Inclusive Fitness

This describes a genetic mathematical model which allows for interactions between relatives on one another’s fitness.

It uses Wright’s Coefficient of Relationship as the measure of the proportion of replica genes in a relative to discover a quantity called “inclusive fitness”.

This “inclusive fitness” incorporates the maximizing property of Darwinian fitness.

Species following the model evolves behaviour that maximizes its inclusive fitness.

This implies a limited restraint on selfish competitive behaviour and possibility of limited self-sacrifices.

Special cases of the model are used to show:

1. selection in newly covered social situations is slower than classical selection
2. how in populations of non-dispersive organisms the model may apply to genes affecting dispersion, and
3. how it may apply approximately to competition between relatives, for example, within sibships.

Introduction

The mathematical models of theory of natural selection do not allow the evolution of anything disadvantageous.

• This has very few exceptions.

If natural selection followed the classical models exclusively, positively social behaviour would be limited to:

• the coming together of the sexes
• parental care.

Sacrifices involved in parental care is based on fitness being the number of adult offspring.

An individual might sacrifice its own materials for the care of its offspring.

A gene for parental care will then leave more replica genes in offspring than an allele of the opposite tendency.

The selective advantage is in the benefits conferred indifferently on a set of relatives.

• Each of those relatives has a half chance of carrying the gene for parental care.

There is nothing special about the parent-offspring relationship except its:

• close degree
• fundamental asymmetry

The full-sib relationship is just as close.

If an individual carries a certain gene then there is a 1/2 chance that a random sib will carry a replica of it.

Similarly, the half-sib relationship is equivalent to that of grandparent and grandchild with the expectation of replica genes, or genes “identical by descent” is 1/4 and so on.

The possibility of the evolution of characters benefitting descendants more remote than immediate offspring has often been noticed.

Opportunities for benefitting relatives, remote or not, in the same or an adjacent generation (i.e. relatives like cousins and nephews) must be much more common than opportunities for benefitting grandchildren and further descendants.

As a first step towards a general theory that would take into account all kinds of relatives this paper will describe a model which is particularly adapted to deal with interactions between relatives of the same generation. The model includes the classical model for “non-overlapping generations” as a special case.

An excellent summary of the general properties of this classical model has been given by Kingman (1961b). It is quite beyond the author’s power to give an equally extensive survey of the properties of the present model but certain approximate deterministic implications of biological interest will be pointed out.