The pot effect

How small is too small? 

One of the central tenets of "functional ecology" is that the performance of plants in a an environment is due to their functional traits. Yet, which traits to measure, how they are measured, and how the plants are grown are sources of endless debate, sometimes paralyzingly so.

It seems inviolable that species must be compared after having been grown under common conditions. This means growing plants either in field plots or pots. I've written a bit about autogenic plasticity involved with field plots and how feedbacks to resource availability affect expressed traits. One of the most enduring criticisms of plants grown in pots is the size of the pots. No pot is ever too big, and almost any pot can be too small.

The bias in results that comes from restriction of roots has been termed "the pot effect". I trace it back to Curtis and Wang's first ecological meta-analysis on elevated CO2. The authors wrote in their abstract "We found no consistent evidence for photosynthetic acclimation to CO2 enrichment except in trees grown in pots <0.5 l (-36%)". The take-home from the paper was that little pots bias the results.

My guess is that would be the wrong conclusion. For that study, photosynthesis acclimates when plants are nutrient-limited. Plants in small pots become nutrient-limited faster than those in the field or in big pots. It's not the pot size at all. But which is more representative of the real world?

Quite likely the pot. As I've shown at Cedar Creek, small plants in big plots at low density are not very nutrient limited and have the traits associated with the high-nutrient strategy. Plants of the same species in more mature plots at higher density resemble more what we seen in small pots--the low-water or low-nutrient strategy.

One could argue pretty easily that the pot effect is essential to mimicking the real world where resources limit plant growth. One could argue too that small pots cause artifacts, but it would take some careful logic chains for the argument to be convincing.

In the mean time, try small plots. They generate water or nutrient limitation faster. And increase your replication if you're tight on space.

Collective intelligence

Does this person feel playful or irritated? 

If you said irritated, you aren't as likely to raise the collective intelligence of a group.

It is a truism that the smartest of all of us is not smarter than all of us, but how much smarter all of us are depends on how we work together. Ecology lives and breathes by group efforts these days--very rarely are papers ever published by a single author. Yet, we have paid scant attention to how to put these groups together and what makes them successful.

A paper last fall in Science actually did experiments to test what factors made groups collectively the most intelligent. The authors assembled a large number of working groups and had them together try to solve a series of complex tasks.

What made some groups the most successful?

It wasn't necessarily how smart the smartest person in the group was. Instead, collective intelligence correlated best with "with the average social sensitivity of group members, the equality in distribution of conversational turn-taking, and the proportion of females in the group" state the authors.

Not all the lessons transfer directly to scientific working groups. The tests the authors used were generic for which there might not always be specialized knowledge--like playing checkers. Deciding sampling strategies or statistical analyses is going to depend on having experts a lot more than checkers does. That said, there seem to be some pretty good lessons from the study. Take turns. Listen to others equally. Have women involved--or at least men who behave like women in the sense they are "socially sensitive". Not sure what that is? Take this test. Didn't score well? Then it's probably even more important to have women involved I would guess.

Woolley, A. W., C. F. Chabris, A. Pentland, N. Hashmi, and T. W. Malone. 2010. Evidence for a Collective Intelligence Factor in the Performance of Human Groups. Science 330:686-688.

Grazer diet

Bison bonasus. They eat a lot of trees. Image from Michael Gäbler, Wikimedia.

The diets of grazers and browsers have not been easy to determine. To determine the diets of animals you have to 1) spend a lot of time watching, 2) use exclosures, 3) grab the food somewhere in the digestive system and try to recognize it. None of these approaches work that well.

Recently Kowalczyk and others published a paper that sequenced plant DNA present in fecal material from Bison bonasus in Bialowieza Forest in Poland. Essentially, a lot of plant DNA makes it through the digestive tract and it can be sequenced to quantitatively assess diet. This all but renders options 1, 2, and 3 vestigial. My guess is that we are going to see a lot of this technique in the near future. It's too powerful and the results are too fascinating.

Right now it costs about $12K to run 96 fecal samples with 454 sequencing. $12K is a lot, but $100 a sample is not.

The specifics of what the authors learned from the technique is interesting. Bison bonasus diet consists of a lot of trees and herbs. And the tree species are not economically important, which makes them great forest gardeners. Compared to Bison bison, Bison bonasus might as well be Alces alces.

Kowalczyk, R., P. Taberlet, E. Coissac, A. Valentini, C. Miquel, T. Kamiński, and J. M. Wójcik. in press. Influence of management practices on large herbivore diet—Case of European bison in Białowieża Primeval Forest (Poland). Forest Ecology and Management.

How to infer importance

Quantifying the relative importance of ecological factors in determining the distribution and abundance of species is one of the most critical endeavors to understand the assembly of communities and ultimately the evolution of different species. Yet, how do we do this?

One approach is experiments. Another is gradient analyses. Each has its pluses and minuses. Yet, is there a way to infer importance without manipulations or gradients. If I go to a single place and determine who is rare and who is abundant, does that offer insight?

Seems like it should.

Let's take drought. Drought has long thought to structure grasslands. We know that it can from the Great Drought. But how important is drought in determining the assembly of extant communities?

One way is to compare a trait that should confer advantage during drought to the relative abundance of species currently. But what are the interpretations of the relationships. Let's say there is a positive relationship between the drought tolerance trait and abundance. Probably good evidence that drought structures the community since those species that do not have the trait are less abundant.

But what if there is no relationship? Does this mean drought is not important since it doesn't confer any net advantage? Or is it equally important as some other factor, since one might expect the drought tolerance trait to penalize plants in wet times? And what if physiologically drought-tolerant species are less abundant than intolerant ones? Is drought not important? Or does drought serve as a disturbance and structure the community in a different way.

In all, using an inferential approach to interpret patterns depends strongly on our mental model of how different factors structure communities. As much as being able to measure the right traits, linking these mental models to testable hypotheses is one of the most limiting steps.

In short, we need to spend more time clarifying our concepts before testing the importance of factors.

R squared irrelevant?

In addition to problems in experimental design, the key results were felt to be weak.  In Fig. 2, the most significant result is the relationship between physiological drought tolerance and abundance for uplands, which has an R2 of 0.12.  The data presented are not strong enough to support the main points in the abstract.


There are two metrics used to judge a particular result: the coefficient of determination (r2) and the P-value, which is the probability that the observed result could have happened by chance. 


For some modelers seeking to replicate observed phenomenon, the coefficient of determination is the key statistic to assess. Eddy covariance modelers often seek to explain observed patterns in carbon flux and when they can generate a high enough r2 by including different independent variables in their model, the feel they've modeled the system well enough and they move on.  


For hypothesis testing in ecology, r2 is irrelevant. Think about the extremes. Let's say we are attempting to test whether a given trait explains the abundance of species in an ecosystem. Trait A explains 90% of the observed variation in abundance among species. P < 0.001. This would generally be considered highly ecologically significant and important to report. 


Now think about the opposite extreme. Trait A explains 2% of the variation. P = 0.9. Pretty high confidence that you can reject the null and state that trait A is not important. Publishable? Absolutely if there are strong hypotheses relating the two. If we beforehand believe that trait A is likely to predict abundance, then it is likely more important to publish that it didn't explain abundance than if it turned out to explain a high proportion of variance. 


There are some cases where the r2's are important to examine. For example, a model result might be r2 = 0.4, P = 0.1. This happens when there isn't much statistical power. This would be one case where the r2 is a helpful parameter.


What about the above-referenced case of r2 = 0.12, which happened to have a P = 0.008? Is the absolute value of the r2 relevant here? We ran a study that compared physiological drought tolerance to the abundance of 60 species. On the one hand, 12% can be a lot. Let's say there are 8 factors that equally explain abundance. None have ever been identified. you identify one of the 8 with high statistical significance. r2 is only 0.12. That seems important. Or there are only two factors that explain abundance, you've identified one of the two, but there is a lot of measurement error or associated random variation that is inherent to the system. r2 will equal 0.12. [see Shipley's work on relativizing r2 to take account for this.] In short, 12% of the variation is 12% more than we knew before and might be about all we can ever hope to know.


On the other hand, 12% can be considered low if you expected a lot more. In our case we showed for one contrast, drought tolerance explained 12% of the variation in abundance, while in a paired contrast, it explained 0.1% (P = 0.8). If you expect that drought it important and that drought tolerance explains a low proportion of the variation, then that's a scientifically important result that is only strengthened by the low r2. 

r2's in and of themselves are irrelevant. They have to be contextualized to expectations. a high r2 that confirms expectations might be considered less important to publish than a low r2 that contradicts explanation.

In the specific case referenced above, we view an r2 of 0.12 both ways. Our statements in the abstract were 1) In this mesic grassland, physiological drought tolerance appears to increase the abundance of plants in xeric uplands, but does not in the mesic lowlands", and 2) "In all, drought appears to have a limited role in structuring the Konza plant community."

At Konza, drought tolerance explains 12% of the variation in abundance of species in uplands and is responsible for explaining 50-fold variation in abundance. that's a lot, but it happens to against a background of 5 orders of magnitude of abundance across species. At the same time, if one's expectation is that drought is very important in a drought-prone ecosystem where production is highly sensitive to interannual variation in precipitation, that same 12% (when paired with 0%) is actually not a lot. 

The Achilles' Heel of modern scientific publishing is the negative result. It would be silly to only publish papers with positive slopes rather than negative ones, but it seems straightforward to reject papers because r2's are low. Time and time again, it's been shown that not publishing negative results (low r2, low P value) biases our scientific understanding. 


Coefficients of determination are certainly not irrelevant, but they are only relevant within the context of expectations and the statistical significance of a test.

The first of a few notes on temperature sensitivity

Probability (r) curves for the energy of collisions between a substrate and an enzyme at 20 °C and 30 °C. Shown are differences in activation energy (Ea) and Q₁₀ required for reaction for a labile substrate (upper figure) and a recalcitrant substrate (lower figure).

Globally, soils contain about twice as much carbon as found in the atmosphere and three times as much found in vegetation. The fate of organic carbon stored in the terrestrial biosphere depends in large part depends on the temperature sensitivity of microbial decomposition. Currently, there is still debate over the relative sensitivity of different carbon pools to increases in temperature. Modelers have largely punted on the issue, assuming that respiration doubles with every 10°C increase in temperature (Q10 = 2).

Decomposition is complex, but proximally decomposition is an enzymatic process. As such, at least short-term responses to temperature changes should be governed by chemical laws. The degree to which they actually do is still up in the air. The Arrhenius equation describes the relationship between the rate of reaction (k), the activation energy of a reaction (Ea) and temperature (T)

k=A*e^(-Ea/RT)

where R is the gas constant and A is the frequency factor that is specific to each reaction and represents how many collisions between reactants have the correct orientation for reaction. The Arrhenius equation can be used to determine the temperature sensitivity of reactions as well as the fundamental chemical principle that the temperature sensitivity of any given reaction will be proportional to the net activation energy of the reaction.

Mathematically, from the Arrhenius equation, Q10 increases with increasing Ea. For example, at an Ea of 51 kJ mol-1, the Q10 of a reaction between 20 and 30 °C is 2, while at 81 kJ mol-1 the Q10 is 3. The reason for this is derived from molecular collision theory. In brief, at a given temperature, only a small number of the collisions between an enzyme and a substrate will be energetic enough for a reaction to occur, as described by the Maxwell-Boltzmann distribution (see figure above). As temperature increases, the number of collisions increases negligibly, but the fraction of collisions with sufficient energy increases significantly, leading to an increase in reaction rate. The ratio of the number of collisions of sufficient energy at two temperatures is the temperature sensitivity of the reaction. And based on teh Maxwell-Boltzman distributions, we can see that this ratio is much higher for higher Ea's.

The Arrhenius equation is a foundational principle for understanding temperature sensitivity. Later, I'll show recent work just now being published in Nature Geoscience that tests whether the temperature sensitivity of microbial decomposition to short-term increases in temperature follows the Arrhenius equation well or whether other factors might be more important. If it does, predicting temperature responses and the fate of terrestrial carbon pools just got a lot easier.

Grassland Climate Change 3.0

Critical climate periods for ANPP, flowering of three grasses, weight gain of calves, yearlings, and adults, as well as calving rates the following year for Konza. Gray bars indicate a negative effect of precipitation on the process, black positive.

If you look at the development of climate change research in grasslands, there have been two main stages. Climate Change 1.0 was trying to understand the importance of changes in growing season precipitation on ecosystem dynamics. Wet years are compared to dry years. Experiments that test climate change in 1.0 modify total precipitation.

We're still largely using Climate Change 1.0. Climate Change 2.0 examines effective precipitation during the growing season. Effective precipitation calculations largely take into account event size and distribution. Light rain events might lower effective precipitation as they are intercepted by canopies. Heavy rain events might lower effective due to greater flow through or runoff. Too light or too heavy and plants might not ever get a chance to use all the rain, hence lower effective precipitation. Some early-adopters are investigating Climate Change 2.0, but it's not mainstream yet. Certainly the projections and climate change models are not built to forecast in a manner that promotes 2.0.

One of my goals has been to push Climate Change 3.0. With 3.0, it's not just how much rain falls during the growing season, nor how much effective rain falls during the growing season. but when the rain falls. If you look at the critical climate periods for aboveground net primary productivity (ANPP), they largely show that 1.0 works--the more precipitation in the growing season, the more ANPP. For flowering of the major grasses, it's largely 1.0. Growing season precipitation largely determines flowering, with some differences among the species in their sensitivity to rainfall.

For Konza bison, there is just no relationship between growing season precipitation and weight gain for any sex or age class. But factor in the timing of precipitation, and you can explain up to 80% of the variation among years in weight gain. Why? It's because mid-season precipitation suppresses weight gain, while late-season precipitation promotes it. The climate-nutrition-performance cascade hits bison hard. Most likely, the same thing applies to cattle, although it hasn't been shown.

Climate Change 3.0 is nothing new conceptually. But in practice, 3.0 is. Training our models to predict when precipitation falls can be more important than how much falls for humid grasslands. Training ecologists to start to examine this will be probably be harder.