Marquet* et al*. have essay in Bioscience entitled “On theory in ecology”, with the main message being *we need more good theory*; I agree 100%. The paper also presents an overview of important ecological theories and some good points about why theory is important. Notable one:

“Theory, etymologically, comes from the ancient Greek theoria, which means “contemplation” or “a viewing”. In that sense, a theory is a way of looking at the world and not necessary a way of knowing how the world is.”

This sounds like a fundamental insight, yet it would perhaps deserve a deeper critical elaboration, maybe with an example – I'd really like to understand exactly what ancient Greeks were up to.

Another important point:

“Efficient theories in ecology provide a known standard against which to measure natural phenomena. By a standard we mean a prediction of how the world would work if only the first principles of the theory are at work... without standards, no deviations or gaps in knowledge would be apparent, which would lead to scientific stagnation.”

All reviewers of scientific manuscripts, bear this in mind before dismissing a theory just because it seems simplistic, naïve, or ignoring local specifics – maybe it is still valuable as a standard.

I was disappointed by the first two sections of the paper where theory is defined; specifically, the central definition on the first page is:

“We define a theory as a hierarchical

frameworkthat contains clearly formulated postulates, based on minimal set of assumptions, from which a set ofpredictionslogically follows.”

First, it is not clear what is meant by “prediction”. I know that we can do “predictions” by (1) calculating probability of a hypothetical observation, given the theory, or (2) we can simulate new data by “drawing” them as artificial outcomes of the theoretical process; or we can (3) take some part of the theory and deduce (predict) other parts of the theory. Am I the only one who finds the concept of prediction ambiguous?

Second, it is not clear what is “framework”. I asked one of the authors (David Storch), and he explained that theory is not just its formal definition, it is also the *interpretation* of the formal definition, and so the formal definition and its interpretation together are the framework of the theory. Pity that it's not in the paper.

After a lengthy argument with David we've discovered of a third aspect of theory: There is also the dark unknown area beyond each theory, where the observations and phenomena are not yet captured by the theory. However, in these cases we often have some *intuition* about the processes in the unknown territory, for example we can assume (using *induction*) that some unspecified random additive processes generate the observed pattern, leading to normal distribution of measurements. Or we have a set of candidate explanations that were not yet tested and compared. All of these guesses and intuitions should also be included as parts of the theoretical framework.

I disagree with:

“Ecologists and other scientists often use the terms model and theory indistinguishably … but they are fundamentally different.”

and

“Inductively revealed patterns do not, themselves, constitute a theory, and neither do statistical representations of data or model-fitting exercises.”

This is very 90'. In the 90' the toolset of available statistical models was limited to general or generalized linear models (t-test, regression, ANOVA, logistic regression, …), and of course these can only serve as a crippled representations of ecological theories. Crippled, but not fundamentally. It certainly *is* possible to derive statistical representation of data from underlaying principles; moreover, since the end of the 90' it has actually been possible to derive very complex statistical representations of data.

What has changed since the 90'? There's been a development (Clark, 2007; Bolker, 2008; Royle & Dorazio, 2008) in which ecological models have been liberated from the simplistic structures such as bivariate regression, now these structures are used as building blocks of what can be called complex models, ... or simple theories. Statistics has been transformed from a set of disparate numerical recipes into a universal construction set of probability distributions and linear algebra. Models of this new generation are often *hierarchical* (sometimes also called *multilevel*), right in line with the Marquet *et al*.'s (2014) concept of theory being implicitly hierarchical.

I propose that this new statistics has the potential to bring ecology closer to the state that physics has seen for ages: In physics, projects of any size, whether theoretical or experimental, require custom software, and scientists achieve a high level of quantitative expertise and everyone is partly a programmer and partly a mathematician (Bialek & Botstein, 2004) – quantitative skills are the essence of science, because they are THE way to formalize and test theories.

This contrasts with biology, where most researchers have only basic quantitative skills, test mostly verbal theories using pre-defined methods in commercial software packages, and require consultations with biostatisticians. Because of the lack of formal mathematical representations, the theories are fragmented, andecdotal, and people outside the specific fields hardly understand them. Sadly, divergent biologists who like to demonstrate their quantitative skills can even be viewed as statistical machos or academic hipsters.

To conclude, I am with Marquet *et* *al*. (2014) concerning the importance of quantitative theories based on first principles. However, I think that the authors have missed important recent developments in statistics that can help to expand the role of quantitative theory in ecology. There is an emerging new generation of scientists that are fluent in this new statistics, and the next step is to bring them together with the world-class theoreticians such as Marquet et al. (2014).

PS: A couple of days after the publication of this post Jeremy Fox wrote an exhaustive treatment of the Marquet. et al.'s paper. Check it out!

PPS: I now have a personal definition of theory which I am happy with: **"****Theory is a set of models plus their relationships with each other, with other theories, and with observations. Model is a representation of an idea about how the observations came to be**" (thanks to David and an anonymous physicist for inspiration).

**Acknowledgement**

I am grateful to David Storch for friendly review and discussions.

**References**

- Bialek, W. & Botstein, D. (2004) Introductory science and mathematics education for 21st-century biologists.
*Science*, 303, 788–790. - Bolker, B.M. (2008)
*Ecological models and data in R.*Princeton University Press, Princeton. - Clark, J.S. (2007)
*Models for ecological data: An Introduction*. Princeton University Press, Princeton. - Marquet, P.A., Allen, A.P., Brown, J.H., Dunne, J.A., Enquist, B.J., Gillooly, J.F., Gowaty, P.A., Green, J.L., Harte, J., Hubbell, S.P., O’Dwyer, J., Okie, J.G., Ostling, A., Ritchie, M., Storch, D. & West, G.B. (2014) On theory in ecology.
*BioScience*, biu098. - Royle, J.A. & Dorazio, R.M. (2008)
*Hierarchical modelling and inference in ecology*, Academic Press.

Nice post. And I broadly agree with you (and the Marquet et al paper) that theory is important. And I think quantitative skills are important in ecology (e.g. see http://dynamicecology.wordpress.com/2014/10/20/what-math-should-ecologists-teach/)

But I am curious if you really think "demonstrate their quantitative skills" is actually a goal that advances science? Because to me, that goal IS statistical machismo.

I also think its important to keep theory and statistics separate. I would argue a really good quantitative theory only needs simple statistics. It's the lack of theory that drives us to complex statistics. Just for example, physicists often don't even use statistics! And arguably ecologists have substituted complex statistics for good quantitative theory.

Just a few thoughts. Thank you for the post.

Hi Brian, an honor have you here!

I think that people should demonstrate exceptional skills of any kind, tendency to show off is useful, should be encouraged, and it is one of important drivers of science's advancement.

With your last points I dare to disagree. I propose that: Theory and statistics should be unified, not separated. Good theory needs ("is") statistics that is very specific and tailored to the theory. Lack of theory drives us to data mining and statistical fishing, not to statistics (by which I mean building of parametric models and their testing).

Physics has the luxury of fine-tuned experimentation and relatively precise measurements, hence the lesser need for stats. But even there: how about statistical physics? Ecology is often (and not by choice) non-experimental, there are observational biases, and there are idiosyncratic sources of variation that we can only approach with probability distributions – hence the central role of stats.