BROKEN BIOLOGICAL SIZE RELATIONSHIPS - A TRUNCATED SEMIPARAMETRIC REGRESSION APPROACH WITH MEASUREMENT ERROR

Biological size relationships (i.e., regression of one size variable o n another) are typically monotone bur often break down at extreme valu es of the variables. Here we study the way in which a plant's biomass is apportioned to reproductive and other life activities. Working with a theory proposed by Weiner (1988) based an analogy between a biologi cal plant and an industrial plant leads to a truncated regression mode l formulation. We consider a dataset involving 542 goldenrod plants th at has been analyzed in a limited fashion by others. Important extensi ons that we provide include nonparametric modeling of the size relatio nship, introduction of covariate information, incorporation of heterog eneity across plant families, and inclusion of measurement error model s for both response and explanatory variables. Our approach is through hierarchical models taking advantage of available prior information o n the magnitudes of the size variables. Models are fitted using simula tion methods enabling a full range of inference. An attractive model c hoice criterion demonstrates the need to accommodate all of the aforem entioned aspects for the given dataset. Oar flexible modeling approach can be adapted to investigate other biological size relationships.