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The acquisition of translation equivalents is often considered a special component of bilingual children's vocabulary development, as bilinguals have to learn words that share the same meaning across their two languages. This study examined three contrasting accounts for bilingual children's acquisition of translation equivalents relative to singlets (i.e., words that are first labels for a referent): the Avoidance Account whereby translation equivalents are harder to learn, the Preference Account whereby translation equivalents are easier to learn, and the Neutral Account whereby translation equivalents and singlets are learned similarly. To adjudicate between these accounts, Study 1 explored patterns of translation equivalent learning under a novel computational model - the Bilingual Vocabulary Model - which quantifies translation equivalent knowledge as a function of the probability of learning words in each language, and includes a bias parameter that varies the difficulty of learning translation equivalents according to each account. Study 2 tested model-derived predictions against vocabulary data from 200 French-English bilingual children aged 18-33 months. Results showed a close match between the model predictions and bilingual children's patterns of translation equivalent learning. At smaller vocabulary sizes, data matched the Preference Account, while at larger vocabulary sizes they matched the Neutral Account. Our findings show that patterns of translation equivalent learning emerge predictably from the word learning process, and potentially reveal a qualitative shift in translation equivalent learning as bilingual children develop and learn more words.