Fig 1.
Big Woods study region with one iteration of spatial cross-validation algorithm displayed.
For this particular iteration of the cross-validation algorithm, we train our models on all 14 unnumbered blocks of trees. We then apply the fitted model to make predictions on block 10. Blocks 1, 2, 3, 9, 11, 13, 14, and 15 act as “buffer” blocks isolating the test block from the training blocks.
Fig 2.
Comparison of the RMSE for all three species-groupings models.
We calculated the RMSE with and without spatial cross-validation. The dotted lines indicate the RMSE value when the competitor species’ identities were not permuted. The histograms indicate the distribution of the RMSE values resulting from 99 permutations of competitor species’ identities.
Fig 3.
Posterior distribution of β0,j for the family-level model.
These distributions display the estimated baseline (diameter-independent) growth (cm y-1) for each family.
Fig 4.
Posterior distribution of βDBH,j for the family-level model.
These distributions display the estimated change in annual growth (cm y-1) per cm of DBH for each family. Positive values indicate that larger individuals grow faster, while negative values indicate that larger individuals growth slower.
Fig 5.
Posterior distribution of λ family-specific competition coefficients.
Read across rows for that family’s competitive effect on other families and down columns for that family’s response to competition from other families. Positive values of λ indicate that trees of the focal group tend to grow faster if they have more neighbors of that competitor group, while negative values of λ indicate that trees of the focal group then to grow slower. For example, almost all groups tend to have slower growth in the presence of more Fagaceae neighbors, but tend to have faster growth in the presence of more Ulmaceae neighbors. Here we display just the 8 families for which there are at least 200 individuals in the plot. For a high resolution version of this image for the full 20-by-20 lambda matrix see S1 Fig. A full list of all species and families in the plot can be found in S2 Appendix. See S2 Fig for a phylogeny of these families and S3 Fig for counts of focal and competitor family pairs.
Fig 6.
Spatial pattern of residuals for the family-level model.
This shows the actual growth y of each tree minus its predicted growth . Blue individuals grew faster than expected by the model and red individuals grew slower. The residuals show clear spatial patterning.