A global envelope test to detect early and late bursts of trait evolution

The joint analysis of species’ evolutionary relatedness and their morphological evolution has offered much promise in understanding the processes that underpin the generation of biological diversity. Disparity through time (DTT) is a popular method that estimates the relative trait disparity within and between subclades at each time point, and compares this to the null hypothesis that trait values follow an uncorrelated random walk along the time calibrated phylogenetic tree. A simulation envelope is normally created by calculating, at every time point, the 95% minimum and 95% maximum disparity values from multiple simulations of the null model on the phylogenetic tree. The null hypothesis is rejected whenever the empirical DTT curve falls outside of this envelope, and these time periods may then be linked to events that may have sparked non-random trait evolution. However, this method of envelope construction leads to multiple testing and a poor, uncontrolled, false positive rate. As a consequence it cannot be recommended. A recently developed method in spatial statistics is introduced that constructs a confidence envelope by giving each DTT curve a single ranking value based upon its most extreme disparity value. This method avoids the pitfalls of multiple testing whilst retaining a visual interpretation. Results using simulated data show this new test has desirable type 1 properties and is at least as powerful in correctly rejecting the null hypothesis as the morphological disparity index and node height test that lack a visual interpretation. Three example datasets are reanalyzed to show how the new test may lead to different inferences being drawn. Overall the results suggest the new rank envelope test should be used in null model testing for DTT analyses, and that there is no need to combine the envelope test with other tests such as has been done previously. Moreover, the rank envelope method can easily be adopted into recently developed posterior predictive simulation methods. More generally, the rank envelope test should be adopted when-ever a null model produces a vector of correlated values and the user wants to determine where the empirical data is different to the null model

A method to detect sub-communities from multivariate spatial associations

1.Species are seldom distributed randomly across a community, but instead show spatial structure that is determined by environmental gradients and/or biotic interactions. Analysis of the spatial co-associations of species may therefore reveal information on the processes that helped to shape those patterns. 2.We propose a multivariate approach that uses the spatial co-associations between all pairs of species to find sub-communities of species whose distribution in the study area are positively correlated. Our method, which begins with the patterns of individuals, is particularly well-suited for communities with large numbers of species, and gives rare species an equal weight. We propose a method to quantify a maximum number of sub-communities that are significantly more correlated than expected under a null model of independence. 3.Using data on the distribution of tree and shrub species from a 50 ha forest plot on Barro Colorado Island (BCI), Panama, we show that our method can be used to construct biologically meaningful sub-communities that are linked to the spatial structure of the plant community. As an example, we construct spatial maps from the sub-communities that closely follow habitats based on environmental gradients (such as slope) as well as different biotic conditions (such as canopy gaps). 4.We discuss extensions and adaptations to our method that might be appropriate for other types of spatially referenced data and for other ecological communities. We make suggestions for other ways to interpret the sub-communities using phylogenetic relationships, biological traits, and environmental variables as covariates, and note that sub-communities that are hard to interpret may suggest groups of species and/or regions of the landscape that warrant further attention

Are Urban Communities in Successional Stasis? A Case Study on Epiphytic Lichen Communities

Urban areas may contain a wide range of potential habitats and environmental gradients and, given the many benefits to human health and well-being, there is a growing interest in maximizing their biodiversity potential. However, the ecological patterns and processes in urban areas are poorly understood. Using a widely applicable ecological survey method, we sampled epiphytic lichen communities, important bioindicators of atmospheric pollution, on host Quercus trees in urban parks of London, UK, to test if common patterns relating to lichen diversity are mirrored in urban green spaces. We found lichen diversity to be dependent on host species identity, and negatively related to local tree crowding. In addition, we found a strong negative effect of tree size on lichen diversity, leaving large trees as unexploited niches. A novel network analysis revealed the presence of only pioneer communities, showing the lichen communities are being held in successional stasis, likely due to the heritage effects of SO2 emissions and current nitrogen pollution and particulate emissions. Our study highlights that jointly assessing species richness, community structure and the successional stage can be key to understanding diversity patterns in urban ecosystems. Subsequently, this may help best determine the optimum conditions that will facilitate biodiversity increase within cities

A global envelope test to detect non‐random bursts of trait evolution

1.: The joint analysis of species’ evolutionary relatedness and their morphological evolution has offered much promise in understanding the processes that underpin the generation of biological diversity. 2.: Disparity through time (DTT) is a popular method that estimates the relative trait disparity within and between subclades, and compares this to the null hypothesis that trait values follow Brownian evolution along the time‐calibrated phylogenetic tree. To visualise the differences a confidence envelope is normally created by calculating, at every time point, the 97.5% minimum and 97.5% maximum disparity values from multiple simulations of the null model. The null hypothesis is rejected whenever the empirical DTT curve falls outside of this envelope, and these time periods may then be linked to events that may have sparked non‐random trait evolution. 3.: Here, simulated data are used to show this pointwise (ranking at each time point) method of envelope construction suffers from multiple testing and a poor, uncontrolled, false‐positive rate. As a consequence it cannot be recommended. Instead, each DTT curve can be given a single rank based upon their most extreme disparity value, relative to all other curves, and across all time points. Ordering curves this way leads to a test that avoids multiple testing, but still allows construction of a confidence envelope. The null hypothesis is rejected if the empirical DTT curve is ranked within the most extreme 5% ranked curves from the null model. Comparison of the rank envelope curve to the Morphological Disparity Index and Node Height tests shows it to have generally higher power to detect non‐Brownian trait evolution. An extension to allow simultaneous testing over multiple traits is also detailed. 4.: Overall the results suggest the new rank envelope test should be used in null model testing for DTT analyses. The rank envelope method can easily be adapted into recently developed posterior predictive simulation methods used in model selection analyses. More generally, the rank envelope test should be adopted whenever a null model produces a vector of correlated values and the user wants to determine where the empirical data are different to the null model

What is the Fourier Transform of a Spatial Point Process?

This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier transform, and what are its spectral moments, second we calculate fourth order moments of the Fourier transform using Campbell’s theorem. Third we determine how to implement tapering, an important component for spectral analysis of other stochastic processes. Fourth we answer the question of how to produce an isotropic representation of the Fourier transform of the process. This determines the basic spectral properties of an observed spatial point process

Visualizing the Wavenumber Content of a Point Pattern

Spatial point patterns are a commonly recorded form of data in ecology, medicine, astronomy, criminology, epidemiology and many other application fields. One way to understand their second order dependence structure is via their spectral density function. However, unlike time series analysis, for point patterns such approaches are currently underutilized. In part, this is because the interpretation of the spectral representation of the underlying point processes is challenging. In this paper, we demonstrate how to band-pass filter point patterns, thus enabling us to explore the spectral representation of point patterns in space by isolating the signal corresponding to certain sets of wavenumbers

Classifying ecosystem stressor interactions: Theory highlights the data limitations of the additive null model and the difficulty in revealing ecological surprises

Understanding how multiple co-occurring environmental stressors combine to affect biodiversity and ecosystem services is an on-going grand challenge for ecology. Currently, progress has been made through accumulating large numbers of smaller-scale empirical studies that are then investigated by meta-analyses to detect general patterns. There is particular interest in detecting, understanding and predicting ‘ecological surprises’ where stressors interact in a non-additive (e.g. antagonistic or synergistic) manner, but so far few general results have emerged. However, the ability of the statistical tools to recover non-additive interactions in the face of data uncertainty is unstudied, so crucially, we do not know how well the empirical results reflect the true stressor interactions. Here, we investigate the performance of the commonly implemented additive null model. A meta-analysis of a large (545 interactions) empirical dataset for the effects of pairs of stressors on freshwater communities reveals additive interactions dominate individual studies, whereas pooling the data leads to an antagonistic summary interaction class. However, analyses of simulated data from food chain models, where the underlying interactions are known, suggest both sets of results may be due to observation error within the data. Specifically, we show that the additive null model is highly sensitive to observation error, with non-additive interactions being reliably detected at only unrealistically low levels of data uncertainty. Similarly, plausible levels of observation error lead to meta-analyses reporting antagonistic summary interaction classifications even when synergies co-dominate. Therefore, while our empirical results broadly agree with those of previous freshwater meta-analyses, we conclude these patterns may be driven by statistical sampling rather than any ecological mechanisms. Further investigation of candidate null models used to define stressor-pair interactions is essential, and once any artefacts are accounted for, the so-called ‘ecological surprises’ may be more frequent than was previously assumed

Disentangling the historical routes to community assembly in the global epicentre of biodiversity

Aim: The exceptional turnover in biota with elevation and number of species coexisting at any elevation makes tropical mountains hotspots of biodiversity. However, understanding the historical processes through which species arising in geographical isolation (i.e. allopatry) assemble along the same mountain slope (i.e. sympatry) remains a major challenge. Multiple models have been proposed including (1) the sorting of already elevationally divergent species, (2) the displacement of elevation upon secondary contact, potentially followed by convergence, or (3) elevational conservatism, in which ancestral elevational ranges are retained. However, the relative contribution of these processes to generating patterns of elevational overlap and turnover is unknown. / Location: Tropical mountains of Central- and South-America. / Time Period: The last 12 myr. / Major Taxa Studied: Birds. / Methods: We collate a dataset of 165 avian sister pairs containing estimates of phylogenetic age, geographical and regional elevational range overlap. We develop a framework based on continuous-time Markov models to infer the relative frequency of different historical pathways in explaining present-day overlap and turnover of sympatric species along elevational gradients. / Results: We show that turnover of closely related bird species across elevation can predominantly be explained by displacement of elevation ranges upon contact (81%) rather than elevational divergence in allopatry (19%). In contrast, overlap along elevation gradients is primarily (88%) explained by conservatism of elevational ranges rather than displacement followed by elevational expansion (12%). Main / Conclusions: Bird communities across elevation gradients are assembled through a mix of processes, including the sorting, displacement and conservatism of species elevation ranges. The dominant role of conservatism in explaining co-occurrence of species on mountain slopes rejects more complex scenarios requiring displacement followed by expansion. The ability of closely related species to coexist without elevational divergence provides a direct and faster pathway to sympatry and helps explain the exceptional species richness of tropical mountains

When do we have the power to detect biological interactions in spatial point patterns

Uncovering the roles of biotic interactions in assembling and maintaining species‐rich communities remains a major challenge in ecology. In plant communities, interactions between individuals of different species are expected to generate positive or negative spatial interspecific associations over short distances. Recent studies using individual‐based point pattern datasets have concluded that (a) detectable interspecific interactions are generally rare, but (b) are most common in communities with fewer species; and (c) the most abundant species tend to have the highest frequency of interactions. However, it is unclear how the detection of spatial interactions may change with the abundances of each species, or the scale and intensity of interactions. We ask if statistical power is sufficient to explain all three key results. We use a simple two‐species model, assuming no habitat associations, and where the abundances, scale and intensity of interactions are controlled to simulate point pattern data. In combination with an approximation to the variance of the spatial summary statistics that we sample, we investigate the power of current spatial point pattern methods to correctly reject the null model of pairwise species independence. We show the power to detect interactions is positively related to both the abundances of the species tested, and the intensity and scale of interactions, but negatively related to imbalance in abundances. Differences in detection power in combination with the abundance distributions found in natural communities are sufficient to explain all the three key empirical results, even if all pairwise interactions are identical. Critically, many hundreds of individuals of both species may be required to detect even intense interactions, implying current abundance thresholds for including species in the analyses are too low. Synthesis. The widespread failure to reject the null model of spatial interspecific independence could be due to low power of the tests rather than any key biological process. Since we do not model habitat associations, our results represent a first step in quantifying sample sizes required to make strong statements about the role of biotic interactions in diverse plant communities. However, power should be factored into analyses and considered when designing empirical studies

Quantifying drivers of supplementary food use by a reintroduced, critically endangered passerine to inform management and habitat restoration

The provision of supplementary food is widely used in the management of endangered species. Typically, food is provided ad libitum and often without a planned exit strategy, which can be costly. The role supplementary food plays within population demography can be challenging to identify and therefore any reduction must be carefully considered to avoid negative impacts. Here we investigate the role supplementary food plays within a reintroduced population of a Critically Endangered passerine species by quantifying its use alongside intrinsic and extrinsic factors. Specifically, we illustrate how the provision of supplementary food could be refined in response to breeding stage and the time of food provisioning and, via habitat restoration, create a long-term exit strategy based on influential plant species. The consumption of supplementary food increases during energetically expensive phases of the breeding cycle, during the morning provision of food and when natural plant resource availability is low. We also show a pattern whereby supplementary food could act as a buffer during periods of low natural resource availability during breeding. Based on these findings short-term management could take a reactive approach; refining supplementary food supply in response to breeding stages of pairs and potentially removing the provision of food in the afternoon. In the long-term key plant species, found to correlate with a decrease in supplementary food consumption, could be incorporated into habitat restoration efforts which could create a continuous natural food supply and contribute to creating a self-sustaining population and a potential exit strategy