Estimation of development properties of stage-classified biological processes using multinomial models: a case study of the Bay of Biscay anchovy (Engraulis encrasicolis, L.) egg development

This paper describes how multinomial models can be used to study developmental rates of biological processes and how these are affected by different factors such as temperature or parental effects. First, the most common multinomial models for ordinal categorical data (namely, proportional odds, continuation-ratio, and extended continuation-ratio models) are described within the particular framework of developmental rates for discrete and ordered stage classified biological processes. Then, the extraction from the fitted models of a series of biologically meaningful parameters is proposed. In particular, maximum probable age and several alternative definitions for stage duration are presented and pros and cons of each of them are discussed. As an example, the methodology is applied to analyze the temperature dependent development of anchovy (Engraulis encrasicolus) eggs in the Bay of Biscay.