Ascendancy vs. Reserve

Why is biodiversity ‘good’? To what extent is this sort of goodness even relevant to ecosystems—as opposed to us humans? I’d like to study this mathematically.

To do this, we’d need to extract some answerable questions out of the morass of subtlety and complexity. For example: what role does biodiversity play in the ability of ecosystems to be robust under sudden changes of external conditions? This is already plenty hard to study mathematically, since it requires understanding ‘biodiversity’ and ‘robustness’.

Luckily there has already been a lot of work on the mathematics of biodiversity and its connection to entropy. For example:

• Tom Leinster, Measuring biodiversity, Azimuth, 7 November 2011.

But how does biodiversity help robustness?

There’s been a lot of work on this. This paper has some inspiring passages:

• Robert E. Ulanowicz,, Sally J. Goerner, Bernard Lietaer and Rocio Gomez, Quantifying sustainability: Resilience, efficiency and the return of information theory, Ecological Complexity 6 (2009), 27–36.

I’m not sure the math lives up to their claims, but I like these lines:

In other words, (14) says that the capacity for a system to undergo evolutionary change or self-organization consists of two aspects: It must be capable of exercising sufficient directed power (ascendancy) to maintain its integrity over time. Simultaneously, it must possess a reserve of flexible actions that can be used to meet the exigencies of novel disturbances. According to (14) these two aspects are literally complementary.

The two aspects are ‘ascendancy’, which is something like efficiency or being optimized, and ‘reserve capacity’, which is something like random junk that might come in handy if something unexpected comes up.

You know those gadgets you kept in the back of your kitchen drawer and never needed… until you did? If you’re aiming for ‘ascendancy’ you’d clear out those drawers. But if you keep that stuff, you’ve got more ‘reserve capacity’. They both have their good points. Ideally you want to strike a wise balance. You’ve probably sensed this every time you clean out your house: should I keep this thing because I might need it, or should I get rid of it?

I think it would be great to make these concepts precise. The paper at hand attempts this by taking a matrix of nonnegative numbers to describe flows in an ecological network. They define a kind of entropy for this matrix, very similar in look to Shannon entropy. Then they write this as a sum of two parts: a part closely analogous to mutual information, and a part closely analogous to conditional entropy. This decomposition is standard in information theory. This is their equation (14).

If you want to learn more about the underlying math, click on this picture:

The new idea of these authors is that in the context of an ecological network, the mutual information can be understood as ‘ascendancy’, while the conditional entropy can be understood as ‘reserve capacity’.

I don’t know if I believe this! But I like the general idea of a balance between ascendancy and reserve capacity.

They write:

While the dynamics of this dialectic interaction can be quite subtle and highly complex, one thing is boldly clear—systems with either vanishingly small ascendancy or insignificant reserves are destined to perish before long. A system lacking ascendancy has neither the extent of activity nor the internal organization needed to survive. By contrast, systems that are so tightly constrained and honed to a particular environment appear ‘‘brittle’’ in the sense of Holling (1986) or ‘‘senescent’’ in the sense of Salthe (1993) and are prone to collapse in the face of even minor novel disturbances. Systems that endure—that is, are sustainable—lie somewhere between these extremes. But, where?

Insect Population Crash

Scary news from Australia:

• Marc Rigby, Insect population decline leaves Australian scientists scratching for solutions, ABC Far North, 23 February 2018.

I’ll quote the start:

A global crash in insect populations has found its way to Australia, with entomologists across the country reporting lower than average numbers of wild insects.

University of Sydney entomologist Dr. Cameron Webb said researchers around the world widely acknowledge that insect populations are in decline, but are at a loss to determine the cause.

“On one hand it might be the widespread use of insecticides, on the other hand it might be urbanisation and the fact that we’re eliminating some of the plants where it’s really critical that these insects complete their development,” Dr Webb said.

“Add in to the mix climate change and sea level rise and it’s incredibly difficult to predict exactly what it is. It’s left me dumbfounded.”

Entomologist and owner of the Australian Insect Farm, near Innisfail in far north Queensland, Jack Hasenpusch is usually able to collect swarms of wild insects at this time of year.

“I’ve been wondering for the last few years why some of the insects have been dropping off and put it down to lack of rainfall,” Mr. Hasenpusch said.

“This year has really taken the cake with the lack of insects, it’s left me dumbfounded, I can’t figure out what’s going on.”

Mr Hasenpusch said entomologists he had spoken to from Sydney, Brisbane, Perth and even as far away as New Caledonia and Italy all had similar stories.

The Australian Butterfly Sanctuary in Kuranda, west of Cairns, has had difficulty breeding the far north’s iconic Ulysses butterfly for more than two years.

“We’ve had [the problem] checked by scientists, the University of Queensland was involved, Biosecurity Queensland was involved but so far we haven’t found anything unusual in the bodies [of caterpillars] that didn’t survive,” said breeding laboratory supervisor Tina Kupke.

“We’ve had some short successes but always failed in the second generation.”

Ms. Lupke said the problem was not confined to far north Queensland, or even Australia. “Some of our pupae go overseas from some of our breeders here and they’ve all had the same problem,” she said. “And the Melbourne Zoo has been trying for quite a while with the same problems.”

Limited lifecycle prefaces population plummet

Dr. Webb, who primarily researches mosquitoes, said numbers were also in decline across New South Wales this year, which was indicative of the situation in other insect populations.

“We’ve had a really strange summer; it’s been very dry, sometimes it’s been brutally hot but sometimes it’s been cooler than average,” he said.

“Mosquito populations, much like a lot of other insects, rely on the combination of water, humidity and temperature to complete their lifecycle. When you mix around any one of those three components you can really change the local population dynamics.”

All this reminds me of a much more detailed study showing a dramatic insect population decline in Germany over a much longer time period:

• Gretchen Vogel, Where have all the insects gone?, Science, 10 May 2017.

I’ll just quote a bit of this article:

Now, a new set of long-term data is coming to light, this time from a dedicated group of mostly amateur entomologists who have tracked insect abundance at more than 100 nature reserves in western Europe since the 1980s.

Over that time the group, the Krefeld Entomological Society, has seen the yearly insect catches fluctuate, as expected. But in 2013 they spotted something alarming. When they returned to one of their earliest trapping sites from 1989, the total mass of their catch had fallen by nearly 80%. Perhaps it was a particularly bad year, they thought, so they set up the traps again in 2014. The numbers were just as low. Through more direct comparisons, the group—which had preserved thousands of samples over 3 decades—found dramatic declines across more than a dozen other sites.

It also mentions a similar phenomenon in Scotland:

Since 1968, scientists at Rothamsted Research, an agricultural research center in Harpenden, U.K., have operated a system of suction traps—12-meter-long suction tubes pointing skyward. Set up in fields to monitor agricultural pests, the traps capture all manner of insects that happen to fly over them; they are “effectively upside-down Hoovers running 24/7, continually sampling the air for migrating insects,” says James Bell, who heads the Rothamsted Insect Survey.

Between 1970 and 2002, the biomass caught in the traps in southern England did not decline significantly. Catches in southern Scotland, however, declined by more than two-thirds during the same period. Bell notes that overall numbers in Scotland were much higher at the start of the study. “It might be that much of the [insect] abundance in southern England had already been lost” by 1970, he says, after the dramatic postwar changes in agriculture and land use.

Here’s the actual research paper:

• Caspar A. Hallmann, Martin Sorg, Eelke Jongejans, Henk Siepel, Nick Hofland, Heinz Schwan, Werner Stenmans, Andreas Müller, Hubert Sumser, Thomas Hörren, Dave Goulson and Hans de Kroon, More than 75 percent decline over 27 years in total flying insect biomass in protected areas, PLOS One, 18 October 2017.

Abstract. Global declines in insects have sparked wide interest among scientists, politicians, and the general public. Loss of insect diversity and abundance is expected to provoke cascading effects on food webs and to jeopardize ecosystem services. Our understanding of the extent and underlying causes of this decline is based on the abundance of single species or taxonomic groups only, rather than changes in insect biomass which is more relevant for ecological functioning. Here, we used a standardized protocol to measure total insect biomass using Malaise traps, deployed over 27 years in 63 nature protection areas in Germany (96 unique location-year combinations) to infer on the status and trend of local entomofauna. Our analysis estimates a seasonal decline of 76%, and mid-summer decline of 82% in flying insect biomass over the 27 years of study. We show that this decline is apparent regardless of habitat type, while changes in weather, land use, and habitat characteristics cannot explain this overall decline. This yet unrecognized loss of insect biomass must be taken into account in evaluating declines in abundance of species depending on insects as a food source, and ecosystem functioning in the European landscape.

It seems we are heading into strange times.

Restoring the North Cascades Ecosystem

In 49 hours, the National Park Service will stop taking comments on an important issue: whether to reintroduce grizzly bears into the North Cascades near Seattle. If you leave a comment on their website before then, you can help make this happen! Follow the easy directions here:

http://theoatmeal.com/blog/grizzlies_north_cascades

Please go ahead! Then tell your friends to join in, and give them this link. This can be your good deed for the day.

But if you want more details:

Grizzly bears are traditionally the apex predator in the North Cascades. Without the apex predator, the whole ecosystem is thrown out of balance. I know this from my childhood in northern Virginia, where deer are stripping the forest of all low-hanging greenery with no wolves to control them. With the top predator, the whole ecosystem springs to life and starts humming like a well-tuned engine! For example, when wolves were reintroduced in Yellowstone National Park, it seems that even riverbeds were affected:

There are several plans to restore grizzlies to the North Cascades. On the link I recommended, Matthew Inman supports Alternative C — Incremental Restoration. I’m not an expert on this issue, so I went ahead and supported that. There are actually 4 alternatives on the table:

Alternative A — No Action. They’ll keep doing what they’re already doing. The few grizzlies already there would be protected from poaching, the local population would be advised on how to deal with grizzlies, and the bears would be monitored. All other alternatives will do these things and more.

Alternative B — Ecosystem Evaluation Restoration. Up to 10 grizzly bears will be captured from source populations in northwestern Montana and/or south-central British Columbia and released at a single remote site on Forest Service lands in the North Cascades. This will take 2 years, and then they’ll be monitored for 2 years before deciding what to do next.

Alternative C — Incremental Restoration. 5 to 7 grizzly bears will be captured and released into the North Casades each year over roughly 5 to 10 years, with a goal of establishing an initial population of 25 grizzly bears. Bears would be released at multiple remote sites. They can be relocated or removed if they cause trouble. Alternative C is expected to reach the restoration goal of approximately 200 grizzly bears within 60 to 100 years.

Alternative D — Expedited Restoration. 5 to 7 grizzly bears will be captured and released into the North Casades each year until the population reaches about 200, which is what the area can easily support.

So, pick your own alternative if you like!

By the way, the remaining grizzly bears in the western United States live within six recovery zones:

• the Greater Yellowstone Ecosystem (GYE) in Wyoming and southwest Montana,

• the Northern Continental Divide Ecosystem (NCDE) in northwest Montana,

• the Cabinet-Yaak Ecosystem (CYE) in extreme northwestern Montana and the northern Idaho panhandle,

• the Selkirk Ecosystem (SE) in northern Idaho and northeastern Washington,

• the Bitterroot Ecosystem (BE) in central Idaho and western Montana,

• and the North Cascades Ecosystem (NCE) in northwestern and north-central Washington.

The North Cascades Ecosystem consists of 24,800 square kilometers in Washington, with an additional 10,350 square kilometers in British Columbia. In the US, 90% of this ecosystem is managed by the US Forest Service, the US National Park Service, and the State of Washington, and approximately 41% falls within Forest Service wilderness or the North Cascades National Park Service Complex.

For more, read this:

• National Park Service, Draft Grizzly Bear Restoration Plan / Environmental Impact Statement: North Cascades Ecosystem.

The picture of grizzlies is from this article:

• Ron Judd, Why returning grizzlies to the North Cascades is the right thing to do, Pacific NW Magazine, 23 November 2015.

If you’re worried about reintroducing grizzly bears, read it!

The map is from here:

• Krista Langlois, Grizzlies gain ground, High Country News, 27 August 2014.

Here you’ll see the huge obstacles this project has overcome so far.

The Quagga

The quagga was a subspecies of zebra found only in South Africa’s Western Cape region. After the Dutch invaded, they hunted the quagga to extinction. While some were taken to zoos in Europe, breeding programs failed. The last wild quagga died in 1878, and the very last quagga died in an Amsterdam zoo in 1883.

Only one was ever photographed—the mare shown above, in London. Only 23 stuffed and mounted quagga specimens exist. There was one more, but it was destroyed in Königsberg, Germany, during World War II. There is also a mounted head and neck, a foot, 7 complete skeletons, and samples of various tissues.

The quagga was the first extinct animal to have its DNA analyzed. It used to be thought that the quagga was a distinct species from the zebra. After some argument, a genetic study published in 2005 convinced most people that the quagga is a subspecies of the zebra. It showed that the quagga diverged from the other zebra subspecies only between 120,000 and 290,000 years ago, during the Pleistocene.

In 1987, a natural historian named Reinhold Rau started the Quagga Project. He was goal was to breed zebras into quaggas by selecting for quagga-like traits, most notably the lack of stripes on the back half of its body.

The founding population consisted of 19 zebras from Namibia and South Africa, chosen because they had reduced striping on the rear body and legs. The first foal was born in 1988.

By now, members of the Quagga Project believe they have recreated the quagga. Here they are:

The new quaggas are called ‘rau–quaggas’ to distinguish them from the original ones. Do they look the same as the originals? It’s hard for me to decide. Old paintings show quite a bit of variability:

This is an 1804 illustration by Samuel Daniell, which served as the basis of a claimed subspecies of quagga, Equus quagga danielli. Perhaps they just have variable coloring.

Why try to resurrect the quagga? Rau is no longer alive, but Eric Harley, a retired professor of chemical pathology at the University of Cape Town, had this to say:

It’s an attempt to try and repair ecological damage that was done a long time ago in some sort of small way. It is also to try and get a representation back of a charismatic animal that used to live in South Africa.

We don’t do genetic engineering, we aren’t cloning, we aren’t doing any particularly clever sort of embryo transfers—it is a very simple project of selective breeding. If it had been a different species the whole project would have been unjustifiable.

The current Quagga Project chairman, Mike Gregor, has this to say:

I think there is controversy with all programmes like this. There is no way that all scientists are going to agree that this is the right way to go. We are a bunch of enthusiastic people trying to do something to replace something that we messed up many years ago.

What we’re not doing is selecting some fancy funny colour variety of zebra, as is taking place in other areas, where funny mutations have taken place with strange colouring which may look amusing but is rather frowned upon in conservation circles.

What we are trying to do is get sufficient animals—ideally get a herd of up to 50 full-blown rau-quaggas in one locality, breeding together, and then we would have a herd we could say at the very least represents the original quagga.

We obviously want to keep them separate from other populations of plains zebra otherwise we simply mix them up again and lose the characteristic appearance.

The quotes are from here:

• Lawrence Bartlett, South Africa revives ‘extinct’ zebra subspecies, Phys.org, 12 February 2016.

This project is an example of ‘resurrection biology’, or ‘de-extinction’:

• Wikipedia, De-extinction.

Needless to say, it’s a controversial idea.

Fires in Indonesia

I lived in Singapore for two years, and I go back to work there every summer. I love Southeast Asia, its beautiful landscapes, its friendly people, and its huge biological and cultural diversity. It’s a magical place.

But in 2013 there was a horrible haze from fires in nearby Sumatra. And this year it’s even worse. It makes me want to cry, thinking about how millions of people all over this region are being choked as the rain forest burns.

This part of the world has a dry season from May to October and then a wet season. In the dry season, Indonesian farmers slash down jungle growth, burn it, and plant crops. That is nothing new.

But now, palm oil plantations run by big companies do this on a massive scale. Jungles are disappearing at an astonishing rate. Some of this is illegal, but corrupt government officials are paid to look the other way. Whenever we buy palm oil—in soap, cookies, bread, margarine, detergents, and many other products—we become part of the problem.

This year the fires are worse. One reason is that we’re having an El Niño. That typically means more rain in California—which we desperately need. But it means less rain in Southeast Asia.

This summer it was very dry in Singapore. Then, in September, the haze started. We got used to rarely seeing the sun—only yellow-brown light filtering through the smoke. When it stinks outside, you try to stay indoors.

When I left on September 19th, the PSI index of air pollution had risen above 200, which is ‘very unhealthy’. Singapore had offered troops to help fight the fires, but Indonesia turned down the offer, saying they could handle the situation themselves. That was completely false: thousands of fires were burning out of control in Sumatra, Borneo and other Indonesian islands.

I believe the Indonesian government just didn’t want foreign troops out their land. Satellites could detect the many hot spots where fires were burning. But outrageously, the government refused to say who owned those lands.

A few days after I left, the PSI index in Singapore had shot above 300, which is ‘hazardous’. But in parts of Borneo the PSI had reached 1,986. The only name for that is hell.

By now Indonesia has accepted help from Singapore. Thanks to changing winds, the PSI in Singapore has been slowly dropping throughout October. In the last few days the rainy season has begun. Each time the rain clears the air, Singaporeans can see something beautiful and almost forgotten: a blue sky.

Rain is also helping in Borneo. But the hellish fires continue. There have been over 100,000 individual fires—mostly in Sumatra, Borneo and Papua. In many places, peat in the ground has caught on fire! It’s very hard to put out a peat fire.

If you care about the Earth, this is very disheartening. These fires have been putting over 15 million tons of carbon dioxide into the air per day – more than the whole US economy! And so far this year they’ve put out 1.5 billion tons of CO₂. That’s more than Germany’s carbon emissions for the whole year—in fact, even more than Japan’s. How can we make progress on reducing carbon emissions with this going on?

For you and me, the first thing is to stop buying products with palm oil. The problem is largely one of government corruption driven by money from palm oil plantations. But the real heart of the problem lies in Indonesia. Luckily Widodo, the president of this country, may be part of the solution. But the solution will be difficult.

Quoting National Public Radio:

Widodo is Indonesia’s first president with a track record of efficient local governance in running two large cities. Strong action on the haze issue could help fulfill the promise of reform that motivated Indonesian voters to put him in office in October 2014.

The president has deployed thousands of firefighters and accepted international assistance. He has ordered a moratorium on new licenses to use peat land and ordered law enforcers to prosecute people and companies who clear land by burning forests.

“It must be stopped, we mustn’t allow our tropical rainforests to disappear because of monoculture plantations like oil palms,” Widodo said early in his administration.

Land recently burned and planted with palm trees is now under police investigation in Kalimantan [the Indonesian part of Borneo].

The problem of Indonesia’s illegal forest fires is so complex that it’s very hard to say exactly who is responsible for causing it.

Indonesia’s government has blamed both big palm oil companies and small freeholders. Poynton [executive director of the Forest Trust] says the culprits are often mid-sized companies with strong ties to local politicians. He describes them as lawless middlemen who pay local farmers to burn forests and plant oil palms, often on other companies’ concessions.

“There are these sort of low-level, Mafioso-type guys that basically say, ‘You get in there and clear the land, and I’ll then finance you to establish a palm oil plantation,'” he says.

The problem is exacerbated by ingrained government corruption, in which politicians grant land use permits for forests and peat lands to agribusiness in exchange for financial and political support.

“The disaster is not in the fires,” says independent Jakarta-based commentator Wimar Witoelar. “It’s in the way that past Indonesian governments have colluded with big palm oil businesses to make the peat lands a recipe for disaster.”

The quote is from here:

• Anthony Kuhn, As Indonesia’s annual fires rage, plenty of blame but no responsibility.

For how to avoid using palm oil, see for example:

• Lael Goodman, How many products with palm oil do I use in a day?

First, avoid processed foods. That’s smart for other reasons too.

Second, avoid stuff that contains stearic acid, sodium palmitate, sodium laureth sulfate, cetyl alcohol, glyceryl stearate and related compounds—various forms of artificial grease that are often made from palm oil. It takes work to avoid all this stuff, but at least be aware of it. These chemicals are not made in laboratories from pure carbon, hydrogen, oxygen and nitrogen! The raw ingredients often come from palm plantations, huge monocultures that are replacing the wonderful diversity of rainforest life.

For more nuanced suggestions, see the comments below. Right now I’m just so disgusted that I want to avoid palm oil.

For data on the carbon emissions of this and other fires, see:

• Global fire emissions data.

1997 was the last really big El Niño.

This shows a man in Malaysia in September. Click on the pictures for more details. The picture at top shows a woman named a woman named Gaye Thavisin in Indonesia—perhaps in Kalimantan, the Indonesian half of Borneo, the third largest island in the world. Here is a bit of her story:

The Jungle River Cruise is run by Kalimantan Tour Destinations a foreign owned company set up by two women pioneering the introduction of ecotourism into a part of Central Kalimantan that to date has virtually no tourism.

Inspired by the untapped potential of Central Kalimantan’s mighty rivers, Gaye Thavisin and Lorna Dowson-Collins converted a traditional Kalimantan barge into a comfortable cruise boat with five double cabins, an inside sitting area and a upper viewing deck, bringing the first jungle cruises to the area.

Originally Lorna Dowson-Collins worked in Central Kalimantan with a local NGO on a sustainable livelihoods programme. The future livelihoods of the local people were under threat as logging left the land devastated with poor soils and no forest to fend from.

Kalimantan was teeming with the potential of her people and their fascinating culture, with beautiful forests of diverse flora and fauna, including the iconic orang-utan, and her mighty rivers providing access to these wonderful treasures.

An idea for a social enterprise emerged , which involved building a boat to journey guests to inaccessible places and provide comfortable accommodation.

Gaye Thavisin, an Australian expatriate, for 4 years operated an attractive, new hotel 36 km out of Palangkaraya in Kalimantan. Gaye was passionate about developing the tourism potential of Central Kalimantan and was also looking at the idea of boats. With her contract at the hotel coming to an end, the Jungle Cruise began to take shape!

Information and Entropy in Biological Systems (Part 5)

John Harte of U. C. Berkeley spoke about the maximum entropy method as a method of predicting patterns in ecology. Annette Ostling of the University of Michigan spoke about some competing theories, such as the ‘neutral model’ of biodiversity—a theory that sounds much too simple to be right, yet fits the data surprisingly well!

We managed to get a video of Ostling’s talk, but not Harte’s. Luckily, you can see the slides of both. You can also see a summary of Harte’s book Maximum Entropy and Ecology:

• John Baez, Maximum entropy and ecology, Azimuth, 21 February 2013.

Here are his talk slides and abstract:

• John Harte, Maximum entropy as a foundation for theory building in ecology.

Abstract. Constrained maximization of information entropy (MaxEnt) yields least-biased probability distributions. In statistical physics, this powerful inference method yields classical statistical mechanics/thermodynamics under the constraints imposed by conservation laws. I apply MaxEnt to macroecology, the study of the distribution, abundance, and energetics of species in ecosystems. With constraints derived from ratios of ecological state variables, I show that MaxEnt yields realistic abundance distributions, species-area relationships, spatial aggregation patterns, and body-size distributions over a wide range of taxonomic groups, habitats and spatial scales. I conclude with a brief summary of some of the major opportunities at the frontier of MaxEnt-based macroecological theory.

Here is a video of Ostling’s talk, as well as her slides and some papers she recommended:

• Annette Ostling, The neutral theory of biodiversity and other competitors to maximum entropy.

Abstract: I am a bit of the odd man out in that I will not talk that much about information and entropy, but instead about neutral theory and niche theory in ecology. My interest in coming to this workshop is in part out of an interest in what greater insights we can get into neutral models and stochastic population dynamics in general using entropy and information theory.

I will present the niche and neutral theories of the maintenance of diversity of competing species in ecology, and explain the dynamics included in neutral models in ecology. I will also briefly explain how one can derive a species abundance distribution from neutral models. I will present the view that neutral models have the potential to serve as more process-based null models than previously used in ecology for detecting the signature of niches and habitat filtering. However, tests of neutral theory in ecology have not as of yet been as useful as tests of neutral theory in evolutionary biology, because they leave open the possibility that pattern is influenced by “demographic complexity” rather than niches. I will mention briefly some of the work I’ve been doing to try to construct better tests of neutral theory.

Finally I’ll mention some connections that have been made so far between predictions of entropy theory and predictions of neutral theory in ecology and evolution.

These papers present interesting relations between ecology and statistical mechanics. Check out the nice ‘analogy chart’ in the second one!

• M. G. Bowler, Species abundance distributions, statistical mechanics and the priors of MaxEnt, Theoretical Population Biology 92 (2014), 69–77.

Abstract. The methods of Maximum Entropy have been deployed for some years to address the problem of species abundance distributions. In this approach, it is important to identify the correct weighting factors, or priors, to be applied before maximising the entropy function subject to constraints. The forms of such priors depend not only on the exact problem but can also depend on the way it is set up; priors are determined by the underlying dynamics of the complex system under consideration. The problem is one of statistical mechanics and it is the properties of the system that yield the correct MaxEnt priors, appropriate to the way the problem is framed. Here I calculate, in several different ways, the species abundance distribution resulting when individuals in a community are born and die independently. In
the usual formulation the prior distribution for the number of species over the number of individuals is 1/n; the problem can be reformulated in terms of the distribution of individuals over species classes, with a uniform prior. Results are obtained using master equations for the dynamics and separately through the combinatoric methods of elementary statistical mechanics; the MaxEnt priors then emerge a posteriori. The first object is to establish the log series species abundance distribution as the outcome of per capita guild dynamics. The second is to clarify the true nature and origin of priors in the language of MaxEnt. Finally, I consider how it may come about that the distribution is similar to log series in the event that filled niches dominate species abundance. For the general ecologist, there are two messages. First, that species abundance distributions are determined largely by population sorting through fractional processes (resulting in the 1/n factor) and secondly that useful information is likely to be found only in departures from the log series. For the MaxEnt practitioner, the message is that the prior with respect to which the entropy is to be maximised is determined by the nature of the problem and the way in which it is formulated.

• Guy Sella and Aaron E. Hirsh, The application of statistical physics to evolutionary biology, Proc. Nat. Acad. Sci. 102 (2005), 9541–9546.

A number of fundamental mathematical models of the evolutionary process exhibit dynamics that can be difficult to understand analytically. Here we show that a precise mathematical analogy can be drawn between certain evolutionary and thermodynamic systems, allowing application of the powerful machinery of statistical physics to analysis of a family of evolutionary models. Analytical results that follow directly from this approach include the steady-state distribution of fixed genotypes and the load in finite populations. The analogy with statistical physics also reveals that, contrary to a basic tenet of the nearly neutral theory of molecular evolution, the frequencies of adaptive and deleterious substitutions at steady state are equal. Finally, just as the free energy function quantitatively characterizes the balance between energy and entropy, a free fitness function provides an analytical expression for the balance between natural selection and stochastic drift.

Biodiversity, Entropy and Thermodynamics

 

I’m giving a short 30-minute talk at a workshop on Biological and Bio-Inspired Information Theory at the Banff International Research Institute.

I’ll say more about the workshop later, but here’s my talk, in PDF and video form:

• Biodiversity, entropy and thermodynamics.

Most of the people at this workshop study neurobiology and cell signalling, not evolutionary game theory or biodiversity. So, the talk is just a quick intro to some things we’ve seen before here. Starting from scratch, I derive the Lotka–Volterra equation describing how the distribution of organisms of different species changes with time. Then I use it to prove a version of the Second Law of Thermodynamics.

This law says that if there is a ‘dominant distribution’—a distribution of species whose mean fitness is at least as great as that of any population it finds itself amidst—then as time passes, the information any population has ‘left to learn’ always decreases!

Of course reality is more complicated, but this result is a good start.

This was proved by Siavash Shahshahani in 1979. For more, see:

• Lou Jost, Entropy and diversity.

• Marc Harper, The replicator equation as an inference dynamic.

• Marc Harper, Information geometry and evolutionary game theory.

and more recent papers by Harper.

Life’s Struggle to Survive

Here’s the talk I gave at the SETI Institute:

When pondering the number of extraterrestrial civilizations, it is worth noting that even after it got started, the success of life on Earth was not a foregone conclusion. In this talk, I recount some thrilling episodes from the history of our planet, some well-documented but others merely theorized: our collision with the planet Theia, the oxygen catastrophe, the snowball Earth events, the Permian-Triassic mass extinction event, the asteroid that hit Chicxulub, and more, including the massive environmental changes we are causing now. All of these hold lessons for what may happen on other planets!

To watch the talk, click on the video above. To see
slides of the talk, click here!

Here’s a mistake in my talk that doesn’t appear in the slides: I suggested that Theia started at the Lagrange point in Earth’s orbit. After my talk, an expert said that at that time, the Solar System had lots of objects with orbits of high eccentricity, and Theia was probably one of these. He said the Lagrange point theory is an idiosyncratic theory, not widely accepted, that somehow found its way onto Wikipedia.

Another issue was brought up in the questions. In a paper in Science, Sherwood and Huber argued that:

Any exceedence of 35 °C for extended periods should
induce hyperthermia in humans and other mammals, as dissipation of metabolic heat becomes impossible. While this never happens now, it would begin to occur with global-mean warming of about 7 °C, calling the habitability of some regions into question. With 11-12 °C warming, such regions would spread to encompass the majority of the human population as currently distributed. Eventual warmings of 12 °C are
possible from fossil fuel burning.

However, the Paleocene-Eocene Thermal Maximum seems to have been even hotter:

So, the question is: where did mammals live during this period, which mammals went extinct, if any, and does the survival of other mammals call into question Sherwood and Huber’s conclusion?

Monarch Butterflies

Have you ever seen one of these? It’s a Monarch Butterfly. Every spring, millions fly from Mexico and southern California to other parts of the US and southern Canada. And every autumn, they fly back. On the first of November, called the Day of the Dead, people celebrate the return of the monarchs to the mountainous fir forests of Central Mexico.

But their numbers are dropping. In 1997, there were 150 million. Last year there were only 60 million. One problem is the gradual sterilization of American farmlands thanks to powerful herbicides like Roundup. Monarch butterfly larvae eat a plant called milkweed. But the amount of this plant in Iowa, for example, has dropped between 60% and 90% over the last decade.

And this year was much worse for the monarchs. They came late to Mexico… and I think only 3 million have been seen so far! That’s a stunning decrease!

Some blame the intense drought that hit the US in recent years—the sort of drought we can expect to become more frequent as global warming proceeds.

Earlier this year, Michael Risnit wrote this in USA Today:

Illegal logging in the Mexican forests where they spend the winter, new climate patterns and the disappearance of milkweed—the only plant on which monarchs lay their eggs and on which their caterpillars feed—are being blamed for their shrinking numbers.

Brooke Beebe, former director of the Native Plant Center at Westchester Community College in Valhalla, N.Y., collects monarch eggs, raises them from caterpillar to butterfly and releases them.

“I do that when they’re here. They’re not here,” she said.

The alarm over disappearing monarchs intensified this spring when conservation organizations reported that the amount of Mexican forest the butterflies occupied was at its lowest in 20 years. The World Wildlife Fund, in partnership with a Mexican wireless company and Mexico’s National Commission of Protected Areas, found nine hibernating colonies occupied almost 3 acres during the 2012-13 winter, a 59% decrease from the previous winter.

Because the insects can’t be counted individually, the colonies’ total size is used. Almost 20 years ago, the colonies covered about 45 acres. A couple of acres contains millions of monarchs.

“The monarch population is pretty strong, except it’s not as strong as it used to be and we find out it keeps getting smaller and smaller,” said Travis Brady, the education director at the Greenburgh Nature Center here.

Monarchs arrived at the nature center later this year and in fewer numbers, Brady said.

The nature center’s butterfly house this summer was aflutter with red admirals, giant swallowtails, painted ladies and monarchs, among others. But the last were difficult to obtain because collectors supplying the center had trouble finding monarch eggs in the wild, he said.

No one is suggesting monarchs will become extinct. The concern is whether the annual migration will remain sustainable, said Jeffrey Glassberg, the North American Butterfly Association’s president.

The record low shouldn’t set off a panic, said Marianna T. Wright, executive director of the National Butterfly Center in Texas, a project of the butterfly association.

“It should certainly get some attention,” she said. “I do think the disappearance of milkweed nationwide needs to be addressed. If you want to have monarchs, you have to have milkweed.”

Milkweed is often not part of suburban landscape, succumbing to lawn mowers and weed whackers, monarch advocates point out. Without it, monarch eggs aren’t laid and monarch caterpillars can’t feed and develop into winged adults.

“Many people know milkweed, and many people like it,” said Brady at the nature center. “And a lot of people actively try to destroy it. The health of the monarch population is solely dependent on the milkweed plant.”

The widespread use of herbicide-resistant corn and soybeans, which has resulted in the loss of more than 80 million acres of monarch habitat in recent years, also threatens the plant, according to the website Monarch Watch. In spraying fields to eradicate unwanted plants, Midwest farmers also eliminate butterflies’ habitat.

The 2012 drought and wildfires in Texas also made butterfly life difficult. All monarchs heading to or from the eastern two-thirds of the country pass through the state.

So—check out Monarch Watch! Plant some milkweed and make your yard insect-friendly in other ways… like mine!

I may seem like a math nerd, but I’m out there every weekend gardening. My wife Lisa is the real driving force behind this operation, but I’ve learned to love working with plants, soil, and compost. The best thing we ever did is tear out the lawn. Lawns are boring, let native plants flourish! Even if you don’t like insects, birds eat them, and you’ve gotta like birds. Let the beauty of nature start right where you live.

Maximum Entropy and Ecology

I already talked about John Harte’s book on how to stop global warming. Since I’m trying to apply information theory and thermodynamics to ecology, I was also interested in this book of his:

• John Harte, Maximum Entropy and Ecology, Oxford U. Press, Oxford, 2011.

There’s a lot in this book, and I haven’t absorbed it all, but let me try to briefly summarize his maximum entropy theory of ecology. This aims to be “a comprehensive, parsimonious, and testable theory of the distribution, abundance, and energetics of species across spatial scales”. One great thing is that he makes quantitative predictions using this theory and compares them to a lot of real-world data. But let me just tell you about the theory.

It’s heavily based on the principle of maximum entropy (MaxEnt for short), and there are two parts:

Two MaxEnt calculations are at the core of the theory: the first yields all the metrics that describe abundance and energy distributions, and the second describes the spatial scaling properties of species’ distributions.

Abundance and energy distributions

The first part of Harte’s theory is all about a conditional probability distribution

which he calls the ecosystem structure function. Here:

• : the total number of species under consideration in some area.

• : the total number of individuals under consideration in that area.

• : the total rate of metabolic energy consumption of all these individuals.

Given this,

is the probability that given if a species is picked from the collection of species, then it has individuals, and if an individual is picked at random from that species, then its rate of metabolic energy consumption is in the interval

Here of course is ‘infinitesimal’, meaning that we take a limit where it goes to zero to make this idea precise (if we’re doing analytical work) or take it to be very small (if we’re estimating from data).

I believe that when we ‘pick a species’ we’re treating them all as equally probable, not weighting them according to their number of individuals.

Clearly obeys some constraints. First, since it’s a probability distribution, it obeys the normalization condition:

Second, since the average number of individuals per species is we have:

Third, since the average over species of the total rate of metabolic energy consumption of individuals within the species is we have:

Harte’s theory is that maximizes entropy subject to these three constraints. Here entropy is defined by

Harte uses this theory to calculate and tests the results against data from about 20 ecosystems. For example, he predicts the abundance of species as a function of their rank, with rank 1 being the most abundant, rank 2 being the second most abundant, and so on. And he gets results like this:

The data here are from:

• Green, Harte, and Ostling’s work on a serpentine grassland,

• Luquillo’s work on a 10.24-hectare tropical forest, and

• Cocoli’s work on a 2-hectare wet tropical forest.

The fit looks good to me… but I should emphasize that I haven’t had time to study these matters in detail. For more, you can read this paper, at least if your institution subscribes to this journal:

• J. Harte, T. Zillio, E. Conlisk and A. Smith, Maximum entropy and the state-variable approach to macroecology, Ecology 89 (2008), 2700–2711.

Spatial abundance distribution

The second part of Harte’s theory is all about a conditional probability distribution

This is the probability that individuals of a species are found in a region of area given that it has individuals in a larger region of area

obeys two constraints. First, since it’s a probability distribution, it obeys the normalization condition:

Second, since the mean value of across regions of area equals we have

Harte’s theory is that maximizes entropy subject to these two constraints. Here entropy is defined by

Harte explains two approaches to use this idea to derive ‘scaling laws’ for how varies with . And again, he compares his predictions to real-world data, and get results that look good to my (amateur, hasty) eye!

I hope sometime I can dig deeper into this subject. Do you have any ideas, or knowledge about this stuff?