Statistics for correlated data: phylogenies, space, and time.

Here we give an introduction to the growing number of statistical techniques for analyzing data that are not independent realizations of the same sampling process--in other words, correlated data. We focus on regression problems, in which the value of a given variable depends linearly on the value of another variable. To illustrate different types of processes leading to correlated data, we analyze four simulated examples representing diverse problems arising in ecological studies. The first example is a comparison among species to determine the relationship between home-range area and body size; because species are phylogenetically related, they do not represent independent samples. The second example addresses spatial variation in net primary production and how this might be affected by soil nitrogen; because nearby locations are likely to have similar net primary productivity for reasons other than soil nitrogen, spatial correlation is likely. In the third example, we consider a time-series model to ask whether the decrease in density of a butterfly species is the result of decreases in its host-plant density; because the population density of a species in one generation is likely to affect the density in the following generation, time-series data are often correlated. The fourth example combines both spatial and temporal correlation in an experiment in which prey densities are manipulated to determine the response of predators to their food supply. For each of these examples, we use a different statistical approach for analyzing models of correlated data. Our goal is to give an overview of conceptual issues surrounding correlated data, rather than a detailed tutorial in how to apply different statistical techniques. By dispelling some of the mystery behind correlated data, we hope to encourage ecologists to learn about statistics that could be useful in their own work. Although at first encounter these techniques might seem complicated, they have the power to simplify ecological research by making more types of data and experimental designs open to statistical evaluation.     

Marine reserve design: optimal size, habitats, species affinities, diversity, and ocean microclimate.

The design of marine reserves is complex and fraught with uncertainty. However, protection of critical habitat is of paramount importance for reserve design. We present a case study as an example of a reserve design based on fine-scale habitats, the affinities of exploited species to these habitats, adult mobility, and the physical forcing affecting the dynamics of the habitats. These factors and their interaction are integrated in an algorithm that determines the optimal size and location of a marine reserve for a set of 20 exploited species within five different habitats inside a large kelp forest in southern California. The result is a reserve that encompasses approximately 42% of the kelp forest. Our approach differs fundamentally from many other marine reserve siting methods in which goals of area, diversity, or biomass are targeted a priori. Rather, our method was developed to determine how large a reserve must be within a specific area to protect a self-sustaining assemblage of exploited species. The algorithm is applicable across different ecosystems, spatial scales, and for any number of species. The result is a reserve in which habitat value is optimized for a predetermined set of exploited species against the area left open to exploitation. The importance of fine-scale habitat definitions for the exploited species off La Jolla is exemplified by the spatial pattern of habitats and the stability of these habitats within the kelp forest, both of which appear to be determined by ocean microclimate.