Arctic Duck Diving Inspires Math Study on Dynamic Patterns

What do eider ducks hunting for sea urchins and bargain shoppers have in common? New research from UBC mathematician Leah Edelstein-Keshet and former post-doctoral fellows Nessy Tania, Ben Vanderlei and Joel Heath analyzes how social interactions can create evolving foraging patterns.

The findings, published in the Proceedings of the National Academy of Sciences this month, might help answer some age old questions: What's the best way to snag that pair of bargain-price shoes? Or, to find those sea urchins.

When it comes to foraging patterns (or perhaps humans finding a gem in a sea of bargain-basement discounts) there are two strategies one can follow. Either look carefully for the desired items, or watch out for other excited shoppers congregating at a promising aisle.

Each behaviour comes with benefits and disadvantages. Methodical searching is more time consuming and costly (in terms of energy spent flying or scanning) but leads to earlier arrival to food and prey. Searching for crowds may be faster but ineffective – especially if the food or bargain items are being snapped up quickly.

Using mathematical modelling and spatially explicit computer simulations, Edelstein-Keshet and her team found that searching-exploiting resource systems exhibit spatial patterns resembling 'waves of pursuit' as individuals rush between resource sites. The authors also discovered that overall strategies may fluctuate over time if individuals switch behaviours either by learning or by reproductive fitness.

"Lots of people have studied so called producer-scrounger strategies, but never in this particular way," says Edelstein-Keshet. "We're showing that these strategies affect – and are affected by – the way food is distributed in space."

The team was originally inspired by Heath's post doctoral work studying eider duck foraging in the Belcher Islands. He introduced the idea of marrying foraging with computer simulations.

Says Edelstein-Keshet: "The work we did is all computational modelling – Joel kept insisting that it should be kept abstract. But there were three skeptical mathematicians who didn't quite see it. It took an ecologist to get us to go in an exciting direction."

The team's findings are of importance to ecologists, conservation biologists and mathematicians. Results of the computational model can be applied to many systems that have inspired social foraging theory, as well as in systems where predators can shape the patchiness of their prey, for example, shorebirds and eider ducks.

"The fact that such producer-scrounger systems can both shape and be shaped by the spatial distribution of resources is an important ecological story that deserves to be told," says Heath, who is also the documentary director of People of a Feather, a film about the changing Arctic landscape.

"Role of social interactions in dynamic patterns of resource patches and forager aggregation" is available at: http://www.pnas.org/content/early/2012/06/25/1201739109.abstract