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Wiktionary
cross-fostering

n. the technique of removing eggs from the nest of one species of bird, to be incubated in the nest of another. Usually done to aid the recovery of endangered species. vb. (present participle of cross-foster English)

Wikipedia
Cross-fostering

Cross-fostering is a technique used in animal husbandry, animal science, genetic and nature versus nurture studies, and conservation, whereby offspring are removed from their biological parents at birth and raised by surrogates. This can also occasionally occur in nature.