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An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…
Improved monitoring and associated inferential tools to efficiently identify declining bird populations, particularly of rare or sparsely distributed species, is key to informed conservation and management across large spatio-temporal…
Polarization issue is generally subject to ideological polarization and affective polarization. In particular, affective polarization usually accelerates the polarization process and transform social interactions into a zero-sum game. Yet,…
Statistical averaging and asynchronous population dynamics as portfolio mechanisms are considered as the most important processes with which biodiversity contributes to ecosystem stability. However, portfolio theories usually regard…
Based on perturbation theory, we study the dynamics of how dark matter and dark energy in the collapsing system approach dynamical equilibrium while interacting. We find that the interaction between dark sectors cannot ensure the dark…
We investigate extremal statistical properties such as the maximal and the minimal heights of randomly generated binary trees. By analyzing the master evolution equations we show that the cumulative distribution of extremal heights…
We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…
Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical…
Tree ensembles are flexible predictive models that can capture relevant variables and to some extent their interactions in a compact and interpretable manner. Most algorithms for obtaining tree ensembles are based on versions of boosting or…
Random matrix theory successfully connects the structure of interactions of large ecological communities to their ability to respond to perturbations. One of the most debated aspects of this approach is the missing role of population…
Patches of vegetation consist of dense clusters of shrubs, grass, or trees, often found to be circular characteristic size, defined by the properties of the vegetation and terrain. Therefore, vegetation patches can be interpreted as…
Random forests are a statistical learning technique that use bootstrap aggregation to average high-variance and low-bias trees. Improvements to random forests, such as applying Lasso regression to the tree predictions, have been proposed in…
Social groups with widely different music tastes, political convictions, and religious beliefs emerge and disappear on scales from extreme subcultures to mainstream mass-cultures. Both the underlying social structure and the formation of…
Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles…
The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local…
Decisions to disperse from a habitat stand out among organismal behaviors as pivotal drivers of ecosystem dynamics across scales. Encounters with other species are an important component of adaptive decision-making in dispersal, resulting…
We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…
In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider the regularly-spaced vegetation bands, on gentle hill-slopes, that survive low rainfall conditions by…
High-dimensional compositional covariates, often derived from count data, are subject to measurement error and are frequently analyzed after aggregation along a prespecified tree to improve interpretability in applications such as…
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…