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**SPEAM** (funded by the City of Vienna Jubilee Fund, Grant No. JF_2021-03_SPEAM) is an agent-based simulation that models the evolution of word stress patterns. Agents in the simulation are stress patterns of di- and trisyllabic words that get together to form phrases. These phrases are then evaluated in terms of their rhythmic quality, and the fitness of the involved words and their stress patterns is changed according to that quality. Stress patterns that contribute to producing good utterance rhythms more often, become more frequent in the lexicon and in use. The simulation shows what types and proportions of stress patterns should be expected in a language, if word stress patterns adapt one another and to the rhythmic constraints on the phrases that result from their combination. The purpose of **SPEAM** is to test hypotheses about the distribution of word stress patterns among words in natural languages. It addresses such questions as why one can stress the English noun research both on the first and on the second syllable, or why the German noun Kaffee is stressed on the first syllables in some varieties, but on the last syllable in others. The central idea on which **SPEAM** is based is that lexical stress patterns are designed (or evolve) to yield rhythmically well-formed (or 'pleasing') phrases when words are combined to form phrases. The **SPEAM** simulation can be used to investigate what patterns this hypothesis predicts, depending on various factors such as how many monosyllabic, disyllabic, or trisyllabic words there are in a language, how likely they are to form different types of phrases with one another, or how pleasant or unpleasant different rhythmic sequences are felt to be. *SPEAM* allows one to construct one's own type of language, to specify one's assumptions about rhythmic well-formedness, and to test what predictions follow about the stress patterns that words in that language are likely to assume. These predictions can then be compared with the stress patterns found in actual languages, so that one can test the plausibility of the hypothesis that they really follow from preferences regarding phrase rhythm.
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