The authors' recent classification of trilinear operations includes four infinite fami-lies; the fourth (with parameter q) consists of [a, b, c] ∞ = abc + acb − bac + 2 bca, [a, b, c] q = 2 abc + q acb + (1−q) bac + q bca + (1−q) cab − cba. Every polynomial identity in degree 3 satisfied by these operations is a consequence of [a, c, b] − [b, a, c] + [b, c, a] − [c, a, b] = 0. In degree 5, for
... [Show full abstract] finite q there is a space of dimension 40 of identities which do not follow from the identity in degree 3. For six special values of q there are further identities: for q = 0, 1, −1, 2 we get dimension 49; for q = ∞, 1 2 we get dimension 54. Using the expansion matrix of the operation to find explicit identities in these six cases gives results with many terms and large coefficients. To simplify these results we apply a new evolutionary algorithm which gives results with fewer terms and much smaller coefficients. Our computations give examples of artificial evolution which combine gradual and punctuational changes.