Causality and persistence in ecological systems: a nonparametric spectral granger causality approach.

Abstract Directionality in coupling, defined as the linkage relating causes to their effects at a later time, can be used to explain the core dynamics of ecological systems by untangling direct and feedback relationships between the different components of the systems. Inferring causality from measured ecological variables sampled through time remains a formidable challenge further made difficult by the action of periodic drivers overlapping the natural dynamics of the system. Periodicity in the drivers can often mask the self-sustained oscillations originating from the autonomous dynamics. While linear and direct causal relationships are commonly addressed in the time domain, using the well-established machinery of Granger causality (G-causality), the presence of periodic forcing requires frequency-based statistics (e.g., the Fourier transform), able to distinguish coupling induced by oscillations in external drivers from genuine endogenous interactions. Recent nonparametric spectral extensions of G-causality to the frequency domain pave the way for the scale-by-scale decomposition of causality, which can improve our ability to link oscillatory behaviors of ecological networks to causal mechanisms. The performance of both spectral G-causality and its conditional extension for multivariate systems is explored in quantifying causal interactions within ecological networks. Through two case studies involving synthetic and actual time series, it is demonstrated that conditional G-causality outperforms standard G-causality in identifying causal links and their concomitant timescales.

Predicting population survival under future climate change: density dependence, drought and extraction in an insular bighorn sheep.

1. Our understanding of the interplay between density dependence, climatic perturbations, and conservation practices on the dynamics of small populations is still limited. This can result in uninformed strategies that put endangered populations at risk. Moreover, the data available for a large number of populations in such circumstances are sparse and mined with missing data. Under the current climate change scenarios, it is essential to develop appropriate inferential methods that can make use of such data sets. 2. We studied a population of desert bighorn sheep introduced to Tiburon Island, Mexico in 1975 and subjected to irregular extractions for the last 10 years. The unique attributes of this population are absence of predation and disease, thereby permitting us to explore the combined effect of density dependence, environmental variability and extraction in a 'controlled setting.' Using a combination of nonlinear discrete models with long-term field data, we constructed three basic Bayesian state space models with increasing density dependence (DD), and the same three models with the addition of summer drought effects. 3. We subsequently used Monte Carlo simulations to evaluate the combined effect of drought, DD, and increasing extractions on the probability of population survival under two climate change scenarios (based on the Intergovernmental Panel on Climate Change predictions): (i) increase in drought variability; and (ii) increase in mean drought severity. 4. The population grew from 16 individuals introduced in 1975 to close to 700 by 1993. Our results show that the population's growth was dominated by DD, with drought having a secondary but still relevant effect on its dynamics. 5. Our predictions suggest that under climate change scenario (i), extraction dominates the fate of the population, while for scenario (ii), an increase in mean drought affects the population's probability of survival in an equivalent magnitude as extractions. Thus, for the long-term survival of the population, our results stress that a more variable environment is less threatening than one in which the mean conditions become harsher. Current climate change scenarios and their underlying uncertainty make studies such as this one crucial for understanding the dynamics of ungulate populations and their conservation.

Understanding strategies for seed dispersal by wind under contrasting atmospheric conditions.

Traits associated with seed dispersal vary tremendously among sympatric wind-dispersed plants. We used two contrasting tropical tree species, seed traps, micrometeorology, and a mechanistic model to evaluate how variation in four key traits affects seed dispersal by wind. The conceptual framework of movement ecology, wherein external factors (wind) interact with internal factors (plant traits) that enable movement and determine when and where movement occurs, fully captures the variable inputs and outputs of wind dispersal models and informs their interpretation. We used model calculations to evaluate the spatial pattern of dispersed seeds for the 16 factorial combinations of four traits. The study species differed dramatically in traits related to the timing of seed release, and a strong species by season interaction affected most aspects of the spatial pattern of dispersed seeds. A rich interplay among plant traits and seasonal differences in atmospheric conditions caused this interaction. Several of the same plant traits are crucial for both seed dispersal and other aspects of life history variation. Observed traits that limit dispersal are likely to be constrained by their life history consequences.