Altruism, the prisoner’s dilemma,
and the components of selection
Jeffrey A. Fletcher and Martin Zwick
Systems
Science Ph.D. Program
The
mechanisms by which altruistic[1]
behavior may evolve in biological systems has been vigorously debated over the
last several decades. Alternative explanations include reciprocal altruism
where the self-interest of individuals is served by the exchange of cooperation
with others, inclusive fitness where the self-interest of genes is served by
benefiting copies of themselves in other organisms (usually relatives), and
multilevel selection (often called group selection) where the self-interest of
groups may favor those with more altruistic, cooperative members. Although
these explanations may to some degree be mathematically equivalent, they
clearly differ in their view of the level at which self-interest can select for
self-sacrifice. The purpose of our research is to demonstrate the usefulness of
game theory as a framework for understanding the evolution of altruistic
behaviors. Previously we have shown that an n-player prisoner’s dilemma (PD)
with minimal group structure can serve as a model of multilevel selection
favoring altruism. This framework highlights the non-zero sum fitness
relationships necessary for selection of altruistic traits as well as the
tension between selection within groups (which favors selfish individuals) and
selection between groups (which favors altruistic individuals). Here we more formally
connect the parameters of a simple n-player PD and these two opposing
components of selection.
Dynamic
evolutionary computer simulations based on a simple n-player PD in multiple
groups are used in which utility payoffs from the PD determine fitness, i.e.
the relative number of progeny in the next generation. We demonstrate how an
altruistic trait can be selected for in a global population despite being
selected against in each sub-population. This is an example of Simpson’s
paradox and is due to the disproportionate contribution to the whole population
by groups containing a higher percentage of cooperators. Using the Price
covariance equation we partition the change in overall altruism frequency into
two components. The first represents the contribution to the global frequency
change due to the disproportionate success of groups; the second component
represents the contribution to change due to the advantage of individual
defectors over cooperators within any group. In the multilevel selection explanation
of altruism, these two components of selection oppose one another, i.e. have
opposite sign.
We
find that the two components of hierarchical selection predicted by the Price
equation can be directly interpreted in terms of two features of our PD model.
Specifically the between group selection component is given by the weighted
average of the utilities for cooperators and defectors within a group. This
value varies with the frequency of cooperators in each group. The within group
individual selection component is given by the difference between cooperator
and defector utilities independent of group cooperator frequency.
Although
computer simulations of the PD including n-player versions have been used to
study reciprocal altruism, surprisingly, the n-player PD has not been used to
model multilevel selection. Previously we have made this connection and here
for the first time we formally demonstrate the connection between PD parameters
in our model and the hierarchical components of selection specified by the
Price equation.
The
tension between hierarchical levels of selection can be modeled by an n-player
PD in multiple groups such that the between and within group selection
components can be precisely represented by two features of the n-player PD.
[1] Here we use the term altruistic to describe any behavior that gives benefit to others at a relative cost to the provider of the benefit. Psychological or moral aspects of altruism are not investigated nor implied by our use of this term.