Basic desiderata (Jaynes)

From E.T. Jaynes with G.L. Bretthorst (2003) Probability theory: the logical of science. Cambridge University Press, Cambridge.

Consider that we build a robot that thinks like us, except that it cannot make qualitative judgements. It can use only Aristotelian logic. What sort of fundamental desirable properties would its thinking have?

Desiderata I.   Degrees of plausibility are represented by real numbers.

Desiderata II.  Qualitative correspondence with common sense.

Desiderata III. Consistency:

• IIIa. If a conclusion can be reasoned out in more than one way, then every plausible way must lead to the same result.
• IIIb. The robot always takes into account all of the evidence it has relevant to a question. It does not arbitrarily ignore some of the information, basing its conclusions only on what remains. In other words, it is not ideological.
• IIIc. The robot always represents equivalent states of knowledge by equivalent plausibility assignments. That is, if in two problems the robot's state of knowledge is the same (except perhaps for the labeling of propositions), then it must assign the same plausibilities in both.

....

I (HS) will note that IIIb makes this robot a Bayesian, just like the rest of us.

Will Bayesian statistics become too easy?

A Bayesian approach to statistical inference has become increasing popular since the advent of increased desktop computing power and the development of tailored software. This is a really really good thing. However, I am concerned that it may, in the not very distant future, become too easy, and too much like frequentist methods as they are currently learned and used by life science undergraduate and graduate students. I am concerned that, in order to make Bayesian methods more accessible, they will be dumbed-down --made too easy-- and their value lost.

Part of the benefit of a Bayesian approach is that it more accurately reflects how Science is done. In a nutshell, the Bayesian approach consists of

1. Prior beliefs: ideas, knowledge, and explicit assumptions about our system, 
2. Collection of new data.
3. Using the new data to update our beliefs.

The result of a Bayesian analysis is not a simple yes-no, significant-not significant kind of answer, but rather a probability distribution that reflects our most informed guesses about our variable of interest.

I believe that there are two potential pitfalls in the over simplification of a Bayesian analysis. I believe that the less serious of these pitfalls concerns the results, the posterior distribution of each model parameter. Each of these distributions is really a massive collection of independent guesses at the parameters of interest, given all of our assumptions and the newly collected data. Thus the result is not "an answer" but rather thousands of answers, with some answers more likely than others. In our efforts to satisfy ourselves, editors, and readers, we may try too hard to simplify our results.

Although we may try too hard to simplify our results, I think there is a greater danger that we will try to simplify the prior knowledge and that assumptions that we start with. In my limited experience, ecologists and statisticians are very quick to fall back into the use of the "uninformative prior," as if this is somehow "unbiased." Statisticians recognize that all priors come with a point of view, so there is no such thing as an objective uninformative prior, sometimes more accurately called a reference prior. However, I see us taking the lazy route too often and using a supposedly unbiased reference prior that reduces the tendency to take seriously the literature we read. Lots of data will overwhelm a weak prior. However, it is my experience that priors derive their weakness out of our tendency to not take seriously the quantitative nature of our literature.

As evidence that Bayesian analyses can be made easy, I can point to the numerous specialized programs for population genetics and phylogenetics that are based upon Bayesian approaches. I have seen many students use these with very little notion of what they are doing.

As learning in general is essentially a Bayesian process, my fears are not too serious. Nonetheless, ecologists need to take their priors seriously. Statisticians can help by encouraging us to make our beliefs both informed and explicit. In the end, it will only strengthen our science.

Fundamental units?

What are the fundamental units in E & E?

Part of the trick to unifying or connecting things is to figure out what the “things” are that can be connected and need connecting. Here I list the elements or “things” that are at the core of ecology and which need connection. We should think of these as the primary state variables of the most distinct subdisciplines:

• Ecosystem variables: elements tracked by ecosystem scientists, such as carbon, or nitrogen; these might be described by the mean, variance and dynamics of grams per meter squared.
• Individual physiological rates: elements tracked by physiologists, such as body mass, resting and active metabolic rates, or the fat reserves in migratory songbirds.
• Populations: elements tracked by population and community ecologists, and evolutionary biologists; these might be tracked as the mean and variance and the dynamics of N, the number of individuals.
• Genes: the elements tracked by evolutionary biologists; these tend to be tracked by either copy number, N, or frequency, p.

We can use similar conceptual and mathematical tools and equations to study all of these. Complicating factors are numerous and in many cases shared across subdisciplines. For instance, one could study “disturbance” in any of these subdisciplines, but but it is the consequence of disturbance that is usually of primary interest. The physical landscape is an important factor as well, whether in landscape ecology, metapopulation dynamics, or in niche partitioning. Again, it is the consequence of the landscape more than the landscape itself which is usually of primary interest.

These elements (ecosystem variables, populations and genes) can be and often are linked in classic levels of biological organisation (e.g., cells, tissues, organs, organ systems, etc.). While this is a comfortable approach, it is not the best we can do. This LBO approach requires the instructor to create all the meaning, connection, and disciplinary thinking and structure. Instead, the Core Elements approach reinforces the type of disciplinary thinking of of ecology and evolutionary biology generally.

The primary cross-cutting feature of these elements that scientists tend to study are statics and dynamics, corresponding to pattern and process. For each element type, we can measure a static pattern such as the amounts of carbon in the atmosphere and the oceans, the abundance an invasive species in its introduced range and its native range, or the relative frequency of rare genotypes in the wild. By the same token, we can measure the dynamics or processes of a system, such as the rate of flow of carbon from the atmosphere to the oceans, how metabolic rate varies with body mass, population growth rate of an invasive species, or changes in particular allele frequency in response to El Nino events.

We often equate pattern with description and process with mechanism, but this is a misleading distinction. We can describe patterns and processes, and use either of such descriptions in either hypothesis-generation or hypothesis falsification/confirmation.

On Robert Ricklefs (2012), American Naturalist Presidential Address

I am one of those ecologists that thinks like a theoretical physicist -- I want to maximize the ratio of explanatory power to the number of parameters in a model. I look for ways to simplify and unify phenomena. I am bad with details. Therefore, I have tremendous respect for and feel humbled by innovative ecologists that emphasize natural history. Robert Ricklefs is a prime example of this type of ecologist. His presidential address to the American Society of Naturalists, recently published in Am Nat, is a rich cornucopia of discussion material.

A somewhat useful summary comes from the penultimate page:

"Neither niche theory nor neutral theory provides a satisfying narrative for ecological communities, and the defense of one or the other (sometimes both) by ecologists has at times slowed progress toward understanding biodiversity."

Earlier in the paper, he argues pretty emphatically that neutral theory is a waste of ecologists' time, because there are examples of it not explaining observed patterns, and because some of its assumptions and/or predictions are not realistic, even in principle. He also argues that niche theory (as typified by Lotka, Hutchinson, MacArthur, Lack, Elton, Gause, and others) is highly limited in its usefulness.

I would say the same thing about natural history, that natural history alone does not provide a satisfying narrative for ecological communities, because, unfortunately, words can sometimes be horribly ambiguous and non-quantitative. I would also argue that we need mathematics because it is the least ambiguous language we have, and that its quantitative nature underlies the nature Ricklefs wants us to spend more time observing.

I heartily agree with his sentiment that we need to spend more time observing nature. The scientific culture needs to find ways to reward useful, organized, and detailed observation of natural history. However, I don't think we should throw the baby out with the bath water.

Josh Tewksbury is one of many examples of an ecologists that seems to have equal respect for, and grasp of, both natural history and theory. Long ago, I had the pleasure of listening to a talk of his at Miami University, in which introduced his thinking about ecology as the combination or unity of natural history, theory, and experiment. He was a bit more dogmatic about it, or perhaps just enthusiastic. Regardless, it struck a positive chord with me, because I think his goal is the goal of all ecology and evolutionary biology. I guess I think not everyone needs to do it all, nor all at once.

The Cockroach

(Inspired by my wife's habit, on Fridays in October, of providing ghastly Halloween treats and poetry in our kids' school lunches. On this day, she provided rubber cockroaches, and we had to come up with some poetry to match the theme. Lacking true creativity, I usually provide different words to poems our kids already knew. Here I update the Raven for my daughter, in the school lunchroom.)
...
Open here I flung the lunchbox, when, so quickly it did outfox,
In there was a stately Cockroach, of the saintly days, once happier.
Not the least obeisance made he; not a minute stopped or stayed he;
But with mien of lord or lady, perched upon my Twinkie wrapper.
Perched upon this food-like substance, digging at my Twinkie wrapper,
Perched, and sat, and nothing more.

Then this tawny roach beguiling, my sad fancy into smiling,
By the buzzing stern decorum of the countenance it wore,
"Though your back is made of rubber, thou," I said, "art sure no tubber!
Ghastly, creepy, and icky cockroach, wand'ring from the lunchroom store.
Tell me what the insect name is on thy lunchroom's Plutonian floor."
Quoth the cockroach, "Nevermore."

Startled at the stillness broken by reply so aptly spoken,
"Doubtless," said I, "what it utters is its only stock and store,
'Scaped from some unhappy master, whom unmerciful disaster
Taught him speech, not love nor laughter, till his songs one burden bore,
Till the words bereft of hope, so that melancholy burden bore
Of life, "No---nevermore."

"Prophet!" said I, "thing of evil--prophet still, if roach or devil!
By the old school building 'round us--by these four walls we both adore--
Tell this soul with sorrow laden, if, within the distant snacktime,
It shall consume a chocolate iced cake, whom the angels name Ding Dong---
Clasp and covet a rare delicious iced cake, whom the angels name Ding Dong?
Quoth the cockroach, "Nevermore."

And the cockroach, never skitt'ring, still is sitting, still is sitting
On the pallid Twinkie food-like substance, me wishing I had more;
And his 'tennae moving, sensing, like a demon's sword in fencing.
Flourescent lights o'er him dancing throws his shadow on the floor;
Like my hope (to eat that Ding Dong) is also dashed on the floor,
To be lifted---nevermore!

Too much or too little?

Ecology seems to me like a hodge-podge of different ideas. A result of this (or a manifestation or a cause?) is that we teach and learn ecology as a hodge-podge. The single overarching theme is levels of organization, typically as individuals, populations, communities, ecosystems, landscapes, and global issues, with a generous dose of climate, geology, and geography at the beginning. Applications, statistics, experimental design, and primary literature are scattered throughout.

Quick perusal of two evolution textbooks (Ridley, and Freeman & Herron) showed me that they do not have chapters on "The Physical Environment" or "Biomes" or "The Earth's Climate System." The evolution textbooks instead focus on the math and biology that is universal.

What if a book laid out ecology completely independently of natural history and environment? Would the books look the same? Do we need context? If we lead with context (e.g., a pond, a forest, a grassland) what do we gain, what do we lose?

Why do we lead with the physical environment? Perhaps because we have been ecologists for at least the past 2 my, and we know a lot?

What if we learned B = aM^z and dX/dt = aX - bX^2 before we learned that trees dominate the eastern US, and deep water bodies are dark?

This same question plagues the niche vs. neutral debate...in ecology. Evolutionary biologists learned long ago that it is both, in different measure. Ecologists and humans generally are plagued with the notion that niche matters. It makes it hard for us to think outside the box.

US Government as Central Dogma of Molecular Biology

Spoiler Alert: There is nothing new here. However, writing it helps to form the thoughts in my own head ....

Complex adaptive systems
A colleague of mine -- a very successful molecular biologist -- recently gave a Sigma Xi Researcher of the Year presentation. In it, he made the relative specific analogy relating the central dogma of biology to the operation of the U.S. federal government. It blew my mind. It was is SO cool to me, because I take seriously those "far fetched" analogies between different complex adaptive systems. I realize that others have made these analogies before, but they are cool to me, because I rarely hear them.

Social institutions, such as governments, are complex adaptive systems under selective pressures. Each governing institution acquires mutations which maybe retained or discarded. Each governing institution competes with other governing institutions for limiting resources. Different institutions exhibit different levels of survival and growth and spread. These institutions tend to be passed on from generation to generation because humans have written records, and also simply and more importantly, humans remember what they did yesterday and twenty years ago, and change is both intellectually challenging, and financially restricted.

Governments exhibit
-- phenotypic variation,
-- heritable phenotypic variation, insofar as governments persist and self-replicate,
-- fitness differences among variants.

As a consequence of these phenomena (1), governments tend to evolve. As you know, evolution does not always optimize performance. Rather, they undergo probabilistic responses to selective pressures,. It is possible for these responses to result in objects which are poorly suited for future conditions. Evolution is always backward-looking.

Social Darwinism? No, not in the original sense.

The above smacks a bit of "Social Darwinism." However, the earlier incarnation of that phenomenon was used as an excuse for greed and imperialism (2). In the past 50 years, however, strong evidence has accrued that cooperation can easily evolve and is an evolutionary stable state (3). All successful societies or nations rely heavily on within-group cooperation. It seems further that cooperation among nation-states provides increased fitness as well. This seems like a no-brainer, given that nation-states are themselves composed of interacting groups that cooperate as well as compete.

One of the primary requirements of the evolution of cooperation is that fitness of individuals within groups is increased through the cooperation. This central criterion is often easily met.

Another important criterion for the emergence and maintenance of cooperation is repeated interactions among the same agents so that "learning" can occur. Repeated interactions is the key difference between the standard Prisoner's dilemma game, where cooperation is not advantageous vs. games in which cooperation is advantageous. [I put "learning" in quotes, because it need not be learning in the usual sense of a cognitive process by an individual, but rather can be an adaptation to respond to cues given by cheaters that they are cheating. "Cheating" is defined as the receipt of benefits of cooperation without incurring the costs of cooperation and reciprocity.]

The ease with which cooperation can arise, and become a stable equilibrium does not exclude the possibility that cheating cannot also arise. However, under easily met conditions, if a "mutation" does give rise to cheating, it can be eliminated, or kept at low levels, depending on the conditions.


References cited


1. Endler, J. Natural Selection in the Wild. Princeton monographs.
2. Wikipedia, 2011, http://en.wikipedia.org/w/index.php?title=Social_Darwinism&oldid=461877577
3.  Nowak, 8 December 2006, Science; Nowak et al. 26 August 2010. Nature.