Timothy H. Keitt

Dispersal, Environmental Correlation, and Spatial Synchrony in Population Dynamics.

Many species exhibit widespread spatial synchrony in population fluctuations. This pattern is of great ecological interest and can be a source of concern when the species is rare or endangered. Both dispersal and spatial correlations in the environment have been implicated as possible causes of this pattern, but these two factors have rarely been studied in combination. We develop a spatially structured population model, simple enough to obtain analytic solutions for the population correlation, that incorporates both dispersal and environmental correlation. We ask whether these two synchronizing factors contribute additively to the total spatial population covariance. We find that there is always an interaction between these two factors and that this interaction is small only when one or both of the environmental correlation and the dispersal rate are small. The interaction is opposite in sign to the environmental correlation; so, in the normal case of positive environmental correlation across sites, the population synchrony will be lower than predicted by simply adding the effects of dispersal and environmental correlation. We also find that population synchrony declines as the strength of population regulation increases. These results indicate that dispersal and environmental correlation need to be considered in combination as explanations for observed patterns of population synchrony.

The dual nature of community variability

Author(s): Micheli, Fiorenza; Cottingham, Kathryn L.; Bascompte, Jordi; Bjornstad, Ottar N.; Eckert, Ginny L.; Fischer, Janet M.; Keitt, Timothy H.; Kendall, Bruce E.; Klug, Jennifer L.; Rusak, James A | Abstract: Community variability has a dual nature. On the one hand, there is compositional variability, changes in the relative abundance of component species. On the other hand, there is aggregate variability, changes in summary properties such as total abundance, biomass, or production. Although these two aspects of variability have received much individual attention, few studies have explicitly? related the compositional and aggregate variability of natural communities. In this paper, we show how simultaneous consideration of both aspects of community variability might advance our understanding of ecological communities.We use the distinction between compositional and aggregate variability to develop an organizational framework for describing patterns of community variability. At their extremes, compositional and aggregate variability combine in four different ways: (I) stasis, low compositional and low aggregate variability; (2) synchrony, low compositional and high aggregate variability; (3) asynchrony, high compositional and high aggregate variability; and (4) compensation, high compositional and low aggregate variability. Each of these patterns has been observed in natural communities, and can be linked to a suite of abiotic and biotic mechanisms. We give examples of the potential relevance of variability patterns to applied ecology, and describe the methodological developments needed to make meaningful comparisons of aggregate and compositional variability across communities. Finally, we provide two numerical examples of how our approach can be applied to natural communities.

Dynamics of North American Breeding Bird Populations

Population biologists have long been interested in the variability of natural populations. One approach to dealing with ecological complexity is to reduce the system to one or a few species, for which meaningful equations can be solved. Here we explore an alternative approach, by studying the statistical properties of a data set containing over 600 species, namely the North American breeding bird survey. The survey has recorded annual species abundances over a 31-year period along more than 3,000 observation routes. We now analyse the dynamics of population variability using this data set, and find scaling features in common with inanimate systems composed of strongly interacting subunits. Specifically, we find that the distribution of changes in population abundance over a one-year interval is remarkably symmetrical, with long tails extending over six orders of magnitude. The variance of the population over a time series increases as a power-law with increasing time lag, indicating long-range correlation in population size fluctuations. We also find that the distribution of species lifetimes (the time between colonization and local extinction) within local patches is a power-law with an exponential cutoff imposed by the finite length of the time series. Our results provide a quantitative basis for modelling the dynamics of large species assemblages.

SCALE‐SPECIFIC INFERENCE USING WAVELETS

Understanding of spatial pattern and scale has been identified as a key issue in ecology, yet ecology has traditionally lacked necessary tools for making inference about relationships between scale-specific patterns. We introduce wavelet-coefficient regression, in which the dependent and independent variables are wavelet transformed prior to analysis, as a means to formalize scale-specific relationships in ecological data. We apply this method to data on vegetation and environmental factors related to water availability from Sequoia-Kings Canyon National Park (California, USA). We find that the wavelet transform and wavelet-coefficient regression efficiently characterize scale-specific pattern in these data. We also find that different environmental factors show up as good predictors of vegetation growth at different scales and that these differences in scale greatly facilitate interpretation of the mechanisms relating water availability to vegetation growth.

Scale invariance and universality: organizing principles in complex systems

This paper is a brief summary of a talk that was designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena – scale invariance and universality – can be useful in guiding research on a broad class of complex phenomena. We shall see that while scale invariance has been tested for many years, universality is relatively more rarely discussed. In particular, we shall develop a heuristic argument that serves to make more plausible the universality hypothesis in both thermal critical phenomena and percolation phenomena, and suggest that this argument could be developed into a possible coherent approach to understanding the ubiquity of scale invariance and universality in a wide range of complex systems.

Coherent ecological dynamics induced by large-scale disturbance

Aggregate community-level response to disturbance is a principle concern in ecology because post-disturbance dynamics are integral to the ability of ecosystems to maintain function in an uncertain world. Community-level responses to disturbance can be arrayed along a spectrum ranging from synchronous oscillations where all species rise and fall together, to compensatory dynamics where total biomass remains relatively constant despite fluctuations in the densities of individual species. An important recent insight is that patterns of synchrony and compensation can vary with the timescale of analysis and that spectral time series methods can enable detection of coherent dynamics that would otherwise be obscured by opposing patterns occurring at different scales. Here I show that application of wavelet analysis to experimentally manipulated plankton communities reveals strong synchrony after disturbance. The result is paradoxical because it is well established that these communities contain both disturbance-sensitive and disturbance-tolerant species leading to compensation within functional groups. Theory predicts that compensatory substitution of functionally equivalent species should stabilize ecological communities, yet I found at the whole-community level a large increase in seasonal biomass variation. Resolution of the paradox hinges on patterns of seasonality among species. The compensatory shift in community composition after disturbance resulted in a loss of cold-season dominants, which before disturbance had served to stabilize biomass throughout the year. Species dominating the disturbed community peaked coherently during the warm season, explaining the observed synchrony and increase in seasonal biomass variation. These results suggest that theory relating compensatory dynamics to ecological stability needs to consider not only complementarity in species responses to environmental change, but also seasonal complementarity among disturbance-tolerant and disturbance-sensitive species.

Spatial Autocorrelation, Dispersal and the Maintenance of Source-Sink Populations

Populations may be regulated by both local density-dependent factors and spatial variation in habitat quality. I explore the influence of spatial autocorrelation in habitat quality on the survival of model populations. Dispersal is modeled as Markov transitions between patches. A finite rate of population increase was assigned to each patch. Total habitat area and mean dispersal distance had strong effects on overall population persistence. The effect of spatial autocorrelation was relatively weak, but interacted with dispersal distance. The results suggest that landscape pattern can play an important role in population survival, but its importance depends crucially on dispersal behavior.