of life-history evolution. Studies aiming to generalise demographic patterns rely on data being derived from a representative sample. However, the data are likely to be taxonomically, geographically and methodologically biased. Matrix population models (MPMs) are widely-used in plant demography, so an assessment of publications using MPMs is a convenient way to assess the distribution of plant demographic knowledge using this modelling approach. We assessed bias in this knowledge using data from the COMPADRE Plant Matrix Database, containing MPMs for > 700 species. We show that tree species and tropical areas are under-represented, while herbaceous perennials and temperate areas are over-represented. There is a positive association between the number of studies per country and per capita GDP. Most studies have low spatiotemporal replication with 43% of studies conducted over three sites. This limited spatiotemporal coverage means existing data may not represent the environmental conditions the species experience. These biases and knowledge gaps inhibit theory development and limit current utility for identifying useful generalities for management decisions, such as typical responses to climate change. It is likely that similar biases extend to other demographic modelling tools such as integral projection models. We urge researchers to address these biases and close these knowledge gaps

Bridging gaps in demographic analysis with phylogenetic imputation

Phylogenetically informed imputation methods have rarely been applied to estimate missing values in demographic data but may be a powerful tool for reconstructing vital rates of survival, maturation, and fecundity for species of conservation concern. Imputed vital rates could be used to parameterize demographic models to explore how populations respond when vital rates are perturbed. We used standardized vital rate estimates for 50 bird species to assess the use of phylogenetic imputation to fill gaps in demographic data. We calculated imputation accuracy for vital rates of focal species excluded from the data set either singly or in combination and with and without phylogeny, body mass, and life‐history trait data. We used imputed vital rates to calculate demographic metrics, including generation time, to validate the use of imputation in demographic analyses. Covariance among vital rates and other trait data provided a strong basis to guide imputation of missing vital rates in birds, even in the absence of phylogenetic information. Mean NRMSE for null and phylogenetic models differed by 0.8). In these cases, including body mass and life‐history trait data compensated for lack of phylogenetic information: mean normalized root mean square error (NRMSE) for null and phylogenetic models differed by <0.01 for adult survival and <0.04 for maturation rate. Estimates of demographic metrics were sensitive to the accuracy of imputed vital rates. For example, mean error in generation time doubled in response to inaccurate estimates of maturation time. Accurate demographic data and metrics, such as generation time, are needed to inform conservation planning processes, for example through International Union for Conservation of Nature Red List assessments and population viability analysis. Imputed vital rates could be useful in this context but, as for any estimated model parameters, awareness of the sensitivities of demographic model outputs to the imputed vital rates is essential

Fast-slow continuum and reproductive strategies structure plant life-history variation worldwide

This is the author accepted manuscript. The final version is available from National Academy of Sciences via the DOI in this record.The identification of patterns in life-history strategies across the tree of life is essential to our prediction of population persistence, extinction, and diversification. Plants exhibit a wide range of patterns of longevity, growth, and reproduction, but the general determinants of this enormous variation in life history are poorly understood. We use demographic data from 418 plant species in the wild, from annual herbs to supercentennial trees, to examine how growth form, habitat, and phylogenetic relationships structure plant life histories and to develop a framework to predict population performance. We show that 55% of the variation in plant life-history strategies is adequately characterized using two independent axes: the fast-slow continuum, including fast-growing, short-lived plant species at one end and slow-growing, long-lived species at the other, and a reproductive strategy axis, with highly reproductive, iteroparous species at one extreme and poorly reproductive, semelparous plants with frequent shrinkage at the other. Our findings remain consistent across major habitats and are minimally affected by plant growth form and phylogenetic ancestry, suggesting that the relative independence of the fast-slow and reproduction strategy axes is general in the plant kingdom. Our findings have similarities with how life-history strategies are structured in mammals, birds, and reptiles. The position of plant species populations in the 2D space produced by both axes predicts their rate of recovery from disturbances and population growth rate. This life-history framework may complement trait-based frameworks on leaf and wood economics; together these frameworks may allow prediction of responses of plants to anthropogenic disturbances and changing environments.M. Franco provided the phylogenetic tree. We thank H. Possingham, D. Koons, and F. Colchero for feedback and the COMPADRE Plant Matrix Database team for data digitalization and error-checking. This work was supported by the Max Planck Institute for Demographic Research, Australian Research Council Grant DE140100505 (to R.S.-G.), and a Marie-Curie Career Integration Grant (to Y.M.B.)

ipmr: flexible implementation of integral projection models in R

1. Integral projection models (IPMs) are an important tool for studying the dynamics of populations structured by one or more continuous traits (e.g. size, height, body mass). Researchers use IPMs to investigate questions ranging from linking drivers to population dynamics, planning conservation and management strategies, and quantifying selective pressures in natural populations. The popularity of stage-structured population models has been supported by R scripts and packages (e.g. IPMpack, popbio, popdemo, lefko3) aimed at ecologists, which have introduced a broad repertoire of functionality and outputs. However, pressing ecological, evolutionary and conservation biology topics require developing more complex IPMs, and considerably more expertise to implement them. Here, we introduce ipmr, a flexible R package for building, analysing and interpreting IPMs. 2. The ipmr framework relies on the mathematical notation of the models to express them in code format. Additionally, this package decouples the model parameterization step from the model implementation step. The latter point substantially increases ipmr's flexibility to model complex life cycles and demographic processes. 3. ipmr can handle a wide variety of models, including those that incorporate density dependence, discretely and continuously varying stochastic environments, and multiple continuous and/or discrete traits. ipmr can accommodate models with individuals cross-classified by age and size. Furthermore, the package provides methods for demographic analyses (e.g. asymptotic and stochastic growth rates) and visualization (e.g. kernel plotting). 4. ipmr is a flexible R package for integral projection models. The package substantially reduces the amount of time required to implement general IPMs. We also provide extensive documentation with six vignettes and help files, accessible from an R session and online

The next Generation of Action Ecology: Novel Approaches towards Global Ecological Research

Advances in the acquisition and dissemination of knowledge over the last decade have dramatically reshaped the way that ecological research is conducted. The advent of large, technology-based resources such as iNaturalist, Genbank, or the Global Biodiversity Information Facility (GBIF) allow ecologists to work at spatio-temporal scales previously unimaginable. This has generated a new approach in ecological research: one that relies on large datasets and rapid synthesis for theory testing and development, and findings that provide specific recommendations to policymakers and managers. This new approach has been termed action ecology, and here we aim to expand on earlier definitions to delineate its characteristics so as to distinguish it from related subfields in applied ecology and ecological management. Our new, more nuanced definition describes action ecology as ecological research that is (1) explicitly motivated by the need for immediate insights into current, pressing problems, (2) collaborative and transdisciplinary, incorporating sociological in addition to ecological considerations throughout all steps of the research, (3) technology-mediated, innovative, and aggregative (i.e., reliant on ‘big data\u27), and (4) designed and disseminated with the intention to inform policy and management. We provide tangible examples of existing work in the domain of action ecology, and offer suggestions for its implementation and future growth, with explicit recommendations for individuals, research institutions, and ecological societies

Experimental drought reduces the productivity and stability of a calcareous grassland

Grasslands, which encompass 40% of terrestrial ecosystems, hold global significance for food production, carbon storage and other ecosystem services. However, grasslands across the biosphere are becoming increasingly exposed to both wet and dry precipitation extremes resulting from climate change. Therefore, understanding how grasslands will respond to precipitation extremes is a pressing issue for managing changes to biodiversity and ecosystem service provision. Here, we use experimental manipulations of precipitation (50% increase and 50% decrease in growing‐season precipitation) over 6 years to investigate the stability and resistance of both productivity and community diversity in a calcareous grassland community. We found that decreased growing‐season precipitation led to reductions in mean productivity (25% decrease in peak above‐ground biomass) and its temporal stability (54% increase in the coefficient of variation of biomass across years). Productivity losses were more pronounced for graminoids and legumes, but this was not reflected in species per cent cover. Community composition was resistant to the precipitation manipulations, with no clear differences in overall community compositional turnover, dissimilarity or biodiversity indices. There was also no detectible effect of increased precipitation on productivity or community composition, which may indicate a lack of efficacy of the irrigation treatment in increasing soil moisture. Finally, the precipitation manipulations had no effect on temporal trends of community change, with an overall increase in richness and shift in grassland community composition across the study period independent of treatment. Synthesis. While the diversity and composition of this calcareous grassland was resistant to precipitation extremes (at least in the short term), sustained reductions in growing‐season precipitation reduced productivity and its temporal stability, particularly for graminoids and legumes. Therefore, we highlight that different properties of grasslands can vary in their responses to changes in precipitation