Category Archives: Thinking Out Loud

This category is for notes and thoughts that come out of research, observations, natural history, and/or reading — the germ of ideas and future work.

Of What Use is a Torus?

Knitted Tori

Knitted Tori

I have been knitting tori. A torus is a doughnut shape. It has particular geometrical and typological properties that make it quite interesting. For instance, in a video game like Pac Man, the Pac Man exits what looks like a flat plane and re-enters on the opposite side: the left and right or top and bottom portions of the screen are connected. This is the geometry of a torus. Pac Man isn’t in a flat plane but is cruising around on a torus. You just get to see a small portion of this. Pretty cool.

It was even more cool when I found that the torus might be a solution to a statistical problem I have. I am an ant ecologist currently studying the local distribution of the colonies of the Comanche harvester ant, Pogonomyrmex comanche. These ants nest in open prairie surrounded by oak forest and nowhere else. The real, hard boundary of the forest presents a difficulty for determining the spatial pattern of colonies since a colony at the boundary cannot have a near neighbor within the forest. By modeling the prairie area as a torus – so connecting the edges like the Pac Man game – may be an appropriate way to remedy the problem.

The torus is also a form that an attractor (from chaos theory – a set of physical properties to which a system moves) can have in a dynamical system, like ecological systems. So, I became even more enamored of the torus. This is a very useful shape besides being a doughnut, a bagel, or a lifesaver candy.

I have been using the book Making Mathematics with Needlework (by Sara-Marie Belcastro and Carolyn Yackel) to explore mathematics through some of my favorite forms of needlework. So far I have only done knitting projects. I have been learning a lot about knitting (knitted my first sock) and the mathematics. There is a project for knitting a torus. So, of course I took this up.

There are only two stitches that will create a torus. Sounds simple but I found the pattern a bit of a challenge to get into my head since it is so different to be knitting in the round with short rows when you are not making a sock, a hat or a sweater sleeve. After many, many hours of pulling things out and beginning again, I now have 2 finished tori and am about to finish a third. I have learned a lot about knitting and mathematics. Then a friend asked, “what exactly does one do with this item?”

Here is the progression of knitting a torus. Cast stitches on and distribute on 3 double pointed needles, then knit in a round using short rows to make the curved shape. When complete, the torus shell is stuffed and the ends of the tube knitted together.

Here is the progression of knitting a torus. Cast stitches on and distribute on 3 double pointed needles, then knit in a round using short rows to make the curved shape. When complete, the torus shell is stuffed and the ends of the tube knitted together.

So, of what use is a torus? My immediate answer is whatever you want. Your imagination and creativity are the limits. After all, a torus is an awesome shape. But I understand the need of many for some obvious utility (though this strikes me as a refusal to play the game, the intellectual game). So, I’ll humor you for a bit.

A knitted torus is great. It has at least these utilities:

1. The construction of the torus is an exciting way to learn knitting and mathematics. The pattern given does not actually tell you how to knit the torus together. So there is quite a bit of creativity and insight required to complete the project. This is a good project in problem solving.

2. The finished torus is the result of a creative process and rightfully is called fiber art and sculpture. It is beautiful.

3. It is also worth contemplating. What kind of shape is this torus? But also, what is the knitting that makes up the torus (It is an unknot! That this torus is made up of an unknot should trip you out. If it doesn’t you are very naïve.). What are the implications? How might this shape be used? Philosophical, craft, mathematical and other considerations are found in the torus.

4. The torus can be used as a discussion starter, as a paperweight, as bagels or doughnuts for dolls, as a coffee table decoration, etc.

5. The torus can be used to teach or demonstrate the math, to demonstrate how Pac Man moves.

6. It can be another example of the accomplishments of a child. My Dad has my first knitted torus on a table in his living room. I imagine he tells visitors that I knitted it and … whatever comments he might want to make about a torus (he is a theoretical physicist) – he probably likes that he can do this since it evens him up with Mom and her posting photos and drawings (like my molecular drawings of endo- and exo- brevicomin) on the refrigerator.

7. Like most items, you can collect and trade them; you can give one as a gift.

8. A torus can be used as a marker, a game piece, a token.

In the end, a torus is functional, abstract, and beautiful,  in some ways akin to poetry: if you ask what one does with it, you haven’t understood.

Here the Comanche harvester ant (Pogonomyrmex comanche) forages  Pecan Sandies at a bait station in the Fort Worth Nature Center, Fort Worth, Texas

A Consideration of Andersen’s Functional Groups for North American Ant Assemblages

(These thoughts came out of an email exchange with noted myrmecologists Dr. James Trager of the Missouri Botanical Garden and Dr. Terry McGlynn of California State University Dominguez Hill).

I understand the concern that we not naively appropriate Andersen’s functional groups and the taxons that go into them – I think I have been on the verge of doing that. I obviously need to be exposed to more ant species.

My understanding is that Andersen tested dominance of the ants with bait stations and looked for aggressive interactions. Terry McGlynn’s questioning of this — that bait stations are artificial situations and do not reflect real ant behaviors/interactions well —  I think is well placed. I had thought to show that Pogonomyrmex comanche was a dominant ant in her habitat based on several observations but Dr. Walter Tschinkel, who is now on my committee, raised questions about this: what does dominance mean? I think this is a stickier issue than some believe.

For instance, there appears to be a trade-off between foragers who come early to baits and then leave and those who come later but seem to “dominate” the baits once they arrive. Are these later arrivals really dominant? I question this interpretation because of observations I have
made such as the interaction between P. comanche and a foraging grasshopper over a dead grasshopper (I have a  video) in which Comanche dealt with the competition by cutting up the grasshopper and foraging faster only at the last, stinging the offending grasshopper. When I see
Comanche dominate bait stations (photo above), I do not see the ants directly interact.

Here’s a photo of fire ant (Solenopsis sp.) at a food resource (though this was a cookie dropped in a parking lot). The fire ants seem to get to food resources quickly and to “swarm” on them effectively dominating them. I have seen fire ants overwhelm bait stations in the Fort Worth Nature Center in a similar manner. It seems a typical ant behavioral response to a desirable food resource is to dominate it indirectly by quick removal of it to the nest rather than more direct aggressive interactions which are probably more costly.

Fire ants (Solenopsis invicta or xyloni) opportunistically foraging on an Oreo cookie. I have seen this kind of "swarming" behavior on bait stations in the field as well.

Fire ants (Solenopsis invicta or xyloni) opportunistically foraging on an Oreo cookie. I have seen this kind of “swarming” behavior on bait stations in the field as well.

In the nestmate discrimination trials I am currently completing, I do not see Comanche often acting aggressively. I do see some gaster wagging in these trials. Gaster wagging is interpreted as am aggressive behavior but I am not so sure that it is always aggressive. In some situations, one ant grabs another and the one grabbed does the gaster wagging which appears more submissive. Other times, it is obvious the ants are curling their abdomens to sting. But mostly, the gaster wagging gives the impression of wafting some pheromone for some kind of communication which I am not able to discern (I need ant antennae, I guess.). Perhaps it is like arm or finger wrestling.

I think these situations are more nuanced than just dominance and perhaps many things are still ill defined.

Dr. Trager raised some important concerns about climate specialists and yet we know that climate contributes significantly to  ant occurrence at regional and continental levels. I think Andersen’s work my fit for these larger scales but not so well for more local scales at which I am working. (Scale is a significant concern and challenge in ecological studies. ) I think the scale issue is a part of the local spatial pattern of Comanche as well – it looks like regionally, they are found in sandy soiled prairies associated with oak forest, etc. but locally, Comanche spatial pattern and location may be a matter of queen dispersal. At first perhaps, new queens are attracted to locations with other colonies (conspecific attraction) but after landing, queens have to move farther away.  Later, negative interactions between colonies may come into play as well. Comanche colonies do move — and apparently, not in response to shading, like Pogonomyrmex badius or P. barbatus. But this is just my hunch based on observation and a few preliminary tests.

I also wonder about this: ant species appear to partition habitat seasonally, spatially, and temporarily in terms of activity patterns and so co-exist. These patterns add a level of
complexity which is a challenge.


Alan Andersen and his colleagues have conducted  many studies of ant assemblages with respect to disturbance (mining and deforestation in paricular) and functional groups especially in Australia. An important paper in consideration of these ideas in North America is:

Andersen, A. N. 1997. Functional groups and patterns of organization in North American ant communities: a comparison with Australia. Journal of Biogeography 24 (4): 433-460.

Ant Antennae

I have been thinking about ant antennae for awhile now. First, I became very interested in antennae because there are so many different forms in insects and also in ants. The form of antennae is a key characteristic in ant identification — how are they attached, how long are they, how many segments, is there a club or not, and if there is a club how many segments make up the club?

While the morphology is important to identification, this variety certainly raises functional questions. What are these differences about physiologically? Why are they important and what do they mean behaviorally?

Recently I have been  raising more questions about antennal physiology and sensory perception because of my observations of interactions between individual Comanche harvester ants. I have been conducting nestmate discrimination tests between individual ants by introducing the ants in an arena and observing the ants’ behavior. While these interactions may vary, the antennae almost always have some role. Sometimes, it has been a brief touch or haphazard encounter but other times, the ants spend some seconds or longer facing each other and running their antennae over each other. This may or may not be accompanied by mandible gaping or gaster waging and the encounters may or may not develop. Mostly, the ants go their own way.

It is obvious that the antennae are more than chemosensory or smelling structures and this is well documented in many insects. Antennae may have sensory receptors for mechanical force, tactile stimuli, chemo-sensation, smell/taste, humidity, and air flow.  This multiplicity of perception is a challenge to understand and to place in the context of behavior: what information does an ant get and how does she respond?

Also, the elbow shape of ant antennae make the antennae particularly mobile, rather like our arms. Perhaps, the sensory structure can be thought of, loosely, like our hands and fingers — very sensitive. Although ants don’t use their antennae to manipulate their environment as we use our hands, these structures are key to how the ants interact with their environment. That they have an antenna on each side of the head gives a kind of stereo view of the world — whatever sense they are using. I find this rather fascinating to think about: the stereo world of the ants along all these perceptual lines.

I wonder what these means for the behaviors I am observing. How much are they detecting just being in proximity to one another, how much if they have a bare encounter, and why do some of them spend many seconds using their antennae on one another and others do not? What can they detect, what do they pay attention to, and why are there such differences in responses? Context matters but there is more to this than context.

For the Comanche ant, these questions seem particularly important because they do not use trunk trails and have poor recruitment to resources, etc. which means that pheromones may not be so key to their communication as it is in other ant species. They seem to be rather visual in their orientation for foraging. So what is their perceptual world?  I wonder.



Comanche harvester ants display some aggression.

Behavioral Model for Comanche harvester ant interactions

(I do not know what led to the situation in the photo of the Comanche harvester ant above but obviously there was an aggressive encounter between these two ants and since the one ant is missing her abdomen, I suspect other ants may have been involved. These ants were not near any nest when I took the photo.)

I am working on a behavioral model for interactions between Comanche harvester ants based on the observations I am making. This is part of my evaluation of nestmate discrimination — that is, the idea that ants discriminate nestmates from non-nestmates by being more aggressive towards non-nestmates. These aggressive behaviors in turn may differ in frequency, form, or some other character according to the association between the interacting colonies. This is often thought of in terms of distance between the two colonies- such that, colonies that are close neighbors my elicit less aggression and colonies farther away may elicit more. How to define/detect that distance threshold is a concern.

This is a first, crude model for stimulating thinking about the sensory (both internal and external) inputs and the decisions resulting in an observable behavioral response.

I am already aware that this model is inadequate and in error. For instance, this is not a linear process and gaster pumping or wagging may not always be aggressive. The intent is to stimulate thinking, the production of hypotheses, and a better model. As I begin to analyze the behavioral sequences, I will be developing further models.

Nestmate Discrimination Test/Neighborhood Definition Thoughts

Old Thoughts

Here are some notes on ideas that I had in May 2013 on colony distribution patterns and nestmate discrimination in the Comanche harvester ant (Pogonomyrmex comanche). I have been working on this for a while but am trying to formulate good hypothesis and tests of these hypotheses.

Here are the thoughts:

Nestmate Discrimination Test/Neighborhood Definition?

General Methods: a focal colony interacting with several other colonies which may make up a kind of neighborhood

Colony a (focal colony)

1) control with self (3 – 5 trials each)

field, at nest


2) with other colonies (3 -5 trials each), nearest 5 or 10 colonies

field, at nest



observation in the field and from video

video record and view, check for bias in original observation

identification # for colonies and colony interactions (trials)

identification #/code for each video

list to connect the colony interaction identification # with the video code for the interaction

possible covariates?

distance between colonies, GIS locations

surface temperature

colony activity level

1 – few ants on the nest yard: 1 – 5

2 – moderate: 5 – 20

3 – active: 20+

rate? – movement level: slow, moderate, fast?

area containing colonies

density of colonies

# of colonies


possible behavioral sequence

avoid or encounter

encounter – physical contact leads to detection which may end the encounter

or detection may lead to display of aggression

grab antennae, leg; mandible flare; gaster movement

which may lead to an attack/fight


Maybe use SWNP site as a comparison?


Create a model of behavioral decisions – possible inputs (sensory/information)

how communicated?


Effect of NMD on colony spatial pattern?

How might NMD affect colony distribution? Are new/younger colonies more aggressive?

What is the colony distribution pattern?

Can the ants tell near neighbors from far neighbors – do they behave differently, more aggression?

How are ant colonies and populations organized?

How do they respond to one another: individual ants; colonies?


Queen/Colony foundation

trying to track new colonies and their survival

Where are the colonies established with respect to other colonies?

Is there an “attraction” to areas with established colonies? (conspecific attraction)

or an avoidance – in other parts of the prairie without conspecifics?

Do these concerns operate at different spatial and decision making levels – queen choice?

perhaps depends on spatial scale?

1) conspecific attraction to general area (good habitat) – so tend to construct nest near other colonies, tend to stay close

2) very locally, away from other nests – space requirements, as colony grows, competition for forage?

If so, queens must discern something in flight or upon landing or both – Is there a way to figure this out? Besides tracking queens which only gives general information? > literature: how to discern  queen habitat preference?

1)  one orientation/preference in flight

2) another one on landing in contact with substrate?

behavioral response switch?

Big Picture: May help us understand how fragmentation affects the persistence of ant populations

So, fragmentation and habitat conversion to human use is known to be problem for many organisms – birds, mammals, plants > relationship to spatial scale?

it may be a problem for insects and ants – or do these smaller organisms operate on such a different spatial scale, that human use has a very different effect?

Why/how does it matter? because ants are nearly ubiquitous in terrestrial habitats and play many significant roles in ecosystems

including as predators and prey and in soil health – processing nutrients, “planting” seeds, turning over soil, facilitating gas and water penetration – better than earthworms since ants are not restricted by soil moisture as earthworms are

Nestmate Discrimination may provide information on how colonies interact

relates to how large are ant populations (how many colonies)

how much space might a population need or use (minimum population size for adequate reproduction)

ecosystem services



Directionality Experiment: The pink pebbles were placed to mark the direction in which Comanche forgers left the nest. The black and silver box is a thermometer used to measure soil temperature.

Diffuse Foraging Communication

Myrmecologists generally talk about ant foraging strategies as either trunk trail or diffuse (also called individual). Ants using a trunk trail mark the trail with a pheromone and other ants will follow this chemical trail to the food source. These species typically have strong recruitment based on pheromone signals. Diffuse foragers go off individually to find food resources and do not use pheromone trails. They usually have poor or no recruitment. There are species of both foraging types in the genus Pogonomyrmex.

Some of my preliminary work on the foraging strategy of the Comanche harvester ant (Pogonomrymex comanche) suggests that this species is a diffuse forager with poor recruitment. However, sometimes it looks like they are following a trail — that is, the ants are going in the same direction and often appear to be in a line, similar to what is seen in trunk trail forgers. This is somewhat puzzling since chemical/pheromone based communication is typically important in ants.

This same work also suggests that the Comanche harvester ant is strongly visual. I saw this indicated when I did a directionality experiment. As foragers left the nest, I placed a pink pebble where they left to indicate in which direction they were headed (photo above). Once several of these pebbles had been placed, ants going in that direction went directly over the pebble, not veering from the direction or they went around but realigned exactly on the other side of the pebble going in the same direction. This indicates that the ants are orienting visually toward their foraging objective. Sounds a bit like honey bees to me: the foragers have been told or remember from a previous trip where the food resource is located by visual cues.  How might they be communicating this information? Does the communication  only contain directional information, or also distance like the honey bee dance?

I need to puzzle out this question into a series of hypotheses and find out.


Thoughts about alates and reproduction in the Comanche harvester ant (Pogonomyrmex comanche)

June 30, 2013: Thoughts on Comanche harvester ant reproduction and especially female alates

For two summers now I have seen alates and the release of alates throughout June (I have also seen alates in nests as late as November and found new queens in August/September)– this is not what is in the published literature, which says Comanche mates in late summer, synchronously, after heavy rain.  The release of alates in late May/June is asynchronous — that is, not all colonies release alates at the same time. I have never found a mating lek nor clouds of alates flying off.  Alates are often released when it has not rained in a week or more.  I am thinking that humidity may be the releasing factor rather than rain.  Today the humidity was about 60%.

Throughout June I have been seeing both alates in the nest and new queens digging their first nests.  It seems as though the alates mate and then a day or two later, the new queens begin to dig a nest.  This suggests that the queens are exposed over night — I wonder if they have some kind of refuge.  A similar situation may be happening to some of the workers who appear to be the last ants to close the nest and stay out over night.  Earlier work I did on the opening and closing of the nest, suggested that some workers close the nest from outside and may be involved in opening it the next day, If these workers are out all night, do they have some kind of refuge?

I have just recently observed one colony that had at least two female alates acting as workers.  This does occur in other species but I am not aware of it occurring in this genus, Pogonomyrmex.  I wonder if there is some kind of genetic switch involved. Could this be related to the cues that cause development into a gyne (female who can mate) versus a worker (who may lack any reproductive function and does lack reproductive function in P. comanche)? — Somehow not a complete shift into one form or the other –> is this a problem for the colony? Is this a general occurrence and I haven’t seen it before? Is it colony specific? Or a rare occurrence at random? If this is the case, it suggests that the reproductive caste system seen in ants in particular, and social hymenoptera more generally, may not be fixed.