Figure 2.

Schematic illustration of two different ways in which phase synchrony might be maintained. (A) A continuous series of phase corrections such that |Δ(φ_i,t+1,_t+1)|<|Δ(φ_i,t,_t)|, and points lie symmetrically around a line of slope less than 1. (B) The majority of phase increments proceed independently of the overall average phase, giving rise to points that fall around a line of slope 1, but a few outliers arise from infrequent occasions on which|Δ(φ_i,t+1,_t+1)|≪|Δ(φ_i,t,_t)|, which result in the best fitting regression line having a slope of less than one. However, on eliminating points associated with large standardized residuals from the regression analysis, a slope of ≈1 would be recovered. A third possibility (not shown) is that the regression indicates no evidence of coupling at all, and the observed synchrony between phases must have arisen from synchronizing events that occurred before the interval over which data were collected. (C) The regression of Δ(φ_i,t+1,_t+1) on Δ(φ_i,t,_t) for muskrat in the eastern region. The slope of the best-fitting-line is 0.906, which is significantly less than 1 (see Table 1), indicating a coupling strength of 0.094. The dotted line indicates the line of slope 1. (D) The change in asynchrony, A_t, with time for mink (dotted line) and muskrat (solid line) in the three regions studied. Because phase can be estimated only from completed cycles, A_t cannot be calculated for the entire duration of the time-series data. A plot of the empirical function A_t reveals a significant upward trend (using the Newey-West test for the trends; ref. 25) in the west (but not in central and eastern regions) for both mink (slope = 0.0024, F_{1, 15} = 40.5, P < 0.0001) and muskrat (slope = 0.0015, F_{1, 14} = 37.2, P < 0.0001).