Dormant life stages are often critical for population viability in stochastic environments, but accurate field data characterizing them are difficult to collect. Such limitations may translate into uncertainties in demographic parameters describing these stages, which then may propagate errors in the examination of population-level responses to environmental variation. Expanding on current methods, we 1) apply data-driven approaches to estimate parameter uncertainty in vital rates of dormant life stages and 2) test whether such estimates provide more robust inferences about population dynamics. We built integral projection models (IPMs) for a fire-adapted, carnivorous plant species using a Bayesian framework to estimate uncertainty in parameters of three vital rates of dormant seeds – seed-bank ingression, stasis and egression. We used stochastic population projections and elasticity analyses to quantify the relative sensitivity of the stochastic population growth rate (log λs) to changes in these vital rates at different fire return intervals. We then ran stochastic projections of log λs for 1000 posterior samples of the three seed-bank vital rates and assessed how strongly their parameter uncertainty propagated into uncertainty in estimates of log λs and the probability of quasi-extinction, Pq(t). Elasticity analyses indicated that changes in seed-bank stasis and egression had large effects on log λs across fire return intervals. In turn, uncertainty in the estimates of these two vital rates explained > 50% of the variation in log λs estimates at several fire-return intervals. Inferences about population viability became less certain as the time between fires widened, with estimates of Pq(t) potentially > 20% higher when considering parameter uncertainty. Our results suggest that, for species with dormant stages, where data is often limited, failing to account for parameter uncertainty in population models may result in incorrect interpretations of population viability.
dataDroso - census data
Demographic transitions of Drosophyllum lusitanicum populations recorded in annual censuses (from 2011 to 2015) in five populations. These data are used to quantify vital rates of above-ground individuals.
dataDroso.csv
dataDrosoSB - seed bank
Seed fates (in a binary format) inferred from two experiments. These data are used to quantify the transitions related to the seed bank and associated parameter uncertainties.
dataDrosoSB.csv
BayModel - Bayesian vital rate GLMMs
Executes and saves the results of a Bayesian model quantifying all vital rates; illustrates basic diagnostics that can be run on the results of an MCMC run (i.e., the posterior parameter distribution) to check for model convergence and autocorrelation of the posterior samples.
BayModel.R
mcmcOUT - parameter samples
In case the reader wishes to forego the step of fitting the Bayesian models, we provided a mcmcOUT.csv file with 1000 posterior parameter values for each of the parameters estimated with Bayesian models using uninformative priors
mcmcOUT.csv
makeIPM
Demonstrates how to construct IPMs including continuous and discrete (seed bank) transitions for (A) mean parameter values and (B) from the parameter distributions of the Bayesian models; saves IPMs for all parameters related to seed-bank ingression, stasis, and ingression. The code is based on the supporting material in Ellner and Rees (2006), Am. Nat., 167, 410-428
perturbVR - vital rate perturbations
Demonstrates how to construct IPMs from perturbed vital rates. Each IPM is obtained by (a) perturbing a vital rate by its mean or standard deviation (see makeVRmu.R on constructing mean vital-rate kernels) and (b) constructing a new IPM kernel incorporating the perturbed vital rate
perturbVR.R
makeIPMmu
function to constructs IPMs for average environments
makeVRmu
functions to constructs vital-rate kernels for average environments.
sLambdaSimul - stochastic lambda simulations
Runs simulations, based on different fire return intervals, of the stochastic population growth rate using IPMs constructed (A) from mean parameter values, (B) from perturbed vital rates, and (C) for each posterior sample of the parameters describing seed-bank ingression (goSB), stasis (staySB) and egression (outSB); calculates the stochastic population growth rate, its elasticities, and the probability of quasi-extinction at time t. The structure of the code is based on Tuljapurkar et al. (2003), Am. Nat., 162, 489-502 and Trotter et al. (2013), Methods Ecol. Evol., 4, 290-298.
sLambdaSimul.R
sLambdaRmpi - stochastic simulations on parallel processors
Implements the simulations of the stochastic population growth rate using parallel processing, where simulations are split into different processors of a supercomputer to greatly speed up computational time.
sLambdaRmpi.R