Dear Marcel
Thank you for your quick response. We hold a great amount of respect for Ecology Letters,
publishing the most novel research in ecology. We understand your reasoning regarding our
manuscript being similar to the objectives of the recent publication of Gouhier et al (2010).
However, according to our findings, we think it would be unfortunate for the advancement of
ecological theory if this article prevents similar manuscripts being published. Our opinion is
based on the incorrect conclusions and methods being presented in Gouhier et al (2010).
Even though both Gudmundson et al. and Gouhier et al. (2010) have similar objectives they
do not present similar results. On the contrary, the results are contradictive and the results of
Gouhier et al. (2010) are based on a severe, yet unintentional, error in their modeling
approach. We do understand that this was not easy to detect during your initial referee
process. Actually it was not clear to us when we submitted. It took us quite a while to realize
that it is an error. This is not the first guess when scrutinizing the results of a paper. The error
refers back to Maser et al. (2007) and is a result of mistreating the model of Hassel & Wilson
(1997).
Gouhier et al. (2010) investigates the effect of a spatial dimension using spatial heterogeneity
induced by dispersal (see Comins et al. 1992, Hastings & Higgins 1994, Hassel et al. 1994,
Kareiva & Wennergren 1995). The aim and assumptions of Gouhier et al. (2010) is to
investigate the effect of environmental variation in a homogenous landscape, defined
according to them as variation synchronized over space. Yet, their dispersal scheme itself
unintentionally desynchronizes the environmental variation. Hence the results they present
completely depend on a non synchronized (spatially) environmental variation. We discovered
the error by first searching for the reason why individuals from populations, with the same
abundance over space, start dispersing when governed by a density dependent dispersal
regime. Based on our careful examination of the method used in Gouhier et al (2010), we
have discovered that they induce a time lag in their dispersal. The error can be found on page
E19. Individuals disperse from a local cell (after growth) to a neighboring cell (with density
as before growth). This error gives rise to a time lag which generates an unsynchronized
environmental variation. Unsynchronized environmental variation gives rise to differences in
abundance between neighboring patches necessary for dispersal. The erroneous method has
its origin in the paper of Maser et al. (2007), which more clearly write out the differences in
time steps between local and neighboring patch.
Maser et al. (2007) refer to Hassel & Wilson (1997) when stating: “The order of update
versus dispersal is not important”, update here is defined as local growth. Yet, Hassel &
Wilson (1997) do not state that a mixture of different densities with regard to time is not
important. To be more precise: Maser et al. (2007) and Gouhier et al. (2010) eq. is as
ZL’= ZLt+1-Dz(ZLt+1-ZN), where L is local cell and N is neighbouring cell. ZL’ denotes the
density after update and dispersal, ZLt+1 denotes only update. The difference (ZLt+1-ZN) makes
a difference and Hassel & Wilson (1997) do not state that such a scheme decouple dispersal
and growth to make the order unimportant. Hence the approach of Gouhier et al, and also
Maser et al, are both non spatial since no dispersal ought to occur yet it does due to their error.
A second strange part of the model of Gouhier et al is the dispersal of all species into only
one randomly selected neighbouring patch. This made us very puzzled and we thought this
was the reason for their strange results. Hence, it unfortunately led us into a sidetrack. Hassel
& Wilson (1997) also use local and neighboring cells yet they do not have a one neighbor
dispersal approach. In our opinion, the dispersal of all species into only one neighboring cell
is more of individually based modeling where one single individual move. Instead, Hassel &
Wilson (1997) have dispersal to all neighboring cells and the density dependence is based on
mean density of all these. Of course, Hassel and Wilson calculate density differences for
populations existing at the same time!
To say, as Gouhier et al. (2010), that dispersal itself stabilize populations situated in a
homogenous environment is according on our results an erroneous one. We do find a
stabilising effect of dispersal, yet it is only apparent when patches are affected by non
synchronous (spatially) environmental variation (Gudmundson et al. manuscript).
We are aware that Gouhier et al. (2010) also investigates the effect of colored noise. However,
Gouhier et al. (2010) do not show the important quantitative effect of this component.
Secondly, colored noise will interact with their induced time lag by the dispersal scheme.
This is apparent in their figures where populations become more synchronized by red than
white noise. Yet this is again a result of their dispersal scheme since autocorrelation, time,
will cause less difference between the two densities in their dispersal scheme.
We agree that we should have a more detailed discussion regarding the differences between
our results and Gouhier et al. (2010). In a reworked version of our manuscript we will
explicitly address Gouhier et al. (2010) and Maser et al. (2007) and properly discuss our
differences. Based on the important differences between our manuscript and Gouhier et al.
(2010) we think it is of major importance for the advancement of ecological theory that our
result are made available for comparison. We hope that this new information combined with
our manuscript presenting important extensions to the investigation by Vasseur & Fox
(Ecology Letters 2007) will result in a reevaluation of our manuscript for publication in
Ecology Letters, yet revised according to our findings outlined above. In short, if you agree
we will resubmit a revised version of our manuscript where the errors in Gouhier et al and
Maser et al is more clearly stated, yet in a decent way. And of course our manuscript must be
dealt with in the peer review process as all manuscript, hence we are aware that it may result
in rejection by other reasons then the publication of Gouhier et al.
The authors
Uno Wennergren, Sara Gudmundson and Frida Lögdberg
References
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