Likelihood and model selection

Ecologists study the way biotic and abiotic interactions affect the distribution and abundance of organisms. Interpreting ecological studies, though, is generally not straightforward because most biological patterns of interest are affected by complex webs of interactions (Hilborn and Mangel 1997). Often, numerous simplifying biological hypotheses can be proposed that describe key processes or relations among variables, and the objective of an ecological study is to identify which hypothesis (or set of hypotheses) is best supported. To achieve this it is usually necessary to formalize the hypotheses using mathematical models and then fit them to the data at hand (Richards 2005; Bolker 2008). Model selection is the process of determining which model(s) best describe the data, and, in turn this provides a way for determining which biological hypotheses have support.