Predictions Of Maximum Entropy Theory Of Ecology Research Articles

Land use change through the lens of macroecology: insights from Azorean arthropods and the maximum entropy theory of ecology

Human activity and land management practices, in particular land use change, have resulted in the global loss of biodiversity. These types of disturbance affect the shape of macroecological patterns, and therefore analyzing these patterns can provide insights into how ecosystems are affected by land use change. We here use arthropod census data from 96 sites at Terceira Island in the Azores archipelago across four different land uses of increasing management intensity: native forest, exotic forest, semi‐natural pasture and intensive pasture, to examine the effects of land use type on three macroecological patterns: the species abundance distribution, the metabolic rate distribution of individuals and the species–area relationship. The maximum entropy theory of ecology (METE) has successfully predicted these patterns across habitats and taxa in undisturbed ecosystems, and thus provides a null expectation for their shapes. Across these patterns, we find that the forest habitats are the best fit by METE predictions, while the semi‐natural pasture is consistently the worst fit, and the intensive pasture is intermediately well fit. We show that the direction of failure of the METE predictions at the pasture sites is likely due to the hyper‐dominance of introduced spider species present there. We hypothesize that the particularly poor fit for the semi‐natural pasture is due to the mix of arthropod communities out of equilibrium, leading to greater heterogeneity in composition and complex dynamics that violate METE's assumption of static state variables. The comparative better fit for the intensive pasture plausibly results from more homogeneous arthropod communities that are well adapted to intensive management, and thus whose state variables are less in flux. Analyzing deviations from theoretical predictions across land use type provides useful information about how land use and disturbance affect ecosystems, and such comparisons could be useful across other habitats and taxa.

Disturbance macroecology: a comparative study of community structure metrics in a high‐severity disturbance regime

AbstractMacroecological studies have established widespread patterns of species diversity and abundance in ecosystems but have generally restricted their scope to relatively steady‐state systems. As a result, how macroecological metrics are expected to scale in ecosystems that experience natural disturbance regimes is unknown. We examine macroecological patterns in a fire‐dependent forest of Bishop pine (Pinus muricata). We target two different‐aged stands in a stand‐replacing fire regime: a mature stand with a diverse understory and with no history of major disturbance for at least 40 yr, and one disturbed by a stand‐replacing fire 17 yr prior to measurement. We compare properties of these stands with macroecological predictions from the Maximum Entropy Theory of Ecology (METE), an information entropy‐based theory that has proven highly successful in predicting macroecological metrics in multiple ecosystems and taxa. Ecological patterns in the mature stand more closely match METE predictions than do data from the more recently disturbed, mid‐seral stage stand. This suggests METE's predictions are more robust in late‐successional, slowly changing, or steady‐state systems than those in rapid flux with respect to species composition, abundances, and organisms’ sizes. Our findings highlight the need for a macroecological theory that incorporates natural disturbance, perturbations, and ecological dynamics into its predictive capabilities, because most natural systems are not in a steady state.

Derivations of the Core Functions of the Maximum Entropy Theory of Ecology.

The Maximum Entropy Theory of Ecology (METE), is a theoretical framework of macroecology that makes a variety of realistic ecological predictions about how species richness, abundance of species, metabolic rate distributions, and spatial aggregation of species interrelate in a given region. In the METE framework, “ecological state variables” (representing total area, total species richness, total abundance, and total metabolic energy) describe macroecological properties of an ecosystem. METE incorporates these state variables into constraints on underlying probability distributions. The method of Lagrange multipliers and maximization of information entropy (MaxEnt) lead to predicted functional forms of distributions of interest. We demonstrate how information entropy is maximized for the general case of a distribution, which has empirical information that provides constraints on the overall predictions. We then show how METE’s two core functions are derived. These functions, called the “Spatial Structure Function” and the “Ecosystem Structure Function” are the core pieces of the theory, from which all the predictions of METE follow (including the Species Area Relationship, the Species Abundance Distribution, and various metabolic distributions). Primarily, we consider the discrete distributions predicted by METE. We also explore the parameter space defined by the METE’s state variables and Lagrange multipliers. We aim to provide a comprehensive resource for ecologists who want to understand the derivations and assumptions of the basic mathematical structure of METE.

MeteR: an r package for testing the maximum entropy theory of ecology

Summary Macroecological patterns appear to follow consistent forms across a range of natural systems; however, the origin of their regularity remains obscured. The maximum entropy theory of ecology (METE) predicts macroecological patterns of abundance, metabolic rates and their distribution within communities and across space using an information theoretic approach. METE's success in predicting empirical patterns demands that we further press the theory's predictions to determine how (or whether) predictability depends on attributes of the system and the temporal, spatial and biological scales at which we study it. Maximum entropy theory of ecology predicts multiple macroecological metrics using statistical idealizations from information theory; thus, confronting METE with data represents a strong test of the underlying biological mechanisms that could drive real communities away from statistical idealizations. METE has remained somewhat inaccessible due to its highly mathematical nature and a lack of software for model construction/evaluation. To remedy this, we have developed an r package implementation of METE. Our open‐source (GNU General Public License v2) r package, meteR (version 1.2; https://cran.r-project.org/package=meteR), (i) directly calculates all of METE's predictions from a variety of data formats; (ii) automatically handles approximations and other technical details; and (iii) provides high‐level plotting and model comparison functions to explore and interrogate models. With these tools in hand, ecologists can more readily test the predictions of METE for their data sets. By facilitating tests of METE, we expect that a better understanding of its strengths and limitations will emerge. A better understanding of the strengths and limitations of METE will offer insight into how biological mechanisms and statistical constraints combine to drive macroecological patterns.

Exploring the spatially explicit predictions of the Maximum Entropy Theory of Ecology

AbstractAimThe maximum entropy theory of ecology (METE) is a unified theory of biodiversity that attempts to simultaneously predict patterns of species abundance, size and spatial structure. The spatial predictions of this theory have repeatedly performed well at predicting diversity patterns across scales. However, the theoretical development and evaluation of METE has focused on predicting patterns that ignore intersite spatial correlations. As a result the theory has not been evaluated using one of the core components of spatial structure. We develop and test a semi‐recursive version of the spatially explicit predictions of METE for the distance–decay relationship of community similarity and compare its performance with the classic random placement model of completely random species distributions. This provides a better understanding and stronger test of the spatial community predictions of METE.LocationNew World tropical and temperate plant communities.MethodsWe analytically derived and simulated the spatially explicit expectations of METE for the Sørensen index of community similarity. We then compared the distance–decay of community similarity of 16 mapped plant communities with METE and the random placement model.ResultsThe version of METE we examined was successful at capturing the general functional form of the observed distance–decay relationships, a negative power function relationship between community similarity and distance. However, the semi‐recursive approach consistently predicted lower intercepts and higher slopes than observed in the empirical distance–decay relationships and yielded worse predictions than the random placement model.Main conclusionsOur results suggest that while the current spatial models of METE accurately predict the spatial scaling of species occupancy, and therefore core ecological patterns like the species–area relationship, its semi‐recursive form does not accurately characterize spatially explicit patterns of correlation. More generally, this suggests that tests of spatial theories based only on the species–area relationship may appear to support the underlying theory despite significant deviations in important aspects of spatial structure.

Empirical tests of within‐ and across‐species energetics in a diverse plant community

Many fundamental properties of ecological systems and interactions are tied to body size and a related metric, the metabolic rate distribution, both within and across species. A previously proposed maximum entropy theory of ecology (METE) predicts numerous interrelated macroecological patterns, including spatial distributions of individuals within species, abundance distributions across species, species area relationships, and distributions of metabolic rates of all individuals within a community. Extensive tests of METE's macroecological predictions generally support the theory, but two related predictions have not been evaluated against full community census data: the distribution of metabolic rates of individuals within species as a function of the abundance of the species and the distribution of average individual metabolic rates across species. We test the metabolic predictions of METE for herbaceous plants in a subalpine meadow and show that while this theory realistically predicts the distribution of individual metabolic rates across the entire community, the within‐ and across‐species predictions generally fail. We also test the energy‐equivalence type prediction that arises as a consequence of the prediction for the distribution of average individual metabolic rates across species. We suggest several possible explanations for the empirical deviations from theory, and distinguish between the expected deviations caused by ecological disturbance and those deviations that might be corrected within the theory.

A strong test of the maximum entropy theory of ecology.

The maximum entropy theory of ecology (METE) is a unified theory of biodiversity that predicts a large number of macroecological patterns using information on only species richness, total abundance, and total metabolic rate of the community. We evaluated four major predictions of METE simultaneously at an unprecedented scale using data from 60 globally distributed forest communities including more than 300,000 individuals and nearly 2,000 species.METE successfully captured 96% and 89% of the variation in the rank distribution of species abundance and individual size but performed poorly when characterizing the size-density relationship and intraspecific distribution of individual size. Specifically, METE predicted a negative correlation between size and species abundance, which is weak in natural communities. By evaluating multiple predictions with large quantities of data, our study not only identifies a mismatch between abundance and body size in METE but also demonstrates the importance of conducting strong tests of ecological theories.