It'll be a Poisson distribution. If the spread is too wide then the chance of spatiotemporally cohabiting civilizations of distinct origins will be diminishing

It'll be a Poisson distribution. If the spread is too wide then the chance of spatiotemporally cohabiting civilizations of distinct origins will be diminishingly small. But I don't actually think that the planetary parameters that allow for replication are (in any way) specific to earth.