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The description of spatial patterns in species distributions is central to research throughout ecology. In this manuscript, we demonstrate that five of the most widely used species‐level spatial patterns are not only related, but can in fact be quantitatively derived from each other under minimal assumptions: the occupancy area curve, Taylor's Law, the neighborhood density function, a two‐plot variant of Taylor's Law and two‐plot single‐species turnover. We present an overarching mathematical framework and derivations for several theoretical example cases, along with a simulation study and empirical analysis that applies the framework to data from the Barro Colorado Island tropical forest plot. We discuss how knowledge of this mathematical relationship can support the testing of ecological theory, suggest efficient field sampling schemes, highlight the relative importance of plot area and abundance in driving turnover patterns and lay the groundwork for future unified theories of community‐level spatial metrics and multi‐patch spatial patterns., We show that several widely used single species spatial metrics (the occupancy area curve, Taylor's Law, the neighborhood density function and plot‐based turnover) are all derivable from each other under minimal assumptions. We provide example equations showing this relationship and demonstrate its application to simulated and empirical data.

The Maximum Entropy Theory of Ecology (METE) predicts the shapes of macroecological metrics in relatively static ecosystems, across spatial scales, taxonomic categories and habitats, using constraints imposed by static state variables. In disturbed ecosystems, however, with time‐varying state variables, its predictions often fail. We extend macroecological theory from static to dynamic by combining the MaxEnt inference procedure with explicit mechanisms governing disturbance. In the static limit, the resulting theory, DynaMETE, reduces to METE but also predicts a new scaling relationship among static state variables. Under disturbances, expressed as shifts in demographic, ontogenic growth or migration rates, DynaMETE predicts the time trajectories of the state variables as well as the time‐varying shapes of macroecological metrics such as the species abundance distribution and the distribution of metabolic rates over individuals. An iterative procedure for solving the dynamic theory is presented. Characteristic signatures of the deviation from static predictions of macroecological patterns are shown to result from different kinds of disturbance. By combining MaxEnt inference with explicit dynamical mechanisms of disturbance, DynaMETE is a candidate theory of macroecology for ecosystems responding to anthropogenic or natural disturbances., The architecture of DynaMETE, a hybrid MaxEnt‐plus‐mechanism theory of macroecology. The time evolution of Macroecological Metrics in ecosystems disturbed by a hypothesised Mechanism is derived iteratively using the MaxEnt inference procedure (step E in the figure).

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. Funding for this project was provided in part by grant DEB 1751380 from the US National Science Foundation, as well as by grants to PAVB FCT-UIDP/00329/2020-2024 (Thematic Line 1 – integrated ecological assessment of environmental change on biodiversity) and MACRISK – PTDC/BIA-CBI/0625/2021, through the FCT – Fundação para a Ciência e a Tecnologia. MB acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) (PGSD2-517114-2018). Data acquisition was provided by the projects: ‘Consequences of land use change on Azorean fauna and flora – the 2010 Target' (Ref: Direcção Regional de Ciência e Tecnologia M.2.1.2/I/003/2008) and ‘Direcção Regional dos Recursos Florestais' (‘Secretaria Regional da Agricultura e Pescas') through the Project ‘Reservas Florestais dos Açores: Cartografia e Inventariação dos Artrópodes Endémicos dos Açores' (PROJ. 17.01 – 080203). info:eu-repo/semantics/publishedVersion

Human activity and land management practices, in particular land use change, have resulted in the global loss of biodiversity. These types of disturbances affect the shape of macroecological patterns, and analyzing these patterns can provide insights into how ecosystems are affected by land use change. The Maximum Entropy Theory of Ecology (METE) simultaneously predicts many of these patterns using a set of ecological state variables: the number of species, the number of individuals, and the total metabolic rate. The theory9s predictions have been shown to be successful across habitats and taxa in undisturbed natural ecosystems, although previous tests of METE in relation to disturbance have focused primarily on systems where the state variables are changing relatively quickly. Here, we assess predictions of METE applied to a different type of disturbance: land use change. We use METE to simultaneously predict the species abundance distribution (SAD), the metabolic rate distribution of individuals (MRDI), and the species--area relationship (SAR) and compare these predictions to arthropod data from 96 sites at Terceira Island in the Azores archipelago across four different land uses of increasing management intensity: 1. native forest, 2. exotic forest, 3. semi-natural pasture, and 4. intensive pasture. Across these patterns, we find that the forest habitats are the best fit by METE predictions, while the semi-natural pasture consistently provided the worst fit. The intensive pasture is intermediately well fit for the SAD and MRDI, and comparatively well fit for the SAR, though the residuals are not normally distributed. 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 and the changing management practices throughout the year, leading to greater heterogeneity in composition and complex dynamics that violate METE9s assumption of static state variables. The comparative better fit for the intensive pasture could then result from more homogeneous arthropod communities that are well adapted to intensive management, and thus whose state variables are less in flux.

The Maximum Entropy Theory of Ecology (METE) predicts the shapes of macroecological metrics in relatively static ecosystems using constraints imposed by static state variables. In disturbed ecosystems, however, with time-varying state variables, its predictions often fail. We extend macroecological theory from static to dynamic by combining the MaxEnt inference procedure with explicit mechanisms governing disturbance. In the static limit, the resulting theory, DynaMETE, reduces to METE but also predicts new scaling relationships among static state variables. Under disturbances, expressed as shifts in demographic, ontogenic growth, or migration rates, DynaMETE predicts the time trajectories of the state variables as well as the time-varying shapes of macroecological metrics such as the species abundance distribution and the distribution of metabolic rates over individuals. An iterative procedure for completely solving the dynamic theory is presented. In a lowest-order iteration, characteristic signatures of the deviation from static predictions of macroecolgoical patterns are shown to result from different kinds of disturbance. Because DynaMETE combines MaxEnt inference with explicit dynamical mechanisms, but does not assume any specific trait distributions over species or individuals, it is widely applicable across diverse ecosystems. This makes it a promising theory of macroecology for ecosystems responding to anthropogenic or natural disturbances.

Accumulating evidence suggests that ecological communities undergoing change in response to either anthropogenic or natural disturbances exhibit macroecological patterns that differ from those observed in similar types of communities in relatively undisturbed sites. In contrast to such cross‐site comparisons, however, there are few empirical studies of shifts over time in the shapes of macroecological patterns. Here, we provide a dramatic example of a plant community in which the species–area relationship and the species‐abundance distribution change markedly over a period of six years. These patterns increasingly deviate from the predictions of the maximum entropy theory of ecology (METE), which successfully predicts macroecological patterns in relatively static systems. The error in the species–area relationship prediction additionally correlates over time with increased stress measured as mortality minus recruitment, providing a link between demography and the failure of macroecological theory. Information on the dynamic state of an ecosystem inferred from snapshot measurements of macroecological community structure can potentially assist in identifying causes and consequences of disturbance and extending the domain of current theories and models to disturbed ecosystems.

Spatial patterns in ecology contain useful information about underlying mechanisms and processes. Although there are many summary statistics used to quantify these spatial patterns, there are far fewer models that directly link explicit ecological mechanisms to observed patterns easily derived from available data. We present a model of intraspecific spatial aggregation that quantitatively relates static spatial patterning to negative density dependence. Individuals are placed according to the colonization rule consistent with the Maximum Entropy Theory of Ecology (METE), and die with probability proportional to their abundance raised to a power α, a parameter indicating the degree of density dependence. Our model shows quantitatively and generally that increasing density dependence randomizes spatial patterning. α = 1 recovers the strongly aggregated METE distribution that is consistent with many ecosystems empirically, and as α → 2 our prediction approaches the binomial distribution consistent with random placement. In between our model predicts less aggregation than METE, but more than random placement. We additionally relate our mechanistic parameter α to the statistical aggregation parameter k in the negative binomial distribution, giving it an ecological interpretation in the context of density dependence. We use our model to analyze two contrasting datasets, a 50 ha tropical forest and a 64 m2 serpentine grassland plot. For each dataset, we infer α for individual species as well as a community α parameter. We find that α is generally larger in the tightly packed forest than the sparse grassland, and the degree of density dependence increases at smaller scales. These results are consistent with current understanding in both ecosystems, and we infer this underlying density dependence using only empirical spatial patterns. Our model can easily be applied to other datasets where spatially explicit data are available.

Interactions of different types of topological defects can play an important role in the aftermath of a phase transition. We study interactions of fundamental magnetic monopoles and stable domain walls in a Grand Unified theory in which $SU(5) \times Z_2$ symmetry is spontaneously broken to $SU(3)\times SU(2)\times U(1)/Z_6$. We find that there are only two distinct outcomes depending on the relative orientation of the monopole and the wall in internal space. In one case, the monopole passes through the wall, while in the other it unwinds on hitting the wall., Comment: 8 pages, 7 figures; new title and minor changes; matches the version accepted to Phys Rev D