The Mismatch between Range and Niche Limits due to Source-Sink Dynamics Can Be Greater than Species Mean Dispersal Distance.

AbstractSpecies distribution models assume that at broad spatial scales, environmental conditions determine species ranges and, as such, source-sink dynamics can be ignored. A rationale behind this assumption is that source-sink dynamics manifest at length scales comparable to species mean dispersal distance, which is much smaller than length scales of species distribution and variation in climate. Using a two-dimensional reaction-diffusion model, we show that species can use sink habitats near the niche limit as stepping-stones to occupy sink habitats much further than the mean dispersal distance, thereby extending the distribution far beyond the environmental niche limit. This mismatch between range and niche limits is mediated by the shape (local curvature) of the niche limit. These curvature effects may be significant for a highly dispersive species with low per capita growth rate sensitivity to changes in the environment. These findings underscore the potential importance of stepping-stone dispersal in determining range limits.

An Empiricist's Guide to Using Ecological Theory.

AbstractA scientific understanding of the biological world arises when ideas about how nature works are formalized, tested, refined, and then tested again. Although the benefits of feedback between theoretical and empirical research are widely acknowledged by ecologists, this link is still not as strong as it could be in ecological research. This is in part because theory, particularly when expressed mathematically, can feel inaccessible to empiricists who may have little formal training in advanced math. To address this persistent barrier, we provide a general and accessible guide that covers the basic, step-by-step process of how to approach, understand, and use ecological theory in empirical work. We first give an overview of how and why mathematical theory is created, then outline four specific ways to use both mathematical and verbal theory to motivate empirical work, and finally present a practical tool kit for reading and understanding the mathematical aspects of ecological theory. We hope that empowering empiricists to embrace theory in their work will help move the field closer to a full integration of theoretical and empirical research.

Dispersal Increases the Resilience of Tropical Savanna and Forest Distributions.

Global change may induce changes in savanna and forest distributions, but the dynamics of these changes remain unclear. Classical biome theory suggests that climate is predictive of biome distributions, such that shifts will be continuous and reversible. This view, however, cannot explain the overlap in the climatic ranges of tropical biomes, which some argue may result from fire-vegetation feedbacks, maintaining savanna and forest as bistable states. Under this view, biome shifts are argued to be discontinuous and irreversible. Mean-field bistable models, however, are also limited, as they cannot reproduce the spatial aggregation of biomes. Here we suggest that both models ignore spatial processes, such as dispersal, which may be important when savanna and forest abut. We examine the contributions of dispersal to determining biome distributions using a 2D reaction-diffusion model, comparing results qualitatively to empirical savanna and forest distributions in sub-Saharan Africa. We find that the diffusion model resolves both the aforementioned limitations of biome models. First, local dispersive spatial interactions, with an underlying precipitation gradient, can reproduce the spatial aggregation of biomes with a stable savanna-forest boundary. Second, the boundary is determined not only by the amount of precipitation but also by the geometrical shape of the precipitation contours. These geometrical effects arise from continental-scale source-sink dynamics, which reproduce the mismatch between biome and climate. Dynamically, the spatial model predicts that dispersal may increase the resilience of tropical biome in response to global change: the boundary continuously tracks climate, recovering following disturbances, unless the remnant biome patches are too small.

A mechanistic statistical approach to infer invasion characteristics of human-dispersed species with complex life cycle.

The rising introduction of invasive species through trade networks threatens biodiversity and ecosystem services. Yet, we have a limited understanding of how transportation networks determine patterns of range expansion. This is partly because current analytical models fail to integrate the invader's life-history dynamics with heterogeneity in human-mediated dispersal patterns. And partly because classical statistical methods often fail to provide reliable estimates of model parameters due to spatial biases in the presence-only records and lack of informative demographic data. To address these gaps, we first formulate an age-structured metapopulation model that uses a probability matrix to emulate human-mediated dispersal patterns. The model reveals that an invader spreads along the shortest network path, such that the inter-patch network distances decrease with increasing traffic volume and reproductive value of hitchhikers. Next, we propose a Bayesian statistical method to estimate model parameters using presence-only data and prior demographic knowledge. To show the utility of the statistical approach, we analyze zebra mussel (Dreissena polymorpha) expansion in North America through the commercial shipping network. Our analysis underscores the importance of correcting spatial biases and leveraging priors to answer questions, such as where and when the zebra mussels were introduced and what life-history characteristics make these mollusks successful invaders.

Reproducible Analysis Pipeline for Data Streams: Open-Source Software to Process Data Collected With Mobile Devices.

Smartphone and wearable devices are widely used in behavioral and clinical research to collect longitudinal data that, along with ground truth data, are used to create models of human behavior. Mobile sensing researchers often program data processing and analysis code from scratch even though many research teams collect data from similar mobile sensors, platforms, and devices. This leads to significant inefficiency in not being able to replicate and build on others' work, inconsistency in quality of code and results, and lack of transparency when code is not shared alongside publications. We provide an overview of Reproducible Analysis Pipeline for Data Streams (RAPIDS), a reproducible pipeline to standardize the preprocessing, feature extraction, analysis, visualization, and reporting of data streams coming from mobile sensors. RAPIDS is formed by a group of R and Python scripts that are executed on top of reproducible virtual environments, orchestrated by a workflow management system, and organized following a consistent file structure for data science projects. We share open source, documented, extensible and tested code to preprocess, extract, and visualize behavioral features from data collected with any Android or iOS smartphone sensing app as well as Fitbit and Empatica wearable devices. RAPIDS allows researchers to process mobile sensor data in a rigorous and reproducible way. This saves time and effort during the data analysis phase of a project and facilitates sharing analysis workflows alongside publications.

Dispersal limitation and fire feedbacks maintain mesic savannas in Madagascar.

Madagascar is regarded by some as one of the most degraded landscapes on Earth, with estimates suggesting that 90% of forests have been lost to indigenous Tavy farming. However, the extent of this degradation has been challenged: paleoecological data, phylogeographic analysis, and species richness indicate that pyrogenic savannas in central Madagascar predate human arrival, even though rainfall is sufficient to allow forest expansion into central Madagascar. These observations raise a question-if savannas in Madagascar are not anthropogenic, how then are they maintained in regions where the climate can support forest? Observation reveals that the savanna-forest boundary coincides with a dispersal barrier-the escarpment of the Central Plateau. Using a stepping-stone model, we show that in a limited dispersal landscape, a stable savanna-forest boundary can form because of fire-vegetation feedbacks. This phenomenon, referred to as range pinning, could explain why eastern lowland forests have not expanded into the mesic savannas of the Central Highlands. This work challenges the view that highland savannas in Madagascar are derived by human-lit fires and, more importantly, suggests that partial dispersal barriers and strong nonlinear feedbacks can pin biogeographical boundaries over a wide range of environmental conditions, providing a temporary buffer against climate change.

Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk.

Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.