This authors re-analyse a well-known dataset on grey-sided vole from Hokkaido using a Bayesian approach allowing for heterogeneity among time series in terms of autoregressive order, parameters, and allowing for a common temporal random effect across time series. They identify three time-series groups of autoregressive orders (2, 3 and 4) and correlate this to climate covariates (temperature, warmth index). They also assess changes in abundance as a function of climate change. The re-analysis of the time-series is a valuable piece of work, but I am not convinced by some of the interpretations.
For example, it is written that “The fact that the AR(2) populations were located in cooler areas where Apodemus wood mouse species were rare” but the differences in the proportion of grey-sided vole are relatively minor: in figure 3 (or lines 341-342), you go from a vole rate of 0.58 for AR2 to 0.46 for AR4, hardly a big change (i.e., statistical significance is not biological significance). The discussion on l. 455-464 is perhaps more relevant if you have data on Vaccinium – ie more information than l. 462 “Vaccinium uliginosum and Vaccinium vitis-idaea are common in the area with AR(2) populations. I think you need to write the discussion in a more “open-minded” way – many factors could explain the difference between the three groups, and it is not because predator-prey interactions could lead to AR2 models that AR2 models have to imply predator-prey relationships. We still know too little about the time delays of the different species involved (plants, voles, predators) to infer anything with confidence from time-series analyses.

The analyses of the relationships with the climate variables are rather messy – eg l. 328 ff, a mixture of non-parametric tests and ANOVA, not clear why both? I did not understand also what you meant by nested anova – AR order is a fixed factor and the weather stations are considered as replicates within each level, right? I would just present results of linear models defined in a clear way and remove all nonparametric tests. If there is anything one could criticize regarding the linear models, it is the non-independence of weather stations or time series (as they are spatially structured), and non-parametric tests are also sensitive to non-independence.
It would have been nice to assess the robustness of the AR models with order 4 (or even 3). The time series are short, so AR4 models may seem like overfitting. Perhaps consider other ways to assess this than the approach you have taken.
It is a bit strange that the simulations used to assess the robustness of the approach are not included at all. I would really appreciate to see some of the results and how they were obtained.
Details:
l. 190: shouldn't it be 1/T as Z is V/T? It will affect the denominator only. Anyway I am not sure I understand the logic here - the growth rate is either Z_t/Z_t-1, or log(Z_t)-log(Z_t-1). Why use (Zt/Zt-1 -1)? It will not affect the AR model (constant) but it is just not the usual growth rate, but a kind of relative growth rate.
l. 457: Vaccinium myrtillus
l. 491-2: note that in Cornulier 2013 we did not identify the causes of the decline in (spring) vole populations – it is still a bit of a mystery why such a decline was observed in places as different as the west coast of France and northern Finland.

Nigel G. Yoccoz

Thanks for a very detailed and thorough revision.
some parts of the discussion could be improved like after l. 450; voles are unlikely to «remember» their density, except if you mean by that physiological mechanisms. l. 452, what is an «adequate» density? l. 458: what dou you mean by adequate mechanism? focal plant species?