Analysis of neighborhood dynamics of forest ecosystems using likelihood methods and modeling.

Advances in computing power in the past 20 years have led to a proliferation of spatially explicit, individual-based models of population and ecosystem dynamics. In forest ecosystems, the individual-based models encapsulate an emerging theory of "neighborhood" dynamics, in which fine-scale spatial interactions regulate the demography of component tree species. The spatial distribution of component species, in turn, regulates spatial variation in a whole host of community and ecosystem properties, with subsequent feedbacks on component species. The development of these models has been facilitated by development of new methods of analysis of field data, in which critical demographic rates and ecosystem processes are analyzed in terms of the spatial distributions of neighboring trees and physical environmental factors. The analyses are based on likelihood methods and information theory, and they allow a tight linkage between the models and explicit parameterization of the models from field data. Maximum likelihood methods have a long history of use for point and interval estimation in statistics. In contrast, likelihood principles have only more gradually emerged in ecology as the foundation for an alternative to traditional hypothesis testing. The alternative framework stresses the process of identifying and selecting among competing models, or in the simplest case, among competing point estimates of a parameter of a model. There are four general steps involved in a likelihood analysis: (1) model specification, (2) parameter estimation using maximum likelihood methods, (3) model comparison, and (4) model evaluation. Our goal in this paper is to review recent developments in the use of likelihood methods and modeling for the analysis of neighborhood processes in forest ecosystems. We will focus on a single class of processes, seed dispersal and seedling dispersion, because recent papers provide compelling evidence of the potential power of the approach, and illustrate some of the statistical challenges in applying the methods.