Random environmental fluctuations pose major threats to wild populations. As patterns of environmental noise are themselves altered by global change, there is growing need to identify general mechanisms underlying their effects on population dynamics. This notably requires understanding and predicting population responses to the color of environmental noise, i.e. its temporal autocorrelation pattern. Here, we show experimentally that environmental autocorrelation has a large influence on population dynamics and extinction rates, which can be predicted accurately provided that a memory of past environment is accounted for. We exposed near to 1000 lines of the microalgae Dunaliella salina to randomly fluctuating salinity, with autocorrelation ranging from negative to highly positive. We found lower population growth, and twice as many extinctions, under lower autocorrelation. These responses closely matched predictions based on a tolerance curve with environmental memory, showing that non-genetic inheritance can be a major driver of population dynamics in randomly fluctuating environments.  

Six strains (or mix of two strains) of the green microalgae Dunaliella salina have been exposed to 164 independant, randomly fluctuating time series of salinity, with four autocorrelation treatments. Populations were transferred twice a week for 37 transfers, and population sizes were measured after each transfer by spectrometry (optical density and fluorescence), and once a week by flow cytometry.

Optical density, fluorescence and cytometer counts are used to analyse Dunaliela population dynamics in stochastic environment. All measurements are integrated into a state-space models, assuming logistic growth between each dilution and transfer, using the R package TMB (Template Model Builder). The provided code estimates:

- the parameters of the distribution of growth rates in autocorrelated environments

- the parameters of the function relating growth to current and previous salinity.

Users can perform the analysis by running the R script (PDFE_analysis.R) after the installation of all packages mentioned in the preamble, then running the Mathematica notebook (moments_predicted.nb) 

This publication contains: 

- 1 dataset with population sizes:  

population_dynamics.csv 

- 1 dataset with glycerol concentrations: 

data_cinetique.csv 

- 5 C++ scripts compiled and run with the R TMB package: 

* density_dependence_cst.cpp : compute the negative loglikelihood of the dynamics of lines maintained in constant environments. This script estimates the growth rates and carrying capacities (constant within but varying between treatment genetic background x constant salinity). 

* logistic_data_K_unkownS_normal_autocorr_all_genotype.cpp : compute the negative loglikelihood for population dynamics of lines under stochastic environment, assuming a normal autocorrelated distribution of the growth rate with parameters (mean, standard deviation and autocorrelation) that depend on the genetic background and the autocorrelation treatment 

* logistic_data_K_unkownS_gamma_rho_all_genotype.cpp : compute the negative loglikelihood for population dynamics of lines under stochastic environment, assuming a reverse gamma distribution of the growth rate with parameters (mean, standard deviation and autocorrelation) that depend on the genetic background and the autocorrelation treatment 

* logistic_data_K: compute the negative loglikelihood for population dynamics of lines under stochastic environment and estimate parameters for the bivariate tolerance curves (parameters depend on the genetic background) 

* logistic_data_K_univariate: compute the negative loglikelihood for population dynamics of lines under stochastic environment and estimate parameters for the univariate tolerance curves (parameters depend on the genetic background) 

- 1 R script: 

PDFE_analysis.R. Performs the population dynamics analysis. Read the data, performs the survival analysis, analyses salinity effect on growth rate and carrying capacity in the constant salinity lines, analyses r distribution and fit bivariate and univariate tolerance curves in the stochastic lines. Code used for the plots is also present jointly with the analysis of the moments of N and r (estimation by treatment + regression). 

- A Mathematica notebook: 

moments_predicted.nb: compute the predicted mean, variance, skewness and autocorrelation of the growth rate given the bivariate and univariate tolerance curve parameters and the distribution of salinity in the different autocorrelation regime.