Posts Tagged ‘biology’

Coral Reefs are 85% Shark?

May 18, 2010

In a recent TED Talk, Enric Sala says that before being sullied by people, a healthy coral reef stores 85% of its biomass in the form of sharks.

He shows this image of the “inverted pyramid” of reef biology:

When reading through these calculations, don't forget that I neglected that sharks eat their own young, and they also eat your own young.

I found this pretty surprising, as did the guy who organizes the talks, Chris Anderson. Anderson asked Sala after the talk:

Your inverted pyramid showing 85% of the biomass is in predators – that seems impossible. How could 85% survive on 15%?

To which Sala replied:

Imagine that you have two gears of a watch – a big one and a small one. The big one is moving very slowly and the small one is moving fast. That’s basically – the animals in the lower parts of the food chain, they reproduce really fast. They grow really fast they produce millions of eggs. And there you have sharks, and large fish that live 25 years. They live very slowly they have very slow metabolism, and basically they just maintain their biomass so basically the producion surplus of these guys down there is enough to maintain this biomass that is not moving…

Everything I know about sharks I learned from old Batman movies, but we don’t need much biological knowledge to see if this makes sense. We’ll simplify things to just two trophic levels – sharks and fish. If there are really 3, that doesn’t matter, because if fish are the entire bottom of the pyramid they’re 15% of the biomass, and if they’re the middle of the pyramid they’re maybe 12%, which is close enough.

The striking fact was the high ratio (about 6) between the sharks’ mass and the fishes’ mass, so let’s try to derive a formula for this ratio based on Sala’s idea that sharks have slow metabolism and don’t eat much compared to fish.

Suppose the biomass fraction of the sharks is B_s (0.85 in the video) and of the fish B_f. The basal metabolic rate of the sharks is M_s and of the fish M_f. “Basal metabolic rate” here means the number of calories per kilogram per day needed to maintain the same mass. The eating rates are E_s and E_f. “Eating rate” means calories eaten per kilogram per day.

According to Sala, the sharks are just chillin’ at the same body mass, so

M_s = E_s .

The fish, on the other hand, need to grow, so that they’ll be more there for the sharks to eat. We can write this as

B_s E_s = C(E_f - M_f)B_f .

The left hand side represents the amount the sharks eat. The right hand side is the extra amount the fish eat, multiplied by some conversion factor C that turns surplus calories eaten by the fish into calories for the sharks. These two equations give the ratio of biomass of sharks to fish.

\frac{B_s}{B_f} = \frac{(E_f - M_f)C_f}{M_s}

To get a high ratio of shark mass to fish mass, we need low shark metabolism (to reduce their appetite and not eat the scant fish away completely), low fish metabolism (which is wasted energy), high fish eating rates (to be converted to shark food), and a high conversion rate (to make shark food efficiently).

I think it would be helpful here to introduce the voraciousness of the fish, V, defined by

V = \frac{E_f - M_f}{M_f} .

This is a number like 2 or 6. A voraciousness of 0 would mean the fish eat just enough to survive if there were no sharks around. A voraciousness of 1 means they eat twice as much as they need, and a voraciousness of 4 means they eat 5 times their minimum diet. We’ll also introduce R, the ratio of shark to fish mass by

R = \frac{B_s}{B_f} .

With these new variables, the equation describing the aquatic eating habits is

R = V C \frac{M_f}{M_s}

We might expect 1 kilogram of fishy-fishy to use more energy than 1 kilogram of death shark because sharks are bigger and they keep their cool, except unless they smell blood in the water. (This is just the first search result for a shark feeding frenzy:)

I remember hearing somewhere that in general, biological organisms that are fairly similar (e.g. all mammals) will follow simple power laws when you scale them. Sharks are basically just big fish, so they should be on the same scaling law. We could try to create a heuristic argument for what this should be for the metabolic rate, but I’m not sure how to do that, and it would likely be wrong. Instead, I turned to wikipedia and found Kleiber’s Law, that total metabolism of the animal scales with the 3/4 power of the mass, or that metabolic rate per kilogram (which we are using) scales with the -1/4 power of the mass of the animal.

So let’s introduce a new variable, S, for the ratio of the sizes of the shark to the fish. Then Kleiber’s law states

\frac{M_f}{M_s} = S^{1/4}

This finally gives us a simple equation for the ratio R of shark mass to fish mass.

R = C V S^{1/4}

Sala gave roughly R = 6, and a reasonable guess is C = 0.1 because the surplus food is getting eaten by fish, turned into new fish, and then eaten by sharks, and that takes a lot of energy.

How big is a shark compared to a fish? I googled this and found that a Caribbean reef shark is a big shark for a reef, and weighs up to 70kg. I’d think a mid-level predator fish would be at least 1kg, but let’s be nice and say just 100g. Then S = 700 so S^{1/4} = 5. That fills in enough to solve for V, the voraciousness of the fish.

V = \frac{6}{0.1*5} = 10

So the fish in Sala’s reef must be eating ten times as much daily as they need just to maintain body weight. I suppose this is a conceivable rate to get the food down the gut, but is it a reasonable rate to have the fishes’ bodies effectively processing all that food? A human base metabolism might be half a pound of dry mass, and a newborn baby is maybe 2.5 pounds of dry mass, so the rate that fish in the coral reefs are eating and growing is roughly equivalent to a woman who eats enough to grow a set of twins every day. You can find animals doing some pretty wild things if you look hard (or just turn on the Discovery Channel), so it might be possible. Nonetheless I find it dubious that coral reefs are 85% shark.


Let’s Read The Internet! Week 1

October 12, 2008

Earth From Above

Sensory overload.  Thirty photographs of socially-relevant scenes from around the world, each of which could easily launch me on a few hours of reading and comparing.  Taken together, they present an overwhelming mosaic of a vibrant, living, interconnected, diverse, and changing planet.

But, damn, I just noticed that the story has gone from displaying 30 photographs to just ten, and the impact is nowhere near as great.  It seems hypocritical that the coordinator of the exhibit (not the artist) should ask the website to take photographs down, when the whole point of the exhibit, as expressed by the artist, is that it be completely free and displayed out on the streets in cities across the world to reach as broad and diverse an audience as possible.

Not the end of evolution again!

  John Wilkins at “Evolving Thoughts”

You might have heard about some guy telling the media that human evolution is over because we now care for our sick.  Wilkins presents a brief, irate counterargument.

I’ve done some reading on evolution from time to time.  What I’ve learned is that’s it’s deceptively difficult to understand.  Although the basic idea that heritable variation and selection pressure combined lead to evolution is straightforward, there are an awful lot of intricacies you find when you begin to look more closely.

There are some things you can do – such as study genomes to see how closely-related two species are, or study fossil records to document the evolutionary history of a species.  But there are a lot of things you can’t do, such as say, “Dinosaurs evolved to be really big because they were in an arms race.  Prey got bigger, so predators were forced to get bigger, and then prey got bigger again and off they went.”  That is not a falsifiable hypothesis, because you can’t go back and test it.

You can study evolution mathematically, and you can make falsifiable predictions, and then compare those predictions to observation.  But statements like, “human evolution is over because we care for our sick” are basically pseudoscience.

Extremely simplistic thinking about evolution leads to paradoxes.  For example, now that we first-world men don’t have to worry much about dying in our mothers’ arms during infancy, getting killed in battle at age 16, or starving to death when the buffalo find a new migration route at age 27, shouldn’t the biggest factor left in our reproductive success be how good we are at attracting women?  And therefore, shouldn’t every man spend all his effort spreading his seed far and wide?  Shouldn’t guys just be thinking about sex all the time…  Oh, never mind.

How We Evolve

Benjamin Phelan at Seed Magazine

A lengthy article about the sort of thing I referenced above – collecting data from genomes to study evolution.  Here, the scientists took genomes from humans of varying ethnic background and looked for characteristic differences in their DNA as evidence of evolution.  Bottom line: Yes, people are still evolving.  For example, as a white man, I am a highly-evolved lactase-producing being, unlike the those primitve, dairy-bloated Asians.

In Defense of Difference

Maywa Montenegro and Terry Glavin at Seed Magazine

In a companion article to the one above, the authors discuss why we might want to save the rainforest, anyway (because we like rain?).  Not just because we like toucans or want to display a World Wildlife Fund bumper sticker on our Prius.  Because it has economic, social, medical, and scientific value to humans.

The idea is that biology is a huge information-gathering system.  From a protein to an organism to an ecosystem, evolution allows biology to record information about how to live in the world, and also provides a ready-made task force 10^30 cells strong that will do its best to find out how to live in a changing world.  The more stuff we destroy, the more Earth loses the ability to adapt to hard times.  Clear the rainforest to raise crops, and disease or natural disaster or pollution find it much easier to brutally rape the new, homogenized biosphere.

The argument is then extended to such things as preserving human languages, which record the results of thousands of experiments in creating human culture.  So nature is basically a billion billion whatever tiny lab books full of experiments, and instead of reading them, we’re throwing them out.

Nobel Sur-prize

Peter Coles at “In The Dark”

Particles are everywhere.  While you read this, particles are in your home, in your infant child’s crib.  In her anus.

I don’t understand them.  But here’s a fairly simple explanation of the work that won this year’s Nobel Prize in physics.  Basically, the uproar is that this guy Cabibbo had a big idea about physics that helped explain a mystery about particles.  Later, Kobayashi and Maskawa solved a mathematical problem that expanded on Cabibbo’s idea.  Both were important – the original idea and the difficult mathematical extension to it – but only one was awarded the prize.

Also check out a more basic article from Mark Chu-Carroll at “Good Math, Bad Math”

What positive psychology can help you become

Martin Seligman on TED

A talk interesting enough that I watched it twice.  The second time while smiling. Seligman decided to break happiness, or life satisfaction, into three categories.  (To me this is rather arbitrary.  It’s not like the categories of happiness are just sitting out there, waiting to be discovered.  But it’s a persistent plague among people who study such things to break them down into categories they believe are fundamental. i.e. “four personality types”, “two political ideologies” (left/right), or even “four kingdoms of life” (some people now say up to 13.  others 2))

The categories are: surface pleasures like active social life, good love life, and sensual pleasure; “flow”, or the state of intense focus and concentration associated with, say, rock climbing or physics sets; and “meaning”, or finding something greater than yourself to dedicate your life to.

Seligman describes the beginnings of a movement to apply a scientific approach to the study of happiness, as opposed to the traditional psychological model of simply curing mental illness and depression.  He claims that it is possible for people to increase the fulfillment they feel in life by a concentrated effort in the right direction.  It’s a summary of the beginning of a quest to understand people in a new way, and apply that understanding to make life better.


A site you may have seen before.  They use maps of the world to visualize data.  For example, compare a map where each country’s size represents the number of personal computers in that country, to a map showing how many people died of “often preventable deaths”.

There are a lot of technically-interesting things about this project.  How did they get the countries to fit together, when their land area needs to be fixed at some arbitrary size?  What sort of properties of the standard world map’s topology were they trying to preserve?

But more interesting are the social, economic, and political insight you can get.  Compare this project to the Gapminder.

Small samples, and the margin of error

Terry Tao at “What’s New”

Terry Tao tones it down a notch to present something even I can understand.  He discusses how a random sampling of just 1000 people can give an accurate picture of the opinions of a nation of 200,000,000 voters.  He also gives a short proof of the accuracy of the sample, without resorting to the binomial distribution.