## 2 Materials and Methods
### Nested Field Partitioning Essays  
As mentioned before, the field partitioning approach implemented by current eSSPM methods shows relevant shortcomings during the delineation of MZ, such as presence zones nested within absence clusters, presence zones insensitive to differentiated levels of pest infestation, more than one pest absence zones, and inaccurately delimitated MZ [8]. To avoid these scenarios, MZ delineation essays implemented in this work were based on a two-step approach that we denominated nested field partitions. The first step consisted of binary field partitions where 500 random and spatially independent points representative of the experimental orchard (in terms of environmental factors relevant to the distribution of each simulated pest) were used to develop clustering essays that facilitated a rough distinction between pest presence and pest absence zones.  
The second step consisted of complementary field partitions where 500 representations of presence-only and absence-only zones were used to implement within-cluster field partitions useful to identify differentiated levels of pest infestation and nested pest presence/absence zones. The main difference between binary and complementary field partitioning essays is that the former aims to partition the target crop field into two sub-field units (i.e., pest presence and pest absence clusters). In contrast, the latter seeks to partition binary sub-field units into several MZ that facilitate whether the \"rescue\" of nested presence/absence zones or the recognition of differentiated levels of pest infestation.  
Ten MC algorithms were used to partition the experimental orchard binarily or complementarily (Table 3). These algorithms were implemented using R statistical software's \"cIValid\" package [50] and were selected on account of their known capability to group biological data sets [10,50]. A more profound explanation of such clustering approaches is presented in Appendix A.  
Since it was not always possible to generate \"perfect\" field partition models (i.e., containing completely homogeneous clusters), binary partitions of the experimental crop field yielded one of four possible scenarios: (1) the partition model included clusters that clearly distinguished between pest presence and pest absence zones, (2) the model included one accurate absence cluster and a presence cluster that incorrectly hosted absence zones, (3) the model included one accurate presence cluster and an absence cluster that incorrectly hosted presence zones, and (4) both clusters in the model included a mixture of presence and absence zones. Complementary partitioning essays were implemented on presence-only clusters for scenarios (1) and (2). This facilitated the differentiation of pest levels (scenario 1) and the isolation of nested pest absence zones (scenario 2), depending on the case. Scenarios (3) and (4) demanded the partitioning of both pest presence and pest absence clusters, which facilitated the isolation of nested pest presence zones (scenario 3) and the distinction between pest presence and pest absence zones (scenario 4).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Acronym** & **Class** & **Reference** & **Package** \\ \hline Average linkage & AL & hierarchical & [51] & fastcluster \\ Clustering large applications & CLA & partitioning & [52] & cluster \\ Complete linkage & CL & hierarchical & [51] & fastcluster \\ Divisive analysis & DIA & hierarchical & [52] & cluster \\ Fuzzy analysis & FNY & partitioning & [52] & cluster \\ Model-based clustering & MCL & model-based & [53] & mclust \\ Partitioning around medoids & PAM & partitioning & [52] & cluster \\ Self-organizing maps & SOM & machine learning & [54] & kohonen \\ Single linkage & SL & hierarchical & [51] & fastcluster \\ Ward’s linkage & WL & hierarchical & [55] & fastcluster \\ \hline \hline \end{tabular}
\end{table}
Table 3: Multivariate clustering (MC) algorithms compared during field partitioning essays developed in this work.