New paper: predicting climate from leaf venation networks

cr 2

If you travel from the alpine zone to the lowland tropics, more than just the climate will change. Species composition follows changing environments: there is a reason why a Cyathea tree fern doesn’t live in Colorado but does live in Costa Rica. (Note of course that many millions of years ago, when the earth was warmer, rain forest could be found even in what is now Antarctica!).

What is it about a tree fern that prevents it from living in a cold environment? A central idea in modern ecology is that measuring properties that reflect an individual’s function, performance (and ultimately fitness) can explain this pattern. My main hypothesis has been that leaf venation networks are the key ‘trait’ to measure. Here’s why. Plant growth requires water loss through transpiration in the leaves, and transpiration requires water supply, which is provided by the leaf veins. If there is a preferred growth rate and water loss rate set by the environment, then only certain leaf venation networks should be viable in each environment.


I just published a paper that tests this idea. I had noticed early on that different vein networks were associated with colder and warmer, or wetter and drier environments, as you see above. To see how general these patterns were, I went in search of leaves from a broad range of climates.

First, Dr. Brad Boyle led a botanical expedition on the western slope of Costa Rica. We started in lowland moist forest, as you see below. Access to one field site required hiking past a beautiful beach, and it was very tempting to ditch our equipment and sweaty clothes in favor of a late-afternoon swim.

cr 1

We collected plants all the way up to cloud forest and páramo vegetation, across an elevation gradient of more than 3000 meters.

cr 3

Second, I made collections in the Colorado Rocky Mountains. Here, sites ranged from high desert to subalpine meadow.


My favorite sites were in aspen forest, where Neill Prohaska helped me with tree climbing (aspen bark is very slippery).

co (1)

We found an intriguing pattern – vein density (length of veins per unit area) decreases with elevation, meaning that lowland sites have higher resource fluxes than montane sites. But the slope of the line wasn’t constant: the relationship depended on whether we were in the tropics or not.


I decided to try to explain this pattern based on plant physiology: perhaps the slope difference reflects differences in climate, i.e. growing season temperature, carbon dioxide availability, or intensity of solar radiation. We developed a mathematical model that uses vein density to quantitatively predict these climate variables, based on the idea I wrote about at the beginning of this piece: there is an optimal physiology for a given environment, so that the water supply in a leaf matches the water supply in the environment.

I was surprised by how well it all worked. Below is an observed-predicted plot: we compare observed values of climate to values predicted from measurements of vein density, such that a perfect fit falls on the diagonal.


You can see that we sometimes over-predict or under-predict – but in all cases, the model explains nearly all the variation in the empirical data, with trends in the correct direction. I think this means that the model is capturing some important aspects of reality. The paper’s main contribution is showing that leaf veins provide an important explanation for why species are only found in certain climates around the world.

You can read the paper in New Phytologist (link, or free PDF reprint). It’s been more than three years between conceiving the project, doing the fieldwork, doing the math, and seeing this published. Science isn’t always fast. We certainly had setbacks, and I’ll close by showing you one of them. Visualization of leaf veins requires some chemical work in the lab, and we had a very exciting hotplate malfunction one day. Fortunately everyone’s eyes and fingers survived the accident, and our dataset is just a little bit smaller as a result!


An early summer for the snakes

wrightson 2

The sound of a rattlesnake is unmistakable once you’ve heard it once. But this sound wasn’t on my mind when I almost stepped on one a few weekends ago. I was in the Santa Rita mountains of southern Arizona. The highest peak, Mt. Wrightson, looms 7000 feet above the Tucson basin.

wrightson 3

In late March, mountaintops like these are in the final clutches of winter. Snow patches and ice survive on north-facing slopes, trees have yet to leaf out, and perennial forbs are just beginning to push through the topsoil. It is a quiet and cold landscape – not the place one would expect to see a snake.

wrightson 1

Yet that snake did appear, at 8800′ elevation on a day that couldn’t have been much warmer than 60°F. Despite its kind and persistent rattling I put a footstep just a few inches away from its body before recognizing that sinuous movement and particular shaking sound.

wrightson 4

Here it is – the twin-spotted rattlesnake, Crotalus pricei (identification by Dennis Caldwell). This species is protected in Arizona, and was a first sighting for me.

I was curious about why a snake like this would be out on such a cold day so early in the season, and asked a few herpetologists who know more than me about the subject. Two ideas came up.

First, drought might have pushed this snake out of its hibernation. Limited moisture in the environment can mean slow dehydration – so better to chance a cold and prey-poor environment than face a sure death from lack of water. Second, microclimate variation means that a chilly air temperature might translate to a reasonably warm temperature immediately above rocks exposed to the sun in just the right way. This snake might have been taking advantage of warmer conditions immediately near its home. I like imagining all the fine-scale variation in an environment that we humans have difficulty perceiving.

Ultimately I don’t know what caused this snake and me to cross paths. I paused for a quick photograph, then left the snake to its business, whatever it may have been.

Connecting Children to Science and Place in the Sonoran Desert

(Re-blogged from a piece I wrote for the White House)


My great-grandfather immigrated to the United States from China in 1915, at the age of 11. He soon became the owner of a corner grocery store in Tucson, Arizona, and stayed in the community for decades. Now, almost a century later, I find myself living in this same desert city, honored to share my experience bringing science education to communities in southern Arizona.

I came to the Sonoran Desert for a graduate program in ecology at the University of Arizona, and became captivated by the border region. Tucson itself brings together Native Americans, more recent immigrants, refugees, military families, students, retirees, and everyone else in between. We share an arid landscape situated between the Coronado National Forest, Saguaro National Park, and the Tohono O’Odham Nation. Living here, I saw that our natural areas are not equally accessed or appreciated, especially by the children who are our next generation of conservation leaders.

When I wasn’t studying ecology, I was teaching science at a middle school in the Tucson Unified School District and leading hiking trips for The Sierra Club Foundation’s Inner City Outings program. These experiences showed me many children who could benefit from a deeper sense of place and scientific focus on our environment. Science education can build broader minds, better jobs, and more thoughtful stewards of the land.

ico trip

In late 2011 I proposed creating the Sky School  a science education program that would connect youth to our environment through inquiry-based outdoor science education. With support from the University of Arizona’s College of Science and the Forest Service, we have made that vision a reality. Our home is the summit of Mt. Lemmon, rising 6000’ above the Tucson basin. We’ve transformed a 25-acre observatory into a residential school, with hiking trails providing access to thousands of acres of public land.

We take school groups to our site for a week at a time, where students work in small groups to conduct original research with graduate students and other scientists. For many, a Sky School trip is their first experience outside their neighborhood, their first visit to public land, and their first contact with a real scientist. I know that these experiences can have a transformative effect on a life.

In our first two years we will have served more than six hundred students from seventeen primarily low-income schools. The community response has been overwhelmingly positive. Students have said, “I enjoyed what I was doing so much that I said I want to become a scientist”; “This has opened my eyes to all of the possibilities for myself in the scientific field”; “This is the best field trip I have ever been on.” Teachers agree, saying “To get them outside seeing what they’re studying is so important” and “this immersive, stimulating and engaging program will become a fixture in our school district’s science curriculum.” We are excited to keep growing and bring this experience to more schools in the Southwest.

My passion for science education was sparked by an AmeriCorps service year with the McCall Outdoor Science School. I lived in central Idaho, where I taught environmental science and saw firsthand the positive impact of environmental education. Much of what we are now doing at the Sky School is inspired by my time there. I hope that this chain of inspiration will continue, so that some of the Arizona youth we now serve will find ways to become the scientific and conservation leaders of tomorrow.

Talking about science education at the White House

skyschool out

I was honored yesterday to speak at the White House about my work with the University of Arizona’s Sky School. We are a residential outdoor science school located in the heart of the Coronado National Forest. Our mission is to connect K-12 students to science and environment, and so inspire the next generation of conservation leaders.

The trip east was part of an Obama administration initiative, Champions of Change, intended to highlight people and projects that are making a difference in communities across the country. My work was highlighted along with thirteen other conservationists from around the country, who I feel inspired to have met.

home 1

We were able to share our work with a diverse audience, including Sally Jewell (Secretary of the Interior, seen above, also with Sky School team member Pacifica Sommers) and Rhea Suh (the assistant Secretary of the Interior, seen below). Both photos are by the Department of the Interior. The Sky School model – connecting underserved students with authentic inquiry-based science education in the outdoors – is a replicable one, and I hope that our trip to DC will inspire others. My own inspiration for the Sky School comes from my AmeriCorps service at the McCall Outdoor Science School in central Idaho, where I was a part of a very similar vision.

home 2

You can read more about our work at the Arizona Daily Star as well as at the Corporation for National and Community Service.

New publication: Explorations in integrated science

Is it more effective to learn science through the common progression of disciplinary science classes or instead through an interdisciplinary approach? The University of Arizona has many students with science course requirements and scientific interests who might still not be planning on science careers or degrees. Narrowly focused courses might not be the most effective way to prepare these students for their future lives and careers. A few years back I was involved in teaching an interdisciplinary science course whose aim was to provide a more broadly integrated understanding of science.

The advantages of this approach is a more synthetic understanding of how knowledge is created. But interdisciplinary science is risky, because it can dilute important concepts and substitute superficial understandings and analogies for deep knowledge. When I was given the opportunity to help create an interdisciplinary course by mathematician Joceline Lega, I was skeptical, but more than intrigued enough to participate. The course’s focus was on scaling relationships across the sciences, including chemistry and physics (IS303: course website). I contributed a biologically focused module, discussing the limits to tree height and scaling laws that might provide a physical explanation to patterns seen in the real world. My part of the course involved a mathematical introduction, followed by field measurements of trees to test the ideas proposed. You can see below some of our students measuring the scaling relationship between tree radius and height on the Arizona campus.


A summary of the course, and a discussion of the learning outcomes, can be found in a paper we just had published at the Journal of College Science Teaching. The paper is paywalled but you can get a PDF from my website here.

So were we successful? By scoring student journals, our evaluator Sanlyn Buxner found that the course did not provide measurable changes in conceptual understandings of scientific concepts. But we did also find (through interviews) that many students did develop more understandings of the connections between fields. On the other hand, many students struggled to master the concepts in the class, had lower grades, and did not articulate interdisciplinary understandings.

My personal opinion on the course is that it was not a success, but it was an important first effort at providing a more useful introduction to science for non-scientists. Yet the challenges are large. First, the University of Arizona student population has very diverse educational backgrounds, making it difficult to teach a course like this effectively. Second, the nature of interdisciplinary teaching means inevitable tradeoffs between depth and breadth of coverage. I don’t know if these challenges can actually be solved by a course like the one we taught. But I think the time and money spent on the course were a worthwhile investment, and that we learned enough about trying that might make a second attempt more successful. You can read our JCST publication and decide for yourself!

Eye on the environment

I want to share a few images that recently were selected by the University of Arizona’s Institute of the Environment. This year’s challenge was ‘People in Action, in the Environment’.

mcut 1

The first image is taken at The Nature Conservancy’s Mexican Cut preserve. The site is a glacial cirque at more than 12000′ elevation. While working at the nearby Rocky Mountain Biological Laboratory last June, I climbed to the preserve with a few other researchers. Will Petry took the opportunity to make a watercolor painting, shortly after the sunrise. I think the beauty of places like this inspires us to love landscapes more deeply and to so do better science.

We visited the site before the summer snow had melted. Galena Lake, enclosed within the Mexican Cut, was still filled with ice, as you see below. I went for a swim and lasted no more than half a minute before needing to escape!

mcut 2

The second prize-winning image comes from fieldwork in Peru last May. Here you see Efrain Lopez Choque navigating an instrument into the canopy of the cloud forest. He was working with Allie Shenkin measuring light levels at different heights in the canopy using sensors attached to the metal pole. Navigating this kind of instrument in the forest isn’t easy. I once had an ant fall out of a branch, then sting me in the eye – a few minutes of painful blindness was the only prize for that misadventure.

peru efrain

The other winning images can be seen here. Check them out!

The ecological niche and the n-dimensional hypervolume

I want to share a story about how a new idea can originate in a chance hallway conversation. The story is about ecological niches.

When you think about a niche, you might imagine something like you see here in the city of Samarkand: the Mirza-Uluk-Bek in the Registan (one of the first color photographs).


The ecological niche is something different, but draws on the metaphor of a recessed space that can hold something. The concept was primarily popularized by G.E. Hutchinson in the late 1950s, and used to describe species. For him, a niche is

An area is thus defined, each point of which corresponds to a possible environmental state… an n-dimensional hypervolume is defined, every point in which corresponds to a state of the environment which would permit the species.. to exist indefinitely.

This reasonable concept makes intuitive sense: for some set of variables that are important to species, the niche is the combination of variables in which the species can live. You might imagine that a ‘real’ niche simultaneously depends on many variables. Unfortunately the definition says nothing about how to measure one.

This brings us a few decades forward, to early 2012. One morning I left my desk to get a drink of water in the hallway. I ran into Brian Enquist and Christine Lamanna, who were there talking about ecological niches. They asked me if I knew of any algorithms to find the overlap between two niches. I said I didn’t, but I was sure that the problem was solved, and a quick search would resolve the question. We did that search, and after some hours it became clear that the problem was actually not solved. Conceptual debates over what a niche is had for several decades obscured the issue of how to measure one.

The trouble is that a niche probably has many dimensions, and the mathematics get bad very quickly. Thinking about the geometry of a high-dimensional object is fundamentally different than thinking about a low-dimensional object. We were surprised by how hard the problem seemed, but also that no one had yet solved it. So we set ourselves the challenge of finding a more efficient way to determine the shape and overlap of high-dimensional ecological niches. We decided to do a thresholded kernel density estimation, which amounts to taking a set of observations of all variables, estimating their overall probability density, then slicing through this density to determine the ‘edge’ of the niche. You can see this illustrated in one dimension below.


Finding a computationally fast way to do this was a challenge. Over the next few months, I wrote five or six different algorithms based on different ideas. Most were a complete failure or were computationally too slow to be effective in more than two or three dimensions. Here’s an early version based on range box-intersections.

Screen Shot 2014-02-26 at 10.02.50 PM

And here’s another version, some weeks later – after I discovered an idea that would form the basis of our final solution.

old matlab

The core innovation is that the entire niche space doesn’t have to be sampled. A good algorithm can avoid doing calculations in the vast regions of niche space that are almost surely ‘out’, and focus instead on the regions that might be ‘in’. The tradeoff is that the niche is only defined in a stochastic sense. We only get approximate answers but we can get them quickly, and can easily visualize the shape and volume of an arbitrary complex niche in any number of dimensions.

I was able to get a usable version working in MATLAB, and after another few weeks of work, rewrote all the code in R, a more commonly used statistical programming language. I won’t go into all the details of the underlying mathematics, but will simply say that everything works – and for reasonably sized datasets, answers can be obtained in seconds or minutes.

Here’s an example of what the algorithms can do. Below you are seeing a three-dimensional niche, the functional hypervolume of tree species in the temperate (blue) or tropical biomes (red) of the New World. The overlapped hypervolume is in orange. We are now able to determine exactly what resources and strategies are unique or shared in different parts of the world.


We had a rough time getting the method published – niches are controversial because of their central importance in ecology. But after some discouraging rejections, our paper is now out! Check it out in Global Ecology and Biogeography (PDF version here). The issues around niche concepts and niche measurement are more complex than I have presented in this short blog post, and I encourage you to read the paper for a full exploration of the topic. As for the algorithms, they are freely available as the ‘hypervolume’ package on CRAN and come with documentation and demonstration analyses.

Here’s an example (in R) of how to use the code – just a few lines to analyze and visualize a complex multidimensional dataset.


I hope these algorithms will open up a whole new range of analyses that weren’t possible before. It has been a long road to see our work come out – and all thanks to a lucky hallway conversation, good collaborators, and the stubbornness to believe that some things that look impossible are not.


Get every new post delivered to your Inbox.

Join 34 other followers