Calculating David's Score

The relevant portion of Gammel et al. describing David's Score (DS) calculation is included below for explanation.

"The proportion of wins by individual i in his interactions with another individual j (P_ij) is the number of times that i defeats j (α_ij) divided by the total number of interactions between i and j (n_ij), i.e. P_ij=α_ij/n_ij. The proportion of losses by i in interactions with j, P_ji=1–P_ij. If n_ij=0 then P_ij = 0 and P_ji = 0 (David 1988; de Vries 1998). DS for each member, i, of a group is calculated with the formula:

DS = w + w₂ - l - l₂

Where w represents the sum of i's Pij values, w₂ represents the summed w values (weighted by the appropriate P_ij values, see below) of those individuals with which i interacted, l represents the sum of i's P_ji values and l₂ represents the summed l values (weighted by the appropriate P_ji values) of those individuals with which i interacted."

An excel spreadsheet was used to calculate David's score. An example template has been attached. In this, results from pairing the 4 animals per cage are plugged into the far left grey boxes, where each row represents results from a separate day. DS will then be calculated and can be found in the far right. Each portion of the formula is calculated separately and has been annotated as such.