Document Type

Article

Publication Date

2014

College/Unit

Davis College of Agriculture, Natural Resources and Design

Department/Program/Center

Division of Forestry and Natural Resources

Abstract

Matrix population models are widely used to study population dynamics but have been criticized because their outputs are sensitive to the dimension of the matrix (or, equivalently, to the class width). This sensitivity is concerning for the population growth rate () because this is an intrinsic characteristic of the population that should not depend on the model specification. It has been suggested that the sensitivity of to matrix dimension was linked to the existence of fast pathways (i.e. the fraction of individuals that systematically move up a class), whose proportion increases when class width increases. We showed that for matrix population models with growth transition only from class to class , was independent of the class width when the mortality and the recruitment rates were constant, irrespective of the growth rate. We also showed that if there were indeed fast pathways, there were also in about the same proportion slow pathways (i.e. the fraction of individuals that systematically remained in the same class), and that they jointly act as a diffusion process (where diffusion here is the movement in size of an individual whose size increments are random according to a normal distribution with mean zero). For 53 tree species from a tropical rain forest in the Central African Republic, the diffusion resulting from common matrix dimensions was much stronger than would be realistic. Yet, the sensitivity of to matrix dimension for a class width in the range 1–10 cm was small, much smaller than the sampling uncertainty on the value of . Moreover, could either increase or decrease when class width increased depending on the species. Overall, even if the class width should be kept small enough to limit diffusion, it had little impact on the estimate of for tree species.

Source Citation

Picard N, Liang J (2014) Matrix Models for Size-Structured Populations: Unrealistic Fast Growth or Simply Diffusion? PLoS ONE 9(6): e98254. https://doi.org/10.1371/journal.pone.0098254

Comments

© 2014 Picard, Liang. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.