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A repeated pattern has three possible causes. Convergent selection is the most interesting one — the same environment produces the same adaptive solution in independently evolving lineages. But it is not the only cause. The same pattern can come from drift or founder effects when small populations sample from shared ancestral variation and diverge in a history-dependent way. Or from shared ancestry when the trait was inherited once from a common ancestor, and the lineages look similar because they never lost it.
The key test is independence of origin. Sister species on nearby islands that share a trait are not independent replicates — they may have inherited the trait once. Species on distant continents that never interbred, sharing the same solution, are. The number of independent origins — measured from the phylogeny, not from surface similarity — is what discriminates the three causes.
Pattern ≠ process. "Six ecomorphs on four islands" is a pattern. "Six ecomorphs evolved independently on four islands" is a process claim that requires the tree. Always ask for the tree before the story.