The Global Amphibian Crisis

There’s a fungus that infects many kinds of amphibians. Some get wiped out entirely—but it’s harbored harmlessly by others, so it’s impossible to eradicate. Over a hundred species have disappeared in the last 20 years!

You’ve got to read this:

• Joseph R. Mendelson III, Lessons of the lost, American Scientist 99 (November-December 2011), 438.

The fungus causes a disease called chytridiomycosis. The effects are gruesome: when spores land on a susceptible amphibian, they quickly sprout and form a vase-shaped structure that harvests energy from the animal’s skin. This produces more spores, which swim around using flagella and spread. The disease progresses as these reinfect the host. The victim may become lethargic, lose skin over its body, go into convulsions, and die.

Amphibian populations have been dropping rapidly worldwide since the 1980s. There were about 6500 species, but now 30% of these are endangered, about 130 are ‘missing’, and about 30 are extinct in the wild.

There were many theories about the cause of this decline, but now we know this disease is playing a big role. As Mendelson says:

Herpetologists and wildlife biologists began observing inexplicable disappearances of amphibians around the globe in the mid-1970s and especially by the mid-1980s but were at a complete loss to explain them. Finally, in the late 1990s, an insightful team of pathologists at the U.S. National Zoo, led by Don Nichols, collaborated with one of the few chytrid fungus scholars in the world, Joyce Longcore, and identified this quite unusual new genus and species.

Conservationists and disease ecologists were unprepared for the reality of a pathogen capable of directly and rapidly—mere months!—causing the elimination of a population or an entire species that was otherwise robust. Classical host-pathogen theory held that such dramatic consequences to the host population or species were only realized when the host population was already drastically reduced in size or otherwise compromised. The concept of a lightning extinction was foreign to researchers and conservationists, and we argued vehemently about it throughout the 1990s at symposia worldwide.

In retrospect, the scenario of a spreading pathogen is parsimonious and clear, but in the midst of the massacre we were entangled in logical quagmires along these lines: “The disappearances cannot be the result of disease; diseases are not capable of such.” Not to mention the fact that the smoking gun, the pathogen itself, was not described until 1999. While we were debating the issue, a terrible lesson was playing out for us around the world as an unknown disease decimated amphibian populations.

What are the ‘lessons’ that Mendelson is talking about? Here are some:

Our powerlessness in this terrible crisis must be balanced by increased efforts in realms that we can control, such as reducing carbon emissions to protect what habitat remains from chemical and physical disruption. We can go further and restore what has been wounded but can still be salvaged. We need to inspire and fund truly innovative research on pathogens in order to better predict and thwart emerging infectious diseases. The lessons we learn here will extend far beyond the amphibians. We must support funding for programs such as the Amphibian Ark and the Amphibian Survival Alliance. We must keep looking for species gone missing, and continue biodiversity surveys, despite the sometimes paralyzing depression that both activities can induce in this era. But especially, we need to pay close attention to the lessons that legions of dead amphibians are teaching us. I note with some satisfaction that our colleagues in bat research and conservation did not spend a decade arguing whether the fungus that causes white-nose syndrome could possibly eliminate entire colonies of bats in a single season. Our colleagues assumed that it was possible and reacted quickly. We can thank the amphibians for leaving us that lesson, but at such cost.

Yes, millions of bats in America have died from a new fungal disease called white-nose syndrome.

What role, if any, do people play in the spread of these new diseases? Why are they happening now?

In the case of amphibians, people helped spread American bullfrogs. These are resistant to the disease, but carry it. They’ve largely taken over here in Singapore.

Global warming seems not to be responsible, because the worst outbreaks happen at high elevations, where it’s cool: that’s where the fungus thrives.

As for the bats, the same fungus that’s killing bats in America is found in healthy bats in Europe, which suggests the disease spread from there. People might carry spores on their clothes from infected caves to not-yet-infected ones, so visitors to caves with bats are being asked to limit their activities, and disinfect clothing and equipment. It’s completely against the rules to visit some caves now.

There have been successful attempts to cure some amphibians of chytridiomycosis:

• Reid Harris of James Madison University has claims that coating frogs with Janthinobacterium lividum protects them from chytridiomycosis.

• A team of scientists published a paper claiming that Archey’s frog (Leiopelma archeyi), a critically endangered species in New Zealand, was successfully cured of chytridiomycosis by applying chloramphenicol topically.

• Don Nichols claims to have cured several species of frogs using a drug called itraconazole.

• Jay Redmond at WWT Slimbridge, Gloucestershire claims that raising poison dart frogs in water containing Rooibos tea (Aspalathus linearis) wards off chytridiomycosis.

The Amphibian Ark is trying to keep populations alive that have died in the wild. They have a list of suggestions on what you can do to help. For starters:

• Don’t ever release pet amphibians into the wild.

• Build a frog pond: here’s how. Even in arid places like Riverside California, our friends who built some ponds soon found them occupied by sweetly chirping frogs.

• Get involved in collaborations that promote sustainable breeding and management, like the Amphibian Steward Network.

• Figure things out. Zoos don’t even know how to breed common toads without using artificial hormone injections! If you could find a way, maybe the same technique could be used with threatened species.

• If you’re a student, go to James Madison University and work with Reid Harris:

or go to the University of Maine and work with Joyce Longcore:

or find a university closer to you with someone leading a group that studies chytridiomycosis!

(Click on the pictures for even more info.)

I thank Allen Knutson for pointing out the American Scientist article. This is the best popular science magazine in the English language, but I let my subscription lapse when I came to Singapore!

Wild Cats of Arizona

Here’s a quick followup to our discussion of the wild cats of Sumatra caught on camera by the World Wildlife Foundation. Recently there have been sightings of rare wild cats in Arizona!

• Marc Lacey, In southern Arizona, rare sightings of ocelots and jaguars send shivers, New York Times, 4 December 2011.

• Guide describes roaring, powerful jaguar, Arizona Daily Star, 23 November 2011.

For example, consider Donnie Fenn, who specializes in hunting and killing mountain lions (also known as cougars or pumas). He was taking his 10-year-old daughter out on her first hunt when his pack of hounds took off and cornered something in a tree. He then saw with the telephoto lens of his camera that it wasn’t a mountain lion—it was a jaguar, which is about twice as big!

“It’s the most amazing thing that’s ever happened to me,” said Fenn, who leads hunters to mountain lions with his dogs. “To be honest with you—I got to see it in real life, my daughter got to see it, but I hope never to encounter it again.

“I was nervous, scared, everything. It was just the aggressiveness—the power it had, the snarling. It wasn’t a snarl like a lion. It was a roar. I’ve never heard anything like it.”

Fenn was thrilled as well as scared. He had never expected to see such a large, endangered cat so early in his life, at age 32, he said. A lifelong hunter and Benson resident, he runs the mountain lion guide service as a sideline while working full time in an excavating business. He described his one-hour encounter with the jaguar as “a dream come true.”

He came away respectful of its power, speed and size.

“All my dogs took a pretty good beating. They had puncture wounds. … I got to see it in real life, and I’m glad, but I hope to never encounter it again,” he repeated.

He crept up close and took photos and a video of the jaguar:

He also notified state wildlife officials, who were later able to find hair samples left behind by the animal and a tree trunk that showed signs of being climbed by a large clawed animal. They believe he saw an adult male jaguar that weighed about 90 kilograms.

The jaguar, Panthera onca, is the third-largest cat in the world, only outranked by the lion and tiger. It’s the only surviving New World member of the genus Panthera. For example, there was once an American lion, but that went extinct 10,000 years ago, along with a lot of other large mammals, after people showed up. DNA evidence shows that the lion, tiger, leopard, jaguar, snow leopard, and clouded leopard share a common ancestor, and that this whole gang is between 6 and 10 million years old. (The so-called ‘mountain lion’, Puma concolor, is not in this group.)

Jaguars have mostly been killed off in the United States, but they survive from Mexico to Central and South America all the way down to Paraguay and northern Argentina. They are listed as ‘near threatened’ by the IUCN, or International Union for the Conservation of Nature.

The Arizona Fish and Game Department has also announced two reliable sightings of ocelots this year!

The ocelot, Leopardus pardalis, is a much smaller fellow, about the size of a domestic cat. Ocelots live in many parts of South and Central America and Mexico, and they’re listed as being of ‘least concern’ by the IUCN. Once their range extended up into the chaparral thickets of the Gulf Coast of south and eastern Texas, as well as part of Arizona, Louisiana, and Arkansas. But by now they are very hard to find in the United States. They seem to eke out an existence only in several small areas of dense thicket in South Texas… and, we now know, Arizona!

Wild Cats of Sumatra

Sumatra is just half an hour from here. I’ve never visited it, but I’m awfully curious. So, I was excited to hear today that the World Wildlife Fund put cameras in the forest there and caught pictures of 5 species of wild cats! You can see them here:

• World Wildlife Fund, Remarkable images of big cats urge forest protection.

I’ve been curious about the smaller wild cats of Asia ever since I met this absurdly sweet thing which belongs to a friend of mine named Julia Strauss:

Julia lives in London, but she went all the way to Wales to buy this cat. Why? Because it’s a Bengal. That means it’s a crossbreed of an ordinary domestic cat with a leopard cat!

The leopard cat, Prionailurus bengalensis, is the most widespread of the Asian small cats. It has a huge range, from the Amur region in the Russian Far East through Korea, China, Indochina, India… all the way to the Pakistan in the west… and to Philippines and some islands in Indonesia in the south. It’s listed as ‘least vulnerable’ to extinction.

So, it’s not surprising that leopard cats are one of the kinds the WWF saw in Sumatra. Here’s one in the Berlin Zoo, photographed by F. Spangenberg:

Ain’t it cute? It’s about the size of a domestic cat, but it has a different number of chromosomes than Felis domesticus, so it’s a bit remarkable that they can interbreed. The resulting Bengals share some traits with the leopard cat: or example, leopard cats like to fish, and Bengals like to play around in their water bowls!

Another cat the WWF saw in Sumatra is the marbled cat, Pardofelis marmorata. It’s again about the same size as a house cat, but it likes to hunt while climbing around in trees!

This feisty fellow is listed as ‘vulnerable;—there are probably about 10,000 of them in the world, not counting kittens. They live from the Himalayan foothills westward into Nepal and eastward into southwest China, and also on Sumatra and Borneo.

Then there’s the Asian golden cat, Pardofelis temminckii. These guys are two to three times as big as a domestic cat! I saw one at the Night Safari in Singapore—a kind of zoo for nocturnal animals. Here’s a picture of one taken by Karen Stout:

They live all the way from Tibet, Nepal, and India to Thailand, Cambodia, Laos, and Vietnam, to down here around Malaysia and Sumatra. However, they’re listed as ‘near threatened’, due to hunting and habitat loss. They’re hunted for the illegal wildlife trade, and some people kill it for eating poultry—and also supposedly sheep, goats and buffalo calves.

Moving further up the size ladder, we meet the Sunda clouded leopard, Neofelis diardi. Here’s a great photo by ‘spencer77’:

These guys are special! They only live on Borneo and Sumatra, they’re listed as “vulnerable”, and scientists only realized they’re a separate species in 2006! Before that, people thought they were the same as the ordinary kind of clouded leopard, Neofelis nebulosa. But genetic testing showed that they diverged from that species about 1.4 million years ago, after having crossed a now submerged land bridge to reach Borneo and Sumatra.

I’ve seen the ordinary kind of clouded leopard at the Night Safari. But calling them ‘ordinary’ is not really fair: they’re beautiful, mysterious, well-camouflaged beasts—very hard to see even if you know they’re right in front of you! Indeed, very little is known about either kind of clouded leopard, because they’re so elusive and reclusive.

And finally, the biggest kitty on the island: the Sumatran tiger, Panthera tigris sumatrae! It’s a subspecies of tiger that only lives on Sumatra. It’s listed as “critically endangered”. The World Wildlife Fund estimates there are fewer than 500 of these tigers left in the wild—maybe a lot fewer.

This beauty was photographed in the Berlin Zoo by ‘Captain Herbert’:

Sumatran tigers have webbing between their toes, which makes them really good swimmers! They get up to 2.5 meters long, but they’re is the smallest of tigers, as you might expect from a species on a hot tropical island. (The biggest is the Siberian tiger, which I talked about earlier.)

There are lots of palm oil plantations in Sumatra. People burn down the jungle to plant palms, and the smoke sometimes creates a thick smelly haze even here in Singapore. It’s horrible. This deforestation is the main threat to the Sumatran Tiger. Also, many tigers are killed every year by poachers.

On the bright side, in 2006 the Indonesia Forestry Service, the Natural Resources and Conservational Agency, and the Sumatran Tiger Conservation Program sat down with companies including Asia Pulp & Paper and set up the Senepis Buluhala Tiger Sanctuary, which is 106,000 hectares in size. There’s also a large area for tigers called the Tambling Wildlife Nature Conservation on the southern tip of Sumatra. And the Australia Zoo has a program of reintroducing tigers to their natural habitat in Sumatra.

Okay, that’s it for now. I’ve got you all softened up, and I’m not even going to ask you for donations. Just be nice to cats, okay? Or better yet, be nice to life in general. We’re all in this together.

Azimuth on Google Plus (Part 4)

Again, some eye candy to start the show. Stare fixedly at the + sign here until the pink dots completely disappear:

In a semiconductor, a ‘hole’ is the absence of an electron, and it can move around a as if it were a particle. If you have a hole moving to the right, in reality you have electrons moving to the left. Here pink dots moving counterclockwise look like a green dot moving clockwise!

A related puzzle: what happens when you hold a helium balloon on a string while you’re driving in a car with the windows closed… and then you make a sharp right turn? I’ve done it, so I know from experience.

Now for the real stuff:

• Tom Murphy, a physics professor at U.C. San Diego, has a blog worth visiting: Do the Math. He uses physics and math to make informed guesses about the future of energy production. Try out his overview on ‘peak oil’.

• Hundreds of top conservation scientists took a survey, and 99.5% felt that a serious loss of biodiversity is either ‘likely’, ‘very likely’, or ‘virtually certain’. Tropical coral ecosystems were perceived as the most seriously affected. A slim majority think we need to decide on rules for ‘triage’: deciding which species to save and which to give up on.

• Climate change is causing a massive change in tree species across Western USA. “Ecosystems are always changing at the landscape level, but normally the rate of change is too slow for humans to notice,” said Steven Running, a co-author of a study on this at the University of Montana. “Now the rate of change is fast enough we can see it.” The study used remote sensing of large areas over a four-year period.

• The James Dyson Award calls on design and engineering students to create innovative, practical, elegant solutions to the challenges that face us. This year, Edward Linacre won for a self-powering device that extracts water from the air for irrigation purposes. Linacre comes from the drought-afflicted continent of Australia. But his invention borrows some tricks from the Namib beetle, which survives some of the driest deserts in Africa by harvesting the moisture that condenses on its back during the early morning. That’s called biomimicry.

• The New York Times has a great profile of Jeremy Grantham. He heads a successful firm managing $100 billion assets, and now he’s 72. So why is he saying this?

… it’s very important to me to make a lot of money now, much more than when I was 40 or 50.

Not because he has a brand new gold-digger ‘trophy wife’ or spendthrift heirs. No, he puts all the money into the Grantham Foundation for the Protection of the Environment. He’s famous for his quarterly letters on future trends—you can read them free online! And thanks to this, he has some detailed ideas about what’s coming up, and what we should do about it:

Energy “will give us serious and sustained problems” over the next 50 years as we make the transition from hydrocarbons—oil, coal, gas—to solar, wind, nuclear and other sources, but we’ll muddle through to a solution to Peak Oil and related challenges. Peak Everything Else will prove more intractable for humanity. Metals, for instance, “are entropy at work . . . from wonderful metal ores to scattered waste,” and scarcity and higher prices “will slowly increase forever,” but if we scrimp and recycle, we can make do for another century before tight constraint kicks in.

Agriculture is more worrisome. Local water shortages will cause “persistent irritation”—wars, famines. Of the three essential macro nutrient fertilizers, nitrogen is relatively plentiful and recoverable, but we’re running out of potassium and phosphorus, finite mined resources that are “necessary for all life.” Canada has large reserves of potash (the source of potassium), which is good news for Americans, but 50 to 75 percent of the known reserves of phosphate (the source of phosphorus) are located in Morocco and the western Sahara. Assuming a 2 percent annual increase in phosphorus consumption, Grantham believes the rest of the world’s reserves won’t last more than 50 years, so he expects “gamesmanship” from the phosphate-rich.

And he rates soil erosion as the biggest threat of all. The world’s population could reach 10 billion within half a century—perhaps twice as many human beings as the planet’s overtaxed resources can sustainably support, perhaps six times too many.

It’s not that he doesn’t take climate change seriously. However, he seems to have almost given up on the US political establishment doing anything about it. So he’s shifted his focus:

Grantham put his own influence and money behind the climate-change bill passed by the House in 2009. “But even $100 million wouldn’t have gotten it through the Senate,” he said. “The recession more or less ruled it out. It pushed anything having to do with the environment down 10 points, across the board. Unemployment and interest in environmental issues move inversely.”

Having missed a once-in-a-generation legislative opportunity to address climate change, American environmentalists are looking for new strategies. Grantham believes that the best approach may be to recast global warming, which depresses crop yields and worsens soil erosion, as a factor contributing to resource depletion. “People are naturally much more responsive to finite resources than they are to climate change,” he said. “Global warming is bad news. Finite resources is investment advice.” He believes this shift in emphasis plays to Americans’ strength. “Americans are just about the worst at dealing with long-term problems, down there with Uzbekistan,” he said, “but they respond to a market signal better than almost anyone. They roll the dice bigger and quicker than most.”

Let’s wrap up with some more fun stuff: impressive volcanos!

Morgan Abbou explains:

Volcanic lightning photograph by Francisco Negroni. In a scene no human could have witnessed, an apocalyptic agglomeration of lightning bolts illuminates an ash cloud above Chile’s Puyehue volcano in June 2011. The minutes-long exposure shows individual bolts as if they’d all occurred at the same moment and, due to the Earth’s rotation, renders stars (left) as streaks. Lightning to the right of the ash cloud appears to have illuminated nearby clouds.hence the apparent absence of stars on that side of the picture. After an ominous series of earthquakes on the previous day, the volcano erupted that afternoon, convincing authorities to evacuate some 3,500 area residents. Eruptions over the course of the weekend resulted in heavy ashfalls, including in Argentine towns 60 miles (a hundred kilometers) away.

Here’s another shot of the same volcano:

And here’s Mount Etna blowing out a smoke ring in March of 2000. By its shadow, this ring was estimated to be 200 meters in diameter!

Measuring Biodiversity

guest post by Tom Leinster

Even if there weren’t a global biodiversity crisis, we’d want to know how to put a number on biodiversity. As Lord Kelvin famously put it:

When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, your knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science.

In this post, I’ll talk about what happens when you take a mass of biological data and try to turn it into a single number, intended to measure biodiversity.

There have been more than 50 years of debate about how to measure diversity. While the idea of putting a number on biological diversity goes back to the 1940s at least, the debate really seems to have got going in the wake of pioneering work by the great ecologist Robert Whittaker in the 1960s.

There followed several decades in which progress was made… but there was a lot of talking at cross-purposes. In fact, there was so much confusion that some people gave up on the diversity concept altogether. The mood is summed up by the title of an excellent and much-cited paper of Stuart Hurlbert:

• S. H. Hurlbert, The nonconcept of species diversity: A critique and alternative parameters. Ecology 52:577–586, 1971.

So why all the confusion?

One reason is that the word “diversity” is used by different people in many different ways. We all know that diversity is important: so if you found a quantity that seemed to measure biological variation in a sensible way, you might be tempted to call it “diversity” and publish a paper promoting your quantity over all other quantities that have ever been given that name. There are literally dozens of measures of diversity in the literature. Here are two simple ones:

• Species richness is simply the number of species in the community concerned.
• The Shannon entropy is , where our community consists of species in proportions .

Which quantity should we call “diversity”? Do all these quantities really measure the same kind of thing? If community A has greater than species richness than community B, but lower Shannon entropy, what does it mean?

Another cause for confusion is a blurring between the questions

Which quantities deserve to be called diversity?

and

Which quantities are we capable of measuring experimentally?

For example, we might all agree that species richness is an important quantity, but that doesn’t mean that species richness is easy to measure in practice. (In fact, it’s not, more on which below.) My own view is that the two questions should be kept separate:

The statistical problem of designing appropriate estimators becomes relevant only after the measure to be estimated is accepted to be meaningful.

(Hans-Rolf Gregorius, Elizabeth M. Gillet, Generalized Simpson-diversity, Ecological Modelling 211:90–96, 2008.)

The problems involved in quantifying diversity are of three types: practical, statistical and conceptual. I’ll say a little about the first two, and rather more about the third.

Practical  Suppose that you’re doing a survey of the vertebrates in a forest. Perhaps one important species is brightly coloured and noisy, while another is silent, shy, and well-camouflaged. How do you prevent the first from being recorded disproportionately?

Or suppose that you’re carrying out a survey, with multiple people doing the fieldwork. Different people have a tendency to spot different things: for example, one person might be short-sighted and another long-sighted. How do you ensure that this doesn’t affect your results?

Statistical  Imagine that you want to know how many distinct species of insect live in a particular area — the “species richness”, in the terminology introduced above. You go out collecting, and you come back with 100 specimens representing 10 species.

But your survey might have missed some species altogether, so you go out and get a bigger sample. This time, you get 200 specimens representing 15 species. Does this help you discover how many species there really are?

Logically, not at all. The only certainty is that there are at least 15 species. Maybe there are thousands of species, but almost all of them are extremely rare. Or maybe there are really only 15. Unless you collect all the insects, you’ll never know for sure exactly how many species there are.

However, it may be that you can make reasonable assumptions about the frequency distribution of the species. People sometimes do exactly this, to try to overcome the difficulty of estimating species richness.

Conceptual  This is what I really want to talk about.

I mentioned earlier that different people mean different things by “diversity”. Here’s an example.

Consider two bird communities. The first looks like this:

It contains four species, one of which is responsible for most of the population, and three of which are quite rare. The second looks like this:

It has only three species, but they’re evenly balanced.

Which community is the more diverse? It’s a matter of opinion. Mostly in the press, and in many scholarly articles too, “biodiversity” is used as a synonym for “species richness”. On this count, the first community is more diverse. But if you’re more concerned with the healthy functioning of the whole community, the presence of rare species might not be particularly important: it’s balance that matters, and the second community has more of that.

Different people using the word “diversity” attach different amounts of significance to rare species. There’s a spectrum of points of view, ranging from those who give rare species the same weight as common ones (as in the definition of species richness) to those who are only interested in the most common species of all. Every point on this spectrum of viewpoints is reasonable. None should have a monopoly on the word “diversity”.

At least, that’s what Christina Cobbold and I argue in our new paper:

• Tom Leinster, Christina A. Cobbold, Measuring diversity: the importance of species similarity, Ecology, in press (doi:10.1890/10-2402.1).

But that’s not actually our main point. As the title suggests, the real purpose of our paper is to show how to measure diversity in a way that reflects the varying differences between species. I’ll explain.

Most of the existing approaches to measuring biodiversity go like this.

We have a “community” of organisms — the fish in a lake, the fungi in a forest, or the bacteria on your skin. This community is divided into groups, conventionally called species, though they needn’t be species in the ordinary sense.

We assume that we know the relative abundances, or relative frequencies, of the species. Write them as . Thus, is the proportion of the total population that belongs to the th species, where “proportion” is measured in any way you think sensible (number of individuals, total mass, etc).

We only care about relative abundances here, not absolute abundances: so . If half of a forest is destroyed, it might be a catastrophe, but on the (unrealistic) assumption that all the flora and fauna in the forest were distributed homogeneously, it won’t actually change the biodiversity. (That’s not a statement about what’s important in life; it’s only a statement about the usage of a word.)

This model is common but crude. It can’t detect the difference between a community of six dramatically different species and a community consisting of six species of barnacle.

So, Christina and I use a refined model, as follows. We assume that we also have a measure of the similarity between each pair of species. This is a real number between 0 and 1, with 0 indicating that the species are as dissimilar as could be, and 1 indicating that they’re identical. Writing the similarity between the th and th species as , this gives an matrix . Our only assumption on is that its diagonal entries are all 1: every species is identical to itself.

There are many ways of measuring inter-species similarity. Probably the most familiar approach is genetic, as in “you share 98% of your DNA with a chimpanzee”. But there are many other possibilities: functional, phylogenetic, morphological, taxonomic, …. Diversity is a measure of the variety of life; having to choose a measure of similarity forces you to get clear exactly what you mean by “variety”.

Christina and I are by no means the first people to incorporate species similarity into the model of an ecological community. The main new thing in our paper is this measure of the community’s diversity:

What does this mean?

• is what we call the diversity of order of the community. Here is a parameter between and , which you get to choose. Different values of represent different points on the spectrum of viewpoints described above. Small values of give high importance to rare species; large values of give high importance to common species.
• is shorthand for the relative abundances , and is the matrix of similarities.
• means .

The expression doesn’t make sense if or , but can be made sense of by taking limits. For , this gives

If you want to know the value at , or any of the other mathematical details, you can read this post at the n-Category Café, or of course our paper. In both places, you’ll also find an explanation of what motivates this formula. What’s more, you’ll see that many existing measures of diversity are special cases of ours, obtained by taking particular values for and/or .

But I won’t talk about any of that here. Instead, I’ll tell you how taking species similarity into account can radically alter the assessment of diversity.

I’ll do this using an example: butterflies of subfamily Charaxinae at a site in an Ecuadorian rainforest. The data is from here:

• P. J. DeVries, D. Murray, R. Lande, Species diversity in vertical, horizontal and temporal dimensions of a fruit-feeding butterfly community in an Ecuadorian rainforest. Biological Journal of the Linnean Society 62:343–364, 1997.

They measured the butterfly abundances in both the canopy (top level) and understorey (lower level) at this site, with the following results:

Species	Canopy	Understorey
Prepona laertes	15	0
Archaeoprepona demophon	14	37
Zaretis itys	25	11
Memphis arachne	89	23
Memphis offa	21	3
Memphis xenocles	32	8

Which is more diverse: canopy or understorey?

We’ve already seen that the answer is going to depend on what exactly we mean by “diverse”.

First let’s answer the question under the (crude!) assumption that different species have nothing whatsoever in common. This means taking our similarity matrix to be the identity matrix: if then (totally dissimilar), and if then (totally identical).

Now, remember that there’s a spectrum of viewpoints on how much importance to give to rare species when measuring diversity. Rather than choosing a particular viewpoint, we’ll calculate the diversity from all viewpoints, and display it on a graph. In other words, we’ll draw the graph of (the diversity of order ) against (the viewpoint). Here’s what we get:

(the horizontal axis should be labelled with a .)

Conclusion: from all viewpoints, the butterfly population in the canopy is at least as diverse as that in the understorey.

Now let’s do it again, but this time taking account of the varying similarities between species of butterflies. We don’t have much to go on: how do we know whether Prepona laertes is very similar to, or very different from, Archaeoprepona demophon? With only the data above, we don’t. So what can we do?

All we have to go on is the taxonomy. Remember your high school biology: for the butterfly Prepona laertes, the genus is Prepona and the species is laertes. We’d expect species in the same genus to have more in common than species in different genera. So let’s define the similarity between two species as follows:

• the similarity is 1 if the species are the same
• the similarity is 0.5 if the species are different but in the same genus
• the similarity is 0 if they are not even in the same genus.

This is still crude, but in the absence of further information, it’s about the best we can do. And it’s better than the first approach, where we ignored the taxonomy entirely. Throwing away biologically relevant information is unlikely to lead to a better assessment of diversity.

Using this taxonomic matrix , and the same abundances, the diversity graphs become:

This is more interesting! For , the understorey looks more diverse than the canopy — the opposite conclusion to our first approach.

It’s not hard to see why. Look again at the table of abundances, but paying attention to the genera of the butterflies. In the canopy, nearly three-quarters of the butterflies are of genus Memphis. So when we take into account the fact that species in the same genus tend to be somewhat similar, the canopy looks much less diverse than it did before. In the understorey, however, the species are spread more evenly between genera, so taking similarity into account leaves its diversity relatively unchanged.

Taking account of species similarity opens up a world of uncertainty. How should we measure similarity? There are as many possibilities as there are quantifiable characteristics of living organisms. It’s much more reassuring to stay in the black-and-white world where distinct species are always assigned a similarity of 0, no matter how similar they might actually be. (This is, effectively, what most existing measures do.) But that’s just hiding from reality.

Maybe you disagree! If so, try the the Discussion section of our paper, where we lay out our arguments in more detail. Or let me know by leaving a comment.

Bioremediation and Ecological Restoration Job

The University of Texas – Pan American (UTPA) Department of Biology is trying to fill an Assistant Professor Faculty position in Bioremediation and Ecological Restoration, which will start in Fall 2012 pending budget approval. They’re looking for someone whose area of research is bioremediation and/or ecological restoration, and they’re especially interested in candidates whose research focuses on environmental issues relevant to the Lower Rio Grande Valley.

For more details, go here.

 

The Malay Archipelago

I live on the fringes of the Malay Archipelago. At least that’s what the naturalist Alfred Russel Wallace called it. In his famous book of that name, he wrote:

The Malay Archipelago extends for more than 4,000 miles in length from east to west, and is about 1,300 in breadth from north to south. It would stretch over an expanse equal to that of all Europe from the extreme west far into Central Asia, or would cover the widest parts of South America, and extend far beyond the land into the Pacific and Atlantic oceans. It includes three islands larger than Great Britain; and in one of them, Borneo, the whole of the British Isles might be set down, and would be surrounded by a sea of forests. New Guinea, though less compact in shape, is probably larger than Borneo. Sumatra is about equal in extent to Great Britain; Java, Luzon and Celebes are each about the size of Ireland. Eighteen more islands are, on the average, as large as Jamaica; more than a hundred are larger than the Isle of Wight; while the isles and islets of smaller size are innumerable.

Wallace claimed to have fond a line running through the Malay Archipelago that separates islands with Asian flora and fauna from those with plants and animals more like those of Austalia. This is now called the ‘Wallace Line’. It runs between Bali (on the western, Asiatic side) and the lesser-known nearby island of Lombok (on the eastern side).

Why does the Wallace Line run right between these two nearby islands? Wallace had a theory: it’s because the ocean between them is very deep! Even when sea levels were much lower—for example during the last ice age—and many islands were connected by land bridges, Bali and Lombok remained separate. Indeed, all the islands on one side of the Wallace Line have been separate from those on the other side for a very, very long time.

How long? Maybe forever, since Australia used to be down near Antarctica. I don’t really know. Do you? I’ve brought Wallace’s book to read with me, but that’s probably not the best way to find out. It should be easy to look up.

However, everything gets more complicated when you examine it carefully. Now the Wallace Line is just one of several important lines dividing biogeographical regions in the Malay Archipelago:

Sundaland is the land shelf containing the Malay Peninsula, Borneo, Java, and Sumatra. Sahul, also known as Australasia or simply Australia, is the land shelf containing Australia and New Guinea. Wallacea is a group of islands between Sundaland and Sahul—islands that haven’t been haven’t been recently connected to either of these land shelves.

The Wallace line is the western boundary of Wallacea, separating it from Sundaland. The Lydekker line, named after Richard Lydekker, is the eastern boundary of Wallacea separating it, from Sahul.

Wallacea is the red, heart-shaped region here:

The blue line through Wallacea is called the ‘Weber line’. Max Carl Wilhelm Weber argued that this line, not the boundary between Bali and Lombok, mark the major boundary between Asiatic and Australian organisms.

I bet the real truth is even more complicated.

Anyway, today my wife and I are going to Lombok. We’ll say there until the 21st, based in Senggigi; then we’ll go to Bali and stay in the town of Ubud until the 25th. So, we’ll have a good chance to see the difference between Asiatic and Wallacean flora and fauna.