Felix May

Moving beyond abundance distributions: neutral theory and spatial patterns in a tropical forest.

Assessing the relative importance of different processes that determine the spatial distribution of species and the dynamics in highly diverse plant communities remains a challenging question in ecology. Previous modelling approaches often focused on single aggregated forest diversity patterns that convey limited information on the underlying dynamic processes. Here, we use recent advances in inference for stochastic simulation models to evaluate the ability of a spatially explicit and spatially continuous neutral model to quantitatively predict six spatial and non-spatial patterns observed at the 50 ha tropical forest plot on Barro Colorado Island, Panama. The patterns capture different aspects of forest dynamics and biodiversity structure, such as annual mortality rate, species richness, species abundance distribution, beta-diversity and the species–area relationship (SAR). The model correctly predicted each pattern independently and up to five patterns simultaneously. However, the model was unable to match the SAR and beta-diversity simultaneously. Our study moves previous theory towards a dynamic spatial theory of biodiversity and demonstrates the value of spatial data to identify ecological processes. This opens up new avenues to evaluate the consequences of additional process for community assembly and dynamics.

Do abundance distributions and species aggregation correctly predict macroecological biodiversity patterns in tropical forests

Abstract Aim It has been recently suggested that different ‘unified theories of biodiversity and biogeography’ can be characterized by three common ‘minimal sufficient rules’: (1) species abundance distributions follow a hollow curve, (2) species show intraspecific aggregation, and (3) species are independently placed with respect to other species. Here, we translate these qualitative rules into a quantitative framework and assess if these minimal rules are indeed sufficient to predict multiple macroecological biodiversity patterns simultaneously. Location Tropical forest plots in Barro Colorado Island (BCI), Panama, and in Sinharaja, Sri Lanka. Methods We assess the predictive power of the three rules using dynamic and spatial simulation models in combination with census data from the two forest plots. We use two different versions of the model: (1) a neutral model and (2) an extended model that allowed for species differences in dispersal distances. In a first step we derive model parameterizations that correctly represent the three minimal rules (i.e. the model quantitatively matches the observed species abundance distribution and the distribution of intraspecific aggregation). In a second step we applied the parameterized models to predict four additional spatial biodiversity patterns. Results Species‐specific dispersal was needed to quantitatively fulfil the three minimal rules. The model with species‐specific dispersal correctly predicted the species–area relationship, but failed to predict the distance decay, the relationship between species abundances and aggregations, and the distribution of a spatial co‐occurrence index of all abundant species pairs. These results were consistent over the two forest plots. Main conclusions The three ‘minimal sufficient’ rules only provide an incomplete approximation of the stochastic spatial geometry of biodiversity in tropical forests. The assumption of independent interspecific placements is most likely violated in many forests due to shared or distinct habitat preferences. Furthermore, our results highlight missing knowledge about the relationship between species abundances and their aggregation.

Monodominance in tropical forests: modelling reveals emerging clusters and phase transitions

Tropical forests are highly diverse ecosystems, but within such forests there can be large patches dominated by a single tree species. The myriad presumed mechanisms that lead to the emergence of such monodominant areas is currently the subject of intensive research. We used the most generic of these mechanisms, large seed mass and low dispersal ability of the monodominant species, in a spatially explicit model. The model represents seven identical species with long-distance dispersal of small seeds, competing with one potentially monodominant species with short-distance dispersal of large seeds. Monodominant patches emerged and persisted only for a narrow range of species traits; these results have the characteristic features of phase transitions. Additional mechanisms may explain monodominance in different ecological contexts, but our results suggest that percolation-like phenomena and phase transitions might be pervasive in this type of system.

Embracing scale-dependence to achieve a deeper understanding of biodiversity and its change across communities

Because biodiversity is multidimensional and scale-dependent, it is challenging to estimate its change. However, it is unclear (1) how much scale-dependence matters for empirical studies, and (2) if it does matter, how exactly we should quantify biodiversity change. To address the first question, we analysed studies with comparisons among multiple assemblages, and found that rarefaction curves frequently crossed, implying reversals in the ranking of species richness across spatial scales. Moreover, the most frequently measured aspect of diversity - species richness - was poorly correlated with other measures of diversity. Second, we collated studies that included spatial scale in their estimates of biodiversity change in response to ecological drivers and found frequent and strong scale-dependence, including nearly 10% of studies which showed that biodiversity changes switched directions across scales. Having established the complexity of empirical biodiversity comparisons, we describe a synthesis of methods based on rarefaction curves that allow more explicit analyses of spatial and sampling effects on biodiversity comparisons. We use a case study of nutrient additions in experimental ponds to illustrate how this multi-dimensional and multi-scale perspective informs the responses of biodiversity to ecological drivers.

What drives the spatial distribution and dynamics of local species richness in tropical forest

Understanding the structure and dynamics of highly diverse tropical forests is challenging. Here we investigate the factors that drive the spatio-temporal variation of local tree numbers and species richness in a tropical forest (including 1250 plots of 20 × 20 m2). To this end, we use a series of dynamic models that are built around the local spatial variation of mortality and recruitment rates, and ask which combination of processes can explain the observed spatial and temporal variation in tree and species numbers. We find that processes not included in classical neutral theory are needed to explain these fundamental patterns of the observed local forest dynamics. We identified a large spatio-temporal variability in the local number of recruits as the main missing mechanism, whereas variability of mortality rates contributed to a lesser extent. We also found that local tree numbers stabilize at typical values which can be explained by a simple analytical model. Our study emphasized the importance of spatio-temporal variability in recruitment beyond demographic stochasticity for explaining the local heterogeneity of tropical forests.

A framework for dissecting ecological mechanisms underlying the island species-area relationship

The relationship between an island’s size and the number of species on that island—the island species-area relationship (ISAR)—is one of the most well-known patterns in biogeography, and forms the basis for understanding biodiversity loss in response to habitat loss and fragmentation. Nevertheless, there is contention about exactly how to estimate the ISAR, and the influence of the three primary ecological mechanisms—sampling, area per se, and heterogeneity— that drive it. Key to this contention is that estimates of the ISAR are often confounded by sampling and estimates of measures (i.e., island-level species richness) that are not diagnostic of potential mechanisms. Here, we advocate a sampling-explicit approach for dissecting the possible ecological mechanisms underlying the ISAR using individual-based rarefaction curves estimated across spatial scales. Specifically, we show how ISAR mechanisms can be inferred by comparing the relationship between island area and diversity indices derived from regional (γ-) and local (α-) individual-based rarefaction curves. If the parameters derived from rarefaction curves at each spatial scale show no relationship with island area, we cannot reject the hypothesis that ISARs result only from sampling effects. However, if the parameters derived from the rarefactions change with island area, effects beyond sampling (i.e., area per se or heterogeneity) are operating. Additionally, if parameters indicative of within-island spatial variation in species composition (i.e., β-diversity) increase with island area, intra-island compositional heterogeneity plays a role in driving the ISAR. We illustrate this approach using representative case studies, including oceanic islands, natural island-like patches, and habitat fragments from formerly continuous habitat, illustrating several combinations of underlying mechanisms. This approach will offer insight into the role of sampling and other processes that underpin the ISAR, providing a more complete understanding of how, and some indication of why, patterns of biodiversity respond to gradients in island area.

The geometry of habitat fragmentation: effects of distribution patterns on short-term species persistence

Land-use changes cause habitat loss and fragmentation and are thus important drivers of anthropogenic biodiversity change. However, there is an ongoing debate about how fragmentation per se affects biodiversity in a given amount of habitat. We illustrate why it is important to distinguish two different aspects of fragmentation to resolve this debate: (i) geometric fragmentation effects, which exclusively arise from the spatial distributions of species and habitat fragments, and (ii) demographic fragmentation effects due to reduced fragment size, increased isolation, or edge effects. While most empirical studies are primarily interested in quantifying demographic fragmentation effects, geometric effects are typically invoked only as post-hoc explanations of biodiversity responses to fragmentation per se. Here, we present an approach to quantify geometric fragmentation effects on species persistence probability. We illustrate this approach using spatial simulations where we systematically varied the initial abundances and distribution patterns (i.e. random, aggregated, and regular) of species as well as habitat amount and fragmentation per se. As expected, we found no geometric fragmentation effects when species were randomly distributed. However, when species were aggregated, we found positive effects of fragmentation per se on persistence probability for a large range of scenarios. For regular species distributions, we found weakly negative geometric effects. These findings are independent of the ecological mechanisms which generate non-random species distributions. Our study helps to reconcile seemingly contradictory results of previous fragmentation studies. Since intraspecific aggregation is a ubiquitous pattern in nature, our findings imply widespread positive geometric fragmentation effects. This expectation is supported by many studies that find positive effects of fragmentation per se on species occurrences and diversity after controlling for habitat amount. We outline how to disentangle geometric and demographic effects of fragmentation, which is critical for predicting the response of biodiversity to landscape change.

MoB (Measurement of Biodiversity): a method to separate the scale‐dependent effects of species abundance distribution, density, and aggregation on diversity change

1Biology Department, College of Charleston, Charleston, South Carolina; 2School of Biology and Ecology, and Senator George J. Mitchell Center of Sustainability Solutions, University of Maine, Orono, Maine; 3Leuphana University Lüneburg, Lüneburg, Germany; 4German Centre for Integrative Biodiversity Research (iDiv), Halle-Jena-Leipzig, Leipzig, Germany; 5Department of Biology, University of Vermont, Burlington, Vermont; 6Institute of Biology, Martin Luther University Halle-Wittenberg, Halle (Saale), Germany; 7Department of Community Ecology, Helmholtz Centre for Environmental Research – UFZ, Halle (Saale), Germany and 8Department of Computer Science, Martin Luther University, Halle-Wittenberg, Leipzig, Germany

Extinction rate has a complex and non-linear relationship with area

Aim. Biodiversity loss, measured as count of extinction events, is a key component of biodiversity change, and can significantly impact ecosystem services. However, estimation of the loss has focused mostly on per-species extinction rates measured over limited numbers of spatial scales, with no theory linking small-scale extirpations with global extinctions. Here we provide such link by introducing the relationship between area and per-species probability of extinction (PxAR) and between area and count of realized extinction events in that area (NxAR). We show theoretical and empirical forms of these relationships, and we discuss their role in perception and estimation of the current extinction crisis. Location USA, Europe, Czech Republic, Barro Colorado Island Methods We derived the expected forms of PxAR and NxAR from a range of theoretical frameworks based on theory of island biogeography, neutral models, and species-area relationships. We constructed PxAR and NxAR in five empirical datasets on butterflies, plants, trees and birds, collected over range of spatial scales. Results Both the theoretical arguments and empirical data support monotonically decreasing PxAR, i.e. per-species extinction probability decreasing with increasing area; however, we also report a rare theoretical possibility of locally increasing PxAR. In contrast, both theory and data revealed complex NxAR, i.e. counts of extinction events follow variety of relationships with area, including nonlinear unimodal, multimodal and U-shaped relationships, depending on region and taxon. Main conclusions The uncovered wealth of forms of NxAR can explain why biodiversity change (the net outcome of losses and gains) also appears scale-dependent. Furthermore, the complex scale dependence of PxAR and NxAR means that global extinctions indicate little about local extirpations, and vice versa. Hence, effort should be made to understand and report extinction crisis as a scale-dependent problem. In this effort, estimation of scaling relationships such as PxAR and NxAR should be central.