All statistical analyses were performed in SAS Statistical Analysis Software v.9.4 (Cary Institute N.C., United States). All data were analyzed using Bayesian regression models with the ‘genmod’ procedure (PROC GENMOD) with the ‘bayes’ option. Values for all data were scaled to z scores prior to running the models. The models had a burn-in size = 2000, MC sample size = 10,000, and a normal prior distribution (mean = 0, SD = 106). For feeding efficiency data, a separate model was run for each feeding efficiency parameter and included host plant effects (P. lanceolata vs Mimulus guttatus) on CI, AD, ECI, and ECD. Similarly, a separate model was run for each immune parameter and included host plant effects on total PO, standing PO, and melanization. Models with host plant effect on development time and pupal mass were also run. Finally, the effect of feeding efficiency parameters (CI, AD, ECI, ECD) on the strength of total PO, standing PO, and melanization was analyzed using multiple regression models for each immune parameter separately. Separate models were run for each host plant.
To summarize the output of models, we used the posterior probability means β) for each comparison (e.g., total PO on P. lanceolata vs Mimulus guttatus) and the 95% highest posterior density interval (HPDI) (McElreath, 2020 ). For figures summarizing models with host plant species as the independent variable, the x-axis displays the effect size (difference in means between host plants) of the response variables displayed on the y-axis. In models comparing the effect of host plant (i.e., where host plant is the independent variable), M. guttatus was used as the reference host plant. Thus, a positive effect size indicates that individuals reared on P. lanceolata had larger values than those reared on M. guttatus for the given response variable. In the same vein, a negative effect size indicates that individuals reared on M. guttatus had larger values than those reared on P. lanceolata for a given response variable. Effect sizes that are close to zero indicate little to no difference between the means of the groups being compared. For simplicity, we refer to P. lanceolata as having a positive or negative effect on the measured response variable. In the case of feeding efficiency effects on immunity, a mean value close to zero indicates no effect of the feeding efficiency parameter on the immune response. Positive and negative mean values indicate that the relationship between the two variables are positive or negative.
The 95% HPDI shows the narrowest portion of the posterior probability distribution corresponding to 95% of the response variable in the distribution (McElreath, 2020 ). Bayesian posterior probabilities (PP) were calculated for pairwise comparisons of host plant and for the effect of feeding efficiency on immunity (e.g., Fordyce et al., 2011 (link); Forister et al., 2013 (link); Smilanich et al., 2016 (link)). Using this approach, if the effect size for a particular set of categories (e.g., total PO for individuals reared on P. lanceolata) is greater than the effect size for a comparable level of categories (e.g., total PO for individuals reared on M. guttatus) for more than 95% of the 10,000 MCMC iterations, then the two effect sizes are considered to be highly different, or highly different from zero in the case of feeding efficiency effects on immunity (Fordyce et al., 2011 (link); Forister et al., 2013 (link); Smilanich et al., 2016 (link)).
To summarize the output of models, we used the posterior probability means β) for each comparison (e.g., total PO on P. lanceolata vs Mimulus guttatus) and the 95% highest posterior density interval (HPDI) (McElreath, 2020 ). For figures summarizing models with host plant species as the independent variable, the x-axis displays the effect size (difference in means between host plants) of the response variables displayed on the y-axis. In models comparing the effect of host plant (i.e., where host plant is the independent variable), M. guttatus was used as the reference host plant. Thus, a positive effect size indicates that individuals reared on P. lanceolata had larger values than those reared on M. guttatus for the given response variable. In the same vein, a negative effect size indicates that individuals reared on M. guttatus had larger values than those reared on P. lanceolata for a given response variable. Effect sizes that are close to zero indicate little to no difference between the means of the groups being compared. For simplicity, we refer to P. lanceolata as having a positive or negative effect on the measured response variable. In the case of feeding efficiency effects on immunity, a mean value close to zero indicates no effect of the feeding efficiency parameter on the immune response. Positive and negative mean values indicate that the relationship between the two variables are positive or negative.
The 95% HPDI shows the narrowest portion of the posterior probability distribution corresponding to 95% of the response variable in the distribution (McElreath, 2020 ). Bayesian posterior probabilities (PP) were calculated for pairwise comparisons of host plant and for the effect of feeding efficiency on immunity (e.g., Fordyce et al., 2011 (link); Forister et al., 2013 (link); Smilanich et al., 2016 (link)). Using this approach, if the effect size for a particular set of categories (e.g., total PO for individuals reared on P. lanceolata) is greater than the effect size for a comparable level of categories (e.g., total PO for individuals reared on M. guttatus) for more than 95% of the 10,000 MCMC iterations, then the two effect sizes are considered to be highly different, or highly different from zero in the case of feeding efficiency effects on immunity (Fordyce et al., 2011 (link); Forister et al., 2013 (link); Smilanich et al., 2016 (link)).
Free full text: Click here
