Geographic range shifts in species’ distributions, due to climate change, imply altered dynamics at both their northern and southern range limits, or at upper and lower elevational limits. There is therefore a need to identify specific weather or climate variable(s), and life stages or cohorts on which they act, and how these affect population growth. Identifying such variables permits prediction of population increase or decline under a changing climate, and shifts in a species’ geographic range. For relatively well studied groups, such as butterflies, geographic range shifts are well documented, but weather variables and mechanisms causing those shifts are not well known. The Holarctic butterfly genus Parnassius (Papilionidae) inhabits northern and alpine environments subject to variable and extreme weather. As such, Parnassius species are vulnerable not only to long-term changes in average conditions but especially to short-term extreme weather events. We use population growth estimates for the alpine butterfly, Parnassius smintheus, from 21 populations in the Rocky Mountains of Canada, over a 20-year interval, combined with techniques of machine learning (randomForests) and parametric modeling to identify the important weather variables determining population growth. We do this to determine the seasons and life-stages of P. smintheus most affected by climate change. Extreme minimum and maximum temperatures in November, in combination with November snowfall, affect annual population growth most, more so than do mean temperatures in November, and more so than weather at any other time of year. Populations decline both in years with low extreme minimum temperatures in November, and especially in years with high extreme maximum temperatures in November, indicating that overwintering eggs are particularly vulnerable to early-winter weather. Snowfall ameliorates the negative effects of extreme temperatures, particularly for extreme warm events. Results provide insight into biological mechanisms by which over-wintering eggs might be affected by early winter weather. Short-term extreme weather in November, acting on a single pivotal life-stage (egg) is a far better predictor of population change of alpine Parnassius smintheus butterflies than is the general index of climate, the Pacific Decadal Oscillation (PDO).