Addressing biases in sliding window analysis gives new insight into the response of parturition date to weather in a wild mammal

Animal breeding phenology in temperate and high latitude regions is often predicted by weather variables, such as temperature. Much work on this topic has focused on taxonomic groups that employ adaptive plastic responses to annual variation in an environmental cue, with analytical approaches developed to determine when weather has an effect and the magnitude of response. However, adaptive responses are not always likely, so it is important to consider the assumptions and limitations of an approach when analysing similar questions in distinct taxonomic groups. The prolonged period between conception and birth means parturition date in seasonally breeding ungulates, such as red deer, is unlikely to show adaptive plastic responses to variation in weather. Prior studies of red deer on the Isle of Rum, Scotland, have documented that parturition date is sensitive to summer temperature and getting earlier over time, while birth weight is sensitive to spring temperature but shows no temporal trend. Here, we reinvestigate this topic with updated statistical methods to establish confidence in previous results by deploying two approaches: permutations, combatting anti-conservative aspects of sliding window analyses, and detrending, a valuable tool for weather attribution studies containing temporal trends. Incorporating detrending within the sliding window analyses of parturition date identified a different window as best fitting with a shallower temperature slope estimate compared to sliding windows that did not detrend. Permutations then showed all our parturition date results could be achieved by chance. In contrast, and consistent with earlier work, birth weight was predicted by spring temperature. Our novel results regarding the environmental sensitivity of parturition date in red deer suggest a lack of plasticity in response to weather and highlight the distinction between the phenology of mammals with long gestations and many more commonly studied taxa. We encourage the use of permutations and detrending within sliding window analyses when a trait shows temporal trends, to prevent inaccurate windows and effect sizes being identified.