Social copying drives a tipping point for nonlinear population collapse.

Sudden changes in populations are ubiquitous in ecological systems, especially under perturbations. The agents of global change may increase the frequency and severity of anthropogenic perturbations, but complex populations' responses hamper our understanding of their dynamics and resilience. Furthermore, the long-term environmental and demographic data required to study those sudden changes are rare. Fitting dynamical models with an artificial intelligence algorithm to population fluctuations over 40 y in a social bird reveals that feedback in dispersal after a cumulative perturbation drives a population collapse. The collapse is well described by a nonlinear function mimicking social copying, whereby dispersal made by a few individuals induces others to leave the patch in a behavioral cascade for decision-making to disperse. Once a threshold for deterioration of the quality of the patch is crossed, there is a tipping point for a social response of runaway dispersal corresponding to social copying feedback. Finally, dispersal decreases at low population densities, which is likely due to the unwillingness of the more philopatric individuals to disperse. In providing the evidence of copying for the emergence of feedback in dispersal in a social organism, our results suggest a broader impact of self-organized collective dispersal in complex population dynamics. This has implications for the theoretical study of population and metapopulation nonlinear dynamics, including population extinction, and managing of endangered and harvested populations of social animals subjected to behavioral feedback loops.

Reviewing the reliability of Land Use and Land Cover data in studies relating human health to the environment.

BACKGROUND: In recent years, research has been increasingly devoted to understanding the complex human health-environment relationship. Nevertheless, many different measurements have been applied to characterize the environment. Among them, the application of Land Use and Land Cover (LULC) data is becoming more noticeable over time. AIMS: This research aims to analyse the reliability of Land Use and Land Cover data (LULC) data as a suitable describer of the environment in studies relating human health to the environment. With a specific focus on the methodologies using LULC data, we also examine the study designs and analytical methods that have been commonly performed so far. MATERIALS AND METHODS: We gathered studies relating human health outcomes to Land Use and Land Cover (LULC) data. A Boolean search limited to reviews was conducted in February 2019 using Web of Science Core Collection search engines. Five reviews were selected as our preliminary starting set of literature and from those, two backward snowballing searches were conducted. The first backward snowballing search used the reference lists of the first 5 reviews and revealed 17 articles. From these, the second search gathered 24 new articles also fulfilling the inclusion criteria established. In total, 41 articles were examined. RESULTS: Our main results reported that Land Use and Land Cover (LULC) data national level data was preferred over LULC international level data. However, this tendency seems to be strongly related to the specific aims of the articles. They essentially defined the living environment either through buffer zones, using the administrative boundaries wherein the individuals reside, or using the specific location of the individuals assessed. As for the characterization of the environment, authors performed 4 principal methodologies: extracting the percentage of green space, computing the "Land Use mix", recording the type of land cover, and using the percentage of tree canopy. Besides, all the articles included measurements in urban contexts and most of them evaluated the accessibility of individuals to their surroundings. Furthermore, it was clearly stated that the complexity of the topic and the challenging data leads authors to carry out advanced statistical methods and mostly cross-sectional designs with no causal relations. DISCUSSION AND CONCLUSIONS: Land Use and Land Cover (LULC) data has been demonstrated to be a versatile tool supporting both local-focused studies with few individuals involved and broad territorial-scoped studies with huge populations. Promising synergy has been highlighted between Electronic Health Records (EHR) and LULC data in studies dealing with massive information and broader scopes with regards to the assessment of territorial realities. As this emerging topic matures, investigators should (1) elucidate subjects of ongoing debate such as the measurement of the living environment and its characterization; (2) explore the whole potential of LULC data, using methodologies that encompass both their biophysical and socioeconomic information; (3) perform innovative designs that are able to establish causal relationships among the studied variables (for example, Cellular Automata models), and (4) expand the current set of studied health outcomes leveraging comprehensive and trustworthy health data sources such as EHR.

Host-virus evolutionary dynamics with specialist and generalist infection strategies: Bifurcations, bistability, and chaos.

In this work, we have investigated the evolutionary dynamics of a generalist pathogen, e.g., a virus population, that evolves toward specialization in an environment with multiple host types. We have particularly explored under which conditions generalist viral strains may rise in frequency and coexist with specialist strains or even dominate the population. By means of a nonlinear mathematical model and bifurcation analysis, we have determined the theoretical conditions for stability of nine identified equilibria and provided biological interpretation in terms of the infection rates for the viral specialist and generalist strains. By means of a stability diagram, we identified stable fixed points and stable periodic orbits, as well as regions of bistability. For arbitrary biologically feasible initial population sizes, the probability of evolving toward stable solutions is obtained for each point of the analyzed parameter space. This probability map shows combinations of infection rates of the generalist and specialist strains that might lead to equal chances for each type becoming the dominant strategy. Furthermore, we have identified infection rates for which the model predicts the onset of chaotic dynamics. Several degenerate Bogdanov-Takens and zero-Hopf bifurcations are detected along with generalized Hopf and zero-Hopf bifurcations. This manuscript provides additional insights into the dynamical complexity of host-pathogen evolution toward different infection strategies.

Theoretical conditions for the coexistence of viral strains with differences in phenotypic traits: a bifurcation analysis.

We investigate the dynamics of a wild-type viral strain which generates mutant strains differing in phenotypic properties for infectivity, virulence and mutation rates. We study, by means of a mathematical model and bifurcation analysis, conditions under which the wild-type and mutant viruses, which compete for the same host cells, can coexist. The coexistence conditions are formulated in terms of the basic reproductive numbers of the strains, a maximum value of the mutation rate and the virulence of the pathogens. The analysis reveals that parameter space can be divided into five regions, each with distinct dynamics, that are organized around degenerate Bogdanov-Takens and zero-Hopf bifurcations, the latter of which gives rise to a curve of transcritical bifurcations of periodic orbits. These results provide new insights into the conditions by which viral populations may contain multiple coexisting strains in a stable manner.

Finite-time scaling in local bifurcations.

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we have made use of the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete (deterministic) dynamical systems. We analytically derive finite-time scaling laws for two ubiquitous transitions given by the transcritical and the saddle-node bifurcation, obtaining exact expressions for the critical exponents and scaling functions. One of the scaling laws, corresponding to the distance of the dynamical variable to the attractor, turns out to be universal, in the sense that it holds for both bifurcations, yielding the same exponents and scaling function. Remarkably, the resulting scaling behavior in the transcritical bifurcation is precisely the same as the one in the (stochastic) Galton-Watson process. Our work establishes a new connection between thermodynamic phase transitions and bifurcations in low-dimensional dynamical systems, and opens new avenues to identify the nature of dynamical shifts in systems for which only short time series are available.

Stable heteroclinic cycles and symbolic dynamics.

Let S(1) (0), S(1) (1),.,S(1) (n-1) be n circles. A rotation in n circles is a map f: union or logical sum (i=0) (n-1)S(1) (i)--> union or logical sum (i=0) (n-1)S(1) (i) which maps each circle onto another by a rotation. This particular type of interval exchange map arises naturally in bifurcation theory. In this paper we give a full description of the symbolic dynamics associated to such maps.