Abstract
History matters when individual prior conditions contain important information about the fate of individuals. We present a general framework for demographic models which incorporates the effects of history on population dynamics. The framework incorporates prior condition into the i-state variable and includes an algorithm for constructing the population projection matrix from information on current state dynamics as a function of prior condition. Three biologically motivated classes of prior condition are included: prior stages, linear functions of current and prior stages, and equivalence classes of prior stages. Taking advantage of the matrix formulation of the model, we show how to calculate sensitivity and elasticity of any demographic outcome. Prior condition effects are a source of inter-individual variation in vital rates, i.e., individual heterogeneity. As an example, we construct and analyze a second-order model of Lathyrus vernus, a long-lived herb. We present population growth rate, the stable population distribution, the reproductive value vector, and the elasticity of λ to changes in the second-order transition rates. We quantify the contribution of prior conditions to the total heterogeneity in the stable population of Lathyrus using the entropy of the stable distribution.
Highlights
Every demographic analysis requires a classification of individuals by age, size, developmental stage, physiological condition, or some other variable
Our goal in this paper is to present a systematic method for constructing such models in which individuals are classified by current stage and prior condition
When does history matter? Population models are based on i-state variables chosen by some mixture of biological intuition, tradition, practical limitations, and formal statistical analyses
Summary
Every demographic analysis requires a classification of individuals by age, size, developmental stage, physiological condition, or some other variable. Because we are considering effects of individual condition at just one prior time, we refer to these as second-order matrix population models. A more general second-order model structure allows transitions and fertility to depend on some function of current and prior stages. The state of the population is given by a s × rarray M where mij represents the number of individuals whose current stage is i and whose prior condition is j. The resulting 56 × 56 matrices are available in the Supplementary Material The columns in this matrix represent transitions out of the following current stages from left to right: seed (SD), seedling (SL), very small (VS), small (SM), vegetative large (VL), flowering (FL), and dormant (DO). Proportional changes in individuals who were small vegetative at the prior time have effects an order of magnitude larger
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
