Saturday, January 28, 2012

Splash-Dunk Analysis

When taking data in the field you have no idea how things will turn out in the end.  The plot shown here presents splash/dunk data for 2011.  When recording the data I had no idea the end result would be so pleasing to the eye.

Here's the idea behind the plot.  When dragonflies are observed to splash/dunk, they often hit the water multiple times – doing one dunk after another after another.  We've observed as many as 6 dunks in a row before the dragonfly gains altitude and does a spin/dry at 1,000 rpm.  The data for 2011 consisted of observations of 148 events combining for a total of 288 dunks.  Most events consisted of only a single dunk (62 such events), and the average number of dunks per event was 1.9.

The exponential drop off in the number of dunks suggests that dunks are independent events – each dunk is independent of the dunks that precede it.  Roughly speaking, once a dragonfly dunks there is about a 50/50 chance that it will dunk again.  This is true whether the dragonfly has only dunked once, or has already dunked 5 times.  The previous history doesn't matter.  In a sense, you might say that dragonflies "live in the moment," deciding after each dunk whether to dunk again with no regard for what has happened in the past.

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