We do not agree with the authors: the discretization of the original differential equation would have resulted in destabilization had we performed synchronous updates. This is why we elected to use asynchronous updates to simulate the original continuous time differential equation model by inducing gradual changes in the system (Durrett and Levin 1994b). The use of asynchronous updates to approximate a continuous time process has a rich history in cellular automata theory (Durrett and Levin 1994a, 1994b, Schonfisch and de Roos 1999, Nehaniv 2002, 2004, Cornforth et al. 2003, 2005, Fates and Morvan 2005). Classical cellular automata have often been

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We have decided to resubmit our comment on Gouhier et al (2010).

The comments by the
authors on our comment were helpful since they were more detailed about their update scheme
and hence we were able to more correctly reproduce their results.

Some of our critique is
thereby
no longer correct yet our main point is still absolutely correct. Our critique is focusing on
two
points: that is the difference equation vs
.

differential equation and the ecological assumptions
made when applying asynchron
ous update.


We are fully aware of the procedure and appreciate
it
since it reduces the risk of
misunderstandings not based on scientific issues.


Our initial submission was MS #52469

Author: Uno Wennergren; Sara Gudmundson


ASSOCIATE EDITOR'S RECOMMENDATI
ON


I have obtained a response to this critique by the original authors. They argue that the critique is
mistaken, largely because of misunderstanding of how the updating schemes used in the
simulations work. This is largely a technical point that I'm not
qualified to fully evaluate.
However it is one that will need to be carefully discussed if the authors wish to submit a suitably
revised version of the ms. Additionally, the response highlights other issues with the theoretical
critique that will need to b
e better discussed.


Mathew Leibold

Associate Editor

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


We have carefully discussed why an asynchronous update doesn’t necessary equal a correct
numerical solution of differential equations. We

have also showed that it doesn’t in this case.
From there we discuss its implications on conclusions and furthermore we argue that the
ecological assumptions made when applying this specific update scheme
are neither correct nor
justified.
Our conclusion
is that the study has an erroneous modeling approach (t
he assumptions)
and also lacks
correct mathematical analysis

(asynchronous updates
do
not equal correct
numerical solution)
.

T
he
ir

conclusions are erroneous, which is somewhat uninteresting since the
s
tudy
relies

on an unsound ecological approach
by

questionable

assumptions.

Below we have
some comments on their reply on our manuscript. We only deal with our two main points and
have disregarded the major part of their reply since its irrelevant either du
e to our previous
misinterpretation of their modelling or simple that they do not deal with the issue.


Comments in the reply of Gouhier et al. on difference equations vs. differential equations:


We do not agree with the authors: the discretization of the

original differential equation would
have resulted in destabilization had we performed synchronous updates. This is why we elected
to use asynchronous updates to simulate the original continuous time differential equation model
by inducing gradual changes

in the system (Durrett and Levin 1994b). The use of asynchronous
updates to approximate a continuous time process has a rich history in cellular automata theory
(Durrett and Levin 1994a, 1994b, Schonfisch and de Roos 1999, Nehaniv 2002, 2004, Cornforth
et

al. 2003, 2005, Fates and Morvan 2005). Classical cellular automata have often been
criticized for using synchronous updates, which are unrealistic since they assume that all
components of the system respond to a common, global clock or trigger (Schonfisc
h and de Roos
1999, Cornforth et al. 2003, 2005, Fates and Morvan 2005). While real spatial ecological
systems may appear synchronous at broad temporal scales (e.g. ecological processes often share
a common response to seasonality, phenology), most locatio
ns typically do not undergo any form
of demographic change (e.g. births, deaths, immigration or emigration) at finer temporal scales
(Schonfisch and de Roos 1999). Hence, at finer temporal scales, real ecological systems can be
perceived and modeled asynch
ronously since some locations may undergo (multiple)
demographic changes while other locations exhibit no changes. In this context, asynchronous
updates can be viewed as the discretization and approximation of the continuous time processes
observed in natu
ral systems (Schonfisch and de Roos 1999).



Our specific comment on this, not

exactly phrased like this

in
our
manuscript
, is intented to help
the editors to clear out some of the technical details
: Please note the exact wording of
Schonfisch
and de Roos
1999
:

asynchronous updates can be
viewed
as the discretization and
approximation of the continuous time
processes
.


From a mat
h
ematical and numerical method
perspective the wording as viewed and processes are very different from more strict

analysis and
Schonfisch and de Roos

have used this wording to address the problem correct yet Gouhier et al
.

have
misinterpreted
these authors
. A
lso note that what is discussed in all this references
abo
v
e
are cellular automata models where cells switch between states,

for example occupied or non
-
occuppied, which is very different from population densities, and
even more so in
a
cell with a
food

web

of several species and their densities. The reasoning above by Gouhier et al
.

is not
justifying their study.


Comments in
the reply of Gouhier et al on critical assumptions in the dispersal:


Wennergren and Gudmundson claim that our dispersal process is not appropriate because all
individuals disperse to the same randomly
-
selected neighboring location, “and such a modeling
fr
amework may cause very specific dynamics” (page 9, lines 202
-
203). They suggest that we
should allow individuals from a focal location to disperse to all neighboring locations, rather
than a single randomly
-
selected location. However, we found that our dis
persal mechanism did
not introduce any particular artifact in our results, as were able to reproduce the results of
Vasseur and Fox (2007) at high rates of dispersal (Fig 1., column 1).


Furthermore, we elected to use this dispersal mechanism because we wa
nted to focus on the
effect of dispersal on food webs at the metacommunity level. Allowing the different components
of the food web (i.e. the resource, the consumers and the predator) to disperse to different
locations would have added another layer of com
plexity (and spatial heterogeneity) that we were
not interested in exploring at the time.



Our comment on th
is

reply:
We do understand that the effect on metacommunity level is
interesting and
that

they want to measure
it.
However,
this

do
es

not justify the
ir

ecological
assumptions made on individual and population level.
The dispersal process as such doesn’t
occur on metacommunity level, it is based on processes on individual and population level
.
Therefore,

the dispersal modeling has to be
based on ecological reasoning at that level.
The only
possible way to transfer this to a metacommunity process would be to
study it as having cells
occupied or non occupied by foodwebs, i. e. cellular automata with rules for update that relate to
a
fo
o
d

we
b. Yet, we can’t understand the purpose and interest of such a crude model. Such a
model is
also
very different from the approach of Gouhier et al..


We have written the comment such that the critique is clear yet not, at least not intended to be,
harsh an
d personal. We were about to finish a study that resembles their work and we were
confused by their results which both contradict our study and previous analogous ones. We are of
course open for suggestions in how this critical review is presented. Based o
n the important
differences between previous publications and the conclusions of Gouhier et al. (2010), and also
to assure that erroneous methodology is not spread within the scientific community, we think it is
of major importance for the advancement of e
cological theory that our comment is made
available for comparison.


Our manuscript that are related, yet not submitted, can be submitted to Am. Nat whenever it is
convenient. Yet, we found it more appropriate to separately solve the issue with Gouhier et
al
.

to
avoid confusion and when that comment is available for reviewers proceed with our manuscript.
Still if you think it is more suitable to review and or publish them in parallel we can of course
submit that manuscript immediately. The title of our manu
script is “
Spatially structured food
webs in colored environments

.


-----------------------------------------------------------------------------------------------------------------

Th
is

work is original and has not been published, accepted or ever submi
tted elsewhere. Neither
has any part of the results been included in any published or submitted work.
Its submission for
publication has been approved by all authors and the institution.


The authors.

Uno Wennergren

and

Sara Gudmundson