Figure 1: Visual representation of
the various hypotheses (via simulated data), where yellow indicates high
growth rates and blue low growth rates. A represents a truly
asynchronous population cycle, where each population (line) cycles
independently of its neighbours. B shows partial synchrony
where the neighbouring populations’ cycle almost simultaneously, though
they are not perfectly synchronised (decomposed into subsequent models).C is a perfectly synchronised population where each population
cycles at precisely the same time (where \(r_{t}\) should best be
represented as varying with time, model N2). Fshows a purely spatial pattern (where any perceived spatio-temporal
pattern is merely spatial, model N3, as Sherratt and
Smith 2008 suggested may be the case for the apparent snowshoe hare
travelling wave). D is a single planar wave at a snapshot in
time (Moss et al . 2000; Lambin et al . 1998, Bjørnstadet al . 2002, Berthier et al . 2014, model P). Erepresents either an expanding or contracting single radial travelling
wave (radially expanding from a central location as suggested by Johnsonet al . 2006 [model RE] or contracting as suggested by
Sherratt & Smith 2008, [model RC]). G shows two isolated
planar waves separated by a physical feature, the Duero river (inferred
from Sherratt & Smith 2008, model PF). H shows two radial
waves separated by the same physical feature but may be either
contracting or expanding (models RFE and RFC). J represents
dual overlapping planar waves, which additively form a single overall
pattern (model PD). K is either dual overlapping contracting or
expanding radial waves, additively forming an overall pattern (models
RDE and RDC). I represents the modelling approach, represented
by the borders and arrows, used by the various parameterisations for
each model, described in Table 1, to recreate a synchronised cycle in
order to infer the form of partial asynchrony.