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Improving structured population models with more realistic representations of non-normal growth

Publication ,  Journal Article
Peterson, ML; Morris, W; Linares, C; Doak, D
Published in: Methods in Ecology and Evolution
September 1, 2019

Structured population models are among the most widely used tools in ecology and evolution. Integral projection models (IPMs) use continuous representations of how survival, reproduction and growth change as functions of state variables such as size, requiring fewer parameters to be estimated than projection matrix models (PPMs). Yet, almost all published IPMs make an important assumption that size-dependent growth transitions are or can be transformed to be normally distributed. In fact, many organisms exhibit highly skewed size transitions. Small individuals can grow more than they can shrink, and large individuals may often shrink more dramatically than they can grow. Yet, the implications of such skew for inference from IPMs has not been explored, nor have general methods been developed to incorporate skewed size transitions into IPMs, or deal with other aspects of real growth rates, including bounds on possible growth or shrinkage. Here, we develop a flexible approach to modelling skewed growth data using a modified beta regression model. We propose that sizes first be converted to a (0,1) interval by estimating size-dependent minimum and maximum sizes through quantile regression. Transformed data can then be modelled using beta regression with widely available statistical tools. We demonstrate the utility of this approach using demographic data for a long-lived plant, gorgonians and an epiphytic lichen. Specifically, we compare inferences of population parameters from discrete PPMs to those from IPMs that either assume normality or incorporate skew using beta regression or, alternatively, a skewed normal model. The beta and skewed normal distributions accurately capture the mean, variance and skew of real growth distributions. Incorporating skewed growth into IPMs decreases population growth and estimated life span relative to IPMs that assume normally distributed growth, and more closely approximate the parameters of PPMs that do not assume a particular growth distribution. A bounded distribution, such as the beta, also avoids the eviction problem caused by predicting some growth outside the modelled size range. Incorporating biologically relevant skew in growth data has important consequences for inference from IPMs. The approaches we outline here are flexible and easy to implement with existing statistical tools.

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Published In

Methods in Ecology and Evolution

DOI

EISSN

2041-210X

Publication Date

September 1, 2019

Volume

10

Issue

9

Start / End Page

1431 / 1444

Related Subject Headings

  • 0603 Evolutionary Biology
  • 0602 Ecology
  • 0502 Environmental Science and Management
 

Citation

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Peterson, M. L., Morris, W., Linares, C., & Doak, D. (2019). Improving structured population models with more realistic representations of non-normal growth. Methods in Ecology and Evolution, 10(9), 1431–1444. https://doi.org/10.1111/2041-210X.13240
Peterson, M. L., W. Morris, C. Linares, and D. Doak. “Improving structured population models with more realistic representations of non-normal growth.” Methods in Ecology and Evolution 10, no. 9 (September 1, 2019): 1431–44. https://doi.org/10.1111/2041-210X.13240.
Peterson ML, Morris W, Linares C, Doak D. Improving structured population models with more realistic representations of non-normal growth. Methods in Ecology and Evolution. 2019 Sep 1;10(9):1431–44.
Peterson, M. L., et al. “Improving structured population models with more realistic representations of non-normal growth.” Methods in Ecology and Evolution, vol. 10, no. 9, Sept. 2019, pp. 1431–44. Scopus, doi:10.1111/2041-210X.13240.
Peterson ML, Morris W, Linares C, Doak D. Improving structured population models with more realistic representations of non-normal growth. Methods in Ecology and Evolution. 2019 Sep 1;10(9):1431–1444.
Journal cover image

Published In

Methods in Ecology and Evolution

DOI

EISSN

2041-210X

Publication Date

September 1, 2019

Volume

10

Issue

9

Start / End Page

1431 / 1444

Related Subject Headings

  • 0603 Evolutionary Biology
  • 0602 Ecology
  • 0502 Environmental Science and Management