Functional data analysis

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In this information age, we often collect continuous time data:  at least conceptually our data sets consist of functions, rather than just real numbers and vectors.   For instance, in lab experiments with wheel-running mice, we can continuously monitor the activity level of each mouse as a function of time.  So for each mouse we observe a function that describes wheel-running.  We may be interested in the wheel-running speed, or how it relates to, e.g., body mass.  The challenges of statistical analyses of such data are the realm of functional data analysis (FDA).Some questions in evolutionary biology are best answered via the FDA approach.  For instance, suppose the above-mentioned wheel-running mice were bred for fast wheel-running at age 8 weeks. We would expect that their progeny would also be fast wheel runners at age 8 weeks. But what about at other ages? Perhaps their progeny would be fast wheel runners at all ages.  Or perhaps being fast when young goes with being slow when old - that is, there is a trade-off for fastness in youth.   One must look at the entire life history of wheel running to understand the effects of  selection, and one should take into account other factors such as body mass and food consumption.