Towards a unified descriptive theory for spatial ecology: predicting biodiversity patterns across spatial scales

Extinction time distributions of populations and genotypes

Ultimately, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been limited exploration of the distributions of extinction times and the likelihood of significant fluctuations. Recently, Hathcock and Strogatz [D. Hathcock and S. H. Strogatz, Phys. Rev. Lett. 128, 218301 (2022)0031-900710.1103/PhysRevLett.128.218301] identified Gumbel statistics as a universal asymptotic distribution for extinction-prone dynamics in a stable environment. In this study we aim to provide a comprehensive survey of this problem by examining a range of plausible scenarios, including extinction-prone, marginal (neutral), and stable dynamics. We consider the influence of demographic stochasticity, which arises from the inherent randomness of the birth-death process, as well as cases where stochasticity originates from the more pronounced effect of random environmental variations. Our work proposes several generic criteria that can be used for the classification of experimental and empirical systems, thereby enhancing our ability to discern the mechanisms governing extinction dynamics. Employing these criteria can help clarify the underlying mechanisms driving extinction processes.

Turnover and nestedness drive plant diversity benefits of organic farming from local to landscape scales

Biodiversity-benefits of organic farming have mostly been documented at the field scale. However, these benefits from organic farming to species diversity may not propagate to larger scales because variation in the management of different crop types and seminatural habitats in conventional farms might allow species to cope with intensive crop management. We studied flowering plant communities using a spatially replicated design in different habitats (cereal, ley and seminatural grasslands) in organic and conventional farms, distributed along a gradient in proportion of seminatural grasslands. We developed a novel method to compare the rates of species turnover within and between habitats, and between the total species pools in the two farming systems. We found that the intrahabitat species turnover did not differ between organic and conventional farms, but that organic farms had a significantly higher interhabitat turnover of flowering plant species compared with conventional ones. This was mainly driven by herbicide-sensitive species in cereal fields in organic farms, as these contained 2.5 times more species exclusive to cereal fields compared with conventional farms. The farm-scale species richness of flowering plants was higher in organic compared with conventional farms, but only in simple landscapes. At the interfarm level, we found that 36% of species were shared between the two farming systems, 37% were specific to organic farms whereas 27% were specific to conventional ones. Therefore, our results suggest that that both community nestedness and species turnover drive changes in species composition between the two farming systems. These large-scale shifts in species composition were driven by both species-specific herbicide and nitrogen sensitivity of plants. Our study demonstrates that organic farming should foster a diversity of flowering plant species from local to landscape scales, by promoting unique sets of arable-adapted species that are scarce in conventional systems. In terms of biodiversity conservation, our results call for promoting organic farming over large spatial extents, especially in simple landscapes, where such transitions would benefit plant diversity most.

How the storage effect and the number of temporal niches affect biodiversity in stochastic and seasonal environments

Temporal environmental variations affect diversity in communities of competing populations. In particular, the covariance between competition and environment is known to facilitate invasions of rare species via the storage effect. Here we present a quantitative study of the effects of temporal variations in two-species and in diverse communities. Four scenarios are compared: environmental variations may be either periodic (seasonal) or stochastic, and the dynamics may support the storage effect (global competition) or not (local competition). In two-species communities, coexistence is quantified via the mean time to absorption, and we show that stochastic variations yield shorter persistence time because they allow for rare sequences of bad years. In diverse communities, where the steady-state reflects a colonization-extinction equilibrium, the actual number of temporal niches is shown to play a crucial role. When this number is large, the same trends hold: storage effect and periodic variations increase both species richness and the evenness of the community. Surprisingly, when the number of temporal niches is small global competition acts to decrease species richness and evenness, as it focuses the competition to specific periods, thus increasing the effective fitness differences.

One of the major challenges of community ecology and population genetics is the understanding of the factors that protect biodiversity. Surprisingly, in many generic cases temporal environmental variations (and the abundance fluctuations associated with it) promote the coexistence of competing species and facilitate genetic polymorphism. Here we present a detailed and quantitative comparison between the stabilizing (and the destabilizing) effects of periodic (seasonal) and stochastic temporal variations. When the number of species is small, we show that persistence times under periodic variations are much longer than the persistence times in a stochastic environment. However, environmental variations facilitate coexistence only when the number of temporal niches is larger than the number of species, whereas in the opposite case the same mechanism acts to increase competition and to decrease species richness. Since it is reasonable to expect the number of temporal niches under seasonal variations to be typically smaller than the corresponding number in stochastic environments, stochastic variations provide a more plausible explanation for the apparent stability of high-diversity assemblages.

A unified framework for species spatial patterns: Linking the occupancy area curve, Taylor's Law, the neighborhood density function and two-plot species turnover

The description of spatial patterns in species distributions is central to research throughout ecology. In this manuscript, we demonstrate that five of the most widely used species‐level spatial patterns are not only related, but can in fact be quantitatively derived from each other under minimal assumptions: the occupancy area curve, Taylor's Law, the neighborhood density function, a two‐plot variant of Taylor's Law and two‐plot single‐species turnover. We present an overarching mathematical framework and derivations for several theoretical example cases, along with a simulation study and empirical analysis that applies the framework to data from the Barro Colorado Island tropical forest plot. We discuss how knowledge of this mathematical relationship can support the testing of ecological theory, suggest efficient field sampling schemes, highlight the relative importance of plot area and abundance in driving turnover patterns and lay the groundwork for future unified theories of community‐level spatial metrics and multi‐patch spatial patterns.

Scaling up biodiversity-ecosystem functioning relationships: the role of environmental heterogeneity in space and time

The biodiversity and ecosystem functioning (BEF) relationship is expected to be scale-dependent. The autocorrelation of environmental heterogeneity is hypothesized to explain this scale dependence because it influences how quickly biodiversity accumulates over space or time. However, this link has yet to be demonstrated in a formal model. Here, we use a Lotka-Volterra competition model to simulate community dynamics when environmental conditions vary across either space or time. Species differ in their optimal environmental conditions, which results in turnover in community composition. We vary biodiversity by modelling communities with different sized regional species pools and ask how the amount of biomass per unit area depends on the number of species present, and the spatial or temporal scale at which it is measured. We find that more biodiversity is required to maintain functioning at larger temporal and spatial scales. The number of species required increases quickly when environmental autocorrelation is low, and slowly when autocorrelation is high. Both spatial and temporal environmental heterogeneity lead to scale dependence in BEF, but autocorrelation has larger impacts when environmental change is temporal. These findings show how the biodiversity required to maintain functioning is expected to increase over space and time.

The mechanisms generating community phylogenetic patterns change with spatial scale

Studies that test community assembly hypotheses in observational communities frequently evaluate patterns for plots or entire communities, yet studies that examine assembly patterns across spatial scales show that they are greatly influenced by scale. Here, we test the spatial dependency of patterns of relatedness and plant height for all individual herbaceous plants along five 40-m old-field transects (Southern Ontario, Canada). We identified each individual plant and measured its distance along the transect and its height, and we constructed a molecular phylogeny for all observed species. To uncover the scale at which community phylogenetic and trait similarities shift, we used partial Mantel correlograms and distance-based Moran Eigenvector Maps (dbMEMs). We found that communities shift from significantly overdispersed at relatively smaller scales (i.e., < 15 m) to spatially clustered at larger scales, showing that assembly mechanism influence depends on scale of observation. This pattern was observed for both phylogeny and height, but was the strongest when considering phylogeny only. These results reveal the importance of spatial scale when examining community phylogenetic or trait patterns, where finding support for one assembly mechanism at a single scale does not necessarily mean that other mechanisms are also not important for structuring community composition and diversity.

Data Integration for Large-Scale Models of Species Distributions

With the expansion in the quantity and types of biodiversity data being collected, there is a need to find ways to combine these different sources to provide cohesive summaries of species' potential and realized distributions in space and time. Recently, model-based data integration has emerged as a means to achieve this by combining datasets in ways that retain the strengths of each. We describe a flexible approach to data integration using point process models, which provide a convenient way to translate across ecological currencies. We highlight recent examples of large-scale ecological models based on data integration and outline the conceptual and technical challenges and opportunities that arise.

A Bayesian-weighted approach to predicting the number of newly discovered rare species

In natural ecological communities, most species are rare and thus susceptible to extinction. Consequently, the prediction and identification of rare species are of enormous value for conservation purposes. How many newly found species will be rare in the next field survey? We took a Bayesian viewpoint and used observed species abundance information in an ecological sample to develop an accurate way to estimate the number of new rare species (e.g., singletons, doubletons, and tripletons) in an additional unknown sample. A similar method has been developed for incidence-based data sets. Five seminumerical tests (3 abundance cases and 2 incidence cases) showed that our proposed Bayesian-weight estimator accurately predicted the number of new rare species with low relative bias and low relative root mean squared error and, accordingly, high accuracy. Finally, we applied the proposed estimator to 6 conservation-directed empirical data sets (3 abundance cases and 3 incidence cases) and found the prediction of new rare species was quite accurate; the 95% CI covered the true observed value very well in most cases. Our estimator performed similarly to or better than an unweighted estimator derived from Chao et al. and performed consistently better than the naïve unweighted estimator. We recommend our Bayesian-weight estimator for conservation applications, although the unweighted estimator of Chao et al. may be better under some circumstances. We provide an R package RSE (rare species estimation) at https://github.com/ecomol/RSE for implementation of the estimators.

The prevalence and impact of transient species in ecological communities

Transient species occur infrequently in a community over time and do not maintain viable local populations. Because transient species interact differently than non-transients with their biotic and abiotic environment, it is important to characterize the prevalence of these species and how they impact our understanding of ecological systems. We quantified the prevalence and impact of transient species in communities using data on over 19,000 community time series spanning an array of ecosystems, taxonomic groups, and spatial scales. We found that transient species are a general feature of communities regardless of taxa or ecosystem. The proportion of these species decreases with increasing spatial scale leading to a need to control for scale in comparative work. Removing transient species from analyses influences the form of a suite of commonly studied ecological patterns including species-abundance distributions, species-energy relationships, species-area relationships, and temporal turnover. Careful consideration should be given to whether transient species are included in analyses depending on the theoretical and practical relevance of these species for the question being studied.

Upscaling species richness and abundances in tropical forests

The quantification of tropical tree biodiversity worldwide remains an open and challenging problem. More than two-fifths of the number of worldwide trees can be found either in tropical or in subtropical forests, but only ≈0.000067% of species identities are known. We introduce an analytical framework that provides robust and accurate estimates of species richness and abundances in biodiversity-rich ecosystems, as confirmed by tests performed on both in silico-generated and real forests. Our analysis shows that the approach outperforms other methods. In particular, we find that upscaling methods based on the log-series species distribution systematically overestimate the number of species and abundances of the rare species. We finally apply our new framework on 15 empirical tropical forest plots and quantify the minimum percentage cover that should be sampled to achieve a given average confidence interval in the upscaled estimate of biodiversity. Our theoretical framework confirms that the forests studied are comprised of a large number of rare or hyper-rare species. This is a signature of critical-like behavior of species-rich ecosystems and can provide a buffer against extinction.

Solution of the spatial neutral model yields new bounds on the Amazonian species richness

Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with spatial structure, but the analytic results presented so far are limited to well-mixed or mainland-island scenarios. Here we combine analytic results and numerics to obtain an approximate solution for the species abundance distribution and the species richness for the neutral model on continuous landscape. We show how the regional diversity increases when the recruitment length decreases and the spatial segregation of species grows. Our results are supported by extensive numerical simulations and allow one to probe the numerically inaccessible regime of large-scale systems with extremely small mutation/speciation rates. Model predictions are compared with the findings of recent large-scale surveys of tropical trees across the Amazon basin, yielding new bounds for the species richness (between 13100 and 15000) and the number of singleton species (between 455 and 690).

The database of the PREDICTS (Projecting Responses of Ecological Diversity In Changing Terrestrial Systems) project

The PREDICTS project-Projecting Responses of Ecological Diversity In Changing Terrestrial Systems (www.predicts.org.uk)-has collated from published studies a large, reasonably representative database of comparable samples of biodiversity from multiple sites that differ in the nature or intensity of human impacts relating to land use. We have used this evidence base to develop global and regional statistical models of how local biodiversity responds to these measures. We describe and make freely available this 2016 release of the database, containing more than 3.2 million records sampled at over 26,000 locations and representing over 47,000 species. We outline how the database can help in answering a range of questions in ecology and conservation biology. To our knowledge, this is the largest and most geographically and taxonomically representative database of spatial comparisons of biodiversity that has been collated to date; it will be useful to researchers and international efforts wishing to model and understand the global status of biodiversity.

Spatial homogeneity of benthic macrofaunal biodiversity across small spatial scales

Spatial heterogeneity of biodiversity has been extensively researched, but its spatial homogeneity is virtually unstudied. An intertidal seagrass system at Knysna (South Africa) known to display spatially homogeneous macrobenthic species density at scales ≥0.0275 m² was re-investigated at four smaller spatial grains (0.0015 m² - 0.0095 m²) via a lattice of 8 × 8 stations within a 0.2 ha area. The aim was to investigate the null hypothesis that spatial homogeneity of species density is not a fixed emergent assemblage property but breaks down at small spatial grains within given spatial extents. Although assemblage abundance was significantly heterogeneous at all spatial grains investigated, both species density and functional-group density were significantly homogeneous across those same scales; observed densities not departing from those expected on the basis of independent assortment. Spatial homogeneity is therefore an emergent assemblage property within given spatial extents at Knysna and probably at equivalent sites elsewhere. Equivalent species density in South Africa, Australia and the UK at spatial grains <0.03 m², however, is a scale-related sampling artefact, as may be temporal homogeneity of species density at Knysna over a 3 year period, but close similarity in shape of their species occupancy distributions remains unexplained.

How domain growth is implemented determines the long-term behavior of a cell population through its effect on spatial correlations

Domain growth plays an important role in many biological systems, and so the inclusion of domain growth in models of these biological systems is important to understanding how these systems function. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations in a continuum approximation of a lattice-based model of cell motility and proliferation. We show that, depending on the way in which domain growth is implemented, different steady-state densities are predicted for an agent population. Furthermore, we demonstrate that the way in which domain growth is implemented can result in the evolution of the agent density depending on the size of the domain. Continuum approximations that ignore spatial correlations cannot capture these behaviors, while those that account for spatial correlations do. These results will be of interest to researchers in developmental biology, as they suggest that the nature of domain growth can determine the characteristics of cell populations.