The Forces That Determine the Size of Groups ("Swarms") of Social

question 12

Essay

The forces that determine the size of groups ("swarms") of social insects and the rates at
which they grow are not well understood. Biologists have observed large variability in the size of swarms across species. In a study of the social wasp, Polybia occidentalis,
investigators dismantled a nest of these insects and marked a few insects for future
identification in new swarms. Twenty-five days after dismantling the original swarm they
had located new swarms of wasps from the original colonies. The data below present the
numbers of adults and workers in the new swarms in two different years. "Drones" are
fertile males that mate with the queen. "Workers" are infertile females that labor in the nest
and defend the colony. $\begin{array}{|c|r|r|r|r|r|}\hline \begin{array}{c}\text { First } \\\text { Year } \\\text { Swarm } \\\#\end{array} & \begin{array}{c}\text { Number } \\\text { of } \\\text { Drones }\end{array} & \begin{array}{c}\text { Number } \\\text { of } \\\text { Workers }\end{array} & \begin{array}{c}\text { Second } \\\text { Year } \\\text { Swarm } \\\#\end{array} & \begin{array}{c}\text { Number } \\\text { of } \\\text { Drones }\end{array} & \begin{array}{c}\text { Number } \\\text { of } \\\text { Workers }\end{array} \\\hline 1 & 598 & 597 & 1 & 355 & 339 \\\hline 2 & 24 & 21 & 2 & 691 & 673 \\\hline 3 & 567 & 557 & 3 & 278 & 252 \\\hline 4 & 371 & 325 & 4 & 719 & 669 \\\hline 5 & 279 & 260 & 5 & 152 & 129 \\\hline 6 & 44 & 35 & 6 & 156 & 140 \\\hline 7 & 42 & 41 & 7 & 41 & 35 \\\hline 8 & 126 & 107 & & & \\\hline 9 & 108 & 101 & & & \\\hline 10 & 79 & 64 & & & \\\hline\end{array}$
-Calculate the values of these numerical summaries for the number of drones in the second year swarms:
a) The mean __________
b) The standard deviation ___________ The table below presents some summary statistics from the distributions of the number of drones.
Partial summary of data
Numbers of drones
$\begin{array}{|c|c|c|c|c|c|}\hline \text { Swarm } & \text { Minimum } & \begin{array}{c}\text { Lower } \\\text { Quartile }\end{array} & \text { Median } & \begin{array}{c}\text { Upper } \\\text { Quartile }\end{array} & \text { Maximum } \\\hline \text { First year } & 24 & 43.5 & 117 & 420 & 598 \\\text { Second year } & 41 & 152 & 278 & 691 & 719 \\\hline\end{array}$

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