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A decomposable strongly critical Galton-Watson branching process with $N$types of particles labelled $1,2,...,N$ is considered in which a type~$i$parent may produce individuals of types $j\geq i$ only. This model may beviewed as a stochastic model for the sizes of a geographically structuredpopulation occupying $N$ islands, the location of a particle being consideredas its type. The newborn particles of island $i\leq N-1$ either stay at thesame island or migrate, just after their birth to the islands $%i+1,i+2,...,N$. Particles of island $N$ do not migrate. We investigate thestructure of the family tree for this process, the distributions of the birthmoment and the type of the most recent common ancestor of the individualsexisting in the population at a distant moment $n.$

Macroscopic and microscopic structures of the family tree for decomposable critical branching processes