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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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This content will become publicly available on May 27, 2026
Evaluating methods for addressing skewness in clustering: a focus on generalized hyperbolic mixture models
In model-based clustering, the population is assumed to be a combination of sub-populations. Typically, each sub-population is modeled by a mixture model component, distributed according to a known probability distribution. Each component is considered a cluster. Two primary approaches have been used in the literature when clusters are skewed: (1) transforming the data within each cluster and applying a mixture of symmetric distributions to the transformed data, and (2) directly modeling each cluster using a skewed distribution. Among skewed distributions, the generalized hyperbolic distribution is notably flexible and includes many other known distributions as special or limiting cases. This paper achieves two goals. First, it extends the flexibility of transformation-based methods as outlined in approach (1) by employing a flexible symmetric generalized hyperbolic distribution to model each transformed cluster. This innovation results in the introduction of two new models, each derived from distinct within-cluster data transformations. Second, the paper benchmarks the approaches listed in (1) and (2) for handling skewness using both simulated and real data. The findings highlight the necessity of both approaches in varying contexts.
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- Award ID(s):
- 2209974
- PAR ID:
- 10621649
- Publisher / Repository:
- Taylor & Francis
- Date Published:
- Journal Name:
- Journal of Statistical Computation and Simulation
- ISSN:
- 0094-9655
- Page Range / eLocation ID:
- 1 to 16
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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