Organisms are built in four dimensions

Here is, I think, one observation, expressed in various and complementary ways:

• All species exhibit an average relative fitness, w, of approximately $w = 1$.
• On average, all organisms leave approximately one descendent.
• Over its lifetime, an organism does the work (joules) required to leave approximately one descendent.
• Over its lifetime, an organism must do the work required to build another organism of the same size. 

Let

• A be the total amount of work required to produce a descendent.
• R be the rate of that work, and
• T be the time over which the work is done, then

RT = A

My "observation" above implies that A depends strongly on body size: It takes longer to build a large organism.

A 3-D organism has to propagate itself through time, at a velocity sufficient to maintain and replicate itself. The 4-D integral of that mass-time event is directly proportional to the mass of the organism. The rate or velocity measured at any instant in time, $t$, will be a 3-D slice of the 4-D mass-time event. As the event is proportional to the size (mass or volume) of the organism, the 3-D slice will scale to the 3/4 power of the 4-D event or size of the organism.

Thinking like an ecologist

Here is some advice for budding young ecologists--useful or not useful?

A blueprint for ecology

Scheiner (and Willig's) general theory of ecology
 Scheiner 2012, QRB; Scheiner and Willig 2011 monograph

Domain

The spatial and temporal patterns of the distribution and abundance or organisms, including causes and consequences.

Principles

1. Organisms are distributed unevenly in space and time.
2. Organisms interact with their abiotic and biotic environments.
3. Variation in the characteristics of organisms results in heterogeneity of ecological patterns and processes.
4. The distributions of organisms and their interactions depend on contingencies.
5. Environmental conditions are heterogeneous in space and time.
6. Resources are finite and heterogeneous in space and time.
7. Birth rates and death rates are a consequence of interactions with the abiotic and biotic environment.
8. The ecological properties of species are the result of evolution. 

 

Stevens' general theory of ecology

Domain  

Life: its constituent entities, causes, and consequences.

Principles

1. All entities are systems, with some internal complexity.
2. All entities change.
3. Some entities may have inputs and outputs.
4. All rates of change, including inputs and outputs, are influenced directly by physical factors.
5. Some entities interact.
6. All observers must choose specific temporal and spatial scales at which to make observations.

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.