Abstract

Urban and rural colonies of odorous house ants (Tapinoma sessile) have very different social structures. Urban colonies are very large with hundreds of cohabiting queens, while rural colonies are small with only one queen. To investigate whether worker ant aggressiveness varies across these two colony types, an experiment was performed using an aggression assay, in which 50 ants from each of two colonies were placed in a petri dish and allowed to fight. The response was the total number of dead ants within 24 hours. Because the ants were all the same species and not marked by colony, the number of dead ants per colony could not be determined.

A total of 138 colony pairings, involving six urban (U) and seven rural (R) colonies, were used in the experiment. Interest was in comparing the three types of pairings (UU, UR, and RR) to see if there is an ordering based on aggressiveness (e.g., μUU < μUR < μRR). A linear mixed model is proposed to account for the fact that multiple assays involve ants from the same colony (i.e., to account for between colony variation in aggressiveness). However, the incorporation of random colony factors is not feasible for this study because of the UU and RR assays. As a result, we perform this mixed model analysis by specifying the covariance matrix (i.e., using the LINEAR covariance structure). A simulation study is used to assess the Type I and Type II errors of this mixed model approach relative to the standard one-way ANOVA. We conclude with an analysis of the real data set.

Keywords

Aggression assay, Paired competition design, Mixed models, Linear covariance structure

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May 1st, 6:00 AM

PAIRED COMPETITION ANALYSIS USING MIXED MODELS

Urban and rural colonies of odorous house ants (Tapinoma sessile) have very different social structures. Urban colonies are very large with hundreds of cohabiting queens, while rural colonies are small with only one queen. To investigate whether worker ant aggressiveness varies across these two colony types, an experiment was performed using an aggression assay, in which 50 ants from each of two colonies were placed in a petri dish and allowed to fight. The response was the total number of dead ants within 24 hours. Because the ants were all the same species and not marked by colony, the number of dead ants per colony could not be determined.

A total of 138 colony pairings, involving six urban (U) and seven rural (R) colonies, were used in the experiment. Interest was in comparing the three types of pairings (UU, UR, and RR) to see if there is an ordering based on aggressiveness (e.g., μUU < μUR < μRR). A linear mixed model is proposed to account for the fact that multiple assays involve ants from the same colony (i.e., to account for between colony variation in aggressiveness). However, the incorporation of random colony factors is not feasible for this study because of the UU and RR assays. As a result, we perform this mixed model analysis by specifying the covariance matrix (i.e., using the LINEAR covariance structure). A simulation study is used to assess the Type I and Type II errors of this mixed model approach relative to the standard one-way ANOVA. We conclude with an analysis of the real data set.