A growing debate over hypervolumes

Do too much fieldwork and a scientific debate can build up without you noticing. I’m wrapping up a summer in the Rockies and have begun to notice the growing interest and controversy over hypervolumes concepts in ecology. The debate has involved my own work, and it is exciting to trace the threads of its origin and current directions.


Hypervolumes have been widely used to describe the Hutchinsonian niches of species – their responses to the environment, via the resources and conditions they depend on. For example the willow shrubs (Salix spp.) in this photo may only be able to grow in locations corresponding to certain combinations of temperature, rainfall, snowpack duration, and nitrogen availability, while the subalpine fir trees (Abies lasiocarpa) in the valley below might require other combinations. Each variable represents an axis, and the combinations used by each species its niche.


Similarly, hypervolumes are also used to describe the functions and traits of species – their morphology and their interactions with the environment. For example the paintbrush (Castilleja rhexifolia x miniata?) flowers could be described by a combination of axes corresponding to height, flower color, photosynthetic rate, and so on, contrasting with values for the daisy (Erigeron glacialis).

Measuring these hypervolumes, whatever the axes, has proven to be of wide interest, with applications from biodiversity conservation, invasion ecology, community assembly, and ecosystem functioning. But there is not yet agreement on the best way to measure them – leading to the present controversy.

The idea of a hypervolume dates back to Hutchinson in 1957 and was originally implemented as a range box that would independently enclose data along each axis. More recent extensions (e.g. Cornwell et al. [2006]) transformed this idea to convex polygons that would minimally enclose the data. In 2014, I worked with Cyrille Violle, Christine Lamanna, and Brian Enquist to extend this idea to multivariate kernel density estimation, an approach that provides a closer ‘wrap’ of the hypervolume to the underlying data (Blonder et al. [2014]), potentially better modeling the true shape of hypervolumes.

Since then, a diversity of approaches have appeared, each with its own philosophical underpinnings and tradeoffs. For example, our hypervolume approach allows the description of arbitrarily complex shapes and is computationally efficient when the number of niche dimensions is large; the tradeoff is that the scientist must specify some additional parameters to control the boundary of the hypervolume.

Swanson et al. (2015) recently published “A new probabilistic method for quantifying n-dimensional ecological niches and niche overlap”. This approach uses multidimensional ellipses to fit the data. It cannot describe complex shapes but if data are thought to be truly rotated ellipses (multivariate normal) then it has excellent performance.

Similarly, Junker et al. (2016), recently published “Dynamic range boxes – a robust nonparametric approach to quantify size and overlap of n-dimensional hypervolumes”. This approach extends range boxes to a quantile-based approach that is computationally fast and should be less sensitive to outliers, although it also only can describe simple shapes (rotated data are potentially problematic as well, though the authors propose an approach to address this). On the other hand, it might have better performance in high dimensions than our approach, at least with default parameter settings.

Alternatively, Carmona et al. (2016) have published “Traits Without Borders: Integrating Functional Diversity Across Scales”, which proposes a fully probabilistic approach to estimating hypervolumes. This approach shares several motivations with our hypervolume approach, but differs primarily in how and when the hypervolume’s boundaries are delineated. It also is implemented via different algorithms.

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We do disagree on several points, and last month had a friendly discussion around these issues in Trends in Ecology and Evolution. You can read my piece (Pushing Past Boundaries for Trait Hypervolumes: A Response to Carmona et al.) and his response (The Density Awakens: A Reply to Blonder) to see the full debate. I reproduce a figure from my piece below, showing the difference between Carmona’s approach for hypervolume overlap on the left and the several approaches for overlap using our approach on the right. You can see that the ability to choose a threshold for overlap on the right (as we propose) yields a range of possible outcomes, which is either beneficial or detrimental depending on your view of hypervolume concepts.

tree figure

Another research group has also just added to this debate. Qiao et al. (2016) just published “A cautionary note on the use of hypervolume kernel density estimators in ecological niche modelling”, which suggests that simpler approaches that proposed by our group or Carmona’s group may be better suited for predicting species’ geographic distributions. They propose that boxes and ellipses are better assumptions for fundamental niches than the complex shapes that kernel density estimation can produce. I agree with this general point, but also think that more complex shape descriptors have important places for describing realized niches and for describing all trait hypervolumes.

To get a better sense of what each of these approach is doing, it can be instructive to look at some data. Here is an example of what each approach does for a simple dataset, with the approximate shape according to each method drawn in red.


In this case all of the methods seem to produce roughly similar results, although ability of each approach to either capture (or remove) complexity in the data is variable. The difference between methods becomes clearer with a more complex and holey dataset seen below.


Here the more complex methods provide a much tighter fit to the data than the simpler methods – but if the reason for holes in the data is actually under-sampling, then potentially the simpler methods are actually better. This example is also illustrated in two dimensions only. Only the methods in the first and third column are computationally feasible in high dimensions.

Is there a ‘right’ method for measuring a hypervolume? I don’t think there is a unique best way to do things. Each of these approaches has certain upsides and downsides, and may be more suitable for certain applications based on the intent of the scientist. For example, our hypervolume approach is probably less suitable for species distribution modeling than the ellipse method, while the converse would be true for assessing overlap in bird morphology.

Try out each of these methods – they all are associated with R packages – and see what works best for your application. In the meantime our group is working on a comparative study of all these methods, and is refining our hypervolume approach in some new ways that I’ll be able to share soon.

It is exciting to see this diversity of approaches, and for the field to engage in active discussion about the assumptions and implications of each. This is exactly the kind of discussion that deepens conceptual understandings and then produces better science.


Rain and renewal

Summer in Gothic has been hot and dry, paralleling warming trends seen globally.


Strong winds have been blowing dust onto every surface, and the biting flies remain.


For two weeks we had no rain at all. Until a few days ago, when the monsoon returned, bringing moisture from the Pacific Ocean, and clouds to the mountains.

cloud making

Three days of rain, thunder, and the magical smell of wet soil were our prize.


The storms brought change to these landscapes. The soil surface rapidly saturated in many places, leading to sheet flow of water. And the subalpine firs (Abies lasiocarpa), many with dry or dead needles, shed most onto the forest floor.


For other species like this sunflower, the rain washed away a thick layer of dust, restoring photosynthetic rates.

dust gone

And for others like this monument plant (Frasera speciosa), were partly blown down, but received much-needed moisture.


The rain has been good for rescuing some plants from drought-induced mortality. This silver lupine (Lupinus argenteus) ramet is now growing well in bare gravel saturated with moisture.


But for others, the rain has come too late. The yellow patch in this photo is a clone of Veratrum tenuipetalum, leaves dead and crisp from the dry period. Its apical meristems have died and it will not grow more this year, though next year will bring another chance to resprout from rooting stock.


I felt deadened by these two weeks of hot and dry conditions. But now the rain has returned, and with it, my joy for working here. There is more life and summer yet to come.


Getting even with the biting flies

flies 1

I spend a few days each week sitting in a meadow waiting for flies to bite me. Not by choice. The reason we are in the meadow is to measure plant thermoregulation with an infrared camera.

flies 2

But the camera, once we set it up, requires very little attention. Every few hours we change the battery, and the rest of the time we sit there to make sure no one steals it or shoots it.

flies 9

Sometimes we make other measurements, but otherwise there is very little to do but sit, and wait for the insects to come.

flies 6

Some are friendly enough.

flies 3

But others, like this snipe fly (Symphoromyia sp. [Rhagionidae]), are not. They swarm our bodies, sit on our datasheets, find our skin, then bite, and draw blood.

flies 5

Every bite causes a painful swelling that lasts for hours and sometimes days.

flies 7

They are surprisingly resistant to being crushed, often flying off after blows that would do in other insects. But they are slow, and most can be killed with a hand. Unfortunately, there seem to be an infinite population of them – no matter how many we kill, more kept coming.

flies 4

I began wondering how many flies there really were. So I started a collection. Every time one landed on me, I tried to kill it. And then I put each of the victims into a plastic bag.

flies 8

By the end of a 15-hour field day I had about a hundred dead flies in a bag. I estimate I was able to kill about a quarter of the ones I tried to hit, and probably ten landed on me for each one I aimed for. That corresponds to about 4000 flies. Far too many.

My fly collection was a small victory against the swelling and the itching, but it helped pass the time on these long days in the field. It made me wonder where all these flies went at night. I looked under all the nearby plants at sunrise and sunset, but didn’t find any flies. Some cursory searching suggests that very little is known about their life cycles – which is fascinating given how abundant they are for a few short weeks each year.

Not a research project I plan to pursue. I think it would be too painful. I’ll stick to collecting flies instead.

The difference a year makes

baldy 18 june 2016

Summer is a risky season in the alpine. Plants can grow only in the limited time after the snow melts, and often die back as soon as the soil becomes too dry or the autumn snows begin again. The timing of snow melt is very unpredictable too. The amount of snow a mountain receives is important, but so too is the amount of dust that settles on it in late winter. This year at my site we had very little snow, but also very little dust. This photo was taken on June 18th by Jacob Heiling, and you can see my research site is still completely covered.

A week later we hiked up to the site to see how things were progressing. Most of the snow was finally gone, but meter-deep patches still remained on the landscape. As the snow contracts in late winter, it picks up gravel on its surface and produces some fascinating geometrical patterns.

last snow

The snow had also damaged my weather station, which I left to over-winter in place. A few of the sensor arms were crushed, either by the weight of the snowpack or through the action of the wind. But the datalogger and sensors were still functional, and I found out the snow only fully melted there on June 25th.

weather station

Despite most of the snow disappearing only a few days prior, the plants had already started growing, with a few Lupinus and Ivesia individuals sending up leaves. The growing season is precious time.

new growth

Now July has come, and we are back to begin intensive monitoring of these plants.


The snow has completely sublimed or melted at the site, and summer is here.

no snow

Last year at this point in July we found hundreds of Lupinus and Senecio seedlings in the permanent plots. But this year things don’t look so good.


Most of the lupines that grew last year failed to produce any above-ground growth, and nearly all of the seedlings are just dead. I counted only three seedlings on a quick walk through the site yesterday.


And many of the other species don’t look very good either – the leaves on this Phacelia are yellowing already. Mortality will be high this year, and I am looking forward to making a full census of the site in another week.

site weather

From a distance, the almost-bare slopes of this mountain seem not to change. But life comes and goes in the alpine. A year does make a difference.

Back to the mountains


How often do an industrial thermal camera and spectroradiometer end up in the hold of a Greyhound bus? The summer has come, and I am back in the Rockies for another summer field season focused on how alpine plant communities respond to climate change. Traveling with heavy research equipment is never easy, but after a full two-day journey by air, bus, and truck, everything is safe and ready for data collection.


The beauty of these mountains makes up for all of the challenges of the work. Every year that I arrive here, I am filled with a sense of joy and wonder for the place. There is still snow covering the high peaks, and the rivers are swollen with snowmelt. But while it may still be late winter up high, the valleys are full of life, with stands of green and white quaking aspen painting the landscape.


My work occurs primarily at high elevation, and one of the first things I did after arriving was go on a hike to scout out the snow line. My long-term research site is a few hundred meters above the snow in this photograph, so I’m lucky to have some extra time to get our equipment and protocols ready before the daily rigors of fieldwork truly begin.


This means getting all of the sensors up and running. I am using an industrial infrared camera to assess microclimate variation in plant communities. The camera can detect the blackbody radiation given off by warm and cold objects, and so determine the temperature of plants – something that may be highly important for growth and survival.


The main challenge is getting the camera in position to monitor the plants. With an international arrival by air I wasn’t able to travel with most of the equipment needed to do this, so the past few days have been filled with trips to hardware and lumber stores, building platforms that can support a heavy camera. But it all works now.


Here is one of the first images I took, with whiter colors corresponding to warmer plant temperatures. It is sharper and more beautiful than I imagined it was going to be, and it reveals a world of thermal ecology that was until now wholly hidden from me. In the coming days we will begin to learn much more about the lives of these plants, and the journey here will begin to yield its rewards.

Waves in the sand

Leaving for fieldwork in a few days – enjoy these videos of standing and traveling waves in a beachside stream. The dynamics look like they are controlled by thresholds reached during the buildup and transport of sand by water.

Squirrel damage


Never underestimate a squirrel. Growing up near the Atlantic coast of North America, I was familiar with the native eastern gray squirrel (Sciurus carolinensis) as a familiar feature of forest and urban environments. It seemed to coexist in both habitats well enough, and I never heard any stories of it causing ecological damage beyond the occasional occupation of a house.


A few weeks ago, I was on a tour of the Forest of Dean in England, led by managers from the government’s Forestry Commission. I knew the eastern gray squirrel was invasive in Europe, displacing the native red squirrel, but was surprised by the level of anger directed at this species by the land managers.

damage 2 1

I learned that it causes dieback of many native species as well. Apparently it strips bark from trees like oak and beech. Because the bark conducts water and sugars to different parts of the trunk, bark loss can easily lead to the death of the whole tree. The downstream consequence is shifts in the dynamics of forest succession and the loss of trees that would otherwise be sold for timber. And there was evidence of these losses throughout the forest.

squirrel damage

For a North American, this was an incredible surprise – to see a species shift so dramatically in its impact in what appeared to be very similar habitat. I don’t know what exactly causes this behavioral shift, and no one else among this group of ecologists seemed to either. Maybe they do actually strip bark in their native range but no one notices, or minds. Regardless, the land managers were certain about the damages caused by these squirrels and the need to control them, and equally surprised to hear that they caused no such problems in North America.

This experience made me reflect on the difficulty of predicting how species interactions will change in novel climates and biotic contexts. And it gave me a new respect for this species. The eastern gray squirrel is full of surprises.


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