Encountering a dilution problem

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Yesterday, Lesley Morrell, talked to us about her research on group living.  She gave a fantastic summary of her work on why animals form groups, focussing on the anti-predator benefits that individuals in groups obtain. The mechanisms driving these benefits include selfish-herd effects, confusion effects, and encounter-dilution effects. Her talk got me thinking about this last point. It was not immediately obvious to me whether encounter-dilution effects alone can drive the evolution of group living.

The encounter-dilution effect has two parts. The first part, 'encounter effect' looks at how often a predator will encounter groups of different size.  If a predator moves randomly in the environment, then there is, on average, no benefit to belonging to a group, or being a loner. This can be observed in the image below. The magenta points represent the path of a 'predator' with a random walk. The blue points represent prey items that have not been eaten (after some time), and the red points represent prey that have been eaten (the predator came within some distance of them). While the amount of prey that are eaten will vary between different simulations, on average, the same number of prey will be consumed in these two scenarios.

distprey-nodetection

But this assumes that predators move 'blindly' in their environment and cannot detect prey until they are right under their noses. This is clearly a poor assumption, given the multitude of refined senses that predators possess. Therefore, we can add to the simulation a 'detection' parameter, which tells the predator to move towards the highest concentration of prey (with some randomness). When this is added, the story changes. Now, it is riskier to be in a group than not:

distprey-detection

Or is it?  Whether being in a group is safer or riskier will also depend on the second part - the 'dilution effect'. This effect suggests that predators will, or cannot, eat all the members of the group, and only select some individuals to eat. In effect, this means that an individual's chance of being eaten decreases as group size increases.  Whether grouping is beneficial crucially depends on the shape of the 'encounter curve' and the 'dilution curve', as shown below:

detectionandselection

Whether grouping is beneficial is determined by how these two curves combine.  If the increased probability of being detected in groups is offset by the reduction in chances of being the selected prey item - group living is beneficial. On the other hand, if you are still likely to be eaten in groups even after you have been detected, you should live on your own.

In an experiment by Lesley and her team, they found that individuals in aggregated groups survived better in the field than more dispersed individuals. This suggests that the increased chances of being detected were indeed offset by dilution benefits in the wild.  What the shape of these curves really looks like in nature is difficult to measure experimentally, but doing so would help our understanding of why some animals form groups, and others do not.