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!
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’.
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!
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.
The other winning images can be seen here. Check them out!
I want to share a story about how a new idea can originate in a chance hallway conversation. The story is about ecological niches.
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.
And here’s another version, some weeks later – after I discovered an idea that would form the basis of our final solution.
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.
You might wonder what we scientists are spending your tax money on, and how our work makes a difference. Federal grants from the National Science Foundation specifically require that we, the grant-holders, justify the value of the work in this way. We are evaluated not only on the intellectual merit of our work, but also the broader impacts. NSF just redefined what it means as:
The Broader Impacts criterion encompasses the potential to benefit society and contribute to the achievement of specific, desired societal outcomes.
This mandate exists because of the founding vision for NSF, laid out by Vannevar Bush to Franklin Roosevelt in 1945. In a report called Science: The Endless Frontier, Bush argues that
Science, by itself, provides no panacea for individual, social, and economic ills. It can be effective in the national welfare only as a member of a team, whether the conditions be peace or war. But without scientific progress no amount of achievement in other directions can insure our health, prosperity, and security as a nation in the modern world.
In the past we have devoted much of our best efforts to the application of such knowledge which has been discovered abroad… New impetus must be given to research in our country. Such impetus can come promptly only from the Government. Expenditures for research in the colleges, universities, and research institutes will otherwise not be able to meet the additional demands of increased public need for research.
The modern justification for basic scientific research is therefore simple: it produces societal benefits including national security, health, and employment. While new discoveries do not each (and should not each) create these opportunities, they make possible the practical advances and applications that then affect society.
The key question is then: what is an individual scientist’s obligation to these broader impacts? Many think that the obligation should be minimal, since any time spent there is time not spent on doing research. Broader impacts are sometimes treated as a necessary but bothersome distraction, an afterthought to a serious research proposal.
I think that this viewpoint is wrong, but arises from a common focus on broader impacts as scientific outreach: disseminating research results to the general public or to students, or engaging youth in research opportunities. Many university’s grant-writing guidelines (an example) support this viewpoint.
But is outreach effective? I see three major issues. First, most scientists don’t have training or experience with youth or with teaching, challenging the impact of the activity. Second, the scientist may not have deep or serious connections with populations who are interested in or would benefit from such outreach. This can produce a mismatch between supply and demand: too much supply of knowledge from the scientist, and too little demand from the target population. And third, such outreach can be scattered – short bursts of activity directed at a given target, only to disappear as soon as grant funding ceases. This approach may not produce real benefits even if short-term assessment instruments indicate change in attitudes or knowledge.
Therefore I don’t think the average scientist should be in the business of outreach: it can waste both the time of the scientist and the audience, as well as the funding agency’s money. It is doing something that the educational system should be doing better already.
It is true that such outreach does have other benefits – it provides personal connections between an individual scientist and different populations, potentially exposing them to new concepts and experiences that would be impossible to get otherwise. It provides unique opportunities for people to enter into the research world. It forces the scientist to examine the key communicable parts of their work. And it may have other intangible downstream benefits that are harder to predict or measure. Good outreach achieves these unique goals.
I think there is a better way to use our limited funding for outreach, and maximize the benefit our work creates. Consider the thought experiment: if the goal is to maximize the knowledge and experience of the public (or youth) with regard to scientific careers and progress, would it be more effective to spend this money on the development of programs staffed by trained educators, with consistent funding and relationships with audiences, focused on core concepts, or instead on a scattered matrix of multiple short-term efforts by untrained experts? I think we often do the latter but should prefer the former. This is not to say that every scientist’s individual outreach program is not valuable – simply that anyone proposing one should think very hard about its value and potential impact before moving forward, because good work is hard to accomplish. There are many roads to broader impacts and direct outreach is only one.
I think we should instead built institutions that can pool resources and share in NSF’s societal mandate. We could allow grant-holders to allocate some fraction of each award toward more unified outreach strategies – building larger and longer-term programs that would hire trained educators and build relationships with different populations. I think we could get more for our investment in this way than in the current system where each scientist is left to justify their own work, when in fact we are all working together.
So much changes with a little water. On a recent trip to Death Valley, a fragment of Eliot’s The Waste Land came to mind:
Here is no water but only rock
Rock and no water and the sandy road
The road winding above among the mountains
Which are mountains of rock without water
If there were water we should stop and drink
Amongst the rock one cannot stop or think
Sweat is dry and feet are in the sand
If there were only water amongst the rock
The menace in these lines is the same menace I felt in this desert. I have explored other barren landscapes across North and South America. But this place felt different. Drier, barer, and more malevolent. On these sand dunes, the annual precipitation averages some fifty millimeters per year, and summer daytime temperatures often exceed 50 °C. My Sonoran desert home (near Tucson), in contrast, averages a pleasant 280 millimeters of rain per year, with summer temperatures usually no worse than 40 °C. It’s enough to support small trees, columnar cacti, and a wide diversity of animals.
Death Valley, on the other hand, pushes life to its extremes. Consider this remote valley – the landscape is dominated by a dry lakebed interrupted by an intrusive igneous rock formation, and bordered by more distant peaks almost lacking any soil. It doesn’t appear to be a place that might hold any life.
Yet rain does fall, and snow melts off of distant peaks. It isn’t much, but occasionally the dry lake becomes wet, and small channels form. It’s enough for the occasional shrub to find a tenuous home. An infinitesimal change in elevation, a few extra millimeters of water, and life finds a way.
Yet it would not always have been so – fifteen thousand years ago, during a period of cooler temperatures and extensive glaciation, much of this landscape was covered by year-round lakes formed by snowmelt runoff from nearby mountain ranges. The desert, geologically speaking, is a very recent phenomenon.
It is easy to have a shorter view of this kind of climate change, and of the tenuous threads on which our lives depend. I can journey through this barren landscape in an air-conditioned car, traversing a hundred miles in a single day, and can drink water pumped from alluvial deposits. I can ignore the facts of climate in a way that the plants cannot.
I don’t like it. It makes us blind, and weak. It builds us ecologically insensitive cities that paint an artificial and controlled scene over an unforgiving and dynamic landscape. The desert is replaced by asphalt and houses – mechanisms to control and stabilize our experience of the world.
As an example, our return trip passed through southern Nevada, where the outskirts of Las Vegas continue to expand. Exurban areas of identical homes pave the desert, and are fed by water from the Colorado River. They exist because water is cheap, and is imagined to remain cheap in the future. But the river is a dynamic thing. Reconstructions for the past thousand years of its flow (based on tree rings) have indicated flows averaging much less than what was seen during the 20th century, with a multi-decade drought during the medieval period that dropped flow levels fifteen percent relative to the present. And projections for flow rates for the coming century are projected (based on climate models) to be fifteen to forty-five percent lower than we are accustomed to.
I think we are building cities that will not survive the coming century. We will have to retreat, and play by the true rules of the desert, just as the plants do. Eliot writes,
Who are those hooded hordes swarming
Over endless plains, stumbling in cracked earth
Ringed by the flat horizon only
and I read it as a challenge to us in the American west. So much changes with a little water.
Someone once asked me if my research collaborations abroad were a worthwhile use of time and money. I had just explained a project, which was effectively desk work – the statistical analysis of a large dataset. Why use public money to fly all the way to Denmark and upend a life to do a project that could easily be achieved by email and videoconferencing?
I have been thinking about this question a lot. I just returned to the United States from a long stay in Denmark, for the second time in two years. The experience of having lived and worked in both Aarhus (with Jens-Christian Svenning) and Copenhagen (with Carsten Rahbek) has been very valuable to me, and wholly different from a collaboration built on digital communication.
There are three reasons why this travel was valuable for me, all of which likely generalize to many other scientists.
First, projects are far easier to complete when all the participants are in the same place. Data are easy to exchange, conversations are easy to have, and ideas are easy to communicate. The bandwidth of any given interaction is far higher, in-person, than by email. New ideas are also easier to develop in a shared environment. The atmosphere of being in a place, interacting with a group of smart and interesting people, provides fertile ground for creativity.
Second, travel to a new institution broadens one’s perspectives and approaches to science. In the United States, my home institution is a broad ecology and evolution department, with only limited focus on macroecology, biogeography, and climate change. Both Danish institutions I visited focus on these areas and recruit a wide range of top people to think about these topics. The result is an informal education in a discipline that fascinates me. Moreover, this education comes from a different perspective than I am used to, because different research traditions and approaches have dominated on both sides of the Atlantic. I have a broader appreciation for the history and breadth of the field than I had before.
Third, investment in a research visit is not just investment in projects – it is also investment in people. These research visits has given me a broader network of collaborators and contacts in the ecology world, people who I know and now know me. Future collaborations and interchanges are now much more likely because of these present-day connections.
From a personal standpoint, these visits have also been wonderfully world-expanding – exposure to a new culture, a new language, and a wholly different landscape. A life away from my home country seems very possible and maybe likely. These impacts are harder to measure or communicate to a funding agency, but they are very real.
So at the end of things, on this trip back to Arizona, I think about the money that the US National Science Foundation and the Danish National Research Foundation have invested in my work. Two major projects are nearly finished, and three or four more are well underway thanks to their investment. But the impact of the money is far greater than that, and I hope you can now see why.
Ecology is often criticized for being a weak science, with limited data, few ideas, and little predictive power. As a practicing scientist, I often feel frustrated by our collective inability to make the same dramatic progress as seen in other fields – for example, physics in the earth 20th century, during the quantum mechanical revolution. But a few weeks ago, I held in my hands a manifest declaration of scientific progress.
The object in question was an atlas of the global distribution of plants, published in the early 1800s in Copenhagen. (Plantegeographisk Atlas, af E.F. Schouw)
At that time, systematic exploration of the world’s natural history had just begun to occur. Both North and South America remained largely unexplored by Western scientists, to say nothing of Africa or most of the closed East. Alexander von Humboldt had only returned from his pioneering explorations in the Andes a decade earlier. Until this time, the broad-scale distribution of species had been an uninteresting or unexplored topic. Either no one knew enough about where species were to think the patterns were worthy of explanation, or no one thought the question was relevant, since the Biblical flood narrative provided a simple explanation for the radiation of species from a single point. But evidence began accumulating that not everything lived everywhere, and that some groups of species had complex ranges spanning continents. Coupled with the discovery of fossilized organisms on mountaintops or in inhospitable areas, science was forced to confront the idea that the distribution of life did not have a simple explanation.
This atlas was one of the world’s very first attempts to synthesize knowledge on plants. It is a beautiful work, printed from engravings onto thick paper, with hand-painted maps for each group of species. But its beauty belies its limitations. You can see that the geography of South America is very fuzzy, with mountain ranges drawn in that don’t exist, and with ambiguous cartography of many rivers systems and coastal borders.
Empirical knowledge of plants was simply quite weak at this time. You can see on this global map, most of the Pacific islands are represented simply as being the ‘land of the breadfruit’ – hardly a comprehensive description. This atlas represents something of the birth of ecology and biogeography.
Since then, thousands more botanists have traveled the world, made collections, established taxonomies, and so synthesized knowledge. We are much better informed about the world than we ever have been, and so we are now able to begin to explain global patterns of biodiversity. We now know roughly how many species there are on Earth, and roughly where they live. We have assembled large databases to standardize and share this information. Every day, more scientists are exploring the wild and not-so-wild corners of the planet, and we are progressively getting closer to the truth.
Holding this atlas made me feel proud of the progress we have collectively made. The road forward is long and difficult, but we are certainly further down it than we have ever been before.