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Canopy gaps are widely recognized as being crucial for maintaining the diversity of forest tree communities. But empirical studies have found mixed results because the differences in diversity between individual gaps and non-gaps are often small and statistically undetectable. One overlooked factor, however, is how small individual gap versus non-gap differences may accumulate across sites and potentially have a large effect on forest diversity at the plot scale. Our study investigated sapling richness, density, and composition in 124 treefall gaps, and 200 non-gap sites in the 50-ha tropical forest plot at Barro Colorado Island (BCI), Panama. Additionally, we analyzed species accumulation curves to understand how species richness increases with increasing stem numbers. We observed that sapling richness and density were only slightly higher in gaps 7 years after formation and statistically indistinguishable from non-gaps after 12 years. However, species accumulation curves across multiple gaps were substantially higher than those across non-gaps. Species composition showed small differences between individual gaps and non-gaps but differed significantly between collections of gaps and non-gaps. Specifically, 55 species specialized in 7-year-old gaps compared with 24 in non-gaps; of these, 23 gap-specialized species and zero non-gap species were pioneers. Our results indicate that tree species richness is higher in gaps because of both higher stem density and the presence of gap-specialized species. Our study has finally provided compelling evidence to support the idea that gaps enhance the overall diversity of tropical forest tree communities., (© 2024 The Author(s). Ecology published by Wiley Periodicals LLC on behalf of The Ecological Society of America.)

Numerous studies have shown reduced performance in plants that are surrounded by neighbours of the same species 1,2 , a phenomenon known as conspecific negative density dependence (CNDD) 3 . A long-held ecological hypothesis posits that CNDD is more pronounced in tropical than in temperate forests 4,5 , which increases community stabilization, species coexistence and the diversity of local tree species 6,7 . Previous analyses supporting such a latitudinal gradient in CNDD 8,9 have suffered from methodological limitations related to the use of static data 10-12 . Here we present a comprehensive assessment of latitudinal CNDD patterns using dynamic mortality data to estimate species-site-specific CNDD across 23 sites. Averaged across species, we found that stabilizing CNDD was present at all except one site, but that average stabilizing CNDD was not stronger toward the tropics. However, in tropical tree communities, rare and intermediate abundant species experienced stronger stabilizing CNDD than did common species. This pattern was absent in temperate forests, which suggests that CNDD influences species abundances more strongly in tropical forests than it does in temperate ones 13 . We also found that interspecific variation in CNDD, which might attenuate its stabilizing effect on species diversity 14,15 , was high but not significantly different across latitudes. Although the consequences of these patterns for latitudinal diversity gradients are difficult to evaluate, we speculate that a more effective regulation of population abundances could translate into greater stabilization of tropical tree communities and thus contribute to the high local diversity of tropical forests., (© 2024. The Author(s).)

Research into the processes governing species richness has often assumed that the environment is fixed, whereas realistic environments are often characterised by random fluctuations over time. This temporal environmental stochasticity (TES) changes the demographic rates of species populations, with cascading effects on community dynamics and species richness. Theoretical and applied studies have used process-based mathematical models to determine how TES affects species richness, but under a variety of frameworks. Here, we critically review such studies to synthesise their findings and draw general conclusions. We first provide a broad mathematical framework encompassing the different ways in which TES has been modelled. We then review studies that have analysed models with TES under the assumption of negligible interspecific interactions, such that a community is conceptualised as the sum of independent species populations. These analyses have highlighted how TES can reduce species richness by increasing the frequency at which a species becomes rare and therefore prone to extinction. Next, we review studies that have relaxed the assumption of negligible interspecific interactions. To simplify the corresponding models and make them analytically tractable, such studies have used mean-field theory to derive fixed parameters representing the typical strength of interspecific interactions under TES. The resulting analyses have highlighted community-level effects that determine how TES affects species richness, for species that compete for a common limiting resource. With short temporal correlations of environmental conditions, a non-linear averaging effect of interspecific competition strength over time gives an increase in species richness. In contrast, with long temporal correlations of environmental conditions, strong selection favouring the fittest species between changes in environmental conditions results in a decrease in species richness. We compare such results with those from invasion analysis, which examines invasion growth rates (IGRs) instead of species richness directly. Qualitative differences sometimes arise because the IGR is the expected growth rate of a species when it is rare, which does not capture the variation around this mean or the probability of the species becoming rare. Our review elucidates key processes that have been found to mediate the negative and positive effects of TES on species richness, and by doing so highlights key areas for future research., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

A central goal in ecology is to understand what maintains species diversity in local communities. Classic ecological theory 1,2 posits that niches dictate the maximum number of species that can coexist in a community and that the richness of observed species will be below this maximum only where immigration is very low. A new alternative theory 3,4 is that niches, instead, dictate the minimum number of coexisting species and that the richness of observed species will usually be well above this because of ongoing immigration. We conducted an experimental test to discriminate between these two unified theories using a manipulative field experiment with tropical intertidal communities. We found, consistent with the new theory, that the relationship of species richness to immigration rate stabilized at a low value at low immigration rates and did not saturate at high immigration rates. Our results suggest that tropical intertidal communities have low niche diversity and are typically in a dispersal-assembled regime where immigration is high enough to overfill the niches. Observational data from other studies 3,5 suggest that these conclusions may generalize to other ecological systems. Our new experimental approach can be adapted for other systems and be used as a 'niche detector' and a tool for assessing when communities are niche versus dispersal assembled., (© 2023. The Author(s).)

The question of whether biodiversity conservation and carbon conservation can be synergistic hinges on the form of the biodiversity-productivity relationship (BPR), a fundamental ecological pattern. The stakes are particularly high when it comes to forests, which at a global level comprises a large fraction of both biodiversity and carbon. And yet, in forests, the BPR is relatively poorly understood. In this review, we critically evaluate research on forest BPRs, focussing on the experimental and observational studies of the last 2 decades. We find general support for a positive forest BPR, suggesting that biodiversity and carbon conservation are synergistic to a degree. However, we identify several major caveats: (i) although, on average, productivity may increase with biodiversity, the highest-yielding forests are often monocultures of very productive species; (ii) productivity typically saturates at fewer than ten species; (iii) positive BPRs can be driven by some third variable, in particular stem density, instead of a causal arrow from biodiversity to productivity; (iv) the BPR's sign and magnitude varies across spatial grains and extents, and it may be weak at scales relevant to conservation; and (v) most productivity estimates in forests are associated with large errors. We conclude by explaining the importance of these caveats for both conservation programmes focussed on protection of existing forests and conservation programmes focussed on restoring or replanting forests., (© 2023. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

AbstractA goal of ecology is to identify the stabilizing mechanisms that maintain species diversity in the face of competitive exclusion and drift. For tropical forest tree communities, it has been hypothesized that high diversity is maintained via Janzen-Connell effects, whereby host-specific natural enemies prevent any one species from becoming too abundant. Here we explore the plausibility of this hypothesis with theoretical models. We confirm a previous result that when added to a model with drift but no competitive exclusion-that is, a neutral model where intrinsic fitnesses are perfectly equalized across species-Janzen-Connell effects maintain very high species richness that scales strongly with community size. However, when competitive exclusion is introduced-that is, when intrinsic fitnesses vary across species-the number of species maintained by Janzen-Connell effects is substantially reduced and scales much less strongly with community size. Because fitness variation is pervasive in nature, we conclude that the potential of Janzen-Connell effects to maintain diversity is probably weak and that the mechanism does not yet provide a sufficient explanation for the observed high diversity of tropical forest tree communities. We also show that, surprisingly, dispersal limitation can further reduce the ability of Janzen-Connell effects to maintain diversity.

Isolating the effects of fragmentation per se (i.e., spatial configuration of habitat patches) on species richness is an ongoing challenge as habitat configuration often covaries with the amount of habitat. Consequently, there is a lack of experimental evidence for configurational effects on species richness in the whole landscape. Here, we developed a novel experimental system for testing the independent and interactive effects of habitat area and configuration on tropical intertidal species richness. Our results confirmed the expectation that average species richness would increase monotonically with habitat area. More intriguingly, we found mixed evidence for a non-monotonic relationship between species richness and fragmentation per se, with the highest richness at intermediate fragmentation configuration, that is, when habitat tiles were placed in a "several-small" configuration. The effect of habitat configuration was not due to passive sampling (since area was controlled for), variation in total individual abundance, or niche specialization of species to different landscape configurations. We postulate that a combination of processes, including local negative density dependence and dispersal limitation, could give rise to the observed pattern. We emphasize the importance of considering configurational effects on biodiversity at broader spatial scales and for more experimental research to delve into the mechanisms driving the patterns seen here., (© 2019 The Authors. Ecology published by Wiley Periodicals, Inc. on behalf of Ecological Society of America.)

To estimate species loss from habitat destruction, ecologists typically use species-area relationships, but this approach neglects the spatial pattern of habitat fragmentation. Here, we provide new, easily applied, analytical methods that place upper and lower bounds on immediate species loss at any spatial scale and for any spatial pattern of habitat loss. Our formulas are expressed in terms of what we name the 'Preston function', which describes triphasic species-area relationships for contiguous regions. We apply our method to case studies of deforestation and tropical tree species loss at three different scales: a 50 ha forest plot in Panama, the tropical city-state of Singapore and the Brazilian Amazon. Our results show that immediate species loss is somewhat insensitive to fragmentation pattern at small scales but highly sensitive at larger scales: predicted species loss in the Amazon varies by a factor of 16 across different spatial structures of habitat loss., (© 2018 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd.)

LaManna et al (Reports, 30 June 2017, p. 1389) found higher conspecific negative density dependence in tree communities at lower latitudes, yielding a possible mechanistic explanation for the latitudinal diversity gradient. We show that their results are artifacts of a selective data transformation and a forced zero intercept in their fitted model. A corrected analysis shows no latitudinal trend., (Copyright © 2018, American Association for the Advancement of Science.)

Natural communities at all spatiotemporal scales are subjected to a wide variety of environmental pressures, resulting in random changes in the demographic rates of species populations. Previous analyses have examined the effects of such environmental variance on the long-term growth rate and time to extinction of single populations, but studies of its effects on the diversity of communities remain scarce. In this study, we construct a new master-equation model incorporating demographic and environmental variance and use it to examine how statistical patterns of diversity, as encapsulated by species-abundance distributions (SADs), are altered by environmental variance. Unlike previous diffusion models with environmental variance uncorrelated in time (white noise), our model allows environmental variance to be correlated at different timescales (colored noise), thus facilitating representation of phenomena such as yearly and decadal changes in climate. We derive an exact analytical expression for SADs predicted by our model together with a close approximation, and use them to show that the main effect of adding environmental variance is to increase the proportion of abundant species, thus flattening the SAD relative to the log-series form found in the neutral case. This flattening effect becomes more prominent when environmental variance is more correlated in time and has greater effects on species' demographic rates, holding all other factors constant. Furthermore, we show how our model SADs are consistent with those from diffusion models near the white noise limit. The mathematical techniques we develop are catalysts for further theoretical work exploring the consequences of environmental variance for biodiversity.

How many species have gone extinct in modern times before being described by science? To answer this question, and thereby get a full assessment of humanity's impact on biodiversity, statistical methods that quantify undetected extinctions are required. Such methods have been developed recently, but they are limited by their reliance on parametric assumptions; specifically, they assume the pools of extant and undetected species decay exponentially, whereas real detection rates vary temporally with survey effort and real extinction rates vary with the waxing and waning of threatening processes. We devised a new, nonparametric method for estimating undetected extinctions. As inputs, the method requires only the first and last date at which each species in an ensemble was recorded. As outputs, the method provides estimates of the proportion of species that have gone extinct, detected, or undetected and, in the special case where the number of undetected extant species in the present day is assumed close to zero, of the absolute number of undetected extinct species. The main assumption of the method is that the per-species extinction rate is independent of whether a species has been detected or not. We applied the method to the resident native bird fauna of Singapore. Of 195 recorded species, 58 (29.7%) have gone extinct in the last 200 years. Our method projected that an additional 9.6 species (95% CI 3.4, 19.8) have gone extinct without first being recorded, implying a true extinction rate of 33.0% (95% CI 31.0%, 36.2%). We provide R code for implementing our method. Because our method does not depend on strong assumptions, we expect it to be broadly useful for quantifying undetected extinctions., (© 2016 Society for Conservation Biology.)

Ecological communities are subjected to stochasticity in the form of demographic and environmental variance. Stochastic models that contain only demographic variance (neutral models) provide close quantitative fits to observed species-abundance distributions (SADs) but substantially underestimate observed temporal species-abundance fluctuations. To provide a holistic assessment of whether models with demographic and environmental variance perform better than neutral models, the fit of both to SADs and temporal species-abundance fluctuations at the same time has to be tested quantitatively. In this study, we quantitatively test how closely a model with demographic and environmental variance reproduces total numbers of species, total abundances, SADs and temporal species-abundance fluctuations for two tropical forest tree communities, using decadal data from long-term monitoring plots and considering individuals larger than two size thresholds for each community. We find that the model can indeed closely reproduce these static and dynamic patterns of biodiversity in the two communities for the two size thresholds, with better overall fits than corresponding neutral models. Therefore, our results provide evidence that stochastic models incorporating demographic and environmental variance can simultaneously capture important static and dynamic biodiversity patterns arising in tropical forest communities.

MacArthur and Wilson's theory of island biogeography predicts that island species richness should increase with island area. This prediction generally holds among large islands, but among small islands species richness often varies independently of island area, producing the so-called 'small-island effect' and an overall biphasic species-area relationship (SAR). Here, we develop a unified theory that explains the biphasic island SAR. Our theory's key postulate is that as island area increases, the total number of immigrants increases faster than niche diversity. A parsimonious mechanistic model approximating these processes reproduces a biphasic SAR and provides excellent fits to 100 archipelago datasets. In the light of our theory, the biphasic island SAR can be interpreted as arising from a transition from a niche-structured regime on small islands to a colonization-extinction balance regime on large islands. The first regime is characteristic of classic deterministic niche theories; the second regime is characteristic of stochastic theories including the theory of island biogeography and neutral theory. The data furthermore confirm our theory's key prediction that the transition between the two SAR regimes should occur at smaller areas, where immigration is stronger (i.e. for taxa that are better dispersers and for archipelagos that are less isolated)., (© 2016 The Author(s).)

The evenness of an ecological community affects ecosystem structure, functioning and stability, and has implications for biodiversity conservation. In uneven communities, most species are rare while a few dominant species drive ecosystem-level properties. In even communities, dominance is lower, with possibly many species playing key ecological roles. The dominance aspect of evenness can be measured as a decreasing function of the proportion of species required to make up a fixed fraction (e.g., half) of individuals in a community. Here we sought general rules about dominance in ecological communities by linking dominance mathematically to the parameters of common theoretical species-abundance distributions (SADs). We found that if a community's SAD was log-series or lognormal, then dominance was almost inevitably high, with fewer than 40% of species required to account for 90% of all individuals. Dominance for communities with an exponential SAD was lower but still typically high, with fewer than 40% of species required to account for 70% of all individuals. In contrast, communities with a gamma SAD only exhibited high dominance when the average species abundance was below a threshold of approximately 100. Furthermore, we showed that exact values of dominance were highly scale-dependent, exhibiting non-linear trends with changing average species abundance. We also applied our formulae to SADs derived from a mechanistic community model to demonstrate how dominance can increase with environmental variance. Overall, our study provides a rigorous basis for theoretical explorations of the dynamics of dominance in ecological communities, and how this affects ecosystem functioning and stability., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

Biogeography seeks to understand the mechanisms that drive biodiversity across long temporal and large spatial scales. Theoretical models of biogeography can be tested by comparing their predictions of quantities such as species ages against empirical estimates. It has previously been claimed that the neutral theory of biodiversity and biogeography predicts species ages that are unrealistically long. Any improved theory of biodiversity must rectify this problem, but first it is necessary to quantify the problem precisely. Here we provide analytical expressions for species ages in neutral biodiversity communities. We analyse a spatially implicit metacommunity model and solve for both the zero-sum and non-zero-sum cases. We explain why our new expressions are, in the context of biodiversity, usually more appropriate than those previously imported from neutral molecular evolution. Because of the time symmetry of the spatially implicit neutral model, our expressions also lead directly to formulas for species persistence times and species lifetimes. We use our new expressions to estimate species ages of forest trees under a neutral model and find that they are about an order of magnitude shorter than those predicted previously but still unrealistically long. In light of our results, we discuss different models of biogeography that may solve the problem of species ages., (Copyright © 2014 Elsevier Inc. All rights reserved.)

Many problems in ecology require the estimation of rates of dispersal of individuals or propagules across physical boundaries. Such problems arise in invasion ecology, forest dynamics, and the neutral theory of biodiversity. In a forest plot, for example, one might ask what proportion of the seed rain originates from outside the plot. A recent study presented analytical approximations that relate the rate of immigration across a boundary to plot geometry and to the parameters of a dispersal kernel in one- and two-dimensional environments. In this study, we provide a more rigorous derivation of these expressions and we derive a more general expression that applies in environments of arbitrary dimension. We discuss potential applications of the one-, two-, and three-dimensional results to ecological problems.

The neutral theory of community ecology can predict diversity and abundances of tropical trees, but only under the assumption of steady input of new species into the community. Without input, diversity of a neutral community collapses, so the theory's predictions are not relevant unless novel species evolve or immigrate. We derive analytically the species input needed to maintain a target tree diversity, and find that a rate close to 1.0 x 10(-4) per recruit would maintain the observed diversity of 291 species in the Barro Colorado 50-ha tree plot in Panama. We then measured the rate empirically by comparing species present in one complete enumeration of the plot to those present five years later. Over six census intervals, the observed rate of input was 0.6 x 10(-4) to 1.8 x 10(-4) species per recruit, suggesting that there is adequate immigration of novel species to maintain diversity. Species interactions, niche partitioning, or density-dependence, while they may be present, do not appear to enhance tree species richness at Barro Colorado.

Previous research into the neutral theory of biodiversity has focused mainly on equilibrium solutions rather than time-dependent solutions. Understanding the time-dependent solutions is essential for applying neutral theory to ecosystems in which time-dependent processes, such as succession and invasion, are driving the dynamics. Time-dependent solutions also facilitate tests against data that are stronger than those based on static equilibrium patterns. Here I investigate the time-dependent solutions of the classic spatially implicit neutral model, in which a small local community is coupled to a much larger metacommunity through immigration. I present explicit general formulas for the eigenvalues, left eigenvectors and right eigenvectors of the models's transition matrix. The time-dependent solutions can then be expressed in terms of these eigenvalues and eigenvectors. Some of these results are translated directly from existing results for the classic Moran model of population genetics (the Moran model is equivalent to the spatially implicit neutral model after a reparameterization); others of the results are new. I demonstrate that the asymptotic time-dependent solution corresponding to just these first two eigenvectors can be a good approximation to the full time-dependent solution. I also demonstrate the feasibility of a partial eigendecomposition of the transition matrix, which facilitates direct application of the results to a biologically relevant example in which a newly invading species is initially present in the metacommunity but absent from the local community., (Copyright © 2011 Elsevier Inc. All rights reserved.)

A fundamental challenge in ecology is to understand the mechanisms that govern patterns of relative species abundance. Previous numerical simulations have suggested that complex niche-structured models produce species abundance distributions (SADs) that are qualitatively similar to those of very simple neutral models that ignore differences between species. However, in the absence of an analytical treatment of niche models, one cannot tell whether the two classes of model produce the same patterns via similar or different mechanisms. We present an analytical proof that, in the limit as diversity becomes large, a strong niche model give rises to exactly the same asymptotic form of SAD as the neutral model, and we verify the analytical predictions for a Panamanian tropical forest data set. Our results strongly suggest that neutral processes drive patterns of relative species abundance in high-diversity ecological communities, even when strong niche structure exists. However, neutral theory cannot explain what generates high diversity in the first place, and it may not be valid in low-diversity communities. Our results also confirm that neutral theory cannot be used to infer an absence of niche structure or to explain ecosystem function.

In the classic spatially implicit formulation of Hubbell's neutral theory of biodiversity a local community receives immigrants from a metacommunity operating on a relatively slow timescale, and dispersal into the local community is governed by an immigration parameter m. A current problem with neutral theory is that m lacks a clear biological interpretation. Here, we derive analytical expressions that relate the immigration parameter m to the geometry of the plot defining the local community and the parameters of a dispersal kernel. Our results facilitate more rigorous and extensive tests of the neutral theory: we conduct a test of neutral theory by comparing estimates of m derived from fits to empirical species abundance distributions to those derived from dispersal kernels and find acceptable correspondence; and we generate a new prediction of neutral theory by investigating how the shapes of species abundance distributions change theoretically as the spatial scale of observation changes. We also discuss how our main analytical results can be used to assess the error in the mean-field approximations associated with spatially implicit formulations of neutral theory.

Preston's classic work on the theory of species abundance distributions (SADs) in ecology has been challenged by Dewdney. Dewdney contends that Preston's veil-line concept, relating to the shape of sample SADs, is flawed. Here, I show that Preston's and Dewdney's theories can be reconciled by considering the differing mathematical properties of the sampling process on logarithmic (Preston) versus linear (Dewdney) abundance scales. I also derive several related results and show, importantly, that one cannot reject the log-normal distribution as a plausible SAD based only on sampling arguments, as Dewdney and others have done.

Numerous studies have shown reduced performance in plants that are surrounded by neighbours of the same species1,2, a phenomenon known as conspecific negative density dependence (CNDD)3. A long-held ecological hypothesis posits that CNDD is more pronounced in tropical than in temperate forests4,5, which increases community stabilization, species coexistence and the diversity of local tree species6,7. Previous analyses supporting such a latitudinal gradient in CNDD8,9 have suffered from methodological limitations related to the use of static data10-12. Here we present a comprehensive assessment of latitudinal CNDD patterns using dynamic mortality data to estimate species-site-specific CNDD across 23 sites. Averaged across species, we found that stabilizing CNDD was present at all except one site, but that average stabilizing CNDD was not stronger toward the tropics. However, in tropical tree communities, rare and intermediate abundant species experienced stronger stabilizing CNDD than did common species. This pattern was absent in temperate forests, which suggests that CNDD influences species abundances more strongly in tropical forests than it does in temperate ones13. We also found that interspecific variation in CNDD, which might attenuate its stabilizing effect on species diversity14,15, was high but not significantly different across latitudes. Although the consequences of these patterns for latitudinal diversity gradients are difficult to evaluate, we speculate that a more effective regulation of population abundances could translate into greater stabilization of tropical tree communities and thus contribute to the high local diversity of tropical forests.

Hyperdiverse tropical forest tree communities illustrate a fundamental problem in ecology: How can many species coexist given relatively few limiting resources? Neutral theory provides a solution by positing that species have equal fitness and hence drift to extinction slowly. However, neutral theory seriously under‐predicts temporal changes in species abundances. This can be remedied by breaking neutrality and adding temporal environmental stochasticity (TES), but the mechanisms mediating the effects of TES on species richness remain unclear. Here, we make progress by analysing a local community model with species competing for a common resource under TES, to derive formulae partitioning species richness according to different mechanisms.By applying our formulae to generic parameter sets for tropical forest tree communities, we found that when the autocorrelation time of TES was short, the dominant mechanism driving species richness was non‐linear averaging of the interspecific competition term over time, which reduced the typical strength of interspecific competition and boosted richness relative to the neutral case. However, greater immigration to the community resulted in more species and hence weaker non‐linear averaging due to the law of large numbers. In contrast, when the autocorrelation time of TES was long, the dominant mechanism driving species richness was strong selection between changes in environmental conditions, which increased the typical strength of interspecific competition and reduced richness relative to the neutral case.By applying our formulae to a specific parameter set for a tropical forest tree community in Panama, we found that TES had minor effects on species richness because (i) the immigration rate was sufficiently large for non‐linear averaging of the interspecific competition term to be weak and (ii) the autocorrelation time was sufficiently short to suppress the effects of selection.Synthesis. We provide a novel mechanistic explanation of how TES affects tree species richness in tropical forests, in particular how TES often has minor effects on richness despite having substantial effects on temporal changes in species abundances. This provides a deeper insight into why a neutral model with added TES can accurately capture static and dynamic aspects of tree community diversity in the tropics. [ABSTRACT FROM AUTHOR]

A long‐standing puzzle in ecology is coexistence of many species despite relatively few limiting resources. Studies using competitive community models have found that temporal environmental stochasticity (TES) can provide a solution by providing a rare‐species advantage, for example by creating temporal niches. However, this appears to contradict studies using population models, which have found that TES‐induced temporal fluctuations in species abundances increase the chance of species becoming rare and hence increase their extinction risk. Here, we clarified how TES affects species richness by analysing a competitive community model using a novel mean‐field approach. We found that when temporal correlation in TES was weak, the dominant effect of TES was to create temporal niches by decreasing the strength of interspecific competition via a temporal averaging effect, thereby increasing species richness relative to the neutral case without TES. In contrast, when temporal correlation was strong, the dominant effect of TES was to increase the strength of selection and hence interspecific competition, thereby decreasing species richness. Compared with these indirect community effects of TES, the direct effects of TES on species richness via temporal fluctuations in abundances of species populations were relatively minor. [ABSTRACT FROM AUTHOR]

Theoretical ecologists have analysed a range of neutral models but few including stage structure. Here we introduce a stage‐structured neutral model, by extending the standard spatial neutral model to have two‐stage classes: a juvenile stage and a reproductive stage. We find that formulas for biodiversity patterns (e.g. species–area relationships and species abundance distributions) of reproductives in the stage‐structured model can be obtained from the corresponding standard formulas via a parameter rescaling, which involves calculating an effective speciation rate parameter and an effective dispersal parameter. This is useful because it means existing knowledge about the non‐stage‐structured model can be transferred to the stage‐structured model, providing that applications focus exclusively on the reproductive stage. One surprising implication is that the presence of a juvenile stage can substantially increase the species richness of reproductive individuals: a juvenile stage with a length fraction k that of the reproductive stage increases reproductive species richness by roughly the same factor. We apply our new formulas to a case study of tropical forest trees in Panama and find that while the stage‐structured model makes different predictions than the standard model, it does not fix known problems with cross‐scale predictions. We speculate that some of our results, in particular the result that the presence of a juvenile stage increases community diversity, likely apply to non‐neutral systems as well. [ABSTRACT FROM AUTHOR]

Neutral theory proposes that some macroscopic biodiversity patterns can be explained in terms of drift, speciation and immigration, without invoking niches. There are many different varieties of neutral model, all assuming that the fitness of an individual is unrelated to its species identity. Variants that are spatially explicit provide a means for making quantitative predictions about spatial biodiversity patterns.We present software packages that make spatially explicit neutral simulations straightforward and efficient. The packages allow the user to customize both dispersal and landscape structure in a wide variety of ways. We provide a Python package pycoalescence and a functionally equivalent R package rcoalescence. In both packages, the core routines are written in C++ and make use of coalescence methods to optimize performance.We explain the technical details of the packages and give examples for their application, with a particular focus on two scenarios of ecological and evolutionary interest—a landscape with habitat fragmentation, and an archipelago of islands.Spatially explicit neutral models represent an important tool in ecology for understanding the processes of biodiversity generation and predicting outcomes at large scales. The effort required to implement these complex spatially explicit simulations efficiently has thus far been a barrier to entry. Our packages increase the accessibility of these models and encourage further investigation of the primary mechanisms underpinning biodiversity. [ABSTRACT FROM AUTHOR]

The relationship between species richness and productivity changes with spatial scale, but the way in which it changes and the underlying mechanisms remain unclear. We address this critical knowledge gap using a new mechanistic model of the spatial scaling of species richness–productivity (SP) relationships for a local community. Our model is neutral and hence assumes that species dynamics are driven by dispersal limitation and demographic stochasticity. We showed analytically that SP relationships predicted by our model are typically unimodal. Consistent with previous simulation-based studies, the positive phase of our unimodal SP relationship was driven by a sampling effect ("more-individuals effect") whereas the negative phase was driven by relatively more propagules being of local as opposed to external origin ("dilution effect"). Our main novel finding related to the spatial scaling of the unimodal SP relationship: the peak shifted to the left with increasing spatial scale, such that the decreasing phase covered a greater range of productivity. This was driven by an increase in the strength of the dilution effect relative to the more-individuals effect, reflecting higher area/perimeter ratios at larger spatial scales. Our theoretical predictions are qualitatively consistent with the spatial scaling of SP relationships documented for trees in localized forest communities across the world. [ABSTRACT FROM AUTHOR]

In a critique of our recent review on measuring habitat complexity in ecology, Madin et al. (2023) advocate the use of fractal dimension in ecology and defend their geometric constraint theory of habitat complexity. We explain the flaws in their arguments and highlight points where they misinterpreted our statements. [ABSTRACT FROM AUTHOR]

Habitat loss leads to species extinctions, both immediately and over the long term as 'extinction debt' is repaid. The same quantity of habitat can be lost in different spatial patterns with varying habitat fragmentation. How this translates to species loss remains an open problem requiring an understanding of the interplay between community dynamics and habitat structure across temporal and spatial scales. Here we develop formulas that characterise extinction debt in a spatial neutral model after habitat loss and fragmentation. Central to our formulas are two new metrics, which depend on properties of the taxa and landscape: 'effective area', measuring the remaining number of individuals and 'effective connectivity', measuring individuals' ability to disperse through fragmented habitat. This formalises the conventional wisdom that habitat area and habitat connectivity are the two critical requirements for long‐term preservation of biodiversity. Our approach suggests that mechanistic fragmentation metrics help resolve debates about fragmentation and species loss. [ABSTRACT FROM AUTHOR]

Species populations are subjected to fluctuations in their surrounding environment, and the strength of these fluctuations has been hypothesized to be a major determinant of the extinction risk of these populations. Therefore, a key question is: How does temporal environmental variance affect the extinction risk of species populations? Previous theory based on the dynamics of single populations typically predicts an increased risk of extinction from the effects of environmental variance. However, previous studies have focused mainly on the case where environmental effects are temporally uncorrelated (white environmental noise), whereas such effects are typically correlated (colored environmental noise) in nature. Thus, further work on the case of colored environmental noise is required, but this has been hindered by the analytical intractability of corresponding stochastic models. In our study, we address this limitation by developing a new discrete-time Markov chain model of a species population fluctuating under colored environmental noise, with the simplification that the effects of demographic variance are manifested indirectly as an extinction threshold. This simplifying assumption allows us to derive analytical solutions, which show that the expected extinction time of model species declines with the strength of environmental variance under a variety of different scenarios, reflecting greater extinction risk. Our study thus clarifies the situations under which environmental variance tends to increase extinction risk, and provides a novel analytically tractable framework for modeling temporal environmental variance. We also discuss the possible implications of our results for species richness in ecological communities. [ABSTRACT FROM AUTHOR]

Assessing the consequences of biodiversity changes for ecosystem functioning requires separating the net effect of biodiversity from potential confounding effects such as the identity of the gained or lost species. Additive partitioning methods allow factoring out these species identify effects by comparing species' functional contributions against the predictions of a null model under which functional contributions are independent of biodiversity., Classic additive partitioning methods quantify biodiversity effects based on a linear relationship between species deviations from the null model and their functional traits. However, based on ecological theory, nonlinear relationships are also possible., Here, we demonstrate how additive-partitioning methods can be extended to describe such nonlinear relationships, and explain how nonlinear biodiversity effects can be interpreted., We apply both linear and nonlinear partitioning methods to the Cedar Creek Biodiversity II experiment. Nonlinear relationships were detected in the majority of plots, and increased with diversity. Nonlinear partitioning thereby identified a convex relationship between species functional traits and their deviations from the null model, driven by strong positive effects of both species with low and high functional trait values trait values on ecosystem functioning., The presented nonlinear extension of additive partitioning methods is therefore essential for revealing more complex biodiversity effects on ecosystem functioning, that are likely to occur in biodiversity experiments. [ABSTRACT FROM AUTHOR]

MacArthur and Wilson's theory of island biogeography predicts that island species richness should increase with island area. This prediction generally holds among large islands, but among small islands species richness often varies independently of island area, producing the so-called 'small-island effect' and an overall biphasic species-area relationship (SAR). Here, we develop a unified theory that explains the biphasic island SAR. Our theory's key postulate is that as island area increases, the total number of immigrants increases faster than niche diversity. A parsimonious mechanistic model approximating these processes reproduces a biphasic SAR and provides excellent fits to 100 archipelago datasets. In the light of our theory, the biphasic island SAR can be interpreted as arising from a transition from a niche-structured regime on small islands to a colonization-extinction balance regime on large islands. The first regime is characteristic of classic deterministic niche theories; the second regime is characteristic of stochastic theories including the theory of island biogeography and neutral theory. The data furthermore confirm our theory's key prediction that the transition between the two SAR regimes should occur at smaller areas, where immigration is stronger (i.e. for taxa that are better dispersers and for archipelagos that are less isolated). [ABSTRACT FROM AUTHOR]

The compositional complexity of an assemblage is not expressible as a single number; standard measures such as diversities (Hill numbers) and entropies (Rényi entropies and Tsallis entropies) vary in their order q which determines the measures' emphasis on rare or common species. Ranking and comparing assemblages depend on the choice of q. Rather than selecting one or a few measures to describe an assemblage, it is preferable to convey the complete story by presenting a continuous profile, a plot of diversity or entropy as a function of q ≥ 0. This makes it easy to visually compare the compositional complexities of multiple assemblages and to judge the evenness of the relative abundance distributions of the assemblages. In practice, the profile is plotted for all values of q from 0 to q = 3 or 4 (beyond which it generally changes little)., These profiles are usually generated by substituting species sample proportions into the complexity measures. However, this empirical approach typically underestimates the true profile for low values of q, because samples usually miss some of the assemblage's species due to under-sampling. Although bias-reduction methods exist for individual measures of order q = 0, 1 and 2, there has been no analytic method that unifies these bias-corrected estimates into a continuous profile., For incomplete sampling data, this work proposes a novel analytic method to obtain accurate, continuous, low-bias diversity and entropy profiles with focus on low orders of q (0 ≤ q ≤ 3). Our approach is based on reformulating the diversity and entropy of any order q in terms of the successive discovery rates of new species with respect to sample size, that is the successive slopes of the species accumulation curve. A bootstrap method is applied to obtain approximate variances of our proposed profiles and to construct the associated confidence intervals., Extensive simulations from theoretical models and real surveys show that the proposed profiles greatly reduce under-sampling bias and have substantially lower bias and mean-squared error than the empirical profile, especially for q ≤ 1. Our method is also extended to deal with incidence data. [ABSTRACT FROM AUTHOR]

The α-, β-, γ-diversity decomposition methodology is commonly used to investigate changes in diversity over space or time but rarely conjointly. However, with the ever-increasing availability of large-scale biodiversity monitoring data, there is a need for a sound methodology capable of simultaneously accounting for spatial and temporal changes in diversity., Using the properties of Chao's index, we adapted Rao's framework of diversity decomposition between orthogonal dimensions to a multiplicative α-, β-, γ-decomposition of functional or phylogenetic diversity over space and time, thereby combining their respective properties. We also developed guidelines for interpreting both temporal and spatial β-diversities and their interaction., We characterized the range of β-diversity estimates and their relationship to the nested decomposition of diversity. Using simulations, we empirically demonstrated that temporal and spatial β-diversities are independent from each other and from α- and γ-diversities when the study design is balanced, but not otherwise. Furthermore, we showed that the interaction term between the temporal and the spatial β-diversities lacked such properties., We illustrated our methodology with a case study of the spatio-temporal dynamics of functional diversity in bird assemblages in four regions of France. Based on these data, our method makes it possible to discriminate between regions experiencing different diversity changes in time. Our methodology may therefore be valuable for comparing diversity changes over space and time using large-scale data sets of repeated surveys. [ABSTRACT FROM AUTHOR]

Individual species are distributed inhomogeneously over space and time, yet, within large communities of species, aggregated patterns of biodiversity seem to display nearly universal behaviour. Neutral models assume that an individual's demographic prospects are independent of its species identity. They have successfully predicted certain static, time-independent patterns. But they have generally failed to predict temporal patterns, such as species ages or population dynamics. We construct a new, multispecies framework incorporating competitive differences between species, and assess the impact of this competition on static and dynamic patterns of biodiversity. We solve this model exactly for the special case of a Red Queen hypothesis, where fitter species are continually arising. The model predicts more realistic species ages than neutral models, without greatly changing predictions for static species abundance distributions. Our modelling approach may allow users to incorporate a broad range of ecological mechanisms. [ABSTRACT FROM AUTHOR]

Long-term surveys of entire communities of species are needed to measure fluctuations in natural populations and elucidate the mechanisms driving population dynamics and community assembly. We analysed changes in abundance of over 4000 tree species in 12 forests across the world over periods of 6-28 years. Abundance fluctuations in all forests are large and consistent with population dynamics models in which temporal environmental variance plays a central role. At some sites we identify clear environmental drivers, such as fire and drought, that could underlie these patterns, but at other sites there is a need for further research to identify drivers. In addition, cross-site comparisons showed that abundance fluctuations were smaller at species-rich sites, consistent with the idea that stable environmental conditions promote higher diversity. Much community ecology theory emphasises demographic variance and niche stabilisation; we encourage the development of theory in which temporal environmental variance plays a central role. [ABSTRACT FROM AUTHOR]

The relationship between species richness and ecosystem function, as measured by productivity or biomass, is of long-standing theoretical and practical interest in ecology. This is especially true for forests, which represent a majority of global biomass, productivity and biodiversity., Here, we conduct an analysis of relationships between tree species richness, biomass and productivity in 25 forest plots of area 8-50 ha from across the world. The data were collected using standardized protocols, obviating the need to correct for methodological differences that plague many studies on this topic., We found that at very small spatial grains (0.04 ha) species richness was generally positively related to productivity and biomass within plots, with a doubling of species richness corresponding to an average 48% increase in productivity and 53% increase in biomass. At larger spatial grains (0.25 ha, 1 ha), results were mixed, with negative relationships becoming more common. The results were qualitatively similar but much weaker when we controlled for stem density: at the 0.04 ha spatial grain, a doubling of species richness corresponded to a 5% increase in productivity and 7% increase in biomass. Productivity and biomass were themselves almost always positively related at all spatial grains., Synthesis. This is the first cross-site study of the effect of tree species richness on forest biomass and productivity that systematically varies spatial grain within a controlled methodology. The scale-dependent results are consistent with theoretical models in which sampling effects and niche complementarity dominate at small scales, while environmental gradients drive patterns at large scales. Our study shows that the relationship of tree species richness with biomass and productivity changes qualitatively when moving from scales typical of forest surveys (0.04 ha) to slightly larger scales (0.25 and 1 ha). This needs to be recognized in forest conservation policy and management. [ABSTRACT FROM AUTHOR]

Carbon credits are a potential source of funding for restoration initiatives that contribute to achieving conservation targets in important biodiversity areas. Here we investigated whether fallowing sequesters carbon; a first step in assessing the viability of using carbon financing to promote restoration of threatened vegetation in agricultural landscapes. We used renosterveld, a critically endangered shrubland vegetation of the Cape Floristic Region, as a case study. Carbon stocks of soil and biomass in active fields, fallow fields and intact renosterveld were compared. The total carbon stocks measured in fallow fields (82 Mg C ha−1) show that fallowing can sequester carbon lost in the conversion from intact renosterveld (84 Mg C ha−1) to active fields (69 Mg C ha−1) and that revenues of US$ 10 - 48 ha−1 yr−1 from carbon credits could accrue. Our findings suggest that carbon financing could be used to incentivise ecological restoration in marginal agricultural landscapes. [ABSTRACT FROM AUTHOR]

This article discusses various issues related to the unified neutral theory of biodiversity and biogeography. The unified neutral theory of biodiversity and biogeography is a formal mathematical theory that seeks to explain observed patterns of relative species abundance (RSA) and species richness in ecological communities. The unified theory is developed by incorporating a speciation rate into the classical theory of island biogeography. Simulations of the theory's dynamics have to date suggested that at equilibrium the local community RSA distribution has a particular lognormal-like shape, one that is commonly observed in natural communities.