Saturday, December 17, 2011

Best use of bootstrapping, ever: the flavor network.

Not too often, a paper comes out that generates so much insight and is presented so elegantly that it induces jealousy.

Ahn et al. published a paper in Scientific Reports (Nature's version of PLOS), "Flavor network and the principles of food pairing". Essentially, the paper mined on-line recipe databases to generate differences in ingredient use and flavor-space among cuisines.

Each figure in the paper has so much that is interesting. At the center of a giant multivariate analysis of flavor is what Kendra called the "triangle of happiness": cocoa, beer, and coffee. At the center of that: katsuobushi--dried, shaved bonito tuna. It must be amazing. Liver by the way shares little in the way of flavors with anything else (thankfully).

The authors also use bootstrapping to see which are the most unique ingredients in different cuisine's recipes. North America clearly stands out for its desserts. Take away: milk, butter, cocoa, vanilla, cream, cream cheese, egg, peanut butter, and strawberries and our recipes are pretty similar to elsewhere in the world. Essentially it's our ice creams and cheese cakes that make us stand out.

So much about the food of the world, jammed into one paper. Blue cheese and chocolate share 73 flavor compounds? Throw away line.

This is an amazing food paper, yet I can't help think about why we can't do this for plants. Substitute regional flora for cuisines,  functional groups for ingredients, and functional traits for flavors and it would be once-in-a-century paper. Yet, you look at the underlying data for this paper and realize that paper is a century away.

Friday, December 9, 2011

Graphs that don't exist: state factors and shade

Shade, drought, and nutrient scarcity are three resource stresses that constrain vegetation globally. Each of these are influenced by state factors as well as other more proximal controls on ecosystem function.

At least theoretically. We've actually never tested these ideas, which constrains our ability to explain and predict a lot about how ecosystems work.

Take shade. Plants produce leaves, which creates shade beneath them. Yet, the amount of shade in different stands varies tremendously. Theoretically, sites that are more limited by water should be able to produce less leaf area, leaving more light to the understory and removing a constraint on the growth of understory vegetation.

Despite decades of light measurements and hemispherical photographs of canopies, the data has never been synthesized to generate a global map of shade that can be analyzed in terms of determinants. Do dry ecosystems have a lower potential for producing shade than wet ecosystems? And how does that vary with temperature? Do forests in colder regions cast less shade, all other things equal?

Part of this echoes Peter Grubb's assertion that higher fertility sites should generate more shade and have more slow-growing shade-tolerant species, which still hasn't been tested directly as far as I can tell.

What holds for shade also holds for nutrient availability and water potentials. We just don't know the basic drivers of resource availability and hence don't know how global change factors like warming will affect the availability of the most limiting resources.

Wednesday, December 7, 2011

Global change and limitation

Ternary diagram showing the inverse relationships among low resource stresses and how global change factors influence the likelihood of resource limitations.
One foundation of ecology lies in the concept of state factors. Borrowed from soil science, state factors are the properties of ecosystems that are independent of the properties of the ecosystems [see earlier post]. The bedrock under a stand of plants is largely independent of whether a forest is there or we cut it down.

Ecosystems are not entirely deterministic from state factors and there are more proximal "interactive controls" like disturbance that are co-influenced by the vegetation. The probability of fire depends on what species are present as well as state factors like macroclimate.

One deficiency in our application of state factors and interactive controls has been to map the influence of state factors and interactive controls onto limitation. What factors and controls promote water-limitation over nutrient-limitation?

I've been trying to diagram this. Terry in his ecosystem book used a flow-control diagram to map the relative influences of state factors, interactive controls, and other controls on processes.

I've tried this approach for generating limitation and my diagrams come out looking like spaghetti. Or fettuccine. Some type of long, linear pasta. At least not fusilli thankfully.

The best I can come up with is a ternary diagram. In short, we want to show that drought, shade, and nutrient scarcity are all inversely related. And that a given global change factor promotes one or two stresses over the other. Precipitation promotes shade and nutrient scarcity over drought stress. Warmer temperatures promote drought and shade over nutrient scarcity. Disturbances reduce resource stress overall (inset).

There are dependencies for the diagram, e.g. chronic vs. catastrophic fire or scarcity of N vs. P.

Still I think this encapsulates the concepts we have about how global change factors alter limitation.

Mapping out other specific state factors is still a challenge. I get more spaghetti diagrams when I do this. Well, diagrams that look like I spilled dried spaghetti.

Thursday, December 1, 2011

The proximal should precede the distal

Relationship between water potential at which a species loses 90% of conductivity and dry season mortality. From Pratt 2008.  

When it comes to explaining patterns associated with the ecology of plants, a simple dictum should apply: the proximal should precede the distal.

I've been working with a few others to try to make this point with plant functional traits and ecological patterns for a review that Science green-lighted. In short, when looking to explain ecological phenomena, the mechanisms explored should be the closest to the mechanisms that generate the pattern. 

If drought is thought to cause mortality in a system and one is trying to understand which plants would survive drought the best, measure whole-plant drought tolerance first. Then begin to examine more distal underlying traits. Don't start measuring traits like SLA or screening genes until drought tolerance has been quantified.

Pratt et al. 2008 show a good example of the approach. The authors grew up a series of chaparral species from seed and monitored their performance over a dry summer. Those species that could withstand low water potentials the best, suffered lower mortality.

The same approach applies for a range of other cases, but each time it is important to be clear about what the processes are that are hypothesized to generate the patterns of interest and then measure the functional traits that are most closely related to them. 

There has been over-reliance on general leaf traits, for example, that has generated a lot of frustration (and frustratingly low explanatory power). In contrast, when ecologists directly measure the ability of plants to tolerate low resource availability, for example, ecological patterns are explained better.

Defining the pattern of interest, generating hypotheses about their causes, and clearly linking form and function is a heck of a lot harder than going out and measuring SLA. 

Ultimately, when the proximal precedes the distal, more explanation is generated.

We'll see how we do making the case for the proximal in this review.

Sunday, November 27, 2011

The Corner (Ecological) Office

I had read this book awhile ago, but Kendra just got to reading it, so we've had more of a chance to chat about it lately.

In ecology, there are a lot of nuts and bolts to master. Statistics, experimental design, the literature...Our discipline is not a quick one to master. Yet, when you get to the highest levels of the functioning of the discipline, success has less and less to do with the nuts and bolts than the more sociological aspects--basically how to get people to work together. As a scientific society, we recognize this a bit--we have fellowships for interacting with the press or Capitol Hill, but not with each other. It's unfortunate, too, because the failures and dysfunction are costly yet utterly preventable.

Any airport bookstore is filled with similar topics, but the best book I've found that provides advice on how to be a leader is Adam Bryant's The Corner Office. Bryant writes a weekly column for The New York Times Sunday Business section called The Corner Office. Weekly, he interviews a CEO of a different company and asks them essentially the same questions. When did you first have to manage people? Where did you learn to manage people? How do you hire people? What recent insights do you have on leadership? Almost every week the column is interesting and there are a lot of people who have thought carefully about how to manage people. The book is a compilation of his interviews to date.

There are many lessons in the book. There should be. Leading and managing is complex and just one thing wrong can trip up any project no less corporation. You have to take care of people and let them know they are appreciated. You have to provide a vision that can be easily translated to day-to-day activities. You go to the lowest levels for unfiltered information and to learn all the aspects of work that surround you. You have to be fair and even. You have to appreciate failure.

William Bond and I were talking about similar issues on our trip through Afri-homa. He remembered his first year at UCT. He said that his department use to have a brilliant chair. William described how after his first year--a year consumed by teaching courses for the first time along starting a research project--his chair found him and said, "Good job, William. You made it." And you could tell how that one recognition meant a lot to him.

So much dysfunction in any group, whether a project, a department, or a scientific society, comes from not feeling appreciated. And it costs so little for leaders to appreciate others and let oxygen be consumed on more important issues.

There are a host of other aspects of being a leader of a team that need to be carried out well. Bryant might not nail them all, but there are stories in there worth learning that help advance our discipline as much, if not more, than the latest statistical technique or meta-analysis.

Wednesday, November 9, 2011

A bit of inspiration to travel

Photo from Wildflower Wonders by Bob Gibbons of Tien Shan Mountains in China (Princeton University Press).
Books can be good for inspiration. Some books inspire with ideas. Others with adventure. Sometimes just photos that inspire one to travel to new places.

I had a chance to read Wildflower Wonders: The 50 best wildflower sites in the world over the past few days. The author, Bob Gibbons, shows off some impressive photography of beautiful grasslands from around the world. From the Tien Shan Mountains to the Outer Hebrides to Namaqualand.

It's more than just a coffee table book of pictures, though. Gibbons does an excellent job weaving together cultural and geological history with the ecology of the areas in ways I wish I could. His discussion of the settlement history of the Julian Alps or the unique geology of the Dolomites in Italy that differentiates its flora from nearby limestone grasslands.

I think we forget to be biogeographers too often and forget that we can learn as much from travels as experimentation. And it's our travels that shape our experiments. Even those that work at the global scale often see just pixels and not the uniqueness of place that truly defines geography.

I have little but praise for this book. It would have been nice to see more pictures of grass rather than the less-than-subtle, somewhat ostentatious wildflowers. But, I guess that's my job on the next trip.

[Thanks to Princeton University Press for the advance copy.]

Wednesday, October 26, 2011

Why trees aren’t taller

The effect of height-induced drought stress on redwood foliage. From Koch et al. 1994.

The tallest tree in the world is about 120 m. One of the most basic questions we have about trees is whether this height represents the tallest possible tree. Are there some fundamental physical constraints that make growing much beyond this height impossible? Or could we grow a 200 m tree?

In 1997, Ryan and Yoder wrote a Bioscience article “Hydraulic limits to tree height and tree growth”. There, they reviewed 4 hypotheses regarding the limits to tree height. In short, they ruled out that as trees get taller their respiration might become too high, nutrients too hard to acquire, or genetic changes associated with maturation (they get too old) limits their growth. These might come into play, but are only contributing factors.

The hypothesis that was left was hydraulic limitation—it’s just too hard to move water much higher. Here, as trees grow taller, the length of xylem from root to leaf increases. Water flow is a function of the ratio of the difference of water potential and resistance. As tree height increases, resistance to water flow increases requiring lower (more negative) water potentials to move water to the top of the tree. As water potentials decline, xylem at the top of the tree is closer to the point of cavitation. Once the string of water snaps at the top of the tree, it’s hard to get water back up there and that part is dead. To be safe, leaves at the top of the tree close their stomata more frequently, which limits carbon gain. Less photosynthesis slows growth, generating a maximum height.

The evidence at the time for this hypothesis was that stomata in any leaf will close if hydraulic resistance increases, hydraulic resistance increases for older trees, and photosynthesis is reduced in older, taller trees.

They end the 1997 review by saying “we may be close to answering some of our oldest questions about tree height.”

Move forward to 2004. Koch et al. studied the tallest tree known on earth, a 113 m redwood in N California. They showed that as one moved progressively up the tree, water potentials declined, photosynthesis declined, and leaf WUE increased as stomates were closed more frequently. Everything fit the hydraulic limitation model.

Yet, when you go to the top of a redwood tree, the water potentials aren’t that low. It only takes 1 MPa to overcome gravity and move water 100 m. Moving water to the top of the redwood tree takes only -2 MPa due to greater resistance in redwood wood. They argue that at this water potential, photosynthesis is essentially zero for the redwoods, which explains why redwoods aren’t much taller.

But it doesn’t explain why other trees that can photosynthesize at tensions below -2 MPa couldn’t build a taller tree.

Subsequent work seems to reinforce this idea. In 2008, Domec et al. assessed xylem design for 85-m tall Douglas fir trees. There, they showed that with increasing height, Doug fir branches had greater resistance to water movement (less efficient) but could with stand greater tensions (more safety). But still, the water potentials at the top of the theoretically tallest Douglas fir (~130 m) did not push the ultimate bounds for plants.

The authors concluded “Mechanisms governing ultimate tree height must be considered in an evolutionary context, and so it is unlikely that the tradeoffs discussed here are identical to those of all other species. A number of coniferous species adapted to arid and semiarid zones can maintain adequate water transport at substantially greater xylem tensions than those normally experienced by the mesic-environment species Douglas-fir and coast redwood.”

Ultimately, the question of tall trees becomes an evolutionary question. Could nature build a 200-m tree? The current limits to tree height might be evolutionary, not physical. If you built a tree with the same plumbing as a drought-tolerant shrub, a 200-m tree might be possible. 

Domec, J. C., B. Lachenbruch, F. C. Meinzer, D. R. Woodruff, J. M. Warren, and K. A. McCulloh. 2008. Maximum height in a conifer is associated with conflicting requirements for xylem design. Proceedings of the National Academy of Sciences of the United States of America 105:12069-12074.
Koch, G. W., S. C. Sillett, G. M. Jennings, and S. D. Davis. 2004. The limits to tree height. Nature 428:851-854.
Ryan, M. G. and B. J. Yoder. 1997. Hydraulic limits to tree height and tree growth. Bioscience 47:235-242.

Friday, October 14, 2011

A lack of fertilization from elevated CO2 in forests

The concentration of CO2 in the atmosphere has been rising steady for some time now. There are two main potential direct effects of this fertilization. The first is a direct increase in photosynthesis, the second a reduced use of water.

At its simplest, the reduced use of water should increase plant production in drier habitats by increasing soil water availability. Less water is used by plants for a given amount of photosynthesis, means more water in the soil, and more productivity before soils dry out.

Theoretically this straightforward, but whether this has happened in ecosystems across the Earth or not is an open question.

Peñuelas, Canadell, and Ogaya synthesized data on two parameters for 47 forests across the world. The first was the C isotope composition of tree rings, which can be used to infer instantaneous water use efficiency. The second was the growth rate of trees themselves--limiting measurements to well-established forests.

Their results are pretty clear. Across a wide range of forests, over the past 40 years trees have been 20% more efficient with water when they photosynthesize.

If trees are primarily limited by water, they should be producing 20% more wood. Yet, there was no significant increase in productivity in tree growth in any region.

If plants are more efficient with water, then what could be holding back plants?

The authors write, "Other factors such as increasing temperature, drought, nutrient limitation and/or plant acclimation may preclude such growth increase."

Which might it be?

The next chapter in this question is going to be pretty interesting.

Peñuelas, J., J. G. Canadell, and R. Ogaya. 2011. Increased water-use efficiency during the 20th century did not translate into enhanced tree growth. Global Ecology and Biogeography 20:597-608.

Wednesday, October 12, 2011

Low resource tolerance traits

General approach for determining physiological drought tolerance. Individual leaves or plants are dried down over time. Periodically the water potential of the soil or leaves, relative water content (RWC) or wilting stage of the plants is assessed. The response variable is generally gas exchange (stomatal conductance or photosynthesis) or hydraulic conductivity of leaves or stems. Different thresholds of the response variable are used as the ultimate metric  for physiological drought tolerance, i.e. A = 0 or KL = 20% of KLmax.

A short note here.

One of the developing trends in functional traits is moving away from traits associated with general stress tolerance syndromes to traits that directly are associated with tolerances of low availability of specific resources.

There has been a lot of work to determine the leaf economic spectrum, for example. Yet, the LES separates fast- and slow-growing species in essence without separating the specific resources that have driven the evolution of the slow-growing species.

For example, drought, shade, and low nutrient availability are all supposed to be associated with the traits on slow-return portion of the LES. Therefore, at its best, the LES would not separate out whether species were adapted to drought or shade, if they aren't adapted to both.

A hopeful trend has been measuring drought-tolerance or shade-tolerance directly. Tolerance of low nutrient availability/competitive ability when nutrients are limiting, not so much, but that might change yet.

Mel Tyree and Tom Kursar's work for tropical species is a good example. Their approach is to let tropical tree seedlings grown in pots wilt and then measure the water potential of plants that are severely wilted. Similar to psi-crit that I've measured.

When you do that, you get a range of drought tolerances:

They've used this pretty successfully to explain patterns of diversity in dry and wet tropical forests.

Again, this is a hopeful trend that should bear fruit in the near future.

Engelbrecht, B. M., L. S. Comita, R. Condit, T. A. Kursar, M. T. Tyree, B. L. Turner, and S. P. Hubbell. 2007. Drought sensitivity shapes species distribution patterns in tropical forests. Nature 447:80-82.
Kursar, T. A., B. M. J. Engelbrecht, A. Burke, M. T. Tyree, B. Ei Omari, and J. P. Giraldo. 2009. Tolerance to low leaf water status of tropical tree seedlings is related to drought performance and distribution. Functional Ecology 23:93-102.
Tyree, M. T. 2003. Desiccation Tolerance of Five Tropical Seedlings in Panama. Relationship to a Field Assessment of Drought Performance. Plant Physiology 132:1439-1447.

Thursday, September 22, 2011

Fire in grasslands and savannas: a trip to Afri-homa

William Bond with a Gulliver post oak at Tallgrass Prairie Preserve.  

I spent four days last week driving around Oklahoma with William Bond from South Africa. I'm not sure why we chose the state, except in many ways it is the area most analogous (ecologically) to southern Africa that we have in North America. Old soils, intermediate precipitation, native prairies and savannas, and fire.

I've spent a fair amount of time over the past decade with William learning about things I never thought cared about. This trip quickly became a study on the roles of fire, drought, and herbivory in vegetation. It's hard to summarize William's view of the world, but he spends a lot of time thinking about how ecosystems and floras have developed over the past hundred million years. It's not a narrow topic.

I'll do my best to summarize, but essentially we visited different ecosystems such as the Cross Timbers to look for evidence of the antiquity of fire in grasslands, if not the antiquity of grasslands themselves. We'd go to a place like Tallgrass Prairie Preserve and look at oaks to see whether they promote fire. We traveled to Wichita Mountains, another old landscape, to look at how trees were coping with drought. We traveled to Black Kettle grasslands to look for plants with spines as evidence of histories with browsing mammals.

You can't necessarily look at a place and see back 10 million years, but you can try. For example, you can look under a Cross Timbers canopy and try to understand whether fire would rely on grass or oak leaf litter to work through the savanna. Or look at the canopy to see whether the oaks try to shade out the understory or not. Things like this provides evidence of the evolutionary history between these plants and fire.

A place like Black Kettle isn't too far from the Cross Timbers, but it's a radically different ecosystem. Grass there is grazed short. All the woody plants are structurally defended. I'm still picking out prickers from that place. It was never likely a fire world. It was likely always an herbivore world.

Long story short, there are still some great syntheses to be made. We haven't mixed everything up enough such that an old-fashioned field trip can't provide insight into the forces that have structured our world.

Monday, September 5, 2011

Drought and stress tolerance

Comparison of photosynthetic rates for seedlings of dry- and wet-habitat tropical tree species. On average, photosynthetic rates were ~1/3rd higher for dry-habitat species. 

I wrote a bit on this just the other day, but here is a new paper that raises questions about whether low-water species should be considered "stress-tolerators". Pineda-Garcia et al. grew seedlings of 10 pairs of closely related tropical tree species and measured a suite of traits. Dry-habitat species had higher photosynthetic rates than wet-habitat species. In addition, dry-habitat species retained their leaves longer after watering was ceased.

There are always a number of ways plasticity can alter relationships. For example, I once showed that high resource species can have lower N concentrations and longer leaf longevity than low-nutrient species due to patterns of feedbacks to N cycling after establishment. Here, there are a number of mechanisms that could generate the higher photosynthetic rates and longer leaf longevity in this particular experiment that could be reversed in another. Parsimony accrues slowly.

Yet, overall, this is another example where drought-tolerant species are not necessarily following the general "stress-tolerator" syndrome. It will be interesting to begin to officially tally the evidence to see whether there is much support for the two to be linked.

Pineda-Garcia, F., H. Paz, and C. Tinoco-Ojanguren. 2011. Morphological and physiological differentiation of seedlings between dry and wet habitats in a tropical dry forest. Plant, Cell & Environment 34:1536-1547.

Monday, August 29, 2011

Drought vs. shade tolerance

The leaf economics spectrum is the modern incarnation of Grime's C-S axis. Without the overarching evolutionary strategies attached, it describes a broad set of correlations that cover species with leaves that have low activity rates, are built tough and live a long time, to those that have high activity rates, are built wimpy, and live a short time.

The evolutionary underpinning of the broad correlations--what ecological forces would select for the correlations--has remained opaque.

Ülo Niinemets has been publishing on this question for a few years. For example, in 2006, he and Valladares compiled rankings of shade and drought tolerance for woody species in the northern continents. The correlation was somewhat weak, but was negative. More importantly it showed that although there were species that had low shade and drought tolerances (x-axis), there were no species with high shade and drought tolerances.

In a follow-up paper, they examined the associations between stress tolerances and functional traits. They concluded that the traits associated with shade tolerance did not consistently have traits associated with stress-tolerance, while drought tolerant species did.

The evidence for drought tolerance being associated with traits that are low on the leaf economics spectrum, though, seemed a lot more mixed when examined individually. For example, across all species the pairwise correlation coefficient was just 0.18 (P <  0.001), which translates to an r2 of 0.04. Plus the relationship was negative for conifers (EC). LMA relationships were all positive and r = 0.3 overall (r2 = 0.09).

What you can see, though, is that most of the leaf economics spectrum are differences between broadleaf deciduous species and evergreen conifers. And these two groups do not differ primarily in terms of drought (or shade) tolerance. Hence, the trait relationships are pretty weak.

They ran a PCA of 4 main leaf economic traits (leaf longevity, %N, LMA, and photosynthetic rate). Overall and within each group, drought tolerant species ranked lower on the leaf economics spectrum. Overall r = 0.29 (P < 0.01).

I'm still working to rectify these results with what we've found for grasses. A few points are important here.

•Drought tolerance scores were rankings derived from observations, and do not necessarily represent physiological drought tolerance.

•The majority of the leaf economics spectrum for trees is associated with broad functional groups, which do not correspond to differences in shade or drought tolerance.

•Shade tolerance was not associated with the LES, mostly because of shade species having low LMA. But this is because shade tolerant species have thin leaves, not because they have low density (a different paper shows this). This also brings up the question whether LMA should be part of the LES [Answer: SLA (and LMA) should R.I.P.--leaf tissue density is much better.]

•If shade tolerance is not associated with the leaf economics spectrum, is drought tolerance? The glass is 10% full here at best.

•For grasses, we just don't see the same results. Drought tolerance is associated with high rates or gas exchange and no difference in leaf tissue density.

Research like this is going to be important for the interpretation of the leaf economic spectrum. Species high on the spectrum probably can be considered modern C species. But what about low? Is there one general stress-tolerant syndrome with variants that correspond to shade-, drought-, and nutrient-stress tolerance? Or are these largely independent of one another, but just never have the traits of high-resource species?

The endpoints definitely form a pyramid. The question is how tall is the pyramid? How different are high resource species from low-water species, compared to low-water to low-nutrient? We'll probably need more than 4 leaf traits to find this out.

Niinemets, U. and F. Valladares. 2006. Tolerance to shade, drought, and waterlogging of temperate Northern Hemisphere trees and shrubs. Ecological Monographs 76:521-547.
Hallik, L., U. Niinemets, and I. J. Wright. 2009. Are species shade and drought tolerance reflected in leaf-level structural and functional differentiation in Northern Hemisphere temperate woody flora? New Phytologist 184:257-274.

Thursday, August 25, 2011

It's hard to tell the difference between the fringe and the frontier

I guess I said this once to Kendra.

We both couldn't remember what the phrase was.

I wished I had Posted this, so I could just look it up.

Then she remembered it.

So now I probably should Post it.

The context for the statement is that if you look at someone's research, it can be difficult to judge whether their work is isolated and unlikely to have much impact (fringe) vs. being a cornerstone to future ways of thinking (frontier). 

How to use the h-index

A few have asked me how to use the h-index in light of what I showed earlier. In many cases, the h-index is used for promotions, for example. For assessments, I would recommend not just looking at a person's h-index, but instead examining the residual h-index and finding good comparables.

Quantity and quality: residual H-index
The H-index is supposed to represent scientific productivity beyond just the number of publications. Yet, 90% of the h-index is the number of publications and the time a person has been publishing. It’s actually the residuals that are the key here. Two individuals with the same number of pubs and years publishing could differ in their h-index, if one is cited more. Assuming the number of citations correlates with publication quality, then the person with the greater residual h-index would have a greater impact.

There are always caveats to this, but it’s clear that for the purposes of assessment, one should examine the number of publications and the time a person has been publishing as well as the residual H-index from scientists in the discipline. This is probably the best metric of impact beyond number of papers.

Find comparables.
One of the benefits of the approach is to be able to find comparables. Just like in real estate, appraisals are used to determine the potential market value of a house and are anchored with the sale value of comparable houses. Just like researchers, no two houses are exactly alike (except in some uninteresting subdivisions), but they can be compared.

My approach to finding comparables is to generate the relationship between the H-index and the number of publications and the number of years publishing. Then, determine the next closest people in the space defined by the actual and predicted H-index. For example, calculating a Euclidean distance between my scores (H-index = 22, predicted = 20.4), the next closest person to me is a friend of mine, actually: 80 pubs in 12 years, H-index of 24, predicted 23.4. Euclidean distance = 3.6.

The person furthest from me? My advisor, Terry Chapin. 321 publications—probably more with some misspellings. H-index of 84. Predicted H-index of 80. Distance of 86.

Here’s a graph of distance from my scores as a function of H-index for reference.  


Even objective metrics have subjective assumptions. Still, there are important lessons to be learned from quantifying scientific productivity. Might as well do it as well as possible. 

Saturday, August 20, 2011

The H index: how many for how long

Relationships between h index and number of papers, log-transformed # citations for highest-cited publication and the # years since the first publication for 38 plant/ecosystem ecologists
I looked at the H indices a little bit more today. In short, I added a number of people to see if I could bust any of the relationships. Again, these are people at different career stages in a similar field as me from the US.

I knew that I could find people that have been published on papers that were highly cited, but they didn't have a high H-index. That wasn't too hard. Being a coauthor on a highly-cited paper isn't as diagnostic as the number of publications and the number of years cited.

The one relationship that is hard to find outliers for is the number of publications. I couldn't think of anyone that had published a lot of papers that had a low h-index. Tilman is really the only outlier for this. Based on the number of publications he has published, his H-index should be 56 not 86.

Outside of Tilman, when you take into account the number of publications and how long they've been publishing, that's 90% of the variation in H-index. National Academy members (red dots) aren't necessarily higher or lower than non-academy members (P = 0.2). You can find individuals 10 points higher than you expect, which is diagnostic of something, but looking at the individuals that are 10 points too low, I don't think one would denigrate their stature because their h-index was 65 not 75. Still, there might be something to the residuals.

The final equation I get is H index = 3.8 + 0.17*#pubs + 0.54*#yearspublishing. r2 = 0.90.

For what it's worth, my h-index is spot on. I've authored or co-authored 57 papers published in 14 years. That predicts an h-index of 21. Mine is 22.

One thing that is interesting here is that the h-index, at least in my discipline and for almost everyone, really doesn't provide much more information than knowing the number of publications and how long they've been publishing.

Another thing is quantifying what it takes to get to an h-index of 45. Just 160 publications in 25 years is all. Or 150 publications in 30 years, if you can wait a bit longer.

For me, that would be 10 papers a year for the next 11 years.

The H index might not necessarily provide more information for most than how many for how long, but what is represented by an H-index of 45 is pretty impressive.

Friday, August 19, 2011

Predictors of publication productivity: h-index

"Hirsch suggested that, for physicists, a value for h of about 10–12 might be a useful guideline for tenure decisions at major research universities. A value of about 18 could mean a full professorship, 15–20 could mean a fellowship in the American Physical Society, and 45 or higher could mean membership in the United States National Academy of Sciences.[3] Little systematic investigation has been made on how academic recognition correlates with h-index over different institutions, nations and fields of study."--Wikipedia.

In some scientific circles, the h-index is the summary figure of productivity. The h index combines the number of publications (h) that have been cited h times. if someone has published 10 papers cited 10 times, their index is 10. 11 papers each cited at least 11 times, the index is 11.

What's interesting to me is that there would be typical values for someone to be considered for the National Academy. Apparently the number is 45--45 papers cited at least 45 times.

One shouldn't get too hung up on metrics of scientific importance--they are too easily skewed and sliding scales are always necessary--but how does one get to 45? Publish a lot of papers? Start publishing early? Publish long? Or just write (or co-write) 45 great papers? 

I told myself I'd only spend 20 minutes on this, so I'll be brief.

I spent 20 minutes looking up h-index values for selected Academy members plus a few others and some early-career scientists (a few friends). In addition to h index, I calculated how long they had published, the number of papers published, and the most cited paper.

This is by no way scientific. Values can be off, etc.

Most of the national academy members were above 45. 

Of the three predictors, the best predictor of h index was number of publications. 

More work would probably blow this relationship apart, but one key take-home point would be to keep publishing, not worrying as much about the golden publication that'll be cited 1000 times. 

Back to real work....

Thursday, August 18, 2011

Leaf architecture and physiological drought tolerance

Patterns of physiological drought tolerance and leaf venation architecture among 10 woody species.

Quick note on a new paper.

Scoffoni et al. determined the physiological drought tolerance and architecture of 10 woody species. The authors test key components of leaf venation architecture to understand the underlying leaf structural mechanisms for drought tolerance. Most work on drought tolerance focuses on stems and highlight xylem geometries, but the authors show that the density of veins in a leaf are the best correlate with its physiological tolerance of drought. High vein density provides insurance against embolism and allows water to continue to be supplied to areas adjacent to veins that have experienced embolisms that necessarily accompany low water potentials. 

The authors highlight the need to separate leaf size and vein density, which were correlated in the study. But, the research raises an interesting question as to whether the need for higher vein densities serves as a constraint on leaf size and ultimately contributes to one of the major biogeographic patterns of plant form.

I also think their figure, shown above, is pretty stunning. 

Scoffoni, C., M. Rawls, A. McKown, H. Cochard, and L. Sack. 2011. Decline of leaf hydraulic conductance with dehydration: relationship to leaf size and venation architecture. Plant Physiology 156:832-843.

Tuesday, August 2, 2011

Evolution of drought tolerance

Phylogenetic tree of 165 grasses. Size is bubble is proportional to physiological drought tolerance (big bubble = lower psi-crit).

We know a bit about the ancestor of Poaceae. All the main defining characters of grasses like the parallel venation, the monocotyledon, and the distinctive grass flowers, were present in the ancestral grass. What did the first grassland look like? What about it's ecology? Did grasses start in the shade and come out in the open? Were they from wet soils and evolved to inhabit the dry? 

We don't have a time machine, but we do have the ability to assemble the phylogentic relationships among grasses and infer origins. Steve Kembel helped out and took Erika Edwards phylogeny from her PNAS paper and arrayed physiological drought tolerance data from 165 species from our experiment that matched with her phylogeny.

The first thing that pops out is there is no phylogenetic signal to the data. Drought tolerance pops up throughout the phylogeny. If true--and our dataset is by no means definitive yet--then drought tolerance might be evolutionary labile. It might not take that many mutations to confer physiological drought tolerance.

But what about the ancestral trait? Was the mother of all grasses physiologically drought tolerant? That specific analysis has yet to be run, but likely not. Most of the modern grasses are not terribly drought tolerant and the most parsimonious explanation for that--as I understand it--is that it is more likely that the relatively small fraction of grasses that are super-drought tolerant hold the derived trait.

As they say, watch this space. We're going to try to prove ourselves wrong in the meantime.

Sunday, July 31, 2011

Streams don't run from dry soils

Konza streamflow and precipitation as a function of soil moisture at 25 cm

The fraction of precipitation retained by soil is a major source of variation in soil water availability to plants. For a given site, much of the variation that we see in this is associated with the pattern of precipitation, external disturbances on vegetation not withstanding. Precipitation pattern is hard to quantify in an ecologically meaningful way, though. A large, intense rainfall event might be lost to the stream if soils are saturated, but if soils are dry might be retained completely. Yet, heavy rain on dry soils might also be associated with heavy runoff if the rain falls faster than the soil can absorb it. You can occasionally see it on your front lawn, but flow paths are pretty short there compared to an intact grassland. Then again, rivers do flood in deserts.

There has been a lot of uncertainty at Konza on this, so I dug into the data to test it. I used the biweekly soil moisture data and matched it up with precipitation and streamflow during April-July (day 105-214 from our critical precipitation periods). 27 years of data here.

First cut analysis shows high precipitation falling a range of soils, but high flows in the major stream draining Konza only when soils are wet. Really no cases of high flows off dry soils.

The data aren't perfect. Soil moisture is only taken biweekly, and I used the interpolated soil moisture for each day rather than actual or the previous soil moisture. We really need daily data on this and that doesn't exist. 

Upshot? Plants get access to all the precipitation that falls when soils are dry, but can lose a significant amount when soils are wet. Losing water from wet soils might not impact plants immediately, but likely does later as the soils dry out.

Turns out we have pretty good evidence of this. More on that later.

Heat waves and drought: it's all in the timing

Distribution from 1984-2010 of (a) mean daily maximum temperatures averaged over 15-d intervals and (b) soil moisture at 25 cm taken approximately every 15 days. Also shown (c) is the sensitivity to grass aboveground net primary productivity (ANPPG) to variation in drought and heat waves assessed every 15 d in 5-d increments. The critical climate period for drought (day of year 105-214) is shown in blue and for heat waves (day of year 190-214) is shown in red.
July in 2011 has been hot. And dry. Supposedly it's suppose to be like this more often in the future as future climates are likely to include more frequent droughts and heat waves. 

It's generally assumed that in most grasslands these events reduce grass production, yet their effects have been viewed somewhat monolithically. When it comes to forecasting the consequences of future climate variability, droughts and heat waves in early-, mid-, or late-summer are not viewed very differently. Absence of evidence is not necessarily evidence of absence though. 

The Konza LTER has built up datasets over the past 25 years that can really test this, though.

27 years of annual productivity
27 years of daily weather
27 years of daily stream discharge
27 years of biweekly soil moisture
17 years of biweekly productivity
11 years of remotely-sensed NDVI

I'll write about some of the datasets another time, but if one examines the annual productivity data and the climate data together with the critical climate period approach, it is clear that the timing of climate variability is just as important--if not more--than the magnitude.

First, grass productivity only responds to drought (or the converse precipitation) during part of the growing season (Apr 10-Aug 2). Drought in August doesn't reduce primary productivity. 

And heat waves? They only reduce productivity during a 25-d window. Jul 10 - Aug 2. Heat waves in August, no less June, just have no impact on productivity. 

We can use these data to come up with new relationships between productivity and climate variability.

A couple of lessons can be learned here, but the most striking is that droughts and heat waves in August just don't affect grass production. It's not that grasses aren't growing then. About 10% of the production happens then and in some years it can be as high as a third of the mean annual productivity. Yet, growth during that time is not tied to climate then.

It's hard to explain why this is so, but the practical consequences are clear. If droughts or heat waves are more likely to happen in August, it doesn't matter for the amount of grass we have. We've shown elsewhere it still impacts the bison, most likely because they cue in on grass quality than quantity. But ANPP is insensitive. If we  want to predict future productivity well, they we better know timing as well as magnitude.

**On a side note, the results are really the highest expression of what the LTER approach can accomplish. I think long-term datasets have fallen out of fashion in the ecological community. When was the last time Science or Nature published a paper that centered on a long time-series from an LTER site. Compared to experiments, models, and cross-site synthesis, long time series seems like a short leg of the table these days. No one has ever set up an experiment to test what natural variability has shown us about the timing of variability.

Monday, July 18, 2011

Advancing plant functional trait science

I struggle at times to understand why we haven’t made much progress in understanding plant functional traits over the past ten years.

As has been well chronicled for over a century, plant functional traits are keys to understanding the evolution of plants, predicting ecosystem response to global change, and interpreting the distribution of species. None of the importance of plant functional traits has changed any time recently.

I would never argue that there has been no progress. For example, Wright et al.’s 2004 Nature paper on the worldwide leaf economic spectrum certainly is a landmark synthesis, but it was largely confirmatory from Reich’s work in the late 90’s. Baraloto’s recent work on the decoupling of leaf and stem economics is a good study that has the potential to be important. At the very least, advances have been sporadic and incremental.

Still, it just doesn’t feel like we’ve learned much in the past ten years about traits.

Regardless of how much advance there has (or hasn’t) been over the past 10 years, why hasn’t there been more?

In some ways I feel like there are a number of Catch-22 chicken-eggs involved in trait research. This isn’t an exhaustive list, but ones that seem to stand out.
  • Funding agencies do not fund trait work. Major screening projects just are not funded. Most of the funding has been into syntheses of extant data while new data has largely come from side projects and student work.
  • Pot-phobia. I’ve talked about the “pot effect” before and no one would deny that plants can sense their environment. Yet, proposing to grow plants in pots inevitably generates criticism. For example, one proposal review recently included the criticism “The plan to compare plants grown in small pots in growth chambers is questionable, since small pot effects will likely cause artifacts”. The word ‘artifact’ is a dismissively loaded term here. Besides, there is never criticism for the “field effect”—the artifact of growing small plants in an unconstrained soil volume with excess resources. Put briefly, intraspecific variation and plasticity is a bugaboo that can kill broader questions.
  • No new conceptual advances to test. There are still exciting untested hypotheses, but there is the perception that the discipline is a bit dead intellectually. CSR has never been modernized while LHS is just three orthogonal traits. Not much new seems to have taken its place. The lack of a exciting toe-hold here hurts.
  • Phylogenies are incomplete. It’s hard to describe what a drag on progress this is. Without a robust phylogeny, species and traits cannot be compared evolutionarily. For example, it’s hard to do congeneric comparisons when it can’t be agreed that species belong in the same genera. And to require ecologists to generate phylogenies is an unnecessary requirement that doesn’t promote long-term growth.
  • Post-SLA research in a SLA paradigm. The leaf economic spectrum is a great advance, but the common perception to many is that SLA is the central trait of plants. Here’s one comment we received recently on a proposal: “It was odd not to see conventional traits like SLA… included in this work”, even though we had proposed to measure the components of SLA: leaf thickness and tissue density. Put briefly, there is too much uncertainty on whether SLA is a central trait that structures plant evolution and ecology, or whether SLA should R.I.P. for a new generation of metrics.
  • The decline of traditional physiological ecology. This one is unquantifiable, but the central importance of physiological ecology to ecology has been diluted. The rise of model organisms and ecosystem ecology/global change biology has at the very least diluted the middle ground that was plant physiological ecology, instead of strengthened it as a discipline. I think there’s been a loss of the perspective that comes from being at the nexus of plant evolution, biogeography, and ecosystem function.

So what to do? I don’t have clear answers here. This post is just a scratchpad for me.  A couple thoughts come to mind.

  • We can’t always wait on phylogenies. If a phylogeny doesn’t exist, it is not helpful to insist that ecologists create one or that we wait. Some aspects of the work might later get revised, but functional trait work can be done in advance of the phylogenies. Especially considering how often phylogenies get revised.
  • We need model species sets. The rise of model organisms—and the resources devoted to their study—has  been quite amazing. Model organisms in and of themselves do not help us understand plant functional traits too much. They aren’t inherently comparative. I think we need model species sets to complement model organisms. For a broad clade, we need to identify a reasonable number of species that represents a broad set of evolutionary and ecological contrasts. This set then needs to be examined by multiple researchers, just like with model species.
  • The pot effect needs to become irrelevant. We will always need to grow plants in containers. We need clear understanding of how containers affect genetic expression and plant functional traits. Direct research is required here.
  • We need better theories. All disciplines need buzz. Plant functional trait research doesn’t have it. It needs it.
  • We need to measure old traits more, but we also need to develop new traits. SLA and rooting depth isn’t enough to help us understand how plants have been shaped and respond to everything from drought to herbivores.
  • We need to encourage breadth in our science. Plants have been shaped and respond to a multitude of environmental factors. You can’t describe an elephant by grabbing its tail, nor by having a number of scientists grabbing individual parts. Some need to try and feel the whole and understand how the parts come together.

Sunday, July 3, 2011

Grasses of the World IV--Taxonomic differences

Relationships between leaf width and physiological drought potential for six genera of grass.

No one know exactly what the ancestral grass looked like or the environments it inhabited. But one could imagine a bright, open wet environment with a narrow leaved bunch grass or weakly rhizomatous grass inhabiting it.  Some tens of millions of years later the BEP and PACMAD clades would have diverged and the major radiations of grasses still a long way off. 

But what were the forces that drove the radiations. Aridity is often cited as one. Fire another. Grazers still a third. But this might be somewhat of a skewed, biased perspective, since there has been little work to characterize the modern ecology of the whole of grasses.

When we look at the global traitscape of grasses, we saw clear patterns for leaf width and drought tolerance. One can imagine some selective force favoring wide-leaved grasses and drought narrow leaved grasses, until an ecological or physiological tradeoff was reached.

But what does the pattern of radiations for individual clades look like?

If I map the distribution of 6 genera in traitspace, clear unique patterns show up. The genus Panicum, for example, has species with wide and narrow leaves, but none that are very drought tolerant. In contrast, Festuca species all have leaves that are narrow, but span the full range of drought tolerance.

We still haven't mapped all this onto a phylogenetic tree. That's coming. But the value of screening programs like this are pretty clear for understanding the ecology and evolution of grasses. 

But why the separation among genera? Are individual genera constrained physiologically, or are they constrained evolutionarily by the presence of other species that lead to the apparent differentiations. 

Part of what we still need to do is understand the importance of traits such as leaf width and understand the benefits (and constraints) of narrow and wide leaves.

Traitscape of drought tolerance for Konza

One of the keys to understanding community assembly will be assembling traitscapes for communities and comparing them to global traitscapes. Earlier, I showed how we could assemble a nitrogen traitscape for Konza and compare that to the global distribution to show that the typical Konza species has higher foliar N concentrations and experiences higher N availability than the typical species at the global scale.

We're getting close to being able to do something similar for Konza, but for physiological drought tolerance. We're working to collect all the grass species of Konza and measure their psi-crit in order to compare them to the global distribution. We've only fully measured 28 of Konza's 86 species of grasses, but the patterns so far our interesting.

Part of the power of the traitscape is to understand inter- vs. intra-site importance of environmental variation. For drought, if we expect Konza to be more likely to experience frequent and severe drought than other grasslands of the world, you could expect to see the typical species be more drought tolerant than the global distribution. We can also look at the distribution of drought tolerance at a site and see how that compares to the global range. Means might be different, but if there is high spatial or temporal variability in water availability, a community could encompass a large part of the global range.

Expectations for Konza are a bit uncertain--it's a humid prairie (835 mm y-1 precip), but can experience severe droughts. Within site, there are dry habitats--south facing slopes with thin soils--and wet ones--seeps, riparian areas, and ditches.

The pattern?

So far the global mean psi-crit is -4.8 MPa. Konza? -4.5 MPa.

The global range is -1.4 to <-14 MPa. Konza? -1.8 to -13 MPa.

Here's the pattern of psicrit with leaf width (red = Konza species):

After 28 species, most of the global trait-space is covered. If anything, Konza might be underrepresented in fine-leaved, drought tolerant grasses. I haven't measured Agrostis hyemalis yet, but it's leaves are about 1mm across--we'll see how drought tolerant it is.

I think there's an amazing range of diversity in drought tolerance at a single site. Konza might be an exception, but the diversity in soil moisture availability at a site can be high.

One question that comes up is that if there can be such high diversity at a site, what are the differences in among sites? How important is drought tolerance in differentiating grasslands and contributing to gamma diversity?

Saturday, July 2, 2011

Grasses of the world III--grasses can be incredibly drought tolerant

I've posted that I've been growing up 500 grass species from around the world to look at the geographic and phylogenetic distribution of physiological drought tolerance. Before we learned we were a bit constrained in quantifying the drought tolerance of grasses because we had grasses that could withstand pressures in excess of our previous pressure bomb, which maxed out at 10 MPa (~1450 psi). Jeff Hamel at PMS Instruments sent us one that goes to 14 MPa (~2000 psi). With that, we've rerun some grasses and measured some new ones, while we wait for some others to grow from seed again.

Still, the first results show that there are grasses that are incredibly drought tolerant.

We've now measured physiological drought tolerance (psi-crit) on 398 species. 13 of those were able to conduct water at pressures in excess of -14 MPa. That's more than 3% of the grasses we surveyed.

3% does not seem like a large number, but that number will only go up as we measure the most drought-tolerant species which are regrowing. 5% might not seem that high, but that'd be 500 species of grasses in the world if you extrapolate out. 

How drought tolerant could some of these species be? If you extrapolate out the lower bound of the width-psicrit relationship, we should have some that hit -17 MPa (~2500 psi).

Friday, June 24, 2011

Extreme weather summary

Just saw this today:

It's an interesting summary of extreme weather events globally over the past year.

Another thing I hadn't know about was NOAA's Climate Extreme Index.

For example, here's a graph of extreme summer precipitation events over the past 100 years. 2010 wasn't the most extreme, but pretty close.

Saturday, June 4, 2011

Heat waves

I've been learning a bit about heat waves.

The WMO defines heat waves as a sequence of five straight days when the daily maximum temperature exceeds the average maximum temperature by 5 °C. Heat waves can extend much longer than 5 days and can exceed average maximums by much more than 5°C. Although heat waves are a categorical classification, they are part of continuous variation in climate.

Here at Konza, over the past 25 years, there has been a lot of variation in climate. We haven't had a major drought since 1980 ( One thing I didn't have in my head is when the heat waves come and how hot they can be. With the standard definition of heat waves, heat waves should be equally likely across the year. Yet, if you look at the climate data for Konza, the strongest heat waves happen a bit later in the year than one might think.

I took the climate data for Konza and averaged the maximum temperature for each day in 15-day periods from early July to early September. It turns out that the hottest mean daily temperatures are in late July (not shown), but the strongest heat waves are in late August.

Here's a graph of the min and max mean daily maximum temperatures for 15-day periods from 1984-2010.

Although the hottest mean temperatures are generally at the end of July (not shown), the greatest heat waves come at the end of August. In 2003, high temps averaged 40°C for 2 weeks in the last two weeks of August.

Ecologically, the interesting questions about heat waves become how plants (and animals) respond to heat waves at different times of year. Most C4 grasses are shutting down in early September. One would think that heat waves at that time of year would have much of an effect compared to ones in July or early August.

At some point, we'll have another summer like 1980. Preparedness is an important topic, but also for ecologists. I wonder if we're measuring the right things so that when it comes around we can understand our ecosystems better.

Drought tolerance: grasses of the world II

After 200 species, there still is a boundary between width and drought tolerance, just with a missing corner.

I haven't seen too many reviews of drought tolerance/cavitation resistance of grasses, but it is generally thought that permanent wilting points for most grasses is about -3MPa. It isn't considered that too many plants can resist below -10 MPa. Why -10 MPa? Because the machines to measure water potential don't go below there.

In the past few weeks, I've continued to measure the drought tolerance of grasses from across the world.
As the species have accumulated, the same tradeoff boundary observed earlier appears to hold. Yet, over 10% of the species appear to be able to conduct water at pressures below -10 MPa. For reference, if you could graft any of these species on the top of the tallest redwood, they could still conduct water.

We still need to nail down the actual psi-crits for the species. The problem is that our pressure bomb stops at -10MPa (100 bar).

The good news is that Jeff Hamel at PMS has been kind enough to build one that goes to -14MPa, which should allow us to determine the drought tolerance of the most drought-tolerant grasses. We'll grow up these species again and let them dry down. Hopefully, Jeff won't have to build one that goes below -14 MPa.

Saturday, May 14, 2011

Drought tolerance: grasses of the world

One of the 500 species that are part of the Poa500 project to examine drought tolerance in grasses of the world.
I'm not sure this one is going to work. I believe that if you measure something interesting and have strong contrasts, you should learn something interesting. I've had pretty crazy schemes work out in the past. Hopped on a plane and measured roots on three continents. Had people send me soil from across the US to look at nutrient limitation. Measured foliar 15N for a couple hundred species at Konza. Even looked at spectroscopic assays of 20,000 cow poop samples to infer continental scale patterns of forage quality.

Each time, we learned something interesting by having strong contrasts and measuring something interesting. But to start to understand global patterns of drought tolerance by growing 500 species of grass in the growth chamber in relatively tiny tubes? I'm just not sure this one is going to work. 

Granted, what we're doing right now is just a pilot project and would be easier with the NSF Dimensions of Biodiversity grant funded. But, questions about the evolution and geographic distribution of drought tolerance are just too important not too try. At the heart of it, we just don't understand the traits that are associated with drought tolerance--what does a drought-tolerant plant consistently look like. In what climates are they most likely to be found. Are some lineages more likely to have evolved drought tolerance than others?

To begin to answer the question, USDA sent me seeds for 500 grass species from their seedbanks and I've serially germinated them over the past 2 months. After about a month, we measure a couple of gas exchange and morphological metrics on the leaves and then stop watering. When they stop conducting water (shut their stomata), we measure their water potential, which we call psi-crit.

A little over 100 species have hit their psi-crit so far. Here's probably the most interesting graph so far--drought tolerance (psi-crit) vs. the maximum width of the largest leaf on the plant. 

It seems like you can have narrow leaves on plants that aren't drought tolerant--species like Enneapogon oblongus. You can also have narrow leaves on plants that are drought tolerant--species like Bouteloua repens. You can also have wide leaves on plants that are not drought tolerant--species like Dichanthelium scoparium. But you can't have wide leaves on plants that are drought tolerant. Doesn't exist.

Of course, it doesn't take more than one species to prove something not impossible.

We still have a few species left to measure, of course.