From the lme4 package, use the command:data(Arabidopsis), to call the data on genetic variation in responses to fertilization and simulated herbivory in Arabidopsis.

• Establish anargument about what effects there are, and whether they are random or fixed. Use the "lmer" function to fit your proposed model to the data.
• Provide residual plots and statistical conclusions regarding extrapolating this model to other data points.
• Explain the mathematical meaning behind each for the input parameters to the "lmer" function.

Explain your reasoning and provide examples where necessary when answering the following questions:

Are all hierarchical models necessarily mixed models?

Are mixed models necessarily hierarchical?