Getting a clue on population variability Two papers were just published in the Proceedings of the National Academy of Sciences by friends and former colleagues of mine from the University of Washington. Both of these papers confront an old and persistent question in fisheries science: what causes fish populations to vary through time?

The classical answer, and the one that still lies at the heart of most fisheries population models, is that fish populations don’t vary unless we humans go fishing. Left alone, the idea goes, populations should increase towards their natural, equilibrium level and, give or take some minor fluctuations, stay there indefinitely. By controlling how many fish we catch each year, we can change the equilibrium population, and with it the rate of population growth and the risk of overfishing.

The problem with this model, however, is that many fish populations display worryingly little resemblance to it. Large population swings are common in fisheries, and not always for reasons related to fishing. Lots of work has been done looking for, and in many cases finding, correlations between fish populations and oceanographic or climatic processes. Likewise, work has been done on indirect ecological effects, like trophic cascades. But it’s rarely clear exactly how these links work, and we can’t really predict beforehand how or if a particular stock will be affected by physical or biological factors outside of itself.

The first of these two papers, authored by my friend Katyana Vert-Pre (and a few other minor figures in the field) looks at the relationship between stock size and productivity. This is one of the key assumptions in the equilibrium model: that a larger adult population will produce more babies. Using a database of 230 fish population records, Katyana tested how well each stock’s productivity was explained by four hypotheses. She found that only about 18% of the stocks seemed to follow the classical abundance-productivity relationship. About 39% of the populations had an equilibrium, but one that changed from time to time (in so-called “regime shifts”). Another 31% of the populations were a mix of regime shifts and classical population dynamics, and the final 12% of stocks just varied randomly. This is very interesting, and more than a little unsettling when you start ask what percentage of fish stocks are managed as if they had a “natural equilibrium.” I don’t know what the percentage is, but I’ll bet you money its higher than 18%.

The second paper deals with one species, sockeye salmon, in a more restricted geographical range in Alaska. This paper also reveals previously-hidden population variability, but by peering back into the mists of distant time. Or, more accurately, by peering into the muck at the bottom of some 40-odd lakes.

Nitrogen is one of the major elements making up living things. It comes as a mix of two varieties (or isotopes), 14N and the much-less-common 15N . These two isotopes behave identically in chemical reactions, but 15N has one more neutron, making it slightly heavier. As it turns out, marine phytoplankton take up 15N a little bit more than land plants do. As a result, they (and the rest of the marine food chain) end up with nitrogen that is just a little heavier (because it has more 15N) than that found on land.

The upshot of all this is that when thousands of salmon, who have spent their entire adult lives eating and growing at sea, swim up a river to a lake to spawn and die, they bring with them a lot of 15N. Some of this oceanic 15N ends up in bears, bugs, and trees, and some ends up at the bottom of the lake. By looking at the 15N:14N ratio in sediment cores from the bottoms of these lakes, the researchers could measure the relative abundance of sockeye salmon going back for 500 years. This is way before any large-scale commercial fishing, and definitely before any kind of systematic record-keeping.

Records of 15N from 24 Alaskan lakes over the past 500 years. Where delta-15N is high, it indicates a lot of marine organic material (i.e., salmon) arrived in the lake. The lines in green are from lakes with no salmon—notice how they’re a lot flatter than the others.

And what did they find? Salmon stocks had big, apparently natural swings in abundance that played out over many decades. Some of these lakes had semi-periodic population fluctuations repeating every 80 or 100 years. The salmon in some of these lakes and rivers have been under scientific study for 50 or 60 years, which is an exceptionally long time–but that entire research history fits comfortably inside one of these centennial cycles that are apparently not at all uncommon. That’s temporal scale for you: centennial cycles may be the largest source of variability in these salmon populations, but two or three human generations of painstaking observation don’t cover enough time to even notice them.

I thought both these papers were really cool for the new insights they give on variability fish populations. The first uses straightforward statistics to give a really informative sense of how well-supported a few common mental models for population dynamics are in the real world. And the second uses an incredibly subtle signal—a difference of a few parts per thousand in the mass of nitrogen atoms at the muddy bottom of a lake—to reconstruct centuries of fish life and death. And perhaps most importantly, both papers give clear warnings that when it comes to natural populations, equilibrium can be a dangerous thing to assume.

Vert-pre, K., Amoroso, R., Jensen, O., & Hilborn, R. (2013). Frequency and intensity of productivity regime shifts in marine fish stocks Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.1214879110

Rogers, L., Schindler, D., Lisi, P., Holtgrieve, G., Leavitt, P., Bunting, L., Finney, B., Selbie, D., Chen, G., Gregory-Eaves, I., Lisac, M., & Walsh, P. (2013). Centennial-scale fluctuations and regional complexity characterize Pacific salmon population dynamics over the past five centuries Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.1212858110

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