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.

Comparing phenology curves

Packera plattensis, which was found first flowering on April 13 in 2010. 

The timing of flowering is a critical component of the ecology of plants. Flowering during environmentally stressful times or when other plants that utilize the same pollinators can lower a plant’s fecundity if not lead to its extirpation from an ecosystem. As such, the timing of flowering should be under strong selection pressure and be an important component of community assembly. 


Over the past two years, Gene Towne and I (mostly Gene) collected first flowering date (FFD) data on 430 Konza herbaceous species. The last species found to start flowering (a gentian) was found in early October, 189 days after the first herbaceous species--Holosteum umbellatum--was found in late March.


The patterns at Konza are interesting. More on those later. The unexpected find was comparing the patterns with two other predominantly grassland flora. The first was from Chinnor, Oxfordshire. The second, Fargo, ND. 

The y-axis is the fraction of each flora flowering on a given day. x-axis is day of year.


Two things pop out. Relative to Konza, the Chinnor flora has an early tail of species, but not a late tail. Is this because species phenology are all shifted earlier, so that the same species would flower ~50 d earlier there? Or is it just a suite of species that flower earlier are found at Chinnor, but  late-flowering species are not?


And relative to Konza, the Fargo phenology is much more compressed. Again, though, why? Does Fargo not have early- and late- flowering species, or are the phenology of individual species compressed.


Turns out we can begin to answer that and the mechanisms that underly the differences between the pairs differ.


Here are the relationships between FFD between the pairs of sites. Dotted line is 1:1.

Species common to Chinnor and Konza flower on roughly the same day. Hence, one would suspect that the differences in curves between the two sites are due to novel types of species at each site. Yet for Konza and Fargo, early flowering species flower later at Fargo, and late-flowering species flower earlier. Phenology gets compressed for individual species.

Theoretically, I'm still getting up to speed, but comparisons between flora just haven't been done like this. Mid-domain theories are prevalent to test, but each site would support the idea of a mid-domain peak. What's more interesting is why sites differ. Right now, hypotheses about functional novelty/plugging of holes in niche space vs. functional stretching/compression are pretty interesting ones to test here. Flowering is interesting to think about, but the really interesting comparisons (at least for me) will come with comparing functional traits associated with resources, not reproduction.

Bison growth curves

Weight of female (lower) and male (upper) bison at Konza Prairie and Ordway with age.

The performance of bison—how much weight they gain, how many calves are produced—is the ultimate expression of the functioning of North American grasslands. If we can compare the performance of bison in different grasslands, we have a window in the functioning of the grassland. Interannual patterns of weight gain show responses to climate variation. Average weights of animals give general indices to the provision of the quantity and quality of grass produced. Yet, no one has ever compared the performance of bison across grasslands in North America. 

We're getting pretty close to doing that. For any one site, we can fit a growth curve to the weights of animals as they age. There are a number of growth curves that are used for these purposes, but a good one is a generalized Michaelis-Menten equation:

where W0 is the birth weight, Wf is the asymptotic weight, K is the age at which animals are half their asymptotic weight, c is a constant describing the shape of the curve, and t is time in years.

If you fit the weights of bison with age with this equation, for each herd you can extract essentially how heavy cows and bulls get, as well as a rate of maturity...or half-maturity as K would represent.

Right now, we have data on weight gain for about six bison herds. There are about 10 herds in the US that have weight data from roundups. 

So far, we see a few basic things about bison. On average, males level off at about 75% greater weights than females (855 vs. 484 kg). It also takes them about 1.5 y longer to reach half their maximal weight. 

We also see that some bison herds are heavier than others. For example, mature bison in Ordway Prairie in South Dakota are 50-100 kg heavier than mature bison from Konza. That's a lot of bison. Is it a fluke? Unlikely. Over 90% of Ordway adult cows produce calves. At Konza, it's only about 60%. 

There must be a big difference in the grass between Konza and Ordway.  Because their bison growth curves are quite different.

Konza flowering phenology and functional groups.

In general, we have little understanding of how communities are assembled and the types of interactions that long-term generate evolutionary pressures, extinctions, and radiations. I'm pretty sure that whole-flora analyses are going to be keys to helping us understand these complex systems and there are precious few datasets on the scale necessary to do this.


With that in mind, here's the latest Konza phenology data by functional group. This is through Sept 1. The x-axis is day of year of first flowering for a species. Based on n = 408 species, which represents about 80% of the herbaceous grassland flora for Konza. We'll probably get another 10-20 species flowering before the year is up.

The y-axis is probability of flowering per day over the year for species of each functional group based on a "smooth" fit of the distribution data. Probabilities are standardized across functional groups. I broke out the Cyperaceae because it was the Carex that flowered early, not any C3 grasses. The C3 grasses that flower late in the year are generally woodland grasses.

This is terribly fascinating, though I'm not sure what the story is yet. For example, why are there C3 forbs that flower in August, but not any C3 grasses? And why are there C4 grasses that begin flowering in March, but not any C4 forbs? 

There certainly is an long-term competitive interactions that sort communities and drive selection. It's almost likely a rock-paper-scissors story. If rock (C4 grasses) then no scissors (C3 grasses), but if paper (grazers) then there are less rocks, so can have knife (C3 forbs).  

The C4 forbs are probably the most interesting story. If high temperatures favor C4 over C3, then why are there so many C3 forbs that are active during the hottest months rather than C4 forbs. Konza's C4 forbs are mostly Chamaesyche (Euphorbiaceae) and Amaranthus. Often they are prostrate forbs and/or weedy species keying in on disturbed areas. The C3 forbs that flower during this time are species like Salvia. Are there C4 forbs that fall into the same niches as these C3 forbs. Is there evolutionary constraint here that allows all the mid- to late-summer C3 forbs to persist? 

As we generate more large-scale trait datasets, more of these patterns should come clear. 

Mycorrhizal fungi and grassland community structure

Relationship between mycorrhizal infection rates and the log-transformed response of species abundance to grazing.

The structuring of plant communities is complex. There are a myriad of proximal and distal factors that can influence the abundance of species. The role of mycorrhizal fungi in structuring grassland communities has always been opaque. In temperate grasslands, many of the species are dependent on arbuscular mycorrhizal fungi, yet many non-mycorrhizal species are found throughout the grasslands. Whether these non-mycorrhizal species tap unique pools or even are facilitated by the mycorrhizal species is really unknown.

Over a decade ago, Wilson and Hartnett (1998) quantified the dependence of ~100 grassland species on mycorrhizal fungi. There had never been a screening study like it. Nor has there been one since. Their work largely compared different functional groups, with the conclusion that C4 grasses are the most dependent on mycorrhizal fungi and legumes the least. The work implied that success at Konza would be dependent on the ability to utilize mycorrhizal fungi, but this was never quantified.

Recently, we've compared the screening data with actual abundances from Konza. It turns out that there is no relationship between abundance and mycorrhizal responsiveness or infection rates. As such, mycorrhizal symbioses are likely not necessary for success.

That said, mycorrhizal symbioses do determine which species perform better under certain conditions. For example, almost 25% of the variation in the response of species abundance to the presence of grazers (bison) was explained by the mycorrhizal infection rate. Grazing promoted non-mycorrhizal species. Similarly, suppression of fire promotes non-mycorrhizal species (data not shown).

In both cases, fire suppression and grazing increase the availability of nutrients relative to other resources. How to think of the role of mycorrhizal under different burning or grazing regimes is still not clear. It's easy to say that fire suppression or grazing increases nutrient availability, which decreases the need for mycorrhizal fungi. But why? Is it because they are too much of a carbon drain? Many of the high-fire, low-grazing species just do not grow at all in the absence of mycorrhizal fungi, so it is unlikely to be associated with competition for nutrients. And why would mycorrhizal responses/infection predict just the responses to grazing/fire, but not abundance overall. In contrast, we see traits like leaf tissue density--which I think of as being associated with low nutrient availability--prediction abundance across Konza, but not the responses to fire and grazing. 

How to proceed on the issue is not easy, but it's a curious pattern to line up with a number of others in understanding how grassland communities are structured.

Wilson, G. W. T. and D. C. Hartnett. 1998. Interspecific variation in plant responses to mycorrhizal colonization in tallgrass prairie. American Journal of Botany 85:1732-1738.

Comparing two measures of leaf tissue density

Relationship between leaf tissue density (RhoL) and leaf dry matter content (DMC) across 42 Konza grassland species.

There has been some debate on how best to represent plant investment into leaves. Specific leaf area, the ratio of area to mass, is at best an imperfect measure. Plants with high SLA certainly produce a lot of leaf area for minimum investment. Yet, high SLA can come as a result of being thin or low density. And it seems that many of the ecological conditions associated with high SLA are really associated with low tissue density rather than thin leaves.

How to measure tissue density is one of the current debates. On the one hand, tissue density (mass per unit volume) can be derived by measuring the thickness of leaves in addition to SLA. Deriving leaf tissue density (LTD) from thickness measurements provide a direct covariate (thickness) and are relatively simple to do. Yet, for some leaves, measuring the average thickness can be problematic. On the other hand, an approximation of tissue density can be derived from the leaf dry matter content (LDMC). Leaves are weighed in a hydrated state and then again dry. The ratio of dry mass to wet mass is LDMC. There are a number of assumptions to equate this ratio to leaf tissue density, but it has been favored.

Across 40+ species at Konza, I measured LTD and LDMC. The two metrics correlated pretty well (r = ~0.8). Some species seemed to have higher LTD than one would expect based on LDMC. In species with a high proportion of veins, thickness is probably underestimated, since it is generally measured between major veins. The Ambrosia artemisiifolia I selected was deeply lobed and did not have much lamina relative to veins. Its LTD was probably too high. On the other hand, both Bothriochloa and Schizachyrium species had higher LTD than expected from LDMC, but this likely would not have been caused by underestimating thickness or area. Instead, these species likely have high silica concentrations that add more mass per unit volume than other species. This is something I still need to confirm.

As to whether LTD or LDMC does a better job of predicting abundance, they both were about the same. Using long-term abundance data, they both had equal predictive power on average.

Whether one metric is better than another is likely equivocal. It depends on the situations as both have their limitations. I’d probably use both for awhile until better consensus can be reached.

I’m not sure I’ll get around to publishing these data, so I thought I’d put so of the results up here. 

Photosynthetic pathway and phenology

Stylized diagram of phenology of first flowering of different functional groups for Konza.

Global change models had often assumed categorical differences between C₃ and C₄ species. Because of the temperature sensitivity of photorespiration, C₃ species are restricted to cooler seasons and C₄ grasses to warmer seasons. The separation between C₃ and C₄ species, especially the grasses, was a standard categorization for plant functional types.

Yet, how much basis is there really for the separation? What role does photosynthetic pathway have to play in the phenology, if not ecology, of temperate grassland species?

At Konza, we’ve been collecting plant species when they begin to flower. It’s a rough estimate of phenology. It doesn’t capture how long they flower, or when leaves grow the most, but it’s an easily measured trait that represents phenology. We have first flowering dates for about 350 of Konza’s 550 herbaceous species.

Generalization #1: C₃ grasses have an earlier phenology than the C₄ grasses. The first grass to flower in 2010 was a C₃ grass Poa pratensis on April 21. Yet the first C₄ grass flowered just a week later. Bouteloua dactyloides flowered on April 27. Tripsacum dactyloides, another C₄ grass, was just a day later—April 28. There really is little offset between C₃ and C₄ grasses in when they start to flower.

Generalization #2. The C₃ photosynthetic pathway restricts the activity of C₃ species when temperatures are high in comparison to C₄ species. It is true that C₄ grasses do flower later than C₃ grasses. The last C₃ grass to start flowering was Diarrhena obovata, a forest understory grass. It didn’t flower until June 28. Many C₄ grasses do not begin to flower until July or August, when midday temperatures are routinely 30°C. Yet, C₃ forbs also flower during the time when only C₄ grasses are flowering. For example, Helianthus maximiliani will not flower until the first week of August.

At this point, I have a few questions.

If C₄ grasses can flower as early as C₃ grasses, and C₃ forbs can be active during the time when C₄ species should have a physiological advantage, then what are the links between photosynthetic pathway and phenology?

How much of phenology is driven by phylogeny rather than photosynthetic pathway? The Andropogoneae C4's flower mid-season, but not the Chloridoid C4's.

Why do C₃ grasses not flower during the middle of the summer, while C₃ forbs do? Can C₃ forbs regulate their leaf temperature via transpiration to reduce photorespiration?

And why the offset for C₃ and C₄ grasses, if C₃ species can flower mid-season? Is this an example of niche conservatism?

The topic of whole-flora analyses of phenology is complex, but some of these patterns seem clear enough to rethink some generalizations--even if they shouldn't happen based on what we know.

How to taxonomically structure comparisons

For a recent grant, we proposed to measure aspects of the nitrogen and water economy of 30 species at Konza. The novelty of the proposed research was in measuring both water- and N-related traits for a wide variety of species, and then test how well they explain the abundance of the species in a native grassland.

One point that came up was how to frame the research. Part of our framing was that the results should help us understand the evolution of plant strategies and selection forces on species. Reviewers seemed to disagree.

One reviewer said, “The problem here is that because of the close evolutionary relationships of many of the selected plants, traits and responses will be co-correlated through evolutionary relationship and will therefore give an inflated estimate of independence.”

Another said, “It seems to me that the work in this project will yield much in the way of an understanding of the influence of resource availability in the evolution of land plants, since gaining such insights would really require a more extensive phylogenetic and perhaps phylobiogeographic sort of approach.”

This is something I still do not understand. How many species does one have to measure to be able to infer selection pressures and evolutionary tradeoffs? Ironically, we had initially proposed to measure 100 species, but were encouraged to measured fewer species. 30 is not enough? Shouldn’t 2 well-contrasted species be sufficient to provide some inference? Most of the initial work on C4 photosynthesis compared 4 species. Granted the work is still being refined, but isn’t 30 a good start? Also, why would 30 species be enough to test ecological processes, but not evolutionary?

I think the standards here have less to do with the science, than the scientist.

The current review is immaterial—the panel summarized that “The placement of this research in evolutionary context was undeveloped but will not affect the quality and novelty of the project outcome.” Yet, the gap in our scientific process is clear in the lack of anabolic comments being paired with the catabolic ones. Experimental designs to test for evolutionary patterns seem to require I-know-it-when-I-see-it tests. Constructively, we need some resolution on standardizing designs. I’ve pushed before for a standard species set, but we also need resolution on some key questions outside of any standardized set.

If there is one question I'd like to see answered, it's "how many species need to be measured and how should they be related?"

I don't expect one answer to this, but if we are serious about wanting to understand the evolution of ecological traits, we have to make the bar visible, rather than always place it just above our leaps.

Comparing bison weight gain

Locations and size classes of bison conservation herd in North America. Historic ranges shown, too. From Gates et al. 2010 IUCN report on bison.

Before European settlement, bison were distributed across North America. From the Atlantic coast almost to the Pacific and from northern Mexico to the Arctic Ocean. But where would have been the best place to be a bison?

There might not be an easy answer to the best metric for determining where the best place was to be a bison. Especially since we can't go back in time. Yet, bison have been reestablished across North America, which gives us some ability to begin to compare populations.

For bison, as with any animal, fecundity is the ultimate metric of fitness. It is almost axiomatic that when we compare individuals, the best metric of fitness is the number of offspring that an animal or population has. Yet, fecundity is density dependent. Fecund populations become dense, which lowers their fecundity. Population density could serve as another metric, depending on how important disease or predation become in limiting population size.

Systematic comparisons of the geographic ecology of bison have not been attempted. Yet, here's an interesting comparison. The latest IUCN report on bison "American Bison: Status Survey and Conservation Guidelines 2010" included a graph on the weights of bison at Wind Cave in South Dakota.  Weights were averaged for males and females by age. Wind Cave bison are considered some of the purest Plains bison and western South Dakota and its short grasses is thought of as prime bison habitat.
By comparison, Konza Prairie in Kansas is tallgrass. And tallgrass is sourgrass to some--not the best habitat for bison. The calving rates of bison at Konza can be pretty low. In some years only 50% of the adult female bison calve, which might not indicate the best nutrition.

Yet, with the data from Wind Cave, we can compare the weights of bison at Wind Cave and Konza. Based on what we know of the habitats and the calving rates, we might expect that Konza bison would weigh less than Wind Cave bison.

Not the case.

Closed symbols are females. Open symbols males. Circles are Konza. Squares are Wind Cave.

The two sites are right on top of one another. 

Either the two sites are equally good for bison or the weight of animals isn't the best metric for habitat quality. 

The model species set

By restricting our own freedom, we gain collective power. It's a tenet of larger society, but also scientific society. 

For some the restriction is in the form of Arabidopsis. Zea for others. Populus, Lotus, Medicago...the list of model organisms that are used to answer fundamental questions about the genetics of plants goes on.

But what about the evolution of plants? To a degree, we can compare the genomes of model organisms to hint at some of the broader evolutionary patterns. But evolutionary patterns are generally derived by comparison with multiple members of a single clade. If one wanted to understand the evolutionary patterns of grass, we couldn't just look at a single model organism. We would need to look at a model set of species.

What would a model species set for grasses look like? It would have to be large enough to cover the major clades (~10), but restricted enough that researchers could measure standardized metrics on every species. Probably about 100 species. For grasses, they should come from different continents, span multiple origins of C3 and C4, and cover a wide range of environmental tolerances. Seed should be readily accessible. Most likely seed sets would have to be collected by a central agency for distribution to willing researchers. A central database would be needed to store all the data for other researchers to use.

Once that happened, an individual researcher that was interested in the cold tolerance of grasses could grow up all 100 species, measure their cold tolerance, and then examine the evolutionary patterns of cold tolerance. The next researcher that wanted to examine stomatal density could do the same, and then would be able to compare it with cold tolerance. Root anatomy, mycorrhizal dependence, genome size, carbonic anhydrase activity, flowering phenology, drought tolerance...the database would build. Each time we would learn more about multivariate trait selection in ways that no one lab could do.

Why doesn't this exist? Hard to say. Part of it is probably some small group just deciding which 100 species to use. Would it be perfect and cover all the potential evolutionary questions? No, but there are researchers that are asking these questions anyways, so they might as well be using the same species. Plus, there always could be a second species set identified to fill the gaps in the first for a second round of measurement.

Why not just keep a database and let researchers work on whatever species they felt best allowed them to examine specific ecological and evolutionary contrasts? Never enough overlap. Brassicaceae has 3700 species and even the Arabidopsis genus has 9 species. But everyone works on thaliana even if other crucifers might be better to answer some questions.

Once the scientific community agrees to encourage the restriction of freedom of inquiry into plant evolution a little more, a large amount of collective power will be realized. How long should it take? A few informed individuals who are not afraid to make political sausage would need to be in the same room for about 2 days. How long will it take to get people in a room for 2 days? Hopefully within a year or two.

Climate-nutrition-performance cascade

Critical climate periods for precipitation for ANPP, flowering of 3 grass species, bison weight gain, and the calving rate of adult females the following year.  

Some ranchers around here know that "a dry June is money in the bank". Supposedly when precipitation in June is low, cattle gain more weight. More cow means more money. I haven't heard it too much around here and I had never seen data to support it (until the work on bison weight gain at Konza), but it exemplifies the climate-nutrition-performance cascade and is a cautionary lesson in understanding climate change.

The performance of grazers--their weight gain and calving rate--is dependent on both the quantity and quality of the grass they eat. The interannual determinants of quantity seem fairly straightforward (for some sites). Quality is less so. Quality encompasses a lot of things, but primarily is protein. And protein is nitrogen.

The cascade links climate to performance through protein. The proximal and distal drivers of variation in protein are complicated enough that they are still being worked out. But as we work through this, it will be important to ask whether there protein at certain times is more important than others. And if so, maybe interannual variation in climate at certain times is more important than others. Rain in June might be more important than May, for example.

We've used the critical climate period approach to begin to tease some of this out at Konza. The figure above shows a broad CCP for ANPP--rain that falls in June or September still is important for determining growing season biomass. The three C4 grass species have different, but overlapping, CCP's. Each is about 80 d. In contrast, bison weight gain and calving rate seems to respond to variation in precipitation for just relatively short periods. One in late June, early July. The other mid- to late August. Calving rate depends on just mid- to late August precipitation.

Between climate and bison performance is protein. And the controls on protein we're still figuring out.

Until we do, we'll have a hard time understanding the dynamics of grazers, no less their fate in a world where climate has changed.

Whole-flora analysis: flowering and community assembly

Distribution of first flowering dates for 265 Konza grassland species (as of mid-May). 

There are some ecological analyses that can only be done by analyzing every species in a flora. Statistical inference aside, if we are to understand ecological sorting and community assembly, we need whole-flora analyses.

For example, we've slowly been accumulating data on first flowering for the Konza flora. For each species,  the day of year it first begins to flower is recorded. We're about half-way to having dates for the entire grassland flora. It's a bit biased now as we're still collecting data this year, but that's why this is on a blog...

There seems like there might be pretty strong selection pressures to flower at times when 1) environmental stress is low and 2) there is little competition for pollinators. I'm not sure if there would be selection against synchrony in flowering time for anemophilous species, but we that would be something to test, too. In this case, deciding what the null model is, is the hardest part.

I like the idea of whole-flora analyses. It's a lot of work though.

N vs. P limitation

Nutrients limit grass growth in native grasslands throughout the world. Yet, which nutrients limit growth should vary. N limitation appears to be pervasive in all nutrient limited grasslands and P is often limiting, too. In Europe, grasslands are often divided into those limited by N vs. those limited by P. In N-limited grasslands some species such as Alopercus predominate, while in low-P grasslands its Molinia. 

Why the sorting though? What traits would have been selected for in low-N vs. low-P soils? Fujita et al. have a new paper coming out in Oikos that I think provides some good data to separate species and shed light on selection when nutrients are limiting. It's long been known that plants can produce phosphatases to increase P availability. Fujita et al. show that low-P species have higher rates of phosphatase production.

With the experiment examining plant growth and activity at a range of N:P supplies, the research has the potential to help understand not only differences in grassland communities but also the response of grasslands to N deposition. Fertilization with N increased phosphatase activity in ways that should further increase the abundance of low-P species.

The authors do a good job for their eight species in linking plant stoichiometry, plant growth, and resource availability, which might ultimately serve as a key trait in understanding selection for success when nutrients are limiting, as well as the functioning of grasslands.

Fujita et al. 2010. Oikos. doi: 10.1111/j.1600-0706.2010.18427.x

Leaf dry matter content: ecologically relevant?

There is still some contention about whether leaf tissue density (mass per unit volume) leaf dry matter content (LDMC; dry mass per unit wet mass) are equivalent and whether past work has shown LDMC to be ecologically relevant, no less more relevant than specific leaf area (SLA).

I've looked through the literature pretty hard. Here's about all I can find:


1. LDMC and leaf tissue density should be positively correlated and there has been some excellent work investigating the underlying causes of variation in LDMC that are relevant for understanding leaf tissue density (Vile et al. 2005, Roderick et al. 1999, Shipley 1995). I still haven't found the perfect test of the two methods, but they should be pretty strongly related.
2. LDMC can predict plant strategies (Vendramini et al. 2002, Wilson et al. 1999). LDMC does a better job than SLA in predicting CSR placement for example.
3. LDMC can predict relative growth rates within species (Ryser and Aeschlimann 1999) and digestibility (Pontes et al. 2007, Ansquer et al. 2009, Duru et al. 2008).
4. LDMC was not correlated with competitive effect or response (Liancourt et al. 2009).
5. LDMC correlated better with soil fertility and sheep grazing intensity than SLA in Norwegian alpine ecosystems (Rusch et al.2009). [Note I still haven't read this paper--it's on order.]

That's about it.

The use of SLA still outnumbers tissue density or LDMC 50 to 1 and there still are essentially no published tests of the utility of either tissue density or LDMC in explaining abundance.

The tyranny of dominance

If you take a walk through a grassland, you are likely to recognize that a few species are more abundant than others. Walk through a nearby grassland and you'll recognize those species again. Dominance of a few species is a hallmark of grasslands. Especially in humid grasslands, species are thought of as dominant, sub-dominant, or rare.

But do grasses evolve to be dominant? Or rare? Dominance might be a common condition for a few species, but how transient is dominance? Or rarity?

This is a topic that easily belies one's inner model of how the world works. More often than not, it's one's view of human society that paints one's ecological canvas. But that's a topic for another day.

Although unstated, there are likely two competing intellectual frameworks at play with discussing dominant species. On the one hand, it is possible that some species have evolved to be dominant and others rare. There are light-demanding canopy trees and there are shade-tolerant understory herbs.  It is the role of the latter to always be underneath.

On the other hand, dominance and rarity are context specific. All species dominate somewhere and at some time. It all depends on the environmental context. If there are species that are dominating it is only because of the prevailing conditions.

Let's look at Konza Prairie. 86 species of grass. Only a few are considered dominants: Andropogon gerardii, Schizachyrium scoparium, Sorghastrum nutans are the big three. Maybe Panicum virgatum if one is feeling inclusive. But what about the other 82? Do they not dominate because they cannot dominate an area, or because they dominate grasslands under conditions that are not prevalent at Konza.

For example, only a portion of Konza is grazed and most of that area not too heavily. All of Konza's Big 4 grasses are less abundant in areas that are grazed than ungrazed. If Konza were grazed more heavily, one would likely assume another set of species were dominants. Bromus arvensis is likely one of those. It is 10,000 times more abundant in grazed than ungrazed areas. It "dominates" grazing lawn areas.

Along these lines, Gene Towne went and calculated that almost half of Konza's grasses have been found to be abundant in at least one of Konza's ~300 10 m2 permanent plots over the past 15 years. The other half? Some of them, such as Elymus virginicus, dominate in wooded areas which just aren't sampled at Konza. Some of them dominate outside of Konza. For example, Panicum coloratum is a dominant in the southwest mesquite woodlands. Poa arida is not common at all at Konza, but Konza is really at its southern range limit. Go to Alberta to find vast stretches of it. Some of the other Konza-rare species are annuals and would likely be a lot more abundant if the ground was pounded by more hooves or we had recently had a major drought.

In all, there's probably too much Berkeley in me to believe that some species are inherently dominant. It seems like, at least for grasses, each species likely dominates somewhere some of the time. That said, it would help to hear a bit more about the assumptions that underlie the concept of dominance. I could accept that grasses would be tyrannical to one another in their quest for resources and reproduction. The idea that some grasses are inherently more likely to dominate than others is a tyranny of thought I am probably not willing to accept yet.

C4 photosynthesis and nitrogen

Comparison of foliar N concentrations among clades.

Since the beginnings of our modern understanding of C4 photosynthesis, it has been set that C4's are more efficient with water and nitrogen. Yet, there have long been unexplained patterns for C4's that didn't match the assertion of greater nitrogen use efficiency. For example, C4 grasses in the field often have lower foliar N concentrations, but also lower root N concentrations. Why would this be? If the leaves need less, shouldn't the roots get more? Also, some C3 grasses like Chionochloa can have foliar N concentrations as low as 6 mg g-1. Most C4's have higher concentrations and only a few have been observed to be below that. Also, foliar N concentrations for any given species are highly plastic and dependent on the balance between C and N supplies and demand. If a given species can have N concentrations that range 30 mg g-1, just how important is the C4 photosynthetic pathway.


Turns out, probably not much. Taylor et al. (2010) used a phylogenetically structured screening experiment to measure a number of morphological and physiological traits of grasses. In doing so, they could compare C3 and C4 species controlling for phylogeny. The research upholds the notion that C4 photosynthesis confers greater water use efficiency to plants. Yet, after controlling for phylogenetic relationships, there were no differences between C3 and C4 species in their foliar nitrogen concentrations. 


By no means the last word on the topic. For example, they only measured ~30 species. Yet, the authors have provided the best experiment to date to address the question and evidence to the contrary will have to be weighed against some strong evidence regarding the ecological consequences of the evolution of C4 photosynthesis.


Taylor, S. H., S. P. Hulme, M. Rees, B. S. Ripley, F. I. Woodward, and C. P. Osborne. Ecophysiological traits in C-3 and C-4 grasses: a phylogenetically controlled screening experiment. New Phytologist 185:780-791.

Do I have to phylogenetically correct my grocery list?

The figure of Westoby et al. (1995) that summarizes their view of the tension between phylogeny and ecology in understanding trait relationships.

For some, a simple grocery list can pose a dilemma. Just yesterday, I went to the store with 21 items to buy. Others would look at my list and suggest I only bought 11 items. Fresh peas and frozen peas shouldn't really be counted as different items--they were both peas. Cauliflower, broccoli, and collard greens are the same species. Mustard part of the same genus as the previous three. Hot dogs and pork chops both from pigs (I hope). So although 21 items went into the cart, one could phylogenetically correct my list and arrive at the conclusion that I only bought 11 unique items.

It might seem silly to phylogenetically correct one's grocery list, but how to consider both phylogenetic and ecological data when examining species relationships lays bare the same fundamental tension as describing my last trip to the grocer.

In 1995, Westoby, Leishman, and Lord published a forum piece, “On misinterpreting the 'phylogenetic correction'”. The genesis for the forum piece came during the review process of a paper on seed mass in plants. Most likely, during the review of that paper, differences in opinions between reviewers and authors were laid bare. In the original paper, the authors showed that tall plants had large seeds. The reviewers likely insisted that the relationships between plant height and seed size could be due to phylogenetic relationship. The authors disagreed. Differences in opinions became forums, which by ecology standards unleashed a bit of a storm.

The questions associated with the topic of how to match ecological and phylogenetic data are ripe, but “phylogenetic correction” essentially adjusts relationships by weighting closely related species less than distantly related species. The fundamental differences of opinion pin whether closely related species hold similar traits because of phylogenetic constraint or ecological constraint. Closely related species might have similar traits because there has been little time for radiation, or because they are under similar ecological selection pressure. Distantly related species might have different traits because initial trait differences have long been conserved due to fundamental difficulties associated with character displacement or because they have been under the same ecological pressures for a long time.

The issues of how to identify adaptations or evolutionarily beneficial relationships cannot be covered here, but these fundamental issues have never been resolved, near as I can tell. The current détente that seems to exist is to examine ahistorical and “phylogenetically corrected” relationships among traits and hope that the patterns are the same. When setting to test relationships among species, choose congeneric species pairs from distantly related genera and hope the patterns work out consistently.

It’s currently an uneasy impasse. Both sides recognize that correlation does not necessarily imply causation. But outside of hoping that the evolutionary and ecological patterns parallel, there is still no resolution to the question of how to compare the traits of species.

I do know that if I want to shrink my grocery list, I'll start by not buying both cauliflower and broccoli rather than phylogenetically downweighting closely related taxa on my list.

The evolution of grasses: phylogeography of C4 photosynthesis

The temperature niches of grasses of the world overlaid onto their phylogenetic relationships.

The two great datasets in biology are the tree of life and the global biogeographic distributions. The first describes the phylogenetic relationships among organisms. The second describes their distributions on our planet. In a rich and well-nuanced paper, Edwards and Smith have brought the two together to shed light on one of the most fundamental questions regarding the evolutionary ecology of plants, namely the origin of C4 photosynthesis. The authors first use an expanded grass phylogeny to describe the origins of C4 photosynthesis in more detail than has done before. They then determine the current distribution of the grass species to determine the climates they occupy.

With regard to the evolution of C4 photosynthesis, the authors conclude that shifts from C3 to C4 photosynthesis did not involve shifts to warmer macroclimates, but instead to drier macroclimates. This results comes as a bit of a surprise--it is less clear that C4 photosynthesis is a response to low water availability as much as high temperatures. Their next logical step is a bit of a leap--namely that these modern geographic differences can be associated with habitat shifts in the past.

As important as the insights into the phylogeography of C4 photosynthesis is that the evolution of cold-tolerance in grasses is more difficult evolutionarily. Cold-tolerance apparently evolved vary early on in the grass radiation and has not been repeated to the degree that C4 photosynthesis has.

In all, this hardly seems like the last word on the topic. The biogeographic data needs to be improved, climatic ranges rather than centers will likely be used, and the grass phylogeny is still relatively unresolved. Also, we still have little understanding of why C4 photosynthesis would benefit plants in dry environments. That said, there is a lot of insight for many types of researchers and a solid step in understanding the strategies of plants to resource scarcity.

Edwards, E. J. and S. A. Smith. 2010. Phylogenetic analyses reveal the shady history of C4 grasses. Proceedings of the National Academy of Sciences 107:2532-2537.