  Aggregated metapopulation lifetime statistics has been used to access
stylized facts that might help identify the underlying patch-level dynamics.
For instance, the emergence of scaling laws in the aggregated probability
distribution of patch lifetimes can be associated to critical phenomena, in
which the correlation length among system units tends to diverge. Nevertheless,
an aggregated approach is biased by patch-level variability, a fact that can
blur the interpretation of the data. Here, I propose a weakly-coupled
metapopulation model to show how patch variability can solely trigger
qualitatively different lifetime probability distribution at the aggregated
level. In a generalized approach, I obtain a two-way connection between the
variability of a certain patch property (e.g. carrying capacity, environment
condition or connectivity) and the aggregated lifetime probability
distribution. Furthermore, for a particular case, assuming that scaling laws
are observed at the aggregated-level, I speculate the heterogeneity that could
be behind it, relating the qualitative features the variability (mean, variance
and concentration) to the scaling exponents. In this perspective, the
application points to the possibility of equivalence between heterogeneous
weakly-coupled metapopulations and homogeneous ones that exhibit critical
behavior.
