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

1. 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. 2. Here we develop a flexible approach to modeling
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 modeled 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. 3. 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 lifespan
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 modeled size
range. 4. 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.