Almost sure invariance principle for random piecewise expanding maps

We prove a fiberwise almost sure invariance principle for random piecewise expanding transformations in one and higher dimensions using recent developments on martingale techniques

Biogeographical Survey Identifies Consistent Alternative Physiological Optima and a Minor Role for Environmental Drivers in Maintaining a Polymorphism

The contribution of adaptive mechanisms in maintaining genetic polymorphisms is still debated in many systems. To understand the contribution of selective factors in maintaining polymorphism, we investigated large-scale (>1000 km) geographic variation in morph frequencies and fitness-related physiological traits in the damselfly Nehalennia irene. As fitness-related physiological traits, we investigated investment in immune function (phenoloxidase activity), energy storage and fecundity (abdomen protein and lipid content), and flight muscles (thorax protein content). In the first part of the study, our aim was to identify selective agents maintaining the large-scale spatial variation in morph frequencies. Morph frequencies varied considerably among populations, but, in contrast to expectation, in a geographically unstructured way. Furthermore, frequencies co-varied only weakly with the numerous investigated ecological parameters. This suggests that spatial frequency patterns are driven by stochastic processes, or alternatively, are consequence of highly variable and currently unidentified ecological conditions. In line with this, the investigated ecological parameters did not affect the fitness-related physiological traits differently in both morphs. In the second part of the study, we aimed at identifying trade-offs between fitness-related physiological traits that may contribute to the local maintenance of both colour morphs by defining alternative phenotypic optima, and test the spatial consistency of such trade-off patterns. The female morph with higher levels of phenoloxidase activity had a lower thorax protein content, and vice versa, suggesting a trade-off between investments in immune function and in flight muscles. This physiological trade-off was consistent across the geographical scale studied and supports widespread correlational selection, possibly driven by male harassment, favouring alternative trait combinations in both female morphs

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems

We extend the recent spectral approach for quenched limit theorems developed for piecewise expanding dynamics under general random driving to quenched random piecewise hyperbolic dynamics. For general ergodic sequences of maps in a neighborhood of a hyperbolic map we prove a quenched large deviations principle (LDP), central limit theorem (CLT), and local central limit theorem (LCLT).</p

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems

We extend the recent spectral approach for quenched limit theorems developed for piecewise expanding dynamics under general random driving to quenched random piecewise hyperbolic dynamics. For general ergodic sequences of maps in a neighborhood of a hyperbolic map we prove a quenched large deviations principle (LDP), central limit theorem (CLT), and local central limit theorem (LCLT)

Sampling bias in multiscale ant diversity responses to landscape composition in a human-disturbed rainforest

Recent studies have shown that several sources of variation can influence our ability to quantify biological responses to environmental variables, and that spatial scales are important in this process. For instance, sampling methods may differ in their efficiency or specificity, leading to different inferred relationships between community responses and landscape composition—i.e., forest cover (%), landscape heterogeneity, edge effects, and functional connectivity. Consequently, this can also influence the predictive power of the models when evaluating organisms as bioindicators of habitat loss and land use modification. Here, we evaluated how sampling methods (i.e., Winkler, pitfall, beating, and baits) influence our capacity to assess the scale of effect of two landscape composition metrics on ant diversity. We conducted ant sampling in 16 landscapes within a Mexican tropical rainforest and assessed the relationship between species richness and landscape composition metrics through buffers with 12 different spatial extents (from 50 to 1000 m). We found that the sampling method influenced the scale of effect when evaluating the relationships between ant species richness and forest cover and landscape heterogeneity. Combining all sampling methods, we found that the scales that best explained ant species richness were 700 m for forest cover and 900 m for landscape heterogeneity. Therefore, we highlight that our ability to detect ant-based diversity responses to environmental variables depends on the sampling method and spatial extent used in the study.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Consejo Nacional de Ciencia y TecnologíaCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Red de Ecoetología Instituto de Ecología A.C., VeracruzCONACYTRed de Ecología Funcional Instituto de Ecología A.C, VeracruzSpatial Ecology and Conservation Lab (LEEC) Biodiversity Department Bioscience Institute Universidade Estadual Paulista, SPCentro de Investigaciones Tropicales Universidad Veracruzana, VeracruzSpatial Ecology and Conservation Lab (LEEC) Biodiversity Department Bioscience Institute Universidade Estadual Paulista, SPFAPESP: 2013/50421-2CNPq: 312045/2013-1CNPq: 312292/2016-3Consejo Nacional de Ciencia y Tecnología: 584340CAPES: 88881.068425/2014-