Inverse modeling for effective dispersal : do we need tree size to estimate fecundity?

• Inverse modeling methods made possible the estimation of the dispersal kernel and of plant fecundity for the seedling and sapling stages of the recruitment process. Current models for the fecundities of adult trees are build on allometric assumptions where the number of successfully estab¬lished offspring produced by an adult is assumed to be in relation to some (easily) measured characteristic of the specific tree (usually the tree’s basal area). However, the allometric assumption relating tree size to reproduc¬tive success in the sapling (or seedling) stage should be questionable when numerous, well-documented, post-dispersal processes such as safe-site limitation for recruitment or negative density-dependent seedling mortality can cancel out the presumably strong relationship between tree size and seed set. In this paper we hypothesize that when the relationship between tree size and reproductive success is not strong enough then its use in in¬verse modeling is counter-productive and may lead to poor model fits and/or unstable solutions for the parameters of the model. We present a new model for effective dispersal termed the unrestricted fecundity (UF) model, which makes no allometric assumptions on the fecundities; instead they are allowed to vary freely and even to be zero. Based on this model, we examine the hypothesis that when fecundities are estimated indepen¬dently of tree size (or any other tree characteristic), the goodness-of-fit and the ecological meaning of dispersal models (in the seedling or sapling stage) may be enhanced. Parameters of the UF model are estimated through the EM algorithm and their standard errors are approximated via the observed information matrix. We fit the UF model to a dataset from an expanding European beech population of central Spain as well as to a set of simulated data. In comparisons with an allometric model, the UF model fitted the data better and the parameter estimates were less biased. The ecological meaning of the UF model results was also superior. We sug¬gest using this new approach for modeling dispersal in the seedling and sapling stages when tree size is not deemed to be in strong relation to the reproductive success of adults.

Nyckelord

EM algorithm

European beech

dispersal kernel

recruitment

reproductive process

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