Split-plot design
Combination of nested and randomized block designs
\[
y_{ijkl} = \rlap{\overbrace{\phantom{\mu + \alpha_i + \beta_{j(i)}}}^\text{Nested component}}\mu + \alpha_i + \underbrace{\beta_{j(i)} + \gamma_k + \alpha\gamma_{ik} + \beta\gamma_{j(i)k}}_\text{Randomized block component} + \varepsilon_{ijkl}
\]
\[
\begin{align}
Abund_{ijkl} = &Base + Shade_i + Block_{j(i)} + Treat_k +\\
&Shade:Treat_{ik} +Block:Treat_{j(i)k} + \varepsilon_{ijkl}
\end{align}
\]
