Timing of maternal exposure to toxic cyanobacteria and offspring fitness in Daphnia magna: Implications for the evolution of anticipatory maternal effects

Abstract Organisms that regularly encounter stressful environments are expected to use cues to develop an appropriate phenotype. Water fleas (Daphnia spp.) are exposed to toxic cyanobacteria during seasonal algal blooms, which reduce growth and reproductive investment. Because generation time is typically shorter than the exposure to cyanobacteria, maternal effects provide information about the local conditions subsequent generations will experience. Here, we evaluate if maternal effects in response to microcystin, a toxin produced by cyanobacteria, represent an inheritance system evolved to transmit information in Daphnia magna. We exposed mothers as juveniles and/or as adults, and tested the offspring's fitness in toxic and non‐toxic environments. Maternal exposure until reproduction reduced offspring fitness, both in the presence and in the absence of toxic cyanobacteria. However, this effect was accompanied by a small positive fitness effect, relative to offspring from unexposed mothers, in the presence of toxic cyanobacteria. This effect was mainly elicited in response to maternal exposure to toxic cyanobacteria early in life and less so during reproduction. None of these effects were explained by changes in egg size. A meta‐analysis using our and others’ experiments suggests that the adaptive value of maternal effects to cyanobacteria exposure is weak at best. We suggest that the beneficial maternal effect in our study is an example of phenotypic accommodation spanning generations, rather than a mechanism evolved to transmit information about cyanobacteria presence between generations.

The models to estimate the maternal effects, egg sizes and related fitness and the model for meta-analysis are described below in full matrix notation. The design matrices for the fixed effects, notated as as well as the poster estimated effect sizes , varied for the maternal effect and meta-analysis model depending on the covariates in the model. In the design matrix for the fixed effects each column contained the values for one covariate, with the first column containing only 1's for the intercept. In the design matrix for the random effects each column represents one class, for which 1 means the observation was within this class and 0 means it was not. All rows of sum to 1.

Maternal effects model
The maternal effects model consists of two general linear mixed models, which have their random effects jointly estimated. The maternal fitness was sampled from the following normal distribution; in which is the design matrix for the fixed effects, is the vector of posterior fixed effect sizes, Is the design matrix for the genetic effects, is the vector of genetic effects for each genotype and with a standard deviation of . The offspring fitness was sampled from the following normal distribution; Maternal effects as channels of inheritance -Supporting Information in which is the design matrix for the fixed effects, is the vector of posterior fixed effect sizes and is the design matrix for the genetic effects. is sampled from a normal distribution, with a mean of zero and a standard deviation . and were drawn from a uniform distribution from -10 to 10 and and were drawn from a half-Cauchy distribution with a mean of zero and a scale parameter of 0.1. For all models, we ran 4 chains of 10,000 iterations, of which we discarded the first 5,000 iterations as burn-in and thinned the iteration chains by only storing every tenth iteration.

Egg size models
The egg size measurements were sampled from the following normal distribution; in which is the design matrix of the maternal identity, is the average egg size produced by the mothers and with a standard deviation of . is sampled from a normal distribution, in which is the design matrix, is the vector of posterior effect sizes, is the design matrix for the genetic effects, is the vector of genetic effects for each genotype and with a standard deviation of . is sampled from a normal distribution, with a mean of zero and a standard deviation . The fitness measurements was sampled from the following normal distribution; in which is the design matrix, is the vector of posterior effect sizes, Is the design matrix for the maternal egg size effects and with a standard deviation of . and were 4/12 drawn from a uniform distribution from -10 to 10 and , , and were drawn from a half-Cauchy distribution with a mean of zero and a scale parameter of 0.1. For all models, we ran 4 chains of 150,000 iterations, of which we discarded the first 50,000 iterations as burn-in and thinned the iteration chains by only storing every hundredth iteration.

Models for meta-analysis
For the meta-analysis, we used a multi-level meta-analytic model (Nakagawa & Santos, 2012).
The effect size estimates were drawn from the following distribution; in which is the fixed effects design matrix, is the vector of posterior fixed effect sizes, are the between-study effects with their corresponding design matrix , are the betweenclone effects with their corresponding design matrix , are the trait-class effects with their corresponding design matrix , are the within-study effects and are the standard errors for the effect size estimates (i.e., sampling variance). -the between-study effects -are drawn from a normal distribution with standard deviation , the between study heterogeneity; ~0, -the between-clone effects -are drawn from a normal distribution with standard deviation , the clone variability; ~0, -the trait-class effects -are drawn from a normal distribution with standard deviation , the trait-class variability; ~0, -the within-study effects -are drawn from a normal distribution with standard deviation , the within-study variability; Maternal effects as channels of inheritance -Supporting Information

5/12
We first ran the model with only an intercept as fixed effect. Next, we ran the model with an intercept and the concentration of microcystin used in the studies as fixed effects. were drawn from a uniform distribution from -10 to 10 and , , , and were drawn from a half-Cauchy distribution with a mean of zero and a scale parameter of 0.1. For all models, we ran 4 chains of 12,000 iterations, of which we discarded the first 2,000 iterations as burn-in and thinned the iteration chains by only storing every tenth iteration. // standard deviations target += cauchy_lpdf(sigma_s | 0, 0.1); target += cauchy_lpdf(sigma_f | 0, 0.1); target += cauchy_lpdf(sigma_m | 0, 0.1); target += cauchy_lpdf(sigma_g | 0, 0.1); } Figure S1. Posterior effect sizes of the full model explaining total number of offspring.

References
Numbers correspond to coloured arrows in Figure 1a. Dots are the means, whiskers are the 95% credible intervals and violins are the distributions of the posterior estimates. In blue are the estimates for direct treatment effects, in red are the estimates for maternal effects and in purple are the interactions of the maternal effects with the offspring environment. On the grey background are the effects on maternal fitness (first generation) and on the white background are the effects on the offspring fitness (second generation). Although the full model was not among the best performing models (see Table S2), it is representative of the best models, in which all covariates are represented by at least 7 out of the 15 models.