We are studying natural selection on size in queens and sexual selection
on size in males as well as the components of selection operating on colonies.
Males
In the mating swarm, males outnumber queens and compete vigorously for access
to females. There is strong sexual selection on male body size, and
to less of an extent on male shape that is due to the increased mating success
of larger males. Mating takes place at the tops of hills following
a significant summer rain. Thousands of males and queens congregate
at the highest point on the hilltop, forming 'mating balls' with about 15-20
males surrounding a single female. At the center of the mating ball
there is usually a male and a queen 'in copula.' These males are nonrandom
subsets of all of the males at the mating swarm--they are larger.
Additionally, males who are successful at mating have different shapes than
'unsuccessful' males. Successful males tend to have a longer, narrower
body and they tend to have shorter mandibles with a smaller tooth surface.
These are differences in the shape of the males that are consistent in more than
one sample. Our interpretation is that successful males can compete with
males of similar body size if they can move the tip of their abdomen (and
genitalia) more effectively and if they can hold onto females more
tightly. Longer thorax and gaster relative to body size may make it easier
for males to engage in copulation. Shorter mandibles with a smaller tooth
surface means that the moment arm of the gripping tool is smaller and a smaller
surface mean that the greater force is applied over a smaller area.
A mating ball 
A copulating pair
Queens
The size of queens influences their ability to found a
colony successfully. We videotape queens in the process of digging burrows,
digitize size from the video images, and monitor survival. We have
found that larger queens survive better than smaller queens. Head size
and thorax size are highly related to survival probability (although gaster
size is not). In the graph below notice that surviving queens (connected
with solid lines) have larger head width than the dying queens (dotted lines).
Virtually all of the selection on queens comes during the first two-three
weeks, with no perceptible further change after two and a half months.
A queen digging the first nest burrow 
Head width changes rapidly
Colonies
The fitness of colonies is strongly related to the
number of times that the queen mates. The greater the genetic diversity
within the colony, the faster the colony grows. The difference between
colonies that grow rapidly and slowly can be seen in some pictures found
here.
We do not know why colonies that are produced by queens that mate
large numbers of times grow rapidly, but they reach reproductive size faster,
survive better, and since reproduction is a function of colony size, reproduce
more. We are investigating the possibility that colonies with greater
genetic diversity are more resistant to the spread of disease or perform
a greater variety of colony tasks.
Colonies that have high relatedness (low genetic diversity, small number
of matings) have almost no standardized growth over a period of five years.
Colonies with low relatedness due to a large number of matings, have
rapid growth rates.
References:
Links to *.pdf files for some relevant papers are given below.
Wiernasz, D.C., J. Yencharis, B.J. Cole. 1995.
Size and mating success in males of the western harvester ant, Pogonomyrmex
occidentalis. The Journal of Insect Behavior 8(4): 523-531.
Abell, A., B.J. Cole, R. Reyes and D.C. Wiernasz.
1999. Sexual selection on body size and shape in the western harvester
ant, Pogonomyrmex occidentalis. Evolution 53(2): 535-545.
Cole, B.J. and D.C. Wiernasz. 1999.
The selective advantage of low relatedness: growth in the harvester ant,
Pogonomyrmex occidentalis. Science 285(5429): 91-493.
Wiernasz, D.C., A. Sater, A. Abell, and B.J.
Cole. 2001. Male size, sperm transfer, and colony fitness in the western
harvester ant, Pogonomyrmex occidentalis. Evolution 55:324-329.
Wiernasz, D.C. and
B.J. Cole 2003. Queen size mediates queen survival and colony fitness in harvester ants. Evolution 57 (9): 2179-2183.
Wiernasz,
D.C., C. Perroni, B.J. Cole. 2004. Polyandry and fitness in the western
harvester ant Pogonomyrmex occidentalis. Molecular Ecology 13:
1601-1606.