Revealing metapopulation heterogeneities from ensemble lifetime dataset
Metapopulation experimental data are limited due to many factors, such as large
ecological time scales and technical difficulties. A common procedure to investigate the
lifetimes of metapopulations is to group samples from different patches, building the
ensemble lifetime dataset, that has sufficient size to go through an statistical analysis.
When applying this procedure, system variability is set aside and information at patch
level is apparently lost. We propose a methodology, assuming a weakly coupled
metapopulation, to reveal the distribution of patch variability. By implementing a
transformation that mixes the patches statistics, we generate the lifetime probability
distribution of the ensemble. Next, we obtain the inverse transformation that reveals
variability at patch level from the ensemble perspective, e.g. environmental conditions
and migration rates. Here, we apply our framework to a generalized case inspired by
experimental records and discuss how power-laws and other distributions can emerge
in the perspective of the ensemble due to patch-level heterogeneity.