Pattern detection in null model analysis

Synthesis The identification of distinctive patterns in species x site presence-absence matrices is important for understanding meta-community organisation. We compared the performance of a suite of null models and metrics that have been proposed to measure patterns of segregation, aggregation, nestedness, coherence, and species turnover. We found that any matrix with segregated species pairs can be re-ordered to highlight aggregated pairs, indicating that these seemingly opposite patterns are closely related. Recently proposed classification schemes failed to correctly classify realistic matrices that included multiple co-occurrence structures. We propose using a combination of metrics and decomposing matrix-wide patterns into those of individual pairs of species and sites to pinpoint sources of non-randomness. Null model analysis has been a popular tool for detecting pattern in binary presence-absence matrices, and previous tests have identified algorithms and metrics that have good statistical properties. However, the behavior of different metrics is often correlated, making it difficult to distinguish different patterns. We compared the performance of a suite of null models and metrics that have been proposed to measure patterns of segregation, aggregation, nestedness, coherence, and species turnover. We found that any matrix with segregated species pairs can be re-ordered to highlight aggregated pairs. As a consequence, the same null model can identify a single matrix as being simultaneously aggregated, segregated or nested. These results cast doubt on previous conclusions of matrix-wide species segregation based on the C-score and into those of individual pairs of species or pairs of sites to pinpoint the sources of non-randomness. © 2012 The Authors. Oikos © 2012 Nordic Society Oikos

Null model analysis of species associations using abundance data

The influence of negative species interactions has dominated much of the literature on community assembly rules. Patterns of negative covariation among species are typically documented through null model analyses of binary presence/absence matrices in which rows designate species, columns designate sites, and the matrix entries indicate the presence (1) or absence (0) of a particular species in a particular site. However, the outcome of species interactions ultimately depends on population-level processes. Therefore, patterns of species segregation and aggregation might be more clearly expressed in abundance matrices, in which the matrix entries indicate the abundance or density of a species in a particular site. We conducted a series of benchmark tests to evaluate the performance of 14 candidate null model algorithms and six covariation metrics that can be used with abundance matrices. We first created a series of random test matrices by sampling a metacommunity from a lognormal species abundance distribution. We also created a series of structured matrices by altering the random matrices to incorporate patterns of pairwise species segregation and aggregation. We next screened each algorithm-index combination with the random and structured matrices to determine which tests had low Type I error rates and good power for detecting segregated and aggregated species distributions. In our benchmark tests, the best-performing null model does not constrain species richness, but assigns individuals to matrix cells proportional to the observed row and column marginal distributions until, for each row and column, total abundances are reached. Using this null model algorithm with a set of four covariance metrics, we tested for patterns of species segregation and aggregation in a collection of 149 empirical abundance matrices and 36 interaction matrices collated from published papers and posted data sets. More than 80% of the matrices were significantly segregated, which reinforces a previous meta-analysis of presence/absence matrices. However, using two of the metrics we detected a significant pattern of aggregation for plants and for the interaction matrices (which include plant-pollinator data sets). These results suggest that abundance matrices, analyzed with an appropriate null model, may be a powerful tool for quantifying patterns of species segregation and aggregation. © 2010 by the Ecological Society of America

Energetics and the evolution of carnivorous plants - Darwin's "most wonderful plants in the world"

Carnivory has evolved independently at least six times in five angiosperm orders. In spite of these independent origins, there is a remarkable morphological convergence of carnivorous plant traps and physiological convergence of mechanisms for digesting and assimilating prey. These convergent traits have made carnivorous plants model systems for addressing questions in plant molecular genetics, physiology, and evolutionary ecology. New data show that carnivorous plant genera with morphologically complex traps have higher relative rates of gene substitutions than do those with simple sticky traps. This observation suggests two alternative mechanisms for the evolution and diversification of carnivorous plant lineages. The “energetics hypothesis” posits rapid morphological evolution resulting from a few changes in regulatory genes responsible for meeting the high energetic demands of active traps. The “predictable prey capture hypothesis” further posits that complex traps yield more predictable and frequent prey captures. To evaluate these hypotheses, available data on the tempo and mode of carnivorous plant evolution were reviewed; patterns of prey capture by carnivorous plants were analyzed; and the energetic costs and benefits of botanical carnivory were reevaluated. Collectively, the data are more supportive of the energetics hypothesis than the predictable prey capture hypothesis. The energetics hypothesis is consistent with a phenomenological cost-benefit model for the evolution of botanical carnivory and also accounts for data suggesting that carnivorous plants have leaf construction costs and scaling relationships among leaf traits that are substantially different from non-carnivorous plants.Organismic and Evolutionary BiologyOther Research Uni

Statistical challenges in null model analysis

This review identifies several important challenges in null model testing in ecology: 1) developing randomization algorithms that generate appropriate patterns for a specified null hypothesis; these randomization algorithms stake out a middle ground between formal Pearson-Neyman tests (which require a fully-specified null distribution) and specific process-based models (which require parameter values that cannot be easily and independently estimated); 2) developing metrics that specify a particular pattern in a matrix, but ideally exclude other, related patterns; 3) avoiding classification schemes based on idealized matrix patterns that may prove to be inconsistent or contradictory when tested with empirical matrices that do not have the idealized pattern; 4) testing the performance of proposed null models and metrics with artificial test matrices that contain specified levels of pattern and randomness; 5) moving beyond simple presence-absence matrices to incorporate species-level traits (such as abundance) and site-level traits (such as habitat suitability) into null model analysis; 6) creating null models that perform well with many sites, many species pairs, and varying degrees of spatial autocorrelation in species occurrence data. In spite of these challenges, the development and application of null models has continued to provide valuable insights in ecology, evolution, and biogeography for over 80 years. © 2011 The Authors. Oikos © 2012 Nordic Society Oikos

Food-Web Models Predict Species Abundances in Response to Habitat Change

Plant and animal population sizes inevitably change following habitat loss, but the mechanisms underlying these changes are poorly understood. We experimentally altered habitat volume and eliminated top trophic levels of the food web of invertebrates that inhabit rain-filled leaves of the carnivorous pitcher plant Sarracenia purpurea. Path models that incorporated food-web structure better predicted population sizes of food-web constituents than did simple keystone species models, models that included only autecological responses to habitat volume, or models including both food-web structure and habitat volume. These results provide the first experimental confirmation that trophic structure can determine species abundances in the face of habitat loss.Organismic and Evolutionary Biolog

The effects of climate change on density-dependent population dynamics of aquatic invertebrates

Global climate change has the potential to alter aquatic communities through changes in evapotranspiration and increased variability in precipitation. We used aquatic mesocosms to test the impacts of variable precipitation on population dynamics of commonn mosquito (Culicidae) and midge (Chironomidae) larvae that inhabit vernal pools. In a mixed deciduous forest in northern Vermont, USA, we orthogonally crossed seven levels of mean water level (increased rainfall) with seven levels of water level coefficient of variation (more variable rainfall) to simulate a broad array of climate change scenarios in 49 experimental mesocosms. The average abundance of Culicidae was highest at low water levels, whereas the average abundance of Chironomidae was highest at higher water levels and low variability in water level. Treatments and environmental and spatial covariates collectively explained 49% of the variance in mean abundance. For both taxa, we fit hierarchical Bayesian models to each 16-week time series to estimate the parameters in a Gompertz logistic equation of population growth with density dependence. We found that Culicidae population growth rate increased with decreasing water levels and that 87% of the variance in Chironomidae density dependence could be explained by treatment. Collectively, these results suggest that climate change can alter abundances aquatic invertebrate taxa but not necessarily through the same mechanism on all populations. In the case of Culicidae the abundance is affected by changes in growth rate, and in Chironomidae by changes in the strength of density dependence. © 2011 The Authors. Oikos © 2011 Nordic Society Oikos

Water quality improvements offset the climatic debt for stream macroinvertebrates over twenty years

Many species are accumulating climatic debt as they fail to keep pace with increasing global temperatures. In theory, concomitant decreases in other stressors (e.g. pollution, fragmentation) could offset some warming effects, paying climatic debt with accrued environmental credit. This process may be occurring in many western European rivers. We fit a Markov chain model to ~20,000 macroinvertebrate samples from England and Wales, and demonstrate that despite large temperature increases 1991–2011, macroinvertebrate communities remained close to their predicted equilibrium with environmental conditions. Using a novel analysis of multiple stressors, an accumulated climatic debt of 0.64 (±0.13 standard error) °C of warming was paid by a water-quality credit equivalent to 0.89 (±0.04)°C of cooling. Although there is finite scope for mitigating additional climate warming in this way, water quality improvements appear to have offset recent temperature increases, and the concept of environmental credit may be a useful tool for communicating climate offsetting

Bi-dimensional null model analysis of presence-absence binary matrices

Ecology, published by Wiley Periodicals, Inc., on behalf of the Ecological Society of America. Comparing the structure of presence/absence (i.e., binary) matrices with those of randomized counterparts is a common practice in ecology. However, differences in the randomization procedures (null models) can affect the results of the comparisons, leading matrix structural patterns to appear either “random” or not. Subjectivity in the choice of one particular null model over another makes it often advisable to compare the results obtained using several different approaches. Yet, available algorithms to randomize binary matrices differ substantially in respect to the constraints they impose on the discrepancy between observed and randomized row and column marginal totals, which complicates the interpretation of contrasting patterns. This calls for new strategies both to explore intermediate scenarios of restrictiveness in-between extreme constraint assumptions, and to properly synthesize the resulting information. Here we introduce a new modeling framework based on a flexible matrix randomization algorithm (named the “Tuning Peg” algorithm) that addresses both issues. The algorithm consists of a modified swap procedure in which the discrepancy between the row and column marginal totals of the target matrix and those of its randomized counterpart can be “tuned” in a continuous way by two parameters (controlling, respectively, row and column discrepancy). We show how combining the Tuning Peg with a wise random walk procedure makes it possible to explore the complete null space embraced by existing algorithms. This exploration allows researchers to visualize matrix structural patterns in an innovative bi-dimensional landscape of significance/effect size. We demonstrate the rational and potential of our approach with a set of simulated and real matrices, showing how the simultaneous investigation of a comprehensive and continuous portion of the null space can be extremely informative, and possibly key to resolving longstanding debates in the analysis of ecological matrices

Statistical challenges in null model analysis.

This review identifies several important challenges in null model testing in ecology: 1) developing randomization algorithms that generate appropriate patterns for a specified null hypothesis; these randomization algorithms stake out a middle ground between formal Pearson-Neyman tests (which require a fully-specified null distribution) and specific process-based models (which require parameter values that cannot be easily and independently estimated); 2) developing metrics that specify a particular pattern in a matrix, but ideally exclude other, related patterns; 3) avoiding classification schemes based on idealized matrix patterns that may prove to be inconsistent or contradictory when tested with empirical matrices that do not have the idealized pattern; 4) testing the performance of proposed null models and metrics with artificial test matrices that contain specified levels of pattern and randomness; 5) moving beyond simple presence-absence matrices to incorporate species-level traits (such as abundance) and site-level traits (such as habitat suitability) into null model analysis; 6) creating null models that perform well with many sites, many species pairs, and varying degrees of spatial autocorrelation in species occurrence data. In spite of these challenges, the development and application of null models has continued to provide valuable insights in ecology, evolution, and biogeography for over 80 years. 'A null model is a pattern generating model that is based on randomization of ecological data or random sampling from a known or imagined distribution. The null model is designed with respect to some ecological or evolutionary process of interest'. (Gotelli and Graves 1996) From its origins in the analysis of species/genus ratios Hypothesis testing and constraints in null model analysis Classical Pearson-Neyman hypothesis testing The null hypothesis varies depending on the details of the test, but it is often a parsimonious expectation that the data are drawn from a single distribution, so that any patterns in the data arise only from random sampling processes. The alternative hypothesis is that patterns in the data are not the result of random variation generated by H 0 . Erroneous rejection of H 0 occurs with probability a and represents a type I statistical error. Conversely, erroneous acceptance of a false null hypothesis is a type II error and occurs with probability b. The quantity 1 -b is the power of the test, the probability of correctly rejecting H 0 given that it is false In ecological null model analysis, 'Null hypotheses entertain the possibility that nothing has happened, that a process has not occurred, or that change has not been produced by a cause of interest&apos