Yukon field work: Arachnids, landscapes, and the inspiring North

It’s a dream for an arthropod ecologist: a dramatic biome transition from boreal forest to subarctic tundra, a beringian landscape, and diverse and abundant insects and spiders. I have just returned from field work along the Yukon’s Dempster Highway, Canada’s only road to cross the Arctic circle. And again, I was not disappointed!

A stretch of the Dempster Highway

A stretch of the Dempster Highway

This year’s expedition was focused on three projects:

1) Tiny, wonderful arachnids:

On this trip, I continued to document the distribution of an arctic Pseudoscorpion, Wyochernes asiaticus. This is a beringian arachnid, known from the old world, and known in North America from almost exclusively unglaciated parts of the Yukon and Alaska. Like wooly mammoths and giant short-faced bears, these tiny arachnids roamed North America while the rest of the top half of the continent was buried under ice. But unlike the mammoths and giant short-faced bears, the Arctic Pseudoscorpion is not extinct! It’s a relict of the past, thriving today under rocks near beringian rivers and streams. I have been working on this species for many years (and a life history paper about this arachnid will appear in the Canadian Field-Naturalist sometime this month), and each time I visit the Yukon, I leave with more questions, and more specimens. This time, I collected some animals to hopefully work on their population genetics: I am curious about the relatedness among the populations from different watersheds along the Dempster Highway (by the way, I am seeking collaborators [phylogeographers!] for this work… If interested, let me know!)

The Arctic pseudoscorpion, Wyochernes asiaticus

The Arctic pseudoscorpion, Wyochernes asiaticus

2) Northern food webs:

I have left my PhD student Shaun Turney up in the Yukon (along with his field assistant) where he is working on characterizing the arthropod-based food webs along the latitudinal gradient of the Dempster Highway. Past research has given some hints that northern food webs may be atypical, but to fully test this we decided to characterize the entire fauna from 1 x 1 m patches of the tundra. This involved placing tents over the tundra, and Shaun collected critters within those tents, and even “vacuumed” the tundra within the square metre. Shaun started this work near the stunning Richardson mountains above the arctic circle, and over the month of July, will repeat the sampling at different locations along the Dempster Highway.

Shaun Turney, vacuuming the Tundra.

Shaun Turney, vacuuming the Tundra.

3) Thermal biology of wolf spiders

Colleagues from Western University joined me in the Yukon to start some projects related to the thermal biology of the extremely abundant Pardosa wolf spiders which inhabit the tundra. There are several species that occur along the Dempster Highway, and when the weather is good, it’s quite possible to collect hundreds of individuals over the span of several hours. Past work has suggested the density of these spiders is about 0.5 per square metre, and those past estimates certainly seemed accurate on this trip also! The spiders will be taken back to their lab, and I am eager to find out how northern Pardosa may be adapted to Yukon conditions.

Searching for wolf spiders on the Tundra

Searching for wolf spiders on the Tundra

All the sciency parts of our field work were exciting and gratifying, but there are other reasons why the Yukon is special*: it is a breathtakingly beautiful place. From stubby black spruce trees to tufts of tundra-dwelling cotton grass, every turn of the highway or footstep over a hummock is a treat. It’s not all easy (hordes of mosquitoes at some of the campgrounds, or being driven off the tundra by cold rains and strong winds), but it is all inspiring.

The lines between science and passion are blurred on the tundra, and that is a good thing. Searching for spiders is work that is fun; seeing a northern shrike or watching two lonely caribou dart up a river valley is fun that comes with the field work. I am immensely grateful for being able to hike under midnight sun, and be a northern researcher during the day. I am delighted to be able to discover some of hidden secrets of the Yukon.

The northern landscape, near the Yukon-Northwest Territory border.

The northern landscape, near the Yukon-Northwest Territory border.

For more photos of the recent trip, check out my Flickr page.

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* my colleague Terry Wheeler shares a passion for the Yukon – here is his post which outlines why he keeps returning to the region.

Beetles from the North

I’m super-excited to announce new research from the lab, published yesterday with lead author Dr. Crystal Ernst.

Crystal’s paper focused on taxonomic and functional diversity of beetles across 12 sites in northern Canada, ranging from Labrador to the Yukon Territory, and from the bottom of James Bay all the way up to the tip of Ellesmere Island. This work is result of the Northern Biodiversity Program: a multi-institutional collaborative project about the ecological structure of northern Arthropods.

Crystal Ernst, on the tundra.

Crystal Ernst, on the tundra.

The paper was titled “Drivers and Patterns of Ground-Dwelling Beetle Biodiversity across Northern Canada” and in this research Crystal sorted and identified over 9,000 beetles from 464 species, and she classified the species by their functional ecology to assess how functional diversity may vary across the large spatial scale of this project. Instead of re-writing a summary here, I thought to use this blog post as an opportunity to reflect on what I see as the critical findings from this work, and why this is a paper that I’m incredible proud to be a part of.

  • To me, one of the more interesting findings of this work was that the functional diversity of beetles varied by latitude: although beetles do many things (e.g., herbivore, decomposers, carnivores), it doesn’t seem like all these functions happen at all latitudes. For example, although we document an impressive number of carnivores at all the sites, they are relatively more common in the more northern locations. This is a bit peculiar, and suggests that food-webs involving arthropods vary in some important ways depending on the biome. We also document that temperature is a major explanatory variable when considering functional diversity, which raises the important question about potential effects due to climate change. Indeed, should temperatures change in the north, this may affect the functional ecology of beetles, which in turn could affect other parts of the system.

 

Figure 1 from the paper: Fig 1. Map of the 12 study locations (North Pole Azimuthal projection), showing the spatial distribution of functional groups. These were pooled into trophic groups, and the pie charts show the proportion of the total site biomass represented by each trophic group

Figure 1 from the paper: Fig 1. Map of the 12 study locations, showing the spatial distribution of functional groups. These were pooled into trophic groups, and the pie charts show the proportion of the total site biomass represented by each trophic group

  • The research generally supported the well-known pattern in biogeography about how species richness decreases at more northern latitudes. When looking at which environmental variable may explain this pattern, temperature again came out on top. In other words, what beetles are found where is in part due to the temperatures in that region. Climate change scenarios therefore have significant potential effects on beetles in the north: beetles, like most other arthropods, are tightly linked to temperature. Even small changes in temperatures in the north may have big consequences for beetles.
  • One of the other big findings, to me, was the fundamental value of species-level data for an important taxa, across vast areas of Canada. Crystal recorded new Territorial and Provincial records for 15 beetle species, increasing knowledge about northern biodiversity. I’m also pleased that the data are fully available on-line, via Canadensys, so other researchers can access the information, re-analyze data, and benefit from and build upon this work.
  • The Arctic is special: it is a vast, cold, treeless landscape, with blankets of tundra, and permafrost underfoot. But it’s also special for beetles. After Crystal analyzed the community-level beetle data, using ordination methods, it became apparent that assemblages from the Arctic Islands of Canada were distinct from the sub-Arctic and north-Boreal sites. From a conservation perspective this is quite important. To some, the Arctic may come across as a big, ‘life-less’ region, with the odd polar bear roaming about, but in reality it hosts thousands of species, including hundreds of beetle species, and that beetle community is very different from what we find in other parts of North America. Special things deserve recognition and protection.
  • Every journalist I talked to has asked “Why beetles?” This is an easy one to answer: they fill virtually all roles in ecosystems, they are diverse, they are of interest to many people, and they are beautiful. The latter point is an important one, as it is important to capture curiosity and fascination about arthropods.

 

Carabus vietinghoffi. Photo by Henri Goulet.

A northern beetle: Carabus vietinghoffi. Photo by Henri Goulet.

In sum, this was a terrific project to be involved with, and our lab (and our collaborators) are thrilled that the efforts from the Northern Biodiversity program are showing up in the literature (for more examples, check out this, or this).

And rest assured, there’s more to come…

Earthworms at the Morgan Arboretum

This is a post written by undergraduate student Jessica Turgeon – she’s finishing up a project about earthworms.

When I was a child, you could always find me either in a tree or in the dirt. I liked to follow the ants up into the trees and back down again, where I would switch over to digging for earthworms. I loved the feeling of soil between my hands and thinking to myself that these little worms were responsible for making the soil the way it is. I now know that the process is a bit more complex than this but overall, five year old me was almost right.

JessicaI spent my whole life loving nature, especially those living in it. By high school I became a strong advocate for environmental protection, even helping a teacher create a bylaw in my municipality to stop parents from idling in front of elementary schools. This experience truly opened my eyes to the will power and determination this generation has when it comes to changing old mentalities about the environment.

When choosing a university to go to, there was no doubt in my mind whether I should apply to Environmental Biology at the Macdonald campus of McGill or not. This program combines both of my passions: nature and its diversity and environmental management. I’ve since embarked on an amazing journey that has shaped me as a person.

Being around so many naturalists rekindled my love for earthworms, so much so that I decided that I wanted to conduct a research project about them. With the help of Chris Buddle (McGill) and NSERC USRA, I decided to take on a project detailing their biodiversity at the Morgan Arboretum, a nearby forest.

Earthworms can greatly affect Southern Quebec soils because all of the species found here are invasive1. Forests have evolved without the help of earthworms, meaning that earthworm burrowing action is somewhat of a new experience for the trees1. The worms break up and mix the soil when they crawl, leaving the soil readily susceptible to erosion2. While earthworms are prized by gardeners as natural tillers, this can have drastic effects on hardwood forests2.

It was important to me to find out where certain earthworms were in the Morgan Arboretum and why they were there. Soils vary in their composition and properties, meaning that some are more suitable for earthworms than others. The goal of my project was to analyze three different soil types (sandy, clay, loam) with regard to earthworm species. I did so by sampling in the three soils and by collecting and analysing the soil using basic soil analyses.

I found no earthworms in the sandy soil over the course of the sampling period, strongly suggesting that no earthworms inhabit sandy soils. Sandy soils are too rough and painful for earthworms to crawl through, therefore they are actively avoided. The clay and loam soils had much higher numbers of individuals, with 9 species each. After statistical testing, it was concluded that there is no significant difference between the two soils and it could be said that they are similar in biodiversity. In addition, a strong correlation between particle density (how dense the soil is) and earthworm abundance was found. As particle density increases, to a certain extent, so does abundance.

Earthworm Sampling

To conclude, my data suggests that the clay and loam soils in the Morgan Arboretum are similar in biodiversity, both supporting an equally diverse number of earthworm species. However, the sandy soil does not contain any earthworms, suggesting that this type of soil is incapable of supporting earthworm activities. This is interesting information for soil management, since, in terms of earthworm abundance and biodiversity, clay and loam soils are similar.

Earthworms are essential ecosystem engineers that change the soil to better suit their lifestyle and this is why they are often studied. Hopefully my story has encouraged readers to respect earthworms a bit more; after all, they do much more than be an excellent fish bait!

 

[1]        Cameron, E. K., Zabrodski, M. W., Karst, J., & Bayne, E. M. (2012). Non-native earthworm influences on ectomycorrhizal colonization and growth of white spruce. Ecoscience, 19(1), 29-37.

[2]        Jouquet, P., Dauber, J., Lagerlöf, J., Lavelle, P., & Lepage, M. (2006). Soil invertebrates as ecosystem engineers: intended and accidental effects on soil and feedback loops. Applied Soil Ecology,  32(2), 153-164.

 

An ode to graduate students

Last week I saw two of my graduate students successfully defend their PhDs. This is wonderful and exciting, and I am delighted that they are both moving on to post-doctoral research positions in other places. I am also saddened by their departures: seeing good students leave the lab creates a vacuum. This has caused me to reflect about the effect graduate students have on their supervisors:

I write, teach, research.

I see classrooms, computers, forests and fields.

I use keyboards, iPads, PowerPoint, and pipettes.

I publish or perish.

LOIs, RFPs, IFs, and h-factors.

Grants, emails, to-do lists and budgets.

Learning?

Always.

Literature and libraries can start the process,

But books and blogs barely break the silence.

It’s the tangible human that makes the difference.

My colleagues, my friends:

You are the Academy.

Do you have the answers?

How to avoid wandering alone in ivory towers?

How to slow the withering on tenured vines?

How to grasp frail tendrils of discovery?

How to find that perfect chorus of voices, words, arguments and insights?

Search again.

Find hope and optimism in our laboratories.

Open the door to the greatest discovery of all:

It’s their keen intellect, smiles, kind words or questions.

It’s crafted by their company.

Caffeine-fuelled conversations critique, criticize, challenge.

(Coffee is never bitter with graduate students)

Embracing curiosity, creativity and collaboration.

Wrangling words together: perform, propose, predict.

Execute, explain, engage.

Fieldwork, funding, fellowship.

Null hypothesis, clear objectives, conceptual frameworks.

Significance and broader impact,

Contributions to knowledge.

Contributions for humanity.

I hope I did enough; I wish for more.

Fleeting moments are now warm memories:

Catching spiders on the tundra, or caterpillars in the canopy.

Thank you, students: you teach me.

We move beyond metrics and money.

We write, we study, we learn.

We discover.

We grow.

Crystal Ernst successfully defended her PhD on 23 Feb.

Crystal Ernst successfully defended her PhD on 23 Feb.

Dorothy Maguire (middle) successfully defended her PhD on 27

Dorothy Maguire (middle) successfully defended her PhD on 27 Feb. Elena Bennett was Dorothy’s co-supervisor.

A naturalist and his moquitoes

This is another in the “meet the lab” series – here’s a feature by MSc student Chris Cloutier:

I can’t remember a time when I wasn’t fascinated by the world of creepy crawly things. For as long as I have been able to grasp and crawl I have been collecting and observing insects and spiders. Although my mother wasn’t always fond of the critters I would trek through the house, my parents were very supportive of my curiosities and did their best to nurture my interests. As a family we would go camping and fishing often, introducing me to the world outside of our backyard and ultimately landing me where I am today.
My passion for studying insects began many years ago with my first entomology course in CEGEP. After completion of that program I enrolled at Macdonald campus of McGill University. Before I even started my first semester I got my first real taste of applied entomology, when Chris Buddle hired me for several months during the summer to be his field and lab technician. Let’s just say that from that point onward I was hooked.

While studying at Mac I really started to discover where my interests were in this very diverse field. I was intrigued with the ecology and natural history of insects and the amazing things that they do. I really enjoyed learning about insect-human interaction, and for some reason I was very interested in disease transmission and parasitism and the amazing enzootic pathways they can take.

Chris Cloutier: the man, the naturalist, the legend.

Chris Cloutier: the man, the naturalist, the legend.

My Master’s research began in early 2014. I had been working for several years at the Morgan Arboretum, a forested property owned by McGill, when my employer, and now co-supervisor, Dr. Jim Fyles approached me with the idea of performing some graduate research using the Arboretum as a study area. I jumped at the idea of doing this, and we got Chris Buddle on board right away. My thesis will be analysing the temporal variation of mosquito community composition across a habitat gradient which includes suburban areas, fields and various forested sites within the Morgan Arboretum. One of the reasons for this research is the fact that in many suburban and forested areas around Montreal, mosquito densities reach near intolerable levels during the summer months. This, coupled with the increasing number of cases of arbovirus (arthropod-borne viruses) infections, such as West Nile Virus, the importance of understanding where mosquitoes are located, and when, as well as which species are present is becoming more and more important.
Collection of mosquitoes takes place for 24h once a week for the entire frost free period, typically from April to November in Montreal. The traps I use to collect mosquitoes are quite specialized and are designed to capture only females which are seeking a blood meal (the ones that we worry about on our strolls through the woods!). These traps use a combination of LED light and carbon dioxide to attract the insects. The LED lights draw in mosquitoes from quite some distance, and the CO2, produced with the help of a few kilograms of dry ice, draws them ever closer to the trap. Once in range, a tiny fan sucks them into a mesh catch-bag and they are trapped.

Chris in the field, checking a trap.

Chris in the field, checking a trap.

When not out in the field, I spend most of my time with my eyes firmly attached to a microscope, sorting, identifying, and counting mosquitoes. After my first field season, I have collected just over 43,000 mosquitoes representing 9 genera and approximately 28 species. I am now faced with the task of analysing the data and making sense of all those numbers, which in fact has revealed some interesting patterns already. I’m looking forward to heading out next spring to start all over again.

The hard work.

The hard work.

I consider myself to be a “geek of all trades” with interests in everything from birding, to plants, herps and pretty much everything in between. I rarely leave home without my binoculars, and during the summer I almost always carry some vials, an aerial net and several field guides (yes, I often get some strange looks…). I’m also a husband and more recently, a father too. My wife still hates mosquitoes but I feel her coming around slowly, and my daughter doesn’t know it yet, but she will be spending an awful lot of time outdoors with us.
Follow me on twitter @C_Cloutier15 or email me at christopher.cloutier@mail.mcgill.ca if you would like to know more about what I am up to and how things are going with my research.

Under the influence: how insecticides affect jumping spider personalities (Part 2)

This post is written by former PhD student Raphaël Royauté, and is a plain-language summary for our most recent article titled: Under the influence: sublethal exposure to an insecticide affects personality expression in a jumping spider

It’s well known that personalities can shift and change when we are ‘under the influence’ of chemicals, be it drugs or alcohol. As entomologists, we also consider this question for the insects and spiders that live among us: although we assume arthropods can similarly be affected by chemicals in their environment, it’s less clear how these chemicals may affect the personalities of these arthropods. We tested the effects of insecticide residues on the personalities of a jumping spider known to live in apple orchards. We found that individual-based personality shifts occurred when spiders were exposed to sub-lethal doses of an insecticide. This mean that even before we might see ‘population-level’ effects of insecticides on an important predator in agro-ecosystems, individual spiders themselves get, um, sort of messed up when under the influence.

How is this cute jumping sipder affected by insecticides? (photo by C. Ernst, reproduced here with permission)

How is this cute jumping sipder affected by insecticides? (photo by C. Ernst, reproduced here with permission)

Insecticides are often used in agriculture for various reasons, but can have negative effects on the ‘non-target’ fauna living in our agricultural fields. One of the most important challenges in evaluating their toxicity is that these chemicals can persist at low concentration in the environment. These concentrations are unlikely to kill exposed organisms but may substantially alter behaviours. Most of our evidence of the toxicity of insecticides on behaviours comes from studies on pollinators and research has shown decreases in spatial memory and learning capacities.

There remain gaps in our knowledge about how other types of organisms respond to these compounds. Studies on insecticide toxicity may be also limited because they tend to ignore how insecticides shape variation in behaviour. This is important because individuals differ in their behavioural tendencies and may not have the same weight in ecological processes: some individuals are more active, show more aggressiveness or consume more food. Personality traits can also be inter-related and form “behavioural syndromes”: clusters of behavioural traits that are correlated and evolve as a package. If personality traits are interconnected, any insecticide modifying one trait is likely to alter the whole syndrome. We’ve shown previously that behavioural syndromes differed between populations exposed and unexposed to insecticides in the Bronze Jumping Spider, a species common in apple orchards and known to prey on several economically important pests. But those populations could be different for a variety of reasons: for example, perhaps the insecticides affect spider behaviours because there is simply less food available in insecticide-exposed areas for example.

We wanted to test if insecticides could be directly responsible for the shifts in personality and behavioural syndromes we noticed. In other words, when a spider is “under the influence” of insecticides, is it still behaving according to its personality type?

The similarities between insecticides and drugs is fascinating: Both types of compounds target the nervous system, both can affect behaviours and both can kill above a certain lethal dose. In fact caffeine and nicotine evolved as natural plant defenses against insect herbivory and the latter was one of the first insecticides ever used. As crazy as it sounds, the effect of psychoactive drugs has been investigated in spiders in the past! The legend goes that, back in 1948, zoologist H. M. Peters was annoyed by his garden spiders spinning webs at “such ungodly hours” (2 am-5am). He wanted to found a compound that would shift the spinning behaviour to more a “decent” schedule, and he asked pharmacologist Peter N. Witt for help. Witt tried different psychoactive compounds on the spiders, including caffeine, LSD and marijuana but couldn’t produce the desired effect. What he found was in fact much more interesting: each compounds produced a distinct type of “drug web”, altering its shape, size or regularity ! (from Foelix’s “Biology of Spiders”) More recent research has shown that some commonly used insecticides affect web building in the same way drugs do.

We focused on how activity and prey capture capacities were affected by exposure to a widely used insecticide (phosmet) in the Bronze Jumping Spider. We tested activity and prey capture before and after exposure the insecticide and compared the amount of behavioural variation with that of a control group. Doing research in ecology sometimes requires using original equipment. In our case we found that the best way to expose our spiders to the insecticide was to use a hotdog warmer! We applied the insecticide solution on test tubes and used the rotation of the hotdog machine to get a homogeneous surface coated with dry insecticide residues. This allowed us to have a more precise control of the dose that each spider received while simulating field exposure conditions.

Unusual research equipment: hot-dog warmer.

Unusual research equipment: hot-dog warmer. (photo by R. Royaute)

One of our study spiders, in its tube. (Photo by R. Royaute)

One of our study spiders, in its tube. (Photo by R. Royaute)

We did not found any effect of the insecticide on average behaviour between treatments but the ranking of individuals was strongly affected after insecticide exposure. In general spiders exposed to the insecticide were more variable in their behavioural tendencies. This suggests that the effects of insecticides on personality differences may manifest before any effects on the population as a whole are detected, in which case scientists may be frequently underestimating the toxicity of insecticides. Another puzzling result was that males and females did not respond in the same way to insecticide exposure. Males were most affected in the way they explored their environment but their capacity to capture prey remained intact. Females instead showed a decrease in the strength of the activity-prey capture syndrome.

Spiders play an important role in agricultural fields as they help regulate pest outbreaks. By altering personality differences and their syndromes, insecticides may limit spiders’ capacity to provide this important ecosystem service in subtle ways. As usual, this research leads to more questions than answers. At the organism’s level, it is important to understand how long these personality shifts last for. Do these shifts vary depending on how frequently spiders get exposed to insecticide or to what types of insecticides they are exposed to? How do they ultimately affect a spider’s capacity to escape predators, capture prey or reproduce depending on the individual’s personality? At the ecosystem level, prey get exposed to insecticides too, what happens to the predator-prey dynamics when the personality of both prey and predator is affected? How does that translate into biocontrol services? These are all important questions that I hope to contribute to in the future. Stay tuned!

A male bronze jumper (Eris militaris). Photo by C. Ernst, reproduced here with permission.

A male bronze jumper (Eris militaris). Photo by C. Ernst, reproduced here with permission.

References:

Royauté, R., CM Buddle & C. Vincent: Under the influence: sublethal exposure to an insecticide affects personality expression in a jumping spider. Functional Ecology. . http://dx.doi.org/10.1111/1365-2435.12413

Godfray, H.C.J., T. Blacquiere, L.M. Field, R.S.Hails, G. Petrokofsky, S.G. Potts, N.E. Raine, A.J. Vanbergen & A.R. McLean. 2014. A restatement of the natural science evidence base concerning neonicotinoid insecticides and insect pollinators. Proc. R. Soc. B 281: 40558 http://dx.doi.org/10.1098/rspb.2014.0558

Royaute, R., C.M. Buddle & C. Vincent. 2014. Interpopulation Variations in Behavioral Syndromes of a Jumping Spider from Insecticide-Treated and Insecticide-Free Orchards. Ethology. 120, 127-139. http://dx.doi.org/10.1111/eth.12185

Nathanson, J.A. 1984. Caffeine and related methylxanthines: possible naturally occurring pesticides. Science. 226, 184-187. http://dx.doi.org/10.1126/science.6207592

Rainer F. Foelix (2010). Biology of spiders. Oxford University Press. p. 179.

Samu & Vollrath. 1992. Spider orb web as bioassay for pesticide side effects. Entomologia Experimentalis et Applicata. 62, 117-124. http://dx.doi.org/10.1111/j.1570-7458.1992.tb00650.x

Meet Shaun Turney and Fuzzy Cognitive Mapping

This is another in the series of “Meet the arthropod ecology lab“: Meet PhD student Shaun Turney, and a neat project he’s been working on…

I joined the lab in September and I’ve been really enjoying my first months as a PhD student. I haven’t done any field work yet so that means no specimens to ID or field data to crunch. Instead I’ve been occupying my time very happily playing on the computer. I recently released an R package on CRAN for Fuzzy Cognitive Mapping called “FCMapper”, in collaboration with Michael Bachhofer. It is based on FCMapper for Excel, distributed at http://www.fcmappers.net/joomla/, developed by Michael Bachhofer and Martin Wildenberg. Fuzzy Cognitive Mapping is really cool and you should try it out!

Shaun, in the lab, thinking about food-webs.

Shaun, in the lab, thinking about food-webs.

Recently I’ve become interested in graph theory and all that it has to offer to ecology. Anything that can be represented as boxes and arrows (or lines) can be represented as a graph (in the graph theory sense) and can be analyzed using graph theory tools. I LOVE box and arrow diagrams. Like, maybe an inappropriate amount. Any paper that I’ve printed out and read has at least two or three box and arrow diagrams scribbled into the margins. My notebook is filled with box and arrow diagrams from lectures that I’ve attended or random thoughts that have passed through my mind while I’m sitting on the train. Some people think in words, some in pictures, but I think in boxes and arrows. So you can imagine my enthusiasm as I’ve discovered over the past year that there exists a whole body of mathematics that can represent and analyze box and arrow diagrams.

My latest favourite graph theory tool is called Fuzzy Cognitive Mapping. It can be understood by breaking down the term into its component words. A “cognitive map” in this case is when you represent a system as interconnected concepts. Boxes and arrows, in other words. The “fuzzy” part refers to fuzzy logic. Fuzzy logic is logic that deals with approximate rather than exact values. So to make a fuzzy cognitive map, you make a box and arrow diagram and assign approximate values to the arrows (positive vs negative, weak vs strong relationship). The concepts are then allowed to affect each other until they come to an equilibrium. The exciting part is that then you can try out scenarios! For instance, you could fix one (or more!) concept to be a high or low value and see how it affects the rest of the system. In the context of ecology, one use is to explore potential ecosystem management scenarios (ex, http://en.vedur.is/media/loftslag/Kok_JGEC658_2009.pdf).

If Fuzzy Cognitive Mapping sounds interesting to you (and it should!), you can download the package from CRAN. Michael Bachhofer and I plan to create a tutorial in the spring, but until then you are welcome to email me if you can’t figure out how to use the package.

Download here: http://cran.r-project.org/web/packages/FCMapper/

A graphics output for a toy example I was playing with the other day. It is a cognitive map of things which might affect spotted owl abundance. FCMapper uses igraph for visualization. The thickness of the arrows represents the strength of the relationship and the color represents the direction (red=negative, black=positive), as assigned by me. The size of the circles represents the "size" of each concept at equilibrium, as determined using the nochanges.scenario function in FCMapper. Think of the fun maps you could make for your favourite study system!

A graphics output for a toy example I was playing with the other day. It is a cognitive map of things which might affect spotted owl abundance. FCMapper uses igraph for visualization. The thickness of the arrows represents the strength of the relationship and the color represents the direction (red=negative, black=positive), as assigned by me. The size of the circles represents the “size” of each concept at equilibrium, as determined using the nochanges.scenario function in FCMapper. Think of the fun maps you could make for your favourite study system!