DOI: 10.5061/dryad.t6c3573
title: Data from: Improving structured population models with more realistic representations of non-normal growth

description: 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.
description: Bistort raw
 dataDemographic data for
 Polygonum viviparum collected at Niwot Ridge, CO from 2001-2011. szs0 =
 size at time t, szs1 = size at time t+1, bulbs0 = number of bulbils
 produced at time t. Details of data collection given in the supporting
 information.Gorgonian raw
 dataDemographic data for
 Paramuricea clavata collected in the NW Mediterranean Sea from 1999-2004.
 Mortality = source of mortality, Site = site, Plot = plot, Year = annual
 transition from time t to time t+1, Ncol = colony id, Size = size at time
 t, Sizenext = size at time t+1, Survnext = dead (0) or alive (1) at time
 t+1. Details of data collection and reproduction given in supporting
 information.Vulpicida raw
 dataDemographic data for
 Vulpicida pinastri collected in Kennicott Valley, AK from 2004-2009. Year
 = year at time t, site = site, t0 = size at time t, t1 = size at time t+1,
 repro = number of offspring assigned based on thallus circumference,
 survival = dead (0) or alive (1) at time t+1. Details of data collection
 and reproduction are given in supporting information.Appendix
 1R
 script for analyses in Figure 2Appendix
 2R
 script for analyses of coralAppendix
 3R
 script to simultaneously fit the minimum, maximum, mean, and precision
 parameters of the beta approach using maximum
 likelihood