What would be a plausible mechanism for conception involving an arbitrary number of gametes?

I am attempting to devise a mechanism whereby a species may reproduce in a communal manner. A number of individuals, ranging from two to arbitrarily high, may contribute gametes to a mass spawning and the resulting offspring will be genetically related to all of the parents who contributed. This would potentially allow for predominantly collectivist social structures as with social insects without limiting the population of reproductive individuals or resorting to an r-selection strategy where paternal relations are unknown and family groups could not develop. The intent is for any given community to function as one gigantic biological family.

As far as I am aware, no such reproductive cycle exists on Earth. Earthly life only ever has one or two parents contributing nuclear DNA.

EDIT: The problem I run into is with the cellular machinery. I assume the process would be similar to alternation of generations where the dominant generation has X-ploidy and the subsidiary generation of syncytia divides into X-ploid zygotes. How would the gametes would merge? How would the syncytia sort the chromosomes into viable zygotes? What would be an ideal ploidy under this system?

EDIT: One of the few examples in fiction I can think of are the Than-Thre-Kull from Gene Roddenberry's Andromeda. Even if it is unlikely to evolve, there must be some logical explanation? I read the paper "Genetic algorithms with multi-parent recombination" which convinced me it's possible, but it was concerned with computer science and not biology.

posted over 8 years ago

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