Familiarity affects social network structure and discovery of prey patch locations in foraging stickleback shoals

Numerous factors affect the fine-scale social structure of animal groups, but it is unclear how important such factors are in determining how individuals encounter resources. Familiarity affects shoal choice and structure in many social fishes. Here, we show that familiarity between shoal members of sticklebacks (Gasterosteus aculeatus) affects both fine-scale social organization and the discovery of resources. Social network analysis revealed that sticklebacks remained closer to familiar than to unfamiliar individuals within the same shoal. Network-based diffusion analysis revealed that there was a strong untransmitted social effect on patch discovery, with individuals tending to discover a task sooner if a familiar individual from their group had previously done so than if an unfamiliar fish had done so. However, in contrast to the effect of familiarity, the frequency with which individuals had previously associated with one another had no effect upon the likelihood of prey patch discovery. This may have been due to the influence of fish on one another's movements; the effect of familiarity on discovery of an empty ‘control’ patch was as strong as for discovery of an actual prey patch. Our results demonstrate that factors affecting fine-scale social interactions can also influence how individuals encounter and exploit resources.

Eqn. S1a In which the rate of social transmission and asocial learning combine additively, or a multiplicative model: Eqn. S1b Where: ( )is the rate of acquisition (or "hazard rate" in survival analysis terminology) of the trait for individual i in group k at time t; ( ) is a baseline rate function for individuals in group k; ( ) is an indicator variable giving the status of i in group k at time t (1= informed; 0=naïve); is the network connection from j to i in group k; s is a parameter giving the strength of social learning ( ; but see section 3, below); and is a linear predictor allowing the modelling of the effect of individual level variables (e.g. size) in a manner analogous to a Cox survival model or generalised linear model (GLM); and is the number of individuals in group k.
OADA makes no assumptions about the shape of ( ), and should therefore be used if a suitable model is not available for ( ) (Hoppitt & Laland, 2011). We decided to use OADA since it makes fewer assumptions about the baseline acquisition function, though modified as described in section 2. The form of OADA for multiple diffusions given by Hoppitt et al. (2010) is only sensitive to the order of acquisition within groups, and so is not sensitive to between group patterns, i.e. it allows for a different ( ) for each group. However, we felt it was reasonable to assume that there is a common baseline rate function for all groups ( ) ( ), since groups were selected from the same population and diffusions run in identical and constant laboratory conditions. We accomplished this by treating the data the order across groups, effectively as a single diffusion, but with zero social network connections between individuals in different groups. (2012) expanded the simple NBDA model given above to a) allow for two options for solving the task, in this case solving either the left or right version of the task, and b) to separate effects on the rate at which individuals first discover each task and the rate at which they subsequently first solve each task. The standard NBDA is a two state model, with individuals moving from a naïve to an informed state (naïve->informed). In the expanded model used here, for each option fish are in one of three states, being naïve, having discovered that option but not solved it, or having solved that option. This allowed us to examine the social effects on each transition (naïve-> discovered and discovered non-solver -> solver). Analysing the rate of discovery (naïve->discovered) and solving (naïve -> solver) separately (e.g. Hoppitt et al 2010) fails to fully tease apart the two transitions. The additive two option model for discovery is expressed generally as follows:

Atton et al
The full additive models for the two-option extension are:

Eqn. S2b
( ) is the rate of discovery of option 1 and ( ) is the rate of discovery of option 2 and ( ) the corresponding baseline function, taken here to be ( ) ( ), see above. s terms are parameters giving the various social effects tested for: subscript DD denotes on effect of discoverers on the rate of discovery, and SD the effect of solvers on discovery rate; the subscript OS indicates that a social effect is option specific, whereas CO indicates that it operates across options ("cross option"). e.g.
is then a parameter giving the social effect of connected individuals who have discovered the same option on rate of discovery, whereas gives the social effect of connected individuals who have solved the different option on rate of discovery. is a linear predictor as above; ( ) is an indicator for whether i in group k has solved the task using option m prior to time t; ( ) is an indicator for whether i in group k has discovered option m prior to time t, regardless of whether i has yet solved the task using option m; is the effect on discovery rate of option m, on the scale of the linear predictor, of having previously discovered the other option; is the effect on discovery rate of option m, on the scale of the linear predictor, of having previously solved the other option; For all NBDA models, we suggest that individual-level variables included in the linear predictor, , are transformed by subtracting the mean across all individuals. This means that the social effects can be interpreted consistently as the increase in rate per unit of network connection, relative to the average asocial rate.
The rate of solving for each option is then given as follows: Eqn. S2c Eqn. S2d where: ( ) is the rate of solving of option m by i in group k at time t and ( ) the corresponding baseline function, taken here to be ( ) ( ), see above. On s parameters, DS denotes the effect of discoverers on solving rate; the subscript SS denotes the effect of solvers on solvers, on OS/CO denote option-specific and cross-option effects as above; is the effect on discovery rate of option m, on the scale of the linear predictor, of having previously discovered the other option; is the effect on discovery rate of option m, on the scale of the linear predictor, of having previously solved the other option.
The common baseline rate functions across options, ( ) and ( ) are taken to be ( ) and ( ) respectively (the same shape across groups). This means that the model for discovery takes as data the order of discovery across groups and options, and the model for solving takes as data the order of solving across groups and options. The ( ( ) ( )) term ensures individuals are only included in the likelihood function for a solving event at time t for options they have discovered, ( ( ) ) but not solved ( ( ) ).