Living in synchrony on Greenland coasts?

Abstract

Vik et al. question whether we documented spatial synchrony between caribou and musk oxen from Greenland, and whether spatial synchrony within each species related to the North Atlantic Oscillation (NAO)¹. Attributing spatial synchrony to climate is difficult but possible², and the questions raised by Vik et al. are readily addressed. Contrary to their incorrect statement of our definition of the NAO effect ratio¹, a strong climatic effect on any pair of populations is not a requisite of climate-induced synchrony. As Moran³ argued, and as our analysis illustrated¹, populations may be synchronized if climate influences each of them similarly, regardless of the magnitude of that influence. Moreover, the standardized NAO effect ratio is associated statistically with the degree of climatic correlation across populations⁴ and hence the degree of synchrony between populations³.

Post and Forchhammer reply

As stated previously¹, we used cross-population covariance (CV) to produce a time-series index of spatial synchrony, an approach validated in empirical⁵ and theoretical⁶ studies, which have demonstrated the relationship of CV to population synchrony⁷. The simplest test of whether the use of log-transformed data confounds our results is to compare them with results obtained using raw (not log-transformed) data. The correlation between the NAO and 1/CV of the raw musk-ox data⁸(r=−0.57, P=0.001) matches exactly the correlation between the NAO and 1/CV of the log-transformed musk-ox data (r=−0.59, P=0.001). Similarly, results do not vary for caribou, using log-transformed (r=0.35, P=0.002) or raw (r=0.24, P=0.04) data. Hence, log-transformation does not influence relationships between the NAO and spatial synchrony.

Moreover, our results were not influenced by addition of a constant to the log-transformed musk-ox data, which Vik et al. describe as analogous to changing units of abundance. Such a problem would be apparent if the means of the N_i, ln(N)_i, or [ln(a)+ln(N)_i] showed significant and inconsistent correlations with the NAO, but none did (r_i values of 0.14, 0.07 and 0.07, respectively; all P values≥0.50). Vik et al. obtained different results because their direct log-transformation of the decimal-form musk-ox data produced negative values, giving statistically invalid CVs^9,10. We added 4 to the log-transformed musk-ox data to convert negative values to positives before calculating the CV precisely to avoid a spurious correlation.

If the NAO–spatial synchrony correlation were, in fact, influenced by the use of log-transformed data, such an artefact should be apparent in two ways, neither of which is discussed by Vik et al. First, the sign of the correlation between the NAO and musk-ox spatial synchrony should change with addition of constants greater than 4. Second, adding constants to log-transformed caribou data (to which none was originally added¹) should also alter the NAO–caribou synchrony correlation. We checked this by adding constants of up to 10, and in neither case was the correlation altered (Fig. 1).

Figure 1: Addition of constants from zero to ten (corresponding to abundance units shown on the x-axis) to ln-transformed density estimates does not influence the sign of the correlation between the NAO index and spatial synchrony for musk oxen or caribou.

Points designated by an arrow are the correlations reported in our original analysis¹. For the ln-transformed musk-ox data, addition of constants less than four, as done by Vik et al., produces spurious correlations because the resulting negative values do not give statistically valid coefficients of variation^9,10. Thus, the blue points indicate the correlations obtained when using the raw musk-ox data⁸ with constants of zero to three added; note that the point denoted as raw data in Fig. 1 of Vik et al. is in fact a direct ln-transformation of the actual raw data.

We conclude that our previous results still stand and that Vik et al. cannot offer a means of analysing or an alternative explanation for spatial synchrony within and across these species.