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Inverse modeling for effective dispersal: do we need tree size to estimate fecundity?
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology.
(English)Manuscript (preprint) (Other (popular science, discussion, etc.))
Abstract [en]

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.

Keyword [en]
EM algorithm, European beech, dispersal kernel, recruitment, reproductive process
URN: urn:nbn:se:umu:diva-33759OAI: diva2:317873
Available from: 2010-05-05 Created: 2010-05-05 Last updated: 2010-05-07Bibliographically approved
In thesis
1. On perfect simulation and EM estimation
Open this publication in new window or tab >>On perfect simulation and EM estimation
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Perfect simulation  and the EM algorithm are the main topics in this thesis. In paper I, we present coupling from the past (CFTP) algorithms that generate perfectly distributed samples from the multi-type Widom--Rowlin-son (W--R) model and some generalizations of it. The classical W--R model is a point process in the plane or the  space consisting of points of several different types. Points of different types are not allowed to be closer than some specified distance, whereas points of the same type can be arbitrary close. A stick-model and soft-core generalizations are also considered. Further, we  generate samples without edge effects, and give a bound on sufficiently small intensities (of the points) for the algorithm to terminate.

In paper II, we consider the  forestry problem on how to estimate  seedling dispersal distributions and effective plant fecundities from spatially data of adult trees  and seedlings, when the origin of the seedlings are unknown.   Traditional models for fecundities build on allometric assumptions, where the fecundity is related to some  characteristic of the adult tree (e.g.\ diameter). However, the allometric assumptions are generally too restrictive and lead to nonrealistic estimates. Therefore we present a new model, the unrestricted fecundity (UF) model, which uses no allometric assumptions. We propose an EM algorithm to estimate the unknown parameters.   Evaluations on real and simulated data indicates better performance for the UF model.

In paper III, we propose  EM algorithms to  estimate the passage time distribution on a graph.Data is obtained by observing a flow only at the nodes -- what happens on the edges is unknown. Therefore the sample of passage times, i.e. the times it takes for the flow to stream between two neighbors, consists of right censored and uncensored observations where it sometimes is unknown which is which.       For discrete passage time distributions, we show that the maximum likelihood (ML) estimate is strongly consistent under certain  weak conditions. We also show that our propsed EM algorithm  converges to the ML estimate if the sample size is sufficiently large and the starting value is sufficiently close to the true parameter. In a special case we show that it always converges.  In the continuous case, we propose an EM algorithm for fitting  phase-type distributions to data.

Place, publisher, year, edition, pages
Umeå: Print & Media, 2010. 29 p.
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300
Perfect simulation, coupling from the past, Markov chain Monte Carlo, point process, Widom-Rowlinson model, EM algorithm, dispersal distribution, fecundity, first-passage percolation
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
urn:nbn:se:umu:diva-33779 (URN)978-91-7264-985-9 (ISBN)
Public defence
2010-06-01, N420, Umeå universitet, Umeå, 13:01 (English)
Available from: 2010-05-07 Created: 2010-05-06 Last updated: 2010-05-07Bibliographically approved

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