Association calculations

In animal networks analysis, association strength is often defined by the “gambit of the group”, i.e. the frequency with which two individuals are found together in the same group (Cairns & Schwager 1987). To determine the frequency of spatio-temporal co-occurrences of tuna in FAD aggregations, we defined a group as all fish present in the receiver range of a given FAD. A pair of individuals (dyad) was therefore considered associated if their acoustic signals were detected by the same receiver within a given time interval, henceforth referred to as the sampling

period. Despite the high temporal resolution of the acoustic data, a sampling period was hereby defined to last 24 hours, as previous tagging studies have shown tuna to exhibit periodic diel movements away from a FAD without breaking the long term association with it (Ohta &

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Kakuma 2005). To test whether ignoring these short term departures from the FAD

aggregations has an impact on association strength between two individuals and to determine the impact of sampling period duration on the association strength between individuals, association indices were also calculated for 1 hour sampling periods and the results compared using a randomized Mantel’s matrix correlation test (Schnell et al. 1985).

To calculate the association index for each dyad, the simple ratio index (SRI), recommended by Ginsberg & Young (1992) was calculated using the SOCPROG 2.4 (Whitehead 2009) extension for MATLAB (MathWorks 2010). For two individuals a and b, the SRI is computed as follows:

Eqn. 1 SRI=X/(X+Yab+Ya+Yb)

With X = the number of sampling periods in which a and b were detected together

Yab= the number of sampling periods in which aand b were observed at different FADs

Ya=the number of sampling periods in which only a was observed

Yb=the number of sampling periods in which only b was observed

For the SRI to be an unbiased measure of the proportion of time two individuals spend together, the dataset has to meet the following assumptions: recorded associations are symmetric and accurate, the probability of identification is independent of whether an

individual is associated or not and if one individual is detected in a given sampling period, all its associates are also detected (Whitehead 2008). Acoustic tagging data is relatively robust to

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these assumptions, with the main source of possible violations stemming from acoustic signal collision. If an acoustic receiver receives the signals of two fish simultaneously, it might not record either of them, or the two colliding signals may overlap and be recorded as the signal of another tag, leading to the false detection of a fish which is not within receiver range. As the risk of signal collision increases with the number of tags present within the receiver range (e.g. Topping & Szedlmeyer 2011), tagged fish are conceivably less likely to be reliably detected when associated with other individuals. This problem is addressed and to some degree alleviated by the tag manufacturer, as tags transmit their acoustic signal at a random time, between 30 and 90 s, reducing the risk of signal collision. Moreover, the potential of signal collisions to bias the association index can be reduced by using a sampling period that is

relatively large (24 hours) compared to the temporal resolution of the data (10s of seconds) and by removing any potential false detections caused by signal collision. This was accomplished by removing all single records which had no additional detections within 1 hour before or after from the raw dataset.

Another potential source of violating the aforementioned assumptions is the variable range of the receivers, which means that the spatial definition of the FAD aggregation changes, hence a tagged individual just outside the receiver range will not be detected despite being part of the aggregation. However, if this bias exists, it is probably small and approximately constant.

Using the SRI allows the computation of a symmetric half matrix of associations between all dyads, with values between 1 and 0, where 1 indicates a constant association of two individuals and 0 indicates no association. This association matrix was used for all subsequent network

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analyses in SOCPROG (Whitehead 2009) and the drawing of sociograms in NetDraw (Borgatti 2002).

2.2.4 Network analysis

To visualize the tuna networks for both 2002/2003 and 2005, the datasets were plotted as sociograms, consisting of nodes and edges, where each node represents an individual and the edge between them an associative link, with the thickness of the lines representing the edges proportional to the given association index.

To test whether the network exhibited preferred associations between individuals rather than being random, we determined if there was a significant difference between real association patterns and those obtained from a large number of random permutations, which were computed as described in Whitehead (2008). As tuna were rarely detected at two different FADs within the same sampling period, the permutation of associations between rather than within sampling periods was chosen, with a null hypothesis of ‘no preferred companionship between sampling periods’. This means that group membership in each sampling period was permuted with the constraint that the number of associations for each animal in each sampling period was kept constant (Whitehead 2009). The coefficient of variation (CV) of the SRI

association matrix for the real and permuted datasets were then compared and the null hypothesis of random association rejected if more than 97.5% of permutations had a lower CV than the observed data (p<0.025). The number of permutations was increased in increments of 10000 over multiple runs until p-values stabilized at 60000 permutations.

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To determine the structure of the network, the individual mean and maximum of the SRI were averaged over all individuals as well as by individual tagging cohorts (fish tagged at the same FAD on the same day). To test whether associations were higher within cohorts than overall, a randomized Mantel’s matrix correlation test (Schnell et al. 1985) between the association matrix and a binary matrix of whether the individuals of each dyad were from the same (1) or different (0) cohorts was carried out.