**By Jeff Rice**

One of the first things that many budding ecologists learn, often to their chagrin, is that they probably should have paid more attention in Math. Of all the biological sciences, ecology may be the most fundamentally rooted in numbers. Not only is it the study of distribution and abundance—where and how many?—but it also tells you how systems and organisms connect and interact, and how they change over time.

For more than 30 years, Dr. Marc Mangel has been a leader in this sort of quantitative ecological research, with an emphasis on the understanding and management of marine resources. He is a Distinguished Professor of Mathematical Biology in the Department of Applied Mathematics and Statistics at UC Santa Cruz, and is currently a Visiting Scientist at the Puget Sound Institute, where he is applying mathematical principles to the population dynamics of Puget Sound forage fish and other species. We spoke with him about some of his work.

**PSI:** Would you classify yourself as a mathematician who does biology, or a biologist who is good at math?

**MM:** I usually call myself either a theoretical ecologist or a quantitative ecologist. But I really think of myself as a biologist who is using mathematical methods. In my career, about half my time has been spent in mathematical science departments and half in biology departments.

**PSI:** What are some of the theoretical questions that interest you, and why is math especially useful for studying Puget Sound ecology?

**MM:** One of my main interests is in understanding and predicting how animals use their resources. Think of a forage fish. If you think of a fish that’s growing, as it eats it can allocate that incoming food to either growing its body mass or growing its length or putting on fat that will be used later for reproduction or overwinter survival. So there’s a life history tradeoff there. I use mathematical methods to characterize that kind of tradeoff and make predictions about how animals will respond to changing environmental conditions.

And the problems of ecology range across a wide spectrum. For example, one can talk about just estimating abundance of a kind of a fish or, say, a bird or a mammal predator. Those are almost always some type of statistical problem. At the most basic level, you put a net in the water and you may pull up some fish or you may not. And you do this a number of times. And then you want to make some inference about what the total population size.

**PSI:** But it gets more complicated, fast, right? Scientists studying forage fish have to measure a moving target, as opposed to someone studying trees, for example.

**MM:** Even when one is trying to estimate the abundance of trees in a forest, one rarely does an exhaustive survey. What you do is you go and count some patch of the forest and then make assumptions about how that represents the entire forest and scale up. For fish populations, the problem is similar but more complicated because even when we sample a certain area of the ocean, we really don’t know that we have caught everything in that area of the ocean. And when we sample multiple areas of the ocean, then there is the question whether the fish one is looking at are new fish or possibly the same fish that have moved. So what basically these studies do is add technical difficulty to making the argument about scale and [abundance], and add additional layers of uncertainty. And that is where the mathematical methods can help sort things out.

**PSI:** So you are modeling uncertainty as well.

**MM:** Very much so. Lots of my work tries to deal with grappling with uncertainty or trying to understand how to characterize it, how to reduce it, how to understand what kind of information our measurements are actually giving to us. I think part of what the mathematical methods can do is allow us to construct models that will give us a sense of the potential range of outcomes of different restoration or preservation activities.

**PSI:** Given math’s usefulness to the field of ecology, do you think math is fundamental to the preservation of Puget Sound?

**MM:** Well, as a theoretician, it would be kind of dumb for me to say anything other than that! But I think part of what the mathematical methods can do is allow us to construct models that will give us a sense of the potential range of outcomes of different restoration and/or preservation activities.

Much of what I think we want to do with Puget Sound—if I understand the problem properly—is move it away from its current state to one that is more ecologically robust. But exactly what that will be will depend on the actions as well as the many interactions that we don’t fully know and some of the mathematical models can help us characterize how those changes might occur depending on what we do.

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For more information, view some of Dr. Mangel’s publications.