Computational protocol: Maternal Effects May Act as an Adaptation Mechanism for Copepods Facing pH and Temperature Changes

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Protocol publication

[…] The combined egg (∑5i = 1EPRi) and nauplii production (∑5i = 1NPRi) data were analyzed using two-way factorial ANOVA with the factors temperature, pH (two levels) and their interaction. Because it varied between days but less within-treatment than between treatment, pH was treated as a factor in the analysis. Model assumptions, i.e., constancy of variance and normality of errors were checked after fitting the model by using the Fligner-Killeen test, and by plotting the residuals against fitted values, and standardized residuals against theoretical quantiles. All statistical analyses were conducted using software R 2.10.1 .Egg production during five consecutive days was analyzed using a linear mixed effects model (LMM) with restricted maximum likelihood (REML) approximation using the nlme-package . Temperature (two-level factor), pH (arithmetic averages for start and end H+ concentrations converted back to the pH scale), day and all their two-way interactions were used as fixed effects. Because the interaction between temperature and pH was significant, indicating that the effect of pH is different in the two temperatures, the model was rerun to establish estimates of pH effect at 17°C and at 20°C . The random effect structure was day (repeated measure) within each bottle. Model simplification was done manually in a backward stepwise manner using Akaike’s information criterion (AIC) and likelihood ratio test for justifying the simplifications. We report F-statistics of the retained fixed effects. After fitting the best possible LMM, residual diagnostics were performed to check that the assumptions were not violated.The cumulative hatching of eggs produced on days 1, 3 and 5 was analyzed using a generalized linear mixed effects model (GLMM) with Laplace likelihood approximation using the lme4-package , with a binomial error structure and a logit link function . The variables used in the full model, and their definitions are listed in . Model simplification was done manually in a backward stepwise manner using AIC and χ2-test. Interactions between the factors egg production temperature and hatching temperature and the covariate hatching time, and the factor day and the covariate |ΔpH| were significant, indicating that the relation between the covariate and hatching success differs between groups, and that a difference between groups depends on the value of the covariate . The interactions prevent interpretation of the main effects of covariates. Since the only covariate of interest is |ΔpH|, we ran the model again for all three factor levels of day without the interaction, and without the day nested within bottles’ random structure. […]

Pipeline specifications

Software tools lme4, nlme
Application Mathematical modeling