Posts Tagged ‘fish’

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:

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 4

November 2, 2008

2008 Eureka Prize for Science Photography
New Scientist

Why Are Female Blue Tits Unfaithful?
from Living the Scientific Life

Okay, so you don’t have to actually read this article, which has something to do with sexual selection in birds (really? birds? after a title like that?). As with Danielle Steele or eviction notices, the first line or two is good enough.

Spooky Images From Outer Space
New Scientist

That’s no Death Star. That’s a small moon!

A Programmer’s View Of the Universe
Steve Yegge on Stevey’s Blog Rants

I can’t figure out what this essay has to do with programming. As far as I can tell, it’s about fish. Also, something with a metaphor. Fish as a metaphor for life. Because we need more things that are metaphors for life. Here’s a question for you: if the fish is a metaphor for life, who’s going to be a metaphor for the fish? See, not even the Lorax dared to ask that one.

I like reading essays in which people attempt to come to grips with the biggest problems they face. Problems of unspeakable complexity are an example, as is fish ownership. What interested me most was the following take on facing big problems:

In time, though, programming eventually humbles you, because it shows you the limits of your reasoning ability in ways that few other activities can match. Eventually every programmer becomes entangled in a system that is overwhelming in its complexity. As we grow in our abilities as programmers we learn to tackle increasingly complex systems. But every human programmer has limits, and some systems are just too hard to grapple with.

When this happens, we usually don’t blame ourselves, nor think any less of ourselves. Instead we claim that it’s someone else’s fault, and it just needs a rewrite to help manage the complexity.

I do not interpret big problems this way. When I face a problem I can’t solve, I generally have one of two reactions. One is to be humbled, but by “humbled” I mean some more along the lines of “temporarily lose all sense of self-worth”. The other is to ignore the problem, or pretend that it is solved, or pretend that it is not important or that I will easily solve it tomorrow. Never do I adopt the tack of assuming that the fault lies in the problem. It’s a novel idea that I’ll certainly have to try out the next time something confuses me. Actually, I’m pretty confused by my toilet right now, but only because it has like a million little pieces in there that some idiot assembled with horribly unnecessary complexity.

Oh, and writing up that last little comment got me wondering they they had ever made an animated “Lorax” like I had seen with “The Butter Battle Book”. They did. Dr. Seuss is pretty much the best thing ever.

You can read more about it elsewhere, and there is controversy about it, but this is the bare bones of what it would be nice to know about how Google Books will change due to their recent settlement. I’d say having access to millions of otherwise-unaccessible books free through the Caltech Library system, and for pay if I’m not at Caltech (or Caltech doesn’t buy in) is a pretty good deal. I’ve been meaning to read a million books, one of these days.

From the title, you might think this page is a bunch of funny jokes about graduate student life. Or you might thinks it’s a bunch of little packages of bullet-pointed wisdom. Actually, it’s just depressing. A grad student complains that grad school, and scientific culture in general, are nothing like what he/she imagined. But the sad part is that in the responses to the thread, the most optimistic advice anyone has is, “Yup. That’s the way it is. I guess you just have to try to deal as best you can.”

Jordan Ellenburg on Slate

I voted for the first time in this election. I was 19 in 2004, and a sophomore in college. Because I’m a legal resident of Maryland, I couldn’t vote on Election Day, but I could certainly have obtained an absentee ballot with a minimal amount of effort.

I didn’t vote then, and I did this year. However, this was not because the mathematical sophistication I’ve gained in the last four years led me to re-assess the probability that my vote would count using a Bayesian analysis. Even with a one-in-a-million chance that your vote could decide the election, it’s not worth my time and effort to vote (i.e., if you take the time it took me to fill out the ballot and multiply by one million, you get my entire life span so far. And I would readily take my life so far over the chance to decide the next President between two major-party candidates.)

So my decision to vote had nothing to do with my estimation of whether or not it matters. Nor, I suspect, do most other voters’. So I disagree with Ellenburg’s thesis that it’s possible your individual ballot has more meaning than you think. However, I think the reasons people vote may vary widely.

One possible reason is explicit delusion: some people actually believe their vote makes a difference in terms of the outcome of the election. The other reasons to vote that come immediately to my mind are other, less direct forms of delusion, at least one of which I am guilty of.

Probably a common reason to vote is a sense of duty. People believe they are obligated to vote by society. I discussed this point before, and I think it’s insane. Voting is so meaningless that people’s obligation cannot possibly be to vote. If people have an obligation to the political system of their country, that obligation must be to a much more active participation than simply filling in some bubbles on an adult Scantron. (Dude, how did I never notice in high school that Scantron is a total Transformer name?) The same people who believe they have an obligation to vote frequently do not feel an obligation to educate themselves about the social, economic, and international issues that bear upon their vote. They do not feel an obligation to think rationally about their vote, to carefully contemplate and question their positions, and to attempt to recognize and grapple with their own prejudices. I would much rather have 25% of the populace vote with conviction backed upon rational thought and sincere concern for the well-being of themselves, their community, their nation, and the world, rather than 90% of the populace voting on what they read in People magazine.

Another possible delusion, and one that likely prompted my decision to vote, is a desire to avoid hypocrisy. How can I hold and argue opinions about political actions or social issues if I refuse even to make the the bare minimum effort to participate in the decision-making process, when that opportunity is offered? Forget the fact that, aside from school assignments, I have never written a letter to a politician, signed a petition, gone to a political rally, attended a town meeting, made a significant effort to express my opinions to fellow citizens, or in any way attempted to utilize one of the many avenues available for common citizens to participate in the political process. Not only do I remain largely ignorant of the proceedings of our government and of local and world politics. Not only do I eschew any personal sacrifice of even an afternoon’s worth of time or a few hours’ wages to help people whose political causes I believe in, I don’t even bother to take the most basic political action available to an American and cast a vote. The desire to avoid this hypocrisy is delusional because if casting a vote is worthless in terms of making a discernible impact on politics, then whether or not I voted should have no bearing on the probity of offering strongly-held opinions on politics.

I also believe many people vote due to a delusion that is essentially ineffable. Even if brushing your teeth were found to be completely useless in terms of oral hygiene, people would still do it, just because that’s what you do before bed (or whenver you happen to brush your teeth.) Similarly, I suspect that many people vote (and vote along party lines) simply because that’s what you do in election season. And they think about it no further.

Friday Sprog Blogging: Ghosts
Janet D. Stemwedel on Adventurers in Science and Ethics

I’ve been reading this stranger’s “sprog” conversations with her children for a couple of months now. I still don’t know what “sprog” means, but I think it has something do with with indoctrination into free-mindedness. The weekly column is hit and miss, but this one has a nice line or two.

Younger offspring: You don’t believe ghosts are real?

Dr. Free-Ride: I guess I just haven’t seen the evidence that would convince me.

Elder offspring: That creaking stair is pretty convincing.

Dr. Free-Ride: Look, at night, when we’re all in bed, our house creaks, but you don’t think it’s haunted, do you?

Younger offspring: No.

Elder offspring: Of course not! No one has died in it yet.

Providing Toilets for 39,000 Runners
John Branch for The New York Times

As soon as we can get the Times to run an article on nipple chafing we’ll really be on the way to getting the public to understand us runners.