The concession model

The first skew model was formulated by Vehrencamp (1983). Vehrencamp’s (1983) model integrates ecological, genetic and social factors into a single theoretical framework that connects the decision to join a group and therefore group size with skew. Inclusive fitness theory (Hamilton, 1964a,b) is incorporated into the model by using relatedness values to analyse how the benefits and costs involved in group living affect skew. The

Chapter 4. Reproductive skew theory model (Vehrencamp, 1983) analyses how skew between a dominant and a subordinate is affected by three factors: the degree of relatedness between a dominant and a subordinate, the ecological constraints on solitary founding by a subordinate, and the productivity advantage of living in a group as opposed to living alone. This analysis was extended by Reeve and Ratnieks’ (1993) to include an extra variable: the relative fighting abilities of group members. The parameters of Reeve and Ratnieks (1993) model are as follows:

X the probability that a potential subordinate will successfully nest independently multiplied by the productivity of an established single-foundress nest

r the relatedness between a potential subordinate and the dominant

k the ratio of the total productivity of a joined nest to that of a single-foundress nest / the probability that the subordinate will win an intensified fight with the dominant

The concession model is built on several key assumptions. These are as follows. Groups are assumed to be more productive than solitary breeders. Within each group there is a dominant individual which has complete control over subordinate reproduction and therefore skew. Dominants maximize their inclusive fitness either by forfeiting some direct reproduction to a subordinate in order to recruit its help, or by evicting it if the association is unprofitable. The forfeited reproduction is often referred to as an incentive or reproductive concession (Clutton-Brock, 1998). The concession is known as a staying incentive when it is given to prevent the subordinate from leaving the association, and as a peace incentive when given to prevent the subordinate from attempting to fight for control of the nest. To avoid manipulation by the dominant, the subordinate has the choice of either leaving the group or of fighting for control of the nest. It will perform one of these strategies if it stands to gain greater inclusive fitness by doing so. For example, if the dominant does not yield any reproductive concessions and the subordinate has a low relative fighting ability compared to the dominant, then it will choose to leave the association if it is more profitable for it to do so, i.e., when x > r(k -1). The model also assumes that group members are able to assess the chances of successfully breeding

Chapter 4. Reproductive skew theory alone, whether the staying and peace incentives are being given, and the degree to which they are related to the other individual. The model generates four predictions. These are explained below and summarized in Table 4.1.

Predictions

1. Skew should increase as the probability of independent reproduction by subordinates decreases. This is because as ecological constraints on solitary breeding increase the dominant can recruit the subordinate’s help with smaller reproductive concessions. For example, iïx < r ( k - 1 ), that is, when ecological constraints are strong, the subordinate will remain in the group without any direct reproduction. However, \ï r(k -1) <x < k - 7, that is, when ecological constraints are moderate, the subordinate will require a staying incentive.

2. Skew is predicted to increase as relatedness between the dominant and subordinate increases. As relatedness increases, the benefits of helping (r(k - 1)) also increase. Therefore, the subordinate will acccept smaller direct reproductive concessions when it obtains larger indirect fitness returns.

3. Some what counter-intuitively the model predicts, that skew should increase as the contribution to colony productivity by a subordinate increases. By helping to raise colony productivity a subordinate increases its indirect fitness and is therefore given a smaller reproductive concession. This prediction is made for all relatedness values except zero.

4. Concerning an individual’s fighting ability. Reeve and Ratnieks (1993) came to several theoretical conclusions. However, in general, when ecological constraints on solitary nesting are strong, skew is predicted to decrease as a subordinate’s relative fighting ability increases. This is because under strong ecological constraints a subordinate with a high relative fighting ability has much to gain by fighting the dominant for control of the nest. For example, a subordinate will gain from fighting when f > x / ( l - r ) . In this situation the dominant will yield a peace incentive to prevent a fight if k > 1 but will

Chapter 4. Reproductive skew theory choose to fight the subordinate iï k ^ 1. If situations where k ^ 1, the association is therefore considered to be unstable.

Table 4.1. Predictions made by Reeve and Ratnieks ’ ( 1993) concession model.

Variable Effect on skew

Increasing relatedness Increases

Increasing ecological constraints Increases Increasing group productivity Increases Increasing fighting ability of subordinate Decreases

Further extensions o f the concession model

Cant and Johnstone (2000) further analysed the relationship between fighting ability and skew. Their analyses have shown that the effect of relative fighting ability on skew is not independent of other factors that are incorporated into the model. For example, they found that higher relatedness usually leads to lower levels of aggression and hence higher skew.

The concession model has also been extended to analyse asymmetries in relatedness (Reeve and Keller, 1995). Reeve and Keller (1995) extended the concessions model to analyse skew in matrifilial (i.e., mother and daughter) societies in which relatednesses to offspring are asymmetrical, and semisocial (i.e., individuals of the same generation) societies in which relatednesses to offspring are symmetrical. They found that skew should tend to be greater in matrifilial societies compared to semisocial ones.

Kokko and Johnstone (1999) and Ragsdale (1999) independently extended the concession model to examine the effect of inheriting the position of dominant breeder on skew. These models (Kokko & Johnstone, 1999; Ragsdale, 1999) differ from other skew analyses in that they explicitly consider lifetime reproductive success. They predict that groups in which dominants completely monopolize reproduction, can be stable, even when

Chapter 4. Reproductive skew theory probability of beating the dominant in a fight for control of the nest. In general these models (Kokko & Johnstone, 1999; Ragsdale, 1999) predict that skew will increase as the probability of inheriting the position of dominance increases.

Relevance to P. alternata

The concession model may be appropriate to explaining patterns of reproduction in P.

alternata. One important assumption of the model is that dominants have complete control

over reproduction. P. alternata may meet this assumption as colonies and nests are small. These features should in theory make it relatively easy for a dominant to control subordinate reproduction. If dominant s have complete control, they may choose to offer reproductive concessions in exchange for help. P. alternata females also have the option of either remaining as group members or of leaving to nest solitarily, as assumed by the concession model. The extention of the concession model to include the effect of resource inheritance on skew may also be relevant to P. alternata, as nest initiation and nesting in this species occur throughout the year. Together with small group size, these life history characteristics make it possible for subordinates to inherit the position of dominant breeder. Nest inheritance is known to be common and important in another hover wasp,

Liostenogaster flavolineata (Shreeves & Field, 2002).