After the paper was published, a writing error was detected in the mathematical formula used to calculate the population increase rates. Because of this error, the statistical analyses of population increase rates were based on erroneous values. We recalculated the population increase rates using a corrected formula:

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where Nt is the catch index for a trapping occasion, Nt+T is the catch index for the following trapping occasion, and T is the time (in months) elapsed between the trapping occasions. To avoid division by zero, zero values were replaced with a value corresponding to a catch of 0.5 individuals in the trapping occasion.

A reanalysis of the population increase rates revealed that the results published under subheading ‘Population increase rate’ (page 336 in the original article) and in Fig. 7 (page 339) were partly misleading. The main difference between the published results and the corrected results can be seen by comparing the previously published Fig. 7 with the corrected Fig. 7. In the corrected results, direct density dependence is more prevalent than in the previously published results. The difference is obvious particularly in autumn (population growth from August to October). In addition to the changes in Fig. 7, the results of regression analyses (page 336 right column) changed somewhat. In contrast to the previously published results, age structure did not explain a significant proportion of the variation in the population increase rates. The only variable that entered the stepwise regression models was productivity (the mean litter size multiplied by the proportion of females breeding), and even this variable could only explain 9% of the current population increase rate of bank voles (F1,48=5.0, P=0.03). In other species none of the variables studied entered the models.


Figure 7. Corrected Fig. 7. Density dependence of the population increase rate. Pearson correlation coefficients for the relationship of the population increase rate with the density of the species studied (dots), pooled density of voles (circles), and regional mean density of voles (squares) with time lags from 0 to 12 months, separately for each species (field voles, sibling voles, bank voles, and common shrews) and season (spring=April to June, summer=June to August, autumn=August to October, and winter=October to April). Data from short line trappings in 1986–1992. Significant correlations are shown with an asterisk above (positive correlations) or below (negative correlations) the line.

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The corrected results reveal clear interspecific and seasonal differences in the relative importance of direct and delayed density dependence. In common shrews and bank voles, direct density dependence appears to prevail throughout the year (Fig. 7). The only exception is a negative relationship with previous vole densities (a time lag of 8–10 months) in bank voles in spring (population growth from April to June). In field voles, direct density dependence dominates in autumn but delayed density dependence from winter to the following summer (October to June). In sibling voles, the results resemble those of field voles with the exception that direct density dependence appears to be relatively more important in spring (Fig. 7). In contrast to the results of the original article, the corrected results suggest that the cessation of population growth at the population peak in August should be attributed to factors operating in a directly density dependent way at that part of the year. The corrected results also suggest that the delayed density dependent feedback loop necessary to generate the 3-year population cycle in Microtus voles operates during the period from late autumn to the following summer (October to June). These corrected results do not change the main conclusion of the original article: our results indicate that changes in survival rather than in reproduction drive the 3-year population cycles of voles.