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Congratulations - your ms is accepted
You are almost through the procedure; some small attention to Figs S1 and D2 is still needed
I see all issues raised in the first round of reviewing sufficiently addressed.
In Figs. S1 and S2, the resolution is too low to read anything properly. This needs to be adjusted, e.g. by providing vector graphic files.
Thank you for submitting your work to our journal. As you can see our reviewers would like to see some improvements of your ms.
I hope to get your revision in due time
Figs. 2 and 3 need manual editing, since floating-number thresholds do not make sense for integer variables.
There is a conflict between the sentence in lines 101 and 102 and the sentence starting in line 269. It needs to clarified how often this approach had been used before in the same field and in the wider area.
The sentence in lines 162-164 needs to be reformulated as it appears as if countries with native ("feral") populations were counted for "number of invaded countries".
Even if the number of invaded countries is correctly defined (see above), the question remains what it tells us biologically that this variable turned out to be the most relevant (and practical). What drove species to have already invaded so many countries? One should re-analyze the data with "number of invaded countries" as response variable.
It is a great achievement to apply this method to this question and dataset. In lines 239-263, the output of decision trees is clearly illustrated.
l. 28: introduction success
l. 122: replace "to establish"
from l. 146: do not use a tilde for a range as it is commonly used for model descriptions (e.g. in R)
l. 250: Fig. 3
My recommendation is to include one more variable: price (monetary value) of 1 individual from each respective bird species. I anticipate it would be difficult to obtain an accurate economical value, and therefore suggest 4 price categories: <50 euro/ US dollars, 50-100, 100-500 and >500.
Although I assume this addition will not change the results significantly, I believe it will help to better explain the main findings.
Line 151 (or 7th line in the “Variables” paragraph) Invcountry_Max(now is 'contry'). I found the same mistake in S1, species list, column Z.
Line 245-246 which had no record / with no record: a word is missing.
The reporting is clear and well written. The concise introduction contains all the information necessary. Overall, the paper complies to the professional standards to be expected for a scientific report.
The statistical methods were described precisely and sufficiently detailed. The decision tree method is not only an interesting alternative to other statistical procedures, it also provides clear rules for practitioners. The results obtained shed light on some important issues in invasion biology and hence conservation.
The findings are based on a well researched data set and are convincing. The discussion does include statements on the discrepancies with previous results by other research groups.
I would like to see a statement on the justification of using a simple sum of (highly non-linear) performance measures for assessing the overall performance of a method. The authors may also want to speculate a bit on the finding that maximum body size was a better predictor than average body size. To me this looks a bit a statistical fluke, possibly caused by one or very few outliers.
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