Category Archives: Miscellaneous

The Spatial Ecology of the Comanche Harvester Ant

I have successfully presented my dissertation work and am currently finishing up the revisions for the final submission to the University of Texas at Arlington for the PhD degree. I expect the final dissertation to be available from the university library by July 2015.

The title of the dissertation is: The Spatial Ecology of the Comanche Harvester Ant, Pogonomyrmex comanche (Hymenoptera, Formicidae)

Dr. Esther Betran was the chair of my committee (UTA).

Other committee members were:

Dr. Jonathan Campbell (UTA)

Dr. Paul Chippindale (UTA)

Dr. Sophia Passy (UTA)

and Dr. Walter Tschinkel (FSU)

Here is the slide presentation and the notes which are numbered to correspond to the slides. I have included some of the corrections that came out of the discussion with my committee and otherwise have noted where there are other problems which I am addressing in the revision.

The slides:

and the notes:

Ants as Ecosystem Engineers

Comanche harvester ant (Pogonomyrmex comanche) nest year

Comanche harvester ant (Pogonomyrmex comanche) nest year

Many ant species are ecosystem engineers. An ecosystem engineer is an organism which structures the environment to suit its needs and in doing so has profound effects on the occurrence, abundance, and spatial pattern of other species. Beavers, who turn streams into ponds, are the textbook example. Ants do exactly the same thing in soil. They are soil engineers. Through their nesting habits, ants are agents of bioturbation, mixing soil horizons and creating avenues for water and gas exchange through the tunnels and chambers that make up their nest architecture. These activities result in soil production and altering soil chemical, physical, and biotic profiles.

nest casts

Their movement of materials from above and below ground concentrates nutrients and minerals in the nest and associated soil. The above ground nest structure is engineered as well. By creating soil or other mound structures, the ants may prevent plant colonization and change soil temperature and moisture profiles. The addition of pebbles to nest mounds done by Pogonomyrmex barbatus and P. rugosus, for instance, changes the temperature of the upper region of the nests. These species intentionally forage pebbles from the environment to do so. The parasitic, commensalist and mutualist organisms which may share these nests change the soil communities since these species would not be present at all without the ants.

Todd Island (TI-1) site at the Fort Worth Nature Center, Fort Worth, Texas. Note the Comanche harvester ant nest in the bare area, lower left.

Todd Island (TI-1) site at the Fort Worth Nature Center, Fort Worth, Texas. Note the Comanche harvester ant nest in the bare area, lower left.

Through all these activities ants engineer the soil to be suitable for the internal environment of their nests insuring the development of their young and their own survival. Because of this soil engineering, the occurrence, abundance, and spatial pattern of soil organisms and therefore the soil community are significantly different in areas with ant nests and those without. In turn, the differences in the soil community affect soil nutrient cycling and availability which affects these communities as well as the plant community which has a large portion of their bodies above ground. When an ant colony dies or moves, the nest area becomes available for colonization. As a result of the far reaching impacts of their engineering, ants have been used as indicators of ecosystem health and function, specifically tracking the progression through climax stages and in remediation of mining sites specifically due to soil production and engineering activities of ants.

The external nest of a Comanche harvester ant. The ants remove any plants from this nest yard area.

The external nest of a Comanche harvester ant. The ants remove any plants from this nest yard area.

Here I have focused mostly on the engineering of ground nesting ants on soil and provided photo of Pogonomyrmex comanche nests. Ant engineering may include many other ant species and other ecosystem impacts such as foraging activities including vegetation clearing on foraging areas and trails and foraging on seed and vegetative parts through which ants can impact plant populations and communities.

Because ants are central place animals, like beaver, their engineering is of local significance and contributes to the importance of spatial ecology for understanding ecosystem function and health.

 

Selected Literature

Andersen, A.N. 1990. The use of ant communities to evaluate change in Australian terrestrial ecosystems: a review and a recipe. Proceedings of the Ecological Society of Australia 16: 347 – 357.

Bucy, A. M. and Breed, M. D. 2006. Thermoregulatory trade-offs result from vegetation removal by a harvester ant. Ecological Entomology 31: 423 – 429.

Carlson, S. R. and Whitford, W. G. 1991. Ant mound influence on vegetation and soils in a semiarid mountain ecosystem. American Midland Naturalist 126: 125 – 139.

Cox, M. G. and Blanchard, G. B. 2000. Gaseous templates in ant nests. Journal of Theoretical Biology 204: 223 -238.

Dean, W. R. J., Milton, S. J., and Klotz, S. 1997. The role of ant nest-mounds in maintaining small-scale patchiness in dry grassland in Central Germany. Biodiversity and Conservation 6: 1293 – 1307.

de Bruyn, L. A. L. 1999. Ants as bioindicators of soil function in rural environments. Agriculture, Ecosystems, and Environment 74: 425 – 441.

Dostal, P., Brezniva, M., Kozlickova, V., Herben, T. and Hovar, P. 2005. Ant-induced soil modification and its effect on plant below-ground biomass. Pedobiologia 49: 127 – 137.

Eldridge, D. J. 1993. Effects on ants on sandy soils in semiarid eastern Australia: local distribution of nest entrances and their effect in the infiltration of water. Australian Journal of Soil Research 31: 509 – 518.

Elmes, G. W. 1991. Ant colonies and environmental disturbance. In: The Environmental Impact of Burrowing Animals and Animal Burrows [Symposium of the Zoological Society of London 63]. Clarendon Press: Oxford, UK. p. 15 – 32. Clarendon Press: Oxford, UK.

Folgarait, P. J. 1998. Ant biodiversity and its relationship to ecosystem functioning: a review. Biodiversity and Conservation 7: 1221 – 1244.

Hendricks, P. and Hendricks, L. M. 1999. Field observations on the myrmecophilous beetle Araeoschizus airmeti Tanner (Coleoptera: Tenebrionidae) at harvester ant mounds (Hymenoptera, Formicidae) mounds. Great Basin Naturalist 59: 297 – 299.

Lesica, P. and Kannowski, P. B. 1998. Ants create hummocks and alter structure and vegetation of a mountain fen. American Midland Naturalist 139: 58 – 68.

MacMahon, J. A., Mull, J. F., and Crist, T. O. 2000. Harvester ants (Pogonomyrmex spp.): their community and ecosystem influences. Annual Review of Ecology and Systematics 31: 265 – 291.

New, T. R. 2000. How useful are ant assemblages for monitoring habitat disturbance on grasslands in south eastern Australia. Journal of Insect Conservation 4: 153 – 159.

Nikem, J. N., Lobry de Bruyn, L. A., Grant, C. D., and Hulugalle, N. R. 2000. The impact of ant bioturbation and foraging activities on surrounding soil properties. Pedobiologia 44: 60 9 – 621.

Pisani, G. R. 2009. Use of an active ant nest as a hibernaculum by small snake species. Transactions of the Kansas Academy of Science 112: 113 – 118.

Ríos-Casanova, L. Valiente-Banuet, and A., Rico-Gray. 2006. Ant diversity and its relationship with vegetation and soil factors in an alluvial fan of the Techuacán Valley, Mexico. Acta Oecologica 29: 316 – 323.

Smith, C. C. 1940. Biotic and physiographic succession on abandoned eroded farmland. Ecological Monographs 10: 421 – 484.

Snyder, S. R. and Friese, C. F. 2001. A survey of arbuscular mycorrhizal fungus root inoculums associated with harvester ant nests (Pogonomyrmex occidentalis) across the western United States. Mycorrhiza 11: 163 – 165.

Trager, J. C. 1990. Restored prairie colonized by native prairie ants (Missouri, Illinois). Restoration and Management Notes 8: 104 – 105.

Underwood, E. C. and Fisher, B. L. 2006. The role of ants in conservation monitoring: if, when, and how. Biological Conservation 132: 166 – 182.

 

Comanche Harvester Ants are Pansies!

As part of investigating nestmate discrimination, I decided to test if Comanche can distinguish other ant species. So I ran behavioral trials between the Comanche harvester ant (Pogonomyrmex comanche) and the Barbatus harvester ant (or harvester ants or big red ants, Pogonomyrmex barbatus) and: !

Comanche are pansies — mostly they did nothing, either in arenas with P. barbatus or when P. barbatus was introduced to their nest mound near the entrance. In fact, P. barbatus sometimes entered the nest seemingly without harm since they also returned to the external nest.

Out of 19 arena encounters, there were 4 with any aggression and only one of these had an extended grabbing encounter. Barbatus was always the aggressor.

Out of 14 on the nest encounters, 2 showed some aggression by Comanche, mostly a kind of harassment. Mostly, Barbatus just left the mound though twice barbatus entered the nest. Once Barbatus showed great difficulty maneuvering over the sandy mound.

All trials were recorded with a camcorder so I am still analyzing them.

 

Prairies in a Changing World: State of the Prairie Conference 2014

Conferene poster

The Native Prairies Association of Texas (and the Coastal Prairie Partnership) had their annual meeting in Fort Worth at the Fort Worth Botanical Garden from May 29 – May 31, 2014.  I was invited to present my research on ants in the prairies of the Fort Worth Nature Center in Fort Worth and the Southwest Nature Preserve in Arlington, Texas.

I also attended most of the meeting and gained a lot from the presentations I attended and especially from hobnobbing with other attendees.

**I want to pass on that Native American Seed is producing a seed mix especially to attract native bees which will be available this fall. Here’s the link to this Seed Source.

Here is the agenda for May 30 and May 31, following which I post my notes on the few talks I was able to attend with some comments and finally my presentation and extensive notes on the slides.

May 30 Agenda

State of the Prairie Agenda for May 30

May 31 Agenda

State of the Prairie Agenda for May 31

My Notes and Comments

State of the Prairie Conference Notes

Demonstration Prairie 5

The Demonstration Prairie at the Fort Worth Nature Center (photo above)

I presented my research on the ant species I have found in 17 sites at the Fort Worth Nature Center and what this means for 1) the possibility of using ants as bioindicators and 2) for the ecology of the Cross Timbers Ecoregion.

“Jills of All Trades: Ant Diversity and Flexibility in the Cross Timbers Ecoregion”

Here are my notes. In these notes I include quite a bit more than I was able to cover, in part, so that if you did not attend, you can follow the slides. If you have questions, message me.

Jills of all Trades_Presentation Notes

And finally, I mention a 10 minute digital recording I made of the Comanche harvester ant “remodeling” a ground bee nest that was too close to the ant nest. Here is a the video:

The Comanche harvester ant in the Southwest Nature Preserve

There is a population of 60 colonies of the Comanche harvester ant (Pogonomyrmex comanche) in a small prairie in the Southwest Nature Preserve in Arlington, Texas. I have been studying this population for several years – mapping the colony nest locations, observing their foraging, and testing nestmate discrimination.

Last week I discovered 4 Comanche colonies not in this prairie but in some of the trails in the preserve. There are also two colonies in the trail that goes by the prairie, separated by a line of trees and grass. Of these new colonies, I believe 3 are 3-4 years old and the other is 1-2 years old. It looked as though something or someone had tried to dig into the second and forth of these nests. I examined the areas around all these colonies but the only colonies were actually in the trails.

Locations of Comanche harvester ant colonies in the Southwest Nature Preserve. Note the colonies in green were located this year and are isolated from the main population in red.

Locations of Comanche harvester ant colonies in the Southwest Nature Preserve. Note the colonies in green were located this year and are isolated from the main population in red.

The colonies are probably located in the trails where the soil was more exposed — so easier for a queen to discern that the soil is sandy, easier to dig in, and lacking in much leaf litter and humus. These ants also use the established trail to start out their foraging journeys — this species does not make much use of pheromone trails but relies on vision for orientation.

Their presence in the trails is a bit intriguing. These colonies are separated by 150 – 440 meters and by dense forest from the population I have been studying. I wonder how these queens made it to these locations, how these queens choose their nest sites and how/if these colonies are (or will be — they might not be mature colonies and so not produce alates yet) involved in a mating lek with the colonies in the prairie. The mating of Comanche has not been studied and I have only some observations which suggest that it is different in timing and occurrence from Johnson’s (2000 and 20001) speculation on this species.

There was a lot of foraging going on at the Preserve on Sunday, May 11, 2014. Here are two digital recordings and photos of the Comanche colonies.

Photos of the 4 Comanche nests found in trails. All of these nests were about 30 – 50 cm in a rough diameter (that is, they were not completely round).

First Colony:

Comanche harvester ant (Pogonomyrmex comanche) colony in a trail at the Southwest Nature Preserve, Arlington, Texas

Comanche harvester ant (Pogonomyrmex comanche) colony in a trail at the Southwest Nature Preserve, Arlington, Texas

Second Colony:

Comanche harvester ant (Pogonomyrmex comanche) colony in a trail at the Southwest Nature Preserve, Arlington, Texas

Comanche harvester ant (Pogonomyrmex comanche) colony in a trail at the Southwest Nature Preserve, Arlington, Texas

Close-ups of the two entrances for the second colony (Full photo above):

Close-up of one nest entrance for Comanche colony 2        Close-up of the other entrance of Comanche colony 2

Third Colony:

Comanche harvester ant (Pogonomyrmex comanche) colony in a trail at the Southwest Nature Preserve, Arlington, Texas

Comanche harvester ant (Pogonomyrmex comanche) colony in a trail at the Southwest Nature Preserve, Arlington, Texas

Forth Colony:

Comanche harvester ant (Pogonomyrmex comanche) colony in a trail at the Southwest Nature Preserve, Arlington, Texas

Comanche harvester ant (Pogonomyrmex comanche) colony in a trail at the Southwest Nature Preserve, Arlington, Texas

Here is a digital recording of some Comanche foragers (third colony) getting a scavenged bee into their nest, The little black ant that comes in at times is an acrobatic ant (Crematogaster). This recording is about 10 minutes.

Finally, here is a digital recording of pollinators and pollen eaters in a prickly pear blossom (about 1 minute):

Ant Presence and Abundance in the Fort Worth Nature Center

I sampled ants using pitfall traps in 17 sites in the Fort Worth Nature Center monthly in June, July, and August 2012.

I used CANOCO to run redundancy analyses (RDA) on ant presence with abiotic and biotic environmental variables and on ant presence and abundance with soil type to look for ant preference for soil. I used forward selection of variables and Monte Carlo significance tests to select the variables for the final RDA models.

RESULTS

1) RDA for ant presence and environmental variables

RDA Summary Table

Axes

1

2

3

4

Total variance

 Eigenvalues                     

0.122

0.062

0.026

0.014

1.000

Species-environment correlations

0.820

0.872

0.672

0.582

Cumulative percentage variance of species data

12.2

18.4

21.0

22.4

Cumulative percentage variance of species-environment relation 

51.5

77.6

88.8

94.5

Sum of all eigenvalues     

1.000

Sum of all canonical eigenvalues     

0.237

Triplot

2) RDA for ant presence and soil type

RDA Summary Table

Axes                                    1      2      3      4 Total variance
Eigenvalues

0.076

0.023

0.011

0.007

1.000

Species-environment correlations 

0.788

0.603

0.424

0.417

Cumulative percentage variance    of species data

7.6

9.9

11.0

11.7

Cumulative percentage variance    of species-environment relation 65.2   84.9   93.8 100.0
Sum of all eigenvalues

1.000

Sum of all canonical eigenvalues

0.117

Triplot

3) RDA for ant abundance and soil type

RDA Summary Table

Axes                                    1      2      3      4 Total variance
Eigenvalues

0.070

0.031

0.016

0.003

1.000

Species-environment correlations 

0.777

0.655

0.456

0.265

Cumulative percentage variance    of species data

7.0

10.1

11.7

12.0

Cumulative percentage variance    of species-environment relation

58.4

84.6

97.9

100.0

Sum of all eigenvalues

1.000

Sum of all canonical eigenvalues

0.120

Triplot

24% of species presence is explained by the environmental variables with percent litter cover and drainage being the significant variables. Sampling sites by date clumped together indicating a lack of seasonality — which seems a bit unusual since late July and August become quite hot and ant activity seems reduced  at this time.

12% of species presence was explained by soil type with the Aquilla soil being the only significant soil. This soil is the only soil type where the Comanche harvester ant (Pogonomyrmex comanche) is found. All other species are more generalist with respect to soil type.

7.4% of species abundance was explained by soil type again with the Aquilla soil being the only significant soil. This result further supports the result with species presence: only the Comanche harvester ant has such narrow soil preference.

CONCLUSIONS

Though the eigenvalues are low this is not unusual for ecological data. The low level of explanatory value of these variables is likely due to the generalist nature of these species (and more temperate species in general) and the below-ground nesting of most ant species.

The Comanche harvester ant (Pogonomyrmex comanche) was the only species to show strict preference for soil type. Exactly what this species’ preference or requirement is remains unresolved.

Ants on Baits at the Fort Worth Nature Center

This is the demonstration prairie located in front of the Hardwicke Interpretative Center of the Fort Worth Nature Center in Fort Worth, Texas. The students set up some bait stations in this area.

This is the demonstration prairie located in front of the Hardwicke Interpretative Center of the Fort Worth Nature Center in Fort Worth, Texas. The students set up some bait stations in this area.

On April 29, 2014, sixth graders from Trinity Valley School (Ms. Julie Frey) in Fort Worth, Texas came to the Fort Worth Nature Center to learn about horned lizards and the ants they eat, mostly Pogonomyrmex ants, commonly called harvester ants because they mostly eat seeds. As part of their time with me, we set up tuna and pecan sandies cookie baits and made observations. At the conclusion, the students collected the ants for identification. I also recorded some video of the ants.

Although we attempted to set this up as a controlled study, it was a good preliminary investigation. The students explored their areas — limestone ridge, woods, or open prairie — and tried alternative ways of placing and using the baits. They did a good job of investigating.

I set them up with a data sheet to record location, weather, type of bait (tuna, cookie, or both), time of first arrival to the bait (and what this was), time for first ant arrival, observations (numbers of ants; rate of foraging, interactions, etc.), and how many ants on the baits after 5 minutes. (I did not get the data sheets so I cannot share that part.)

I recommend this kind of exercise for teaching about science method, forming hypotheses, investigating insects and foraging. It is easy to do and can be done anywhere. You can develop all kinds of ideas and possible experiments from this kind of work — myrmecologists do so all the time.

Here is a summary of the ants the students collected and some short clips from the video.

METHODS for Identification:

The students collected the ants from the baits and put the ants and bait into jars. In the Formanowicz lab at the University of Texas-Arlington, I separated the ants from the baits, rinsed them and placed them in 95% ethanol. They were identified to species using various on-line and published identification keys.

The lab bench: using a Nikon dissecting microscope with 40X magnification.

Lab bench for ant identification

Lab bench for ant identification

Sorting the ants from the baits

Sorting ants collected on tuna bait

Sorting ants collected on tuna bait

Some photos of the ants: Photos were taken using a dissecting microscope at 40X with a cell phone.

Camponotus americanus: This is a carpenter ant that nests in wood and is mostly found in woodland though they may wander into prairie. These ants are large, 1.5 cm.

Camponotus americanus collected from baits at the Fort Worth Nature Center.

Camponotus americanus collected from baits at the Fort Worth Nature Center.

Crematogaster sp.: Crematogaster is called an acrobatic ant because their gaster (part of the abdomen) is attached such that the ants can carry it above their heads — in a rather acrobatic posture.

Crematogaster

Dorymyrmex flavus: Ants in the genus Dorymyrmex are easily recognized by a cone shaped structure on the their dorsal surface (just before the gaster). Their common name is cone or pyramid ants. The cones differ in size and shape. These differences are used to identify species.

Forelius mccooki (above) and Dorymyrmex flavus (below)

Forelius mccooki (above) and Dorymyrmex flavus (below)

The red arrow indicates the cone or pyramid on Dorymyrmex. This structure is diagnostic for the genus.

The red arrow indicates the cone or pyramid on Dorymyrmex. This structure is diagnostic for the genus.

Forelius mccooki

Forelius

Solenopsis invicta: This is the invasive, red imported fire ant. Note the antennae have a two-part club at the end and altogether there are 10 segments on each antennae. These features are diagnostic for the genus.

Solenopsis invicta collected from baits in the Fort Worth Nature Center.

Solenopsis invicta collected from baits in the Fort Worth Nature Center.

RESULTS:

Sample # Species Count
1 Solenopsis invicta  3
2 Crematogaster cerasi 2
3 Crematogaster cerasi 2
Dorymyrmex flavus  1
Forelius mccooki 18
4 Forelius mccooki 18
5 Crematogaster lineolata 6
Forelius mccooki 16
6 Camponotus americanus 1
Solenopsis invicta 1
Unknown 1
7 Forelius mccooki 3
Solenopsis invicta 1
8 Forelius mccooki 47
9 Solenopsis xyloni 3
10 Forelius mccooki 89
11 Crematogaster lineolata 4
Forelius mccooki 1
12 Solenopsis invicta 1
13 Forelius mccooki 2

Video clip #1: “Bug and Ants”

This clip shows many Forelius ants on a tuna bait. An insect, perhaps a bug, lands on the bait and interacts with these ants, then leaves. It looks like the ants may be performing a cleaning service which has been suggested for Forelius ants in some situations.

Video clip #2: “Crematogaster Waggle”

This clip shows many Forelius ants on tuna bait. A Crematogaster forager is in the lower right hand side. As this forager leaves the bait, she waggles her gaster indicating that she is dispensing a pheromone.
Here are the two short clips from tuna baits that the Trinity Valley School of Fort Worth, Texas set out at the Fort Worth Nature Center.

Looking for ants that define prairies

My analysis right now is focused on considerations of alpha and beta diversity. I have been held up by computer issues but here are the initial results of a form of discriminant analysis on ant species occurrence in 21 sites over 3 months in the Fort Worth/Arlington, Texas area.

I used both a biplot scaling (for short gradients — which I think is most appropriate) and a Hill’s scaling (which is meant for long gradients) and got the same results. So, I will continue these analyses with the biplot scaling.  This initial work was done using soil type as the clustering category. (I will continue DA using ecological group, habitat type (disturbance), and the presence of the Comanche harvester ant as clustering groups. So, several more analyses to do.)

This first summary table and plots are for species occurrence data from 21 sites. The analysis called a CCA in CANOCO, the program I am running (CCA is a general form of CVA, and otherwise called a discriminant analysis). I am using this as a clustering analysis: do the ants cluster by soil type basically. Turn it the other way round: Knowing the ants present, can I say what the soil is? Are the ants bioindicators?  This first analysis uses all the species presence data.

Here is the summary table:

**** Summary **** of CCA for Soil Clustering, biplot scaling, all species

Axes                                    1      2      3      4  Total inertia
Eigenvalues 1.000  0.970  0.770  0.706         6.000
Species-environment correlations  1.000 0.985 0.877 0.840 6.000
Cumulative percentage variance of species data                16.7   32.8   45.7   57.4
Cumulative percentage variance of species-environment relation   22.9   45.1   62.7   78.8
Sum of all eigenvalues      6.000
Sum of all canonical eigenvalues      4.370

And the biplot of data: messy, messy, messy. The red are the species, the triangles with the S followed by a number are the soils.

For the second analysis, I only included species that made up more than 1% of the total ants collected from that sample.

Here’s the summary table:

**** Summary Of CCA with Ecological Descriptors ****

Axes

1

2

3

4

Total inertia

 Eigenvalues                     

0.864

 0.776

 0.717

 0.608

        6.000

Species-environment correlations 

0.929

 0.881

 0.846

 0.780

Cumulative percentage variance of species data

14.4

  27.3

  39.3

  49.4

 Cumulative percentage variance of species-environment relation

24.7

  46.9

  67.4

  84.8

Sum of all  eigenvalues

 

 

 

 

  6.000

Sum of all canonical     eigenvalues     

 

 

 

 

  3.494

And the triplot — here with the addition of circles with numbers — these are the samples.

I haven’t reached interpretations or conclusions yet. This is still pretty raw data…

Stratford and Tandy Hills Prairie Ants

I am completing the ant identifications for the prairie and forest in the Southwest Nature Preserve in Arlington, Texas and the additional prairies, Statford  and Tandy Hills, in Fort Worth, Texas. I believe I have found another Temnothorax species which I have not been able to identify and another Pheidole species. This is quite exciting. No Pogonomyrmex ants are found in the Stratford or Tandy Hills Prairies.

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.