Statistical modeling of patterns in annual reproductive rates

Abstract

Reproduction by individuals is typically recorded as count data (e.g., number of fledglings from a nest or inflorescences on a plant) and commonly modeled using Poisson or negative binomial distributions, which assume that variance is greater than or equal to the mean. However, distributions of reproductive effort are often underdispersed (i.e., variance < mean). When used in hypothesis tests, models that ignore underdispersion will be overly conservative and may fail to detect significant patterns. Here we show that generalized Poisson (GP) and Conway‐Maxwell‐Poisson (CMP) distributions are better choices for modeling reproductive effort because they can handle both overdispersion and underdispersion; we provide examples of how ecologists can use GP and CMP distributions in generalized linear models (GLMs) and generalized linear mixed models (GLMMs) to quantify patterns in reproduction. Using a new R package, glmmTMB, we construct GLMMs to investigate how rainfall and population density influence the number of fledglings in the warbler Oreothlypis celata and how flowering rate of Heliconia acuminata differs between fragmented and continuous forest. We also demonstrate how to deal with zero‐inflation, which occurs when there are more zeros than expected in the distribution, e.g., due to complete reproductive failure by some individuals.

Bird‐friendly wine country through diversified vineyards

“…The GLMM was performed using lme4 package (Bates et al. 2015) with a Poisson log‐link distribution to model the relationship among species‐guild detections and site covariates, and we used glmmTMB package for zero‐inflated Poisson models (Brooks et al., 2017, 2019). We conducted these statistical analyses with R, packages unmarked (Fiske & Chandler 2011) and AICcmodavg (Mazerolle 2017), and used ggplot (Wickham 2016) for plotting.…”

Phenotypic and environmental predictors of reproductive success in painted turtles

“…We included plastron length, as body size is an important predictor of clutch size in female painted turtles (e.g., Hoekstra et al 2018). Clutch size was under-dispersed, as is typical of reproductive data (Brooks et al 2019), and three females that were recovered from the ponds did not oviposit. Thus, to account for a zero-inflated, under-dispersed count distribution, we assessed generalized linear models using 'glmmTMB' v 1.0.2.1 (Brooks et al 2017;Brooks et al 2019).…”

“…Clutch size was under-dispersed, as is typical of reproductive data (Brooks et al 2019), and three females that were recovered from the ponds did not oviposit. Thus, to account for a zero-inflated, under-dispersed count distribution, we assessed generalized linear models using 'glmmTMB' v 1.0.2.1 (Brooks et al 2017;Brooks et al 2019). We used an all-subset approach to model selection, which included every combination of variables from the full model and intercept-only models which assess only the constant and residual variance (Grueber et al 2011), with a zero-inflated Conway-Maxwell-Poisson error distribution to account for under-dispersion and zero-inflation in clutch size using 'dredge' from 'MuMIn' v 1.43.17 (Bartoń 2020).…”

Multigenerational downregulation of insulin/IGF-1 signalling in adulthood improves lineage survival, reproduction, and fitness inC. eleganssupporting the developmental theory of ageing

“…We determined the percentage of eggs that developed into adult males (n= 75 eggs assayed/treatment), one egg per individual Day 2 worm, as above, to determine if the stress induced by irradiation or mutation accumulation would increase male production above standard N2 wild-type levels, as seen previously for heat stress and starvation in C. elegans 51,52 . Age-specific reproduction was analysed using generalised linear mixed effects models to account for temporal pseudoreplication of repeated measures on the same individuals across lifetime, with the template model builder package ('glmmTMB' in R 93,94 ). Models fitted with Poisson, Zero-Inflated Poisson, Generalised…”

“…Poisson and Zero-Inflated Generalised Poisson error structure were compared using AIC values of model fit ('AICtab' function in 'bbmle' package), following 94 , to account for under-or over-dispersion and for zero-inflation, when it was found to occur in simulated residuals generated with the 'DHARMa' package 95 . Age and a quadratic form of age (age 2 ) were fitted as fixed effects in both the conditional and zeroinflation model formula, and significance assessed in each case.…”