Sequences of alternate, second nearest neighbors, in rows and columns, effect an exhaustive decomposition of an initial lattice into four smaller lattices with no points in common. The expected second neighbor joins count, and the second neighbor variance, for the initial lattice are found by simple addition of these values from Krishna-Iyer joins tests performed separately upon each of the four smaller, independent lattices. The same principle extends to decompositions into nine independent lattices by third nearest neighbors, 16 independent lattices by fourth nearest neighbors, and so on. A simplifying feature is that the same sets of nearest neighbor decompositions invariably arise regardless of the starting point. Example calculations and results from a 19 × 28 = 532-tree lattice of 17 y (postplanting age) red pine (Pinus resinosa) are presented for first nearest neighbors (the standard Krishna-Iyer test), and for second and third nearest neighbors. In this example analysis, pockets of soils inimical to early survival are indicated by positive associations of first-year deaths across first, second and third nearest neighbors. Some possible “wave” effects are suggested by such recurrent associations as the largest trees with the empty spaces left by first-year deaths, as first and third nearest neighbors, but not as second neighbors.