UC Davis marine biologist Laura Rogers-Bennett is searching for the best way to preserve California's vanishing abalone populations. Two challenges confront her research team: tracking the ocean-dwelling mollusks, and determining how scarce conservation dollars should be spent to save them.

"When conservation funds are limited, we have to make decisions about where best to put our resources," said Rogers-Bennett.

Rogers-Bennett and her colleagues will make those decisions with the help of a mathematical matrix model — an organizing tool that makes predictions about a population's future from many tiny bits of data about its past.

Rogers-Bennett's team has spent five years assembling data to describe the life histories of two of California's abalone species.

The white abalone variety has been so severely over-fished that, in 2001, they became the first endangered marine invertebrate. In contrast, Northern California's red abalone, long protected by commercial fishing bans, are still abundant enough to support a limited recreational fishery north of San Francisco. The team's data will be used to fuel species-specific conservation efforts: to manage the existing red abalone while recovering the white abalone.

"Since abalone fisheries have collapsed all over the world, our goal is to see that our management measures keep the recreational red abalone fishery sustainable," said Rogers-Bennett, whose work is being funded by a California Sea Grant. Many management measures are already in place. In addition to a size limit, divers must restrict their red abalone collection to areas north of San Francisco, and may not catch abalone using SCUBA gear. It is also illegal to sell abalone caught in the wild.

"We don't want to go the route that other states and countries have gone, where population collapses have forced fishery closures," Rogers-Bennett said.

Life cycles

To understand the life cycles of both red and white abalone, the team combined measurements on current populations with archived data collected during the 1970s and '80s, when populations were larger. The data set includes statistics on several "vital rates": the growth, reproduction and survival rates for many different sizes of red and white abalone.

The next step, currently under way, is to build the mathematical matrix model. The matrix — a grid of rows and columns of numbers — is a structure for organizing and manipulating data. Since it preserves relationships between different types of population data, it can be used to explore the future of the model abalone population.

Rogers-Bennett notes that this is the first attempt to use matrix models in abalone conservation.

The model is constructed in several steps. Many possible matrices exist, so scientists must first decide which one fits the biology of their organism. Rogers-Bennett's team chose a size-based matrix, since an abalone's success at reproduction, growth and survival depends largely on its size. (Human demographic data, in contrast, are usually based on an individual's age.)

"The red abalone fishery has a size limit — animals less than seven inches can't be fished," Rogers-Bennett explained. "With our models, we can ask whether that limit protects the size classes that contribute most to population growth."

Elasticity analysis

Her team will answer this question with an "elasticity analysis." They will change one value in the model's data by a small amount, perhaps 10 percent, and watch whether the change affects the total size of the model population. The scientists will compare many elasticity analyses to predict which measures might work best.

Rogers-Bennett does not yet know whether her work will suggest modified size limits for the red abalone fishery. But she notes that a similar analysis was used to plan sea turtle conservation in Florida. In that case, matrix models suggested that saving big, old females with high egg-laying potential would be more cost-effective than enhancing the survival of turtle hatchlings.

She anticipates that the suggestions that come from her models will be similarly useful.

For endangered white abalone, whose numbers have already collapsed, the focus is on population restoration. For this species, the scientists will use matrix models to answer questions on conservation strategies and threat management.

"One threat we are proposing to assess is poaching," Rogers-Bennett said. "It's a very challenging threat to tackle, but it's within the realm of enforcement and education." With the matrix models, the team will find out which pockets of the white abalone population would benefit most from reduced poaching, giving them clues about where enforcement and education should be targeted.

Threat analysis will also help her team figure out where it might not be efficient to direct conservation resources.

"For example," she said, "if we know that sea otters, eating certain sizes of abalone, will increase in a particular location, we might target restoration efforts somewhere else. Understanding threats is critical to smart recovery planning."

Recovery plans

Rogers-Bennett's results will be used by both state and federal agencies. The California Department of Fish and Game, which oversees the red abalone fishery, will incorporate her work into its forthcoming red abalone recovery and management plan.And the National Marine Fisheries Service will use her results in its recovery plan for white abalone.

"Mathematical modeling lets us ask practical conservation and restoration questions," Rogers-Bennett said. "When we manipulate the model population, we can explore which management and conservation measures might have the largest impacts in the wild."