Description:
<jats:title>Abstract</jats:title><jats:p>In this paper we analyse the migration process in connection with the birth and death process. We assume that the populations are distributed spatially and are subject to birth, death and migration to or from neighbouring populations. Furthermore, we distinguish between populations with infinite and finite number of colonies. By this way we calculate the cumulant of first order.</jats:p><jats:p>First this problem was studied by B<jats:sc>AILEY</jats:sc> and A<jats:sc>DKE</jats:sc> for time‐dependent rates. Similarly P<jats:sc>URI</jats:sc> has specialized the problem for right migration (<jats:italic>v</jats:italic><jats:sub><jats:italic>ij</jats:italic></jats:sub> = 0 for <jats:italic>i</jats:italic> ≢ <jats:italic>j</jats:italic>). Finally R<jats:sc>ENSHAW</jats:sc> had the same result with other procedures.</jats:p>