Superposition construction
To study superpositions we select all populations at locations
with S0vS. The randomized surrogate data set is created by
shuffling these entries, and creating a time series from these
shuffled entries as follows.
(1) From the set of populations with S0vS we select randomly
a population and add up its initial population size S0, irrespective
of its location. (2) We repeat (1) until the sum exceeds S. This
results in a set of locations whose total initial population size equals
or slightly exceeds S. We call this set of locations one realization
of a superposition. (3) For each realization we study the temporal
development with respect to total populations size of the thereafter
fixed selected locations. For each superposition we construct a time
series, that is, the population growth rates in monthly resolution,
from t0 to t1. For this set of time series we obtain the ensemble
averaged ACF.