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Abstract Integral projection models (IPMs) are widely used for studying continuously size‐structured populations. IPMs require a growth sub‐model that describes the probability of future size conditional on current size and any covariates. Most IPM studies assume that this distribution is Gaussian, despite calls for non‐Gaussian models that accommodate skewness and excess kurtosis. We provide a general workflow for accommodating non‐Gaussian growth patterns while retaining important covariates and random effects. Our approach emphasizes visual diagnostics from pilot Gaussian models and quantile‐based metrics of skewness and kurtosis that guide selection of a non‐Gaussian alternative, if necessary. Across six case studies, skewness and excess kurtosis were common features of growth data, and non‐Gaussian models consistently generated simulated data that were more consistent with real data than pilot Gaussian models. However, effects of “improved” growth modeling on IPM results were moderate to weak and differed in direction or magnitude between different outputs from the same model. Using tools not available when IPMs were first developed, it is now possible to fit non‐Gaussian models to growth data without sacrificing ecological complexity. Doing so, as guided by careful interrogation of the data, will result in models that better represent the populations for which they are intended.
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Improving structured population models with more realistic representations of non‐normal growth
Abstract 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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- PAR ID:
- 10447900
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Methods in Ecology and Evolution
- Volume:
- 10
- Issue:
- 9
- ISSN:
- 2041-210X
- Page Range / eLocation ID:
- p. 1431-1444
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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