List on corrections:
Larger editing:
We have moved som technicalites into an appendix
We have combined results and discussion into one section (as proposed by ref 2)
Referee: 1
1. The measure used for speed of spread was the ratio between a pre-specified
distance and the time it took the invasion to spread that distance. Given the
possibility of accelerating invasions with the higher kurtosis values, it is not
clear that "time to reach one specified distance" is really the best way to
capture the effects of kurtosis.
Unfortunately we are not able to measure accelerating invasions in these
systems. It could be possible but the computational power is still a
limiting factor in this case. Another choice is one dimensional studies
yet they behave very different from the two dimensional ones. We have
commented this in section 3.2 paragraph 6.
2. The methods section, particularly section 2.2, was difficult to follow.
Several terms go unexplained (e.g. N_p, N_F, M, PSDF(origo), many of the
subscripts), and it is hard to keep track of when the narrative is dealing with
parameters used to generate landscapes and when it is dealing with parameters
used to describe the landscapes. This section should be edited for clarity. The
verbal descriptions of the continuity and contrast on lines 179-184 are very
helpful and should come much earlier in the discussion of these quantities.
We’ve made a substantial revision of this section. Including more details
on variables and also moved some sections to an appendix. More verbal
descriptions, also postioned earlier.
A few minor comments:
The explanation of relative distance dependence (lines 512-221) was confusing.
The phrase "colonization potential" should either be defined or avoided -although it made perfect sense once I stared at the equations and figured out
what relative distance dependence actually was, I found the phrase very confusing
initially because it sounded like the authors were trying to describe distanceindependence.
Rephrased to invasion process and new explanation of relative distance in
section 3.2 paragraph 4.
2. The "/a" in eqn 2.10 shouldn't appear as part of the subscript.
fixed
3. Figure 6 was missing from the pdf, and in its place was a high-res version of
figure 2.
fixed
Referee: 2
Comments to the Author(s)
I am writing to comment on "The shape of the spatial kernel and its implications
for biological invasions in patchy environments", by Lindstrom et al. This is an
interesting and sophisticated paper, but I had difficulty understanding the
authors' approach and its significance.
I therefore believe that ultimately the
paper will turn into a widely cited publication, but first I think that it must
be substantially rewritten. My preliminary impression is that the results are
novel and of widespread importance, but it is difficult for me to clearly
understand what is novel and what is not, and the larger significance is also
somewhat unclear to me.
A final point is that, in my opinion at least, the
authors assume that the reader is quite familiar with mathematical approaches to
invasions, and such an assumption is problematic for a biological journal like
Proceedings B. I hasten to add that I make these comments as a biologist with
perhaps above-average mathematical training and experience, which means that I
may have misinterpreted some of what is going on.
…
…
I nevertheless have two basic problems with the presentation of the methods and
the results. First, I could not tell whether the algorithm for constructing
neutral point patterns is novel. It certainly sounds like it is, and I can
appreciate that the algorithm itself is not the point of the paper, but the
algorithm is nevertheless a major focus, and so clarity on this point is
important.
We have been more clear with novelty, especially regarding the
construction of the NPPL, and also moved some technicalities out of the
manuscript into an appendix. We have included more verbal descriptions. We
have stressed the implications, see for example conclusions.
Second, in general the authors tend to refer to parameters using symbols without
text. This becomes almost a crippling problem in the figures, where the axes are
labeled with symbols only.
Fixed (will be)
the explanation in the Results of what the figures mean was very terse, and did a
very poor job of explaining the significance of the Results.
Fixed (check it)
I can appreciate that the traditional approach is to explain things in the
Discussion, but my opinion is that a more modern and indeed more useful approach
is to explain the figures and their meaning in the Results section itself.
Fixed.
I also had difficulty with the lack of explanation in the Introduction, where the
authors refer to "a spatial kernel" in the first paragraph without explaining
what they mean. They then continue this approach in the second paragraph, where
they define the moments of the kernel, still without an explanation of what they
mean by the word "kernel". It is certainly true that, within the literature on
models of invasion, the word is widely used, but I would argue that in the
context of Proceedings B a definition is necessary, and indeed that empirical
examples would be extremely helpful.
This basic problem aside, I repeat that
the authors' main point that dispersal is usually modeled using a Gaussian
probability function is well taken.
A large revision is made se four first paragraphs in introduction
Two final points are that the description of the algorithm for landscape
construction did not help me to understand what was going on. Equations 2.5-2.8
in particular were unhelpful. It might make more sense to move the technical
details to an appendix, and instead to simply describe the approach verbally. On
the other hand, I think I understand what is happening in equations 2.1-2.3, but
it is certainly true that more explanation is needed to point out the differences
between an ordinary Gaussian kernel and a generalized Gaussian kernel. It is
nevertheless possible that these equations should also be moved to an appendix,
and replaced with text explaining the kernel. Lastly, I would move Fig.~6
forward to the Methods section.
We have rewritten this, moved some mathematics to an appendix, moved
figure 6. Vi skall nog ploppa in något kring generalized vs normal I
section 2.2