## Wednesday, December 28, 2016

### Relict Ecosystems

Part of what I like about biology is that it includes topics ranging in scale from the analysis of how a single protein functions all the way to how species and whole ecosystems change over geological time. At every level, there is dramatic complexity to be explored.

As the glaciers from the last Ice Age retreated northwards, a whole landscape of ecosystems followed them. Along the way, isolated fragments of those moving ecosystems were sometimes left behind as a species found a microclimate to their liking. The first such relict ecosystems I learned of are the Lost Pines and Lost Maples areas of central Texas. Each of these locales are known for the large numbers of a type of tree not seen over a wide area around them. More recently I learned about Texas Wild Rice, a tiny relict of the ecosystem that northern Minnesota is now known for.

If these relics persevere long enough, they may rejoin the parental populations when the next ice age happens. The relict populations may then blend back into the larger population, or (if they have fully speciated) they may retain a distinct biological identify. American Sycamore trees and their old-world cousins can hybridize, so it isn't certain the extended time apart would result in speciation.

References:
• Relict ecosystems in Texas:
• Relict ecosystems elsewhere:
• General information:

## Saturday, December 24, 2016

### Science Outreach

Though I haven't been writing much here lately, I have been active with another modern form of science outreach. You can follow my Twitter feed @thebiologistisn for links of interest, observations, and other short-form expressions that don't really fit here on my blog.

The topics covered will be pretty much the same as here. Though you will probably get more of a hint about my political stances, as Twitter's soundbite format is so fitting to politics.

I have connected the blog with my Twitter feed, so new posts here will be automatically linked there. This will make it easy to keep track of when I post. It will also make it easy for you to ask me questions about the topics I discuss, unlike here.

## Tuesday, December 6, 2016

### Unstable Genetics

Collecting germplasm is a key step for any plant breeding project. For the amateur plant breeder, this can seem like an arduous task. Fortunately, you can take a quick shortcut by saving seeds from hybrid plants. A hybrid plant will be heterozygous for many alleles, because it was made by crossing two (more or less) unrelated plants. The seeds produced by a hybrid will be segregating out a diverse set of different combinations of the alleles.

Growing these seeds means you may get some plants that are simply worthless, or wonderful in your eyes. Farmers (or others wanting a precise and predictable crop) won't generally accept this uncertainty. (This is probably why there is so much online dismissing the idea of saving seeds from hybrids.) However, if you're ok with each plant being unique and changing from year to year, this may be exactly the sort of thing you're looking for.

Some small plant breeders sell seeds from the unstable early stages of their breeding projects. The good ones will be entirely clear about the unstable nature of the seeds they're selling. The bad ones won't even let you know there is an issue. I have no connection to the breeders I've linked to below, but they seem to be up-front about how their seeds are not a stable end-product of a breeding program. Their seeds should give you plenty of variation to work with.

Seed Sources:

If you know of any other vendors offering similar seeds, please let me know!

More sources added after first posting:

References:

## Tuesday, November 29, 2016

### Botanizing in Alaska: Low-Bush Cranberry

I still have some photos from my last trip up to central Alaska to go through. I found this plant on a drive in the vicinity of Fairbanks-AK. We drove up a mountain until we were at the tree-line. While walking around, we saw lots of this plant woven through thick mats of moss and other small plants. Though it didn't have any berries yet, I was able to find a few flowers.

Called Lingonberry or Low-Bush Cranberry (Vaccinium vitis-idaea), this plant has a circumpolar distribution. It is prominent in Scandinavian cuisine and is one of the plants I fondly remember from my childhood in Anchorage-AK. I was hoping to find a small specimen I could transplant to grow in Minnesota. The plants I found, however, spread over several feet wide (though most was hidden in the thick moss). I haven't found any research into how long the plants can live, but these were undoubtedly many years old. I didn't take any cuttings or plant samples, as doing so would have been too disruptive to the fragile plant community.

References:

## Saturday, November 26, 2016

### Future of the Guinea Worm

Guinea worm (Dracunculus medinensis) is one of those parasites that nightmares are made of. Juvenile worms infect freshwater copepods, which invariably end up getting ingested [by humans] when drinking contaminated water. The adult female grows up to a few feet long. It migrates to the skin (usually in the lower leg) and induces an extremely painful blister about a year after infection. The blister is described like being set on fire. The pain is alleviated best by standing in water, which is exactly what the worm wants. When the blister is in water, the female worm releases hundreds or thousands of babies into the water.

Former US President Jimmy Carter has been leading an organization working to make the worm go extinct. As a disease organism, few people are going to lament its extinction. When I first learned about this organism, it was invariably described as infecting humans only. This would make the process of wiping it out so much simpler. Unfortunately, the story isn't quite so simple. The worm has other plans.

 Figure 1 from paper.
Increasingly, dogs in Chad are being found with lower-leg lesions that have worms hanging out of them. Genetic analysis has shown it is the same species as the Guinea worm which infects people. Even if we prevent all human infections for long enough to interrupt the parasite's life cycle, it can still persist in other animals. It looks like it would take continuing diligence to keep it from erupting into an active human disease again.

Over the last several years, the number of infections observed in dogs has been going up and up, while human infections have been minimal. This pattern of yearly increases suggests the worms have been adapting to their new hosts.

The researchers did find evidence for human behavior that helped give the parasite the opportunity to make this transition. At the end of the dry season, the locals do a mass harvest of fish. The fish are processed and dried/smoked for later use. The guts and other undesirable bits are discarded for the dogs, chickens, etc. to deal with. The dogs are then getting infected by eating the fish guts. It also appears that uncooked/undercooked fish are responsible for the human cases of infection.

 Adapted from Figure 9 of paper.
Historically, most human infections by this parasite were due to ingestion of water contaminated by infected copepods (an host to an earlier stage of the worm). With increasing knowledge about this mode of transmission, it became dramatically less useful of a pathway for the parasite. At the same time, any alternate pathway for the parasite to get into its main host would have been positively selected. Essentially, we've just seen a parasite go from a life-cycle with one intermediate host to a life-cycle with two intermediate hosts.

Many parasites are known to have complicated life-cycles passing through several intermediate hosts, but this is the first case I've come across that helps to illustrate how those complex life-cycles could have evolved.

Better control of the fish discards will help minimize the infection pathway through dogs, but it won't necessarily get rid of the problem. While adapting to their new hosts, the worms have had to evolve to better escape notice by the canine immune system. A consequence of this is that they will be better prepared to infect dogs later by other pathways, even if fish discards aren't available. Maybe dogs will start getting infected by ingesting infected copepods like humans used to. Maybe dogs will start getting infected by eating scavenged fish that died in the dry season. I can't predict what will happen exactly, but I understand the power of natural selection and very much believe the worm will find another way to survive even if we completely prevent transmission to humans in the near future.

References:

## Friday, November 18, 2016

### Frosty Physalis

This has been a long and relatively warm fall season. There have been a few frosts, but most days the sun came out and it warmed up nicely. This is all over now that it is snowing. It might melt away and we might have some warmish days still, but after it has snowed I really can't convince myself that winter hasn't begun.

I grew a couple different types of tomatillos (Physalis ixocarpa) this year. I collected seeds for the first one from a medium-sized, dark purple fruit I got from a local CSA. The plants didn't thrive, but they did pretty good considering the lack of care I gave them. The plants have lots of purple pigment on the stems and the fruit husks, but the fruit themselves remain bright green on the plant. Once the fruit are picked and the husk is removed, the green fruit start developing intense purple pigment in response to light. The original fruit was purple all the way through, but no fruit this year have such a pigment pattern. I'm hoping the coloration of these plants indicates they are hybrids and so the darker color may turn up again in the F2 generation next year.

I collected seeds for the second type from a very large, green fruit I got at the grocery store. It didn't have a name associated with it, but it matches one of a few commercial varieties grown in Mexico. The plants did about as well as the other type. The fruit they grew weren't anywhere near as large as the original fruit, but they were much larger than the fruit from the other variety.

A couple days ago, I noticed the large-green variety had been killed back by one of the recent frosts... while the purple variety showed absolutely no damage. The above photos were taken at the same time and well illustrate the differences in frost-sensitivity.

Tomatillos are profligate outcrossers, due to the self-incompatibility mechanisms in their flowers. A consequence of this is that it is much harder to develop stable strains than it is with tomatoes and peppers, because you always have heterogeneity in at least the incompatability locus genes (and likely any nearby genes). The flip side of this is that it should be relatively easy to mix up the genetics of different strains that you happen to be growing next to each other.

I'd really like to develop a strain with the large fruit of the Mexican strain, but with the purple color and frost-resistance of the CSA strain. I expect I'll be able to find some hybrid seedlings with extra purple color among the masses I can grow out from the seeds in a few of the green fruit. These hybrids would have all of the alleles I'm interested in, though it would probably take several years to stabilize them in the homozygous condition.

A close relative of the tomatillo is the Cape Gooseberry (P. peruviana). I grew out this plant from a couple different seed sources. The plants ended up looking identical to each other early in the season, so I assumed they were essentially the same.

After I noticed the different frost-sensitivities of the tomatillo types, I checked on the Cape Gooseberry plants. Several plants were in perfect health (at left), while one was heavily damaged from frost (at right). The condition of the damaged plant indicates it was harmed by a more recent frost than the green tomatillo, suggesting that it has a greater resistance (even though it wasn't enough to matter).

There doesn't seem to be much trait diversity in these plants to do much breeding with. I'll probably only save seeds from the more frost resistant plants to grow next year.

If I had only grown the large-green tomatillo, I wouldn't have realized there was variation in frost resistance that could be bred with. This highlights the importance of collecting diverse germplasm when starting a breeding project. That I collected seeds from a local CSA and grocer shows it doesn't have to be a very difficult process.

If no or very limited genetic diversity is available, like in P. peruviana, it can take more dramatic efforts to collect sufficient germplasm. International travel or nurturing wide-flung collaborations may be necessary. I like the concept of mutation breeding, the use of chemical or radiological means to damage DNA of the plant to generate usefull diversity to breed with. Each approach has its own costs and difficulties, so the direction a breeder chooses will depend on what makes sense for them and the specific plant they're working with.

References:

## Tuesday, November 1, 2016

### Aphids in Red

I've found myself very busy lately. The little free time I've had after work and on the weekends has been consumed with the process of repairing some windows in my old house as well as sundry other necessary tasks. The main consequence for this blog has been that I haven't found myself able to sit down in front of my computer for long enough to write a post.

I have no plans to end this blog, but I do expect that life will occasionally get in the way like it has lately. To get myself back into the swing of things, I'm probably going to have a few light posts while I work on some more intensive ones.

Earlier in the summer, my wife and I went camping with some friends. Early one of the mornings, I was wandering around looking for photographic subjects when I noticed a bright red color along the stems of some plants. On closer examination, I realized the red color was a mass of aphids.

Aphids may be the bane of many a gardener, but they illustrate some really interesting biology. Aphids have a very complicated life cycle. During most of the year they're all females and don't have sex. Instead they multiply through parthenogenesis. They're so efficient at this that new baby aphids are born (not hatched) already pregnant. Most of the new babies don't waste energy growing wings, instead every calorie is dedicated to growing the swarm. When food starts to run out or the aphids get too crowded some babies will grow wings and fly off to other plants and continue their parthenogenic ways. When the weather starts turning colder in fall, winged male babies are produced. The males then mate with females to produce eggs which can survive more extreme winters than the adults.

Aphids come in a whole range of colors, from pale white to yellow, green, red, or even black. These red ones are really interesting because their color is due to high levels of carotenoid pigments (lycopene and related compounds) that are normally only synthesized by plants and fungi. Since the plants the aphids feed on don't have high levels of these compounds, it was at first confusing as to where they would get them. I turned out that the aphids have the genes needed to produce carotenoids and they seem to have acquired them from a fungus via horizontal gene transfer.

The really bizarre thing about these aphids is that they seem to be using the carotenoids to harvest energy from light. It isn't exactly photosynthesis the way plants do it since they're not incorporating CO2 to build sugars, but they do seem to produce more ATP when they're in sunlight compared to when they're not. This ability might help them survive tough times when other tiny insects would perish, but it really isn't at all clear.

## Tuesday, September 27, 2016

### When A Fly Dies, Do We Question Why?

While recently visiting with my brother, he mentioned he had a biology question for me. He was wondering what might be behind the dead flies he was finding stuck to the basil and other plants in his garden. I asked him to show me what he was talking about, as there are many reasons a dead bug could end up stuck to a plant.

What he ended up pointing out was several house-flies that had become deceased while visiting floral structures on the various plants. Now, flies are dieing all the time and they are often found feeding on flowers, so it wouldn't be surprising for them to die while at flowers. That these dead flies seemed to have a stubborn grip on the flowers they passed-on at made me consider an alternate model for their demise.

There are certain types of fungus that infect ants and take over the minds of the ants in the process, leading the ant to behave in a manner to help spread the fungus. Zombie ants. The zombie ants will clamp their jaws onto stems above where a colony of the host ant species has major highways, whereupon the fungus grows its spore-body and drops infectious spores on other unsuspecting ants. The ant-zombie-fungus in turn has its own parasite. This hyperparasite will help keep the zombie-fungus in check, thus supporting the health of the ant colonies. (Similar to the population dynamics between plankton and large fish.)

 Closer.
 Even closer.
So, how does this relate to the flies? They were all found deceased and holding securely to flowers. Close-up photos of the fly (at left) reveal the body to be covered with strands (fibers, webs?) and splotches that look like tiny yeast (single-celled fungus) colonies. Being stuck on a flower means that another fly dropping by for a feed would have a decent chance of getting exposed to whatever is on this fly. One type of fungus can make zombies out of ants, and there are many types of fungi that do this with different tropical insects, but I've never heard of one being found this far north.

It could easily be that dead flies, wherever they are, end up growing microbial colonies like this. It really isn't clear. To see if this is unusual, I'd have to collect a bunch of dead flies from different environments and determine what the normal decay process is for a fly cadaver. If ones like this are unusual, then I can imagine exposing lab-living flies to whatever is growing on the dead and seeing if they have altered behavior due to becoming a zombie.

References:

## Tuesday, September 20, 2016

### Ichneumon Wasp

Between recently traveling on vacation and subsequent computer issues, I haven't posted much lately. I'm back from vacation and have fixed most of the computer issues. This has allowed me to produce the images I wanted to for my last post on the status of my carrot breeding efforts.

I've got several posts in the works, but for now I'm just going to show you this cool wasp I found a few months back. It, like most wasps, is female. When I found her she was probing the wood surface with her dramatically extended ovipositor. The ovipositor, and my limited entomological knowledge, identifies this as an ichneumon wasp of the family Ichneumonoidea.

Wasps in this family are parasitoids, meaning they inject their eggs into other insects for their larva to feed upon. I suspect this lady was trying to find a wood-boring beetle larvae to inject her eggs into, since the wood itself wouldn't provide for her children.

References:

## Thursday, September 1, 2016

### Making My Own Carrots 6

 The only surviving roots.
My ongoing project to breed my own carrot variety had a couple of unexpected twists this year. At the end of last year I saved all the roots which appeared to be grown by F1 hybrid plants. Such roots were the most interesting to me because they were the ones that could later produce diverse F2 seeds. I was most pleased with the ones that had some purple or red coloring, since I want my carrot population to be full of rich red/purple colored roots in later years. Most of the roots seemed to make it through winter, but when I warmed them up this spring to start growing, most proceeded to rot. This left me with only two large roots that had a lovely blush color (at right). Two plants is a limited genetic pool to work with, but I figured it would be fine because they were both F1s.

During the growing season, one of these potential mother plants bloomed and seeded furiously. The second potential mother plant grew luxuriantly, but decided not to bloom at all. My population has gone through a severe genetic bottleneck. One individual.

 The sterile and floriferous mother plants.
Fortunately, this one plant is a F1 hybrid, so it is likely to have a relatively high amount of genetic heterozygosity. One of the parents was likely an intense red/purple, while the other was likely pale/white. White roots are generally a dominant trait over orange in carrots, but it seems the red/purple trait has a co-dominant expression pattern. The result of this is the next generation of carrots will likely have a widely diverse mix of phenotypes for me to select from, even with the genetic population having been reduced down to one individual. Next year, I plan to save many more roots to minimize the chance of this happening again.

I'll try to keep the non-blooming plant alive over this next winter. Maybe it will flower next year, maybe it won't. Either way, I won't be allowing its genetics to contaminate my main carrot breeding project. If it lives long enough and grows monstrous enough...  I might decide to initiate a new carrot breeding project. We shall see.

References:

## Thursday, August 25, 2016

### A Travelling Scientist

I just returned from a week of traveling in Nevada and California. We visited with my wife's grandmother for a few days, then headed out on the road. We stopped by the Luther Burbank house and hiked through several botanical gardens. The inevitable consequence of this trip is that I took many photos (of plants, animals, and geology) that will be appearing in posts over the coming months.

For a first sample, the photo at left is a specimen of Oxalis gigantea in the desert house at the San Francisco Botanical Gardens. The species is interesting to me because it is another example of how readily trees can evolve from within groups of plants otherwise composed of herbaceous forms. I also like it because it is one of the many cool looking succulents around.

Next week I'll get back to my regular schedule of more lengthy postings.

## Monday, August 15, 2016

### Mathematical Recreations : Ramanujan's Nested Radical 3

I've previously discussed an interesting math problem posed by Srinivasa Ramanujan way back in 1911.

In this third posting on this topic, I'll present a proof that there are an infinite number of valid solutions to his puzzle.

$$x = \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}}$$

Ramanujan said the solution was $$\{x=3\}$$. I'm claiming the proper solution is $$\{x=3+n : n \ge 0\}$$. Lets see how that works out.

$$3+n = \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}}$$

We start by unwrapping the first few radicals and simplifying a bit.

$$\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}} = \frac{(3+n)^2 -1}{2} = \frac{9+6n+n^2-1}{2} = 4+3n+\frac{1}{2}n^2$$

$$\sqrt{1+4\sqrt{1+5\sqrt{\cdots}}} = \frac{(4+3n+\frac{1}{2}n^2)^2 -1}{3} = \frac{16+24n+13n^2+3n^3+\frac{1}{4}n^4-1}{3} = 5+8n+\frac{13}{3}n^2+n^3+\frac{1}{12}n^4$$

If we work out the full radical at each step, we rapidly end up with very high-order polynomials on the right side of the equation. However, the 0th and 1st order terms will always only depend on the 0th and 1st order term of the polynomial for the previous radical. Since we're only working with values of n greater than zero, all of the higher-order terms [in red] will have positive values.

$$\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}} = 4+3n \color{red}{+ \frac{1}{2}n^2}$$

$$\sqrt{1+4\sqrt{1+5\sqrt{\cdots}}} = 5+8n \color{red}{+ \frac{13}{3}n^2+n^3+\frac{1}{12}n^4}$$

This allows us to simply discard them, converting the equations into inequalities. This cleans up our work a lot.

$$\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}} \ge 4+3n$$

$$\sqrt{1+4\sqrt{1+5\sqrt{\cdots}}} \ge 5+8n$$

Unwrap another radical. I'm using a bit of an unusual notation in the right half of the inequality, where I'm using equalities inside of the large parentheses for keeping track of a few steps of simplification.

$$\sqrt{1+5\sqrt{1+6\sqrt{\cdots}}} \ge \left(\frac{(5+8n)^2 -1}{4} = \frac{25+80n+64n^2-1}{4} = 6+20n+16n^2\right)$$

$$\sqrt{1+5\sqrt{1+6\sqrt{\cdots}}} \ge 6+20n\color{red}{+16n^2}$$

$$\sqrt{1+5\sqrt{1+6\sqrt{\cdots}}} \ge 6+20n$$

The first order terms of the polynomials increase with each unwrapping of a radical. These terms form a series that has very simple behavior.

$$\left[ k_0 = 1; k_m = 2k_{m-1}+2^{m-1} \right]$$

$$\lim\limits_{m \to \infty} k_m = \infty$$

Because the trimmed polynomials representing each successive radical are <= the true polynomials, and they increase towards infinity, the true polynomials also increase towards infinity.

Unwrapping successive radicals from Ramanujan's solution results in a simple series that races upwards to infinity.

$$[3, 4, 5, 6, 7, \cdots, \infty ]$$

Unwrapping successive radicals from my solution results in a more complicated series that also races upwards to infinity.

$$[3+1n, 4+3n\color{red}{[+\cdots]}, 5+8n\color{red}{[+\cdots]}, 6+20n\color{red}{[+\cdots]}, 7+48n\color{red}{[+\cdots]}, \cdots, \infty ]$$

As long as the value of 'n' is greater than zero, no contradictions (such as negative values for a radical) arise, thus Ramanujan's solution to his puzzle is incomplete.

 Profiles from valid solutions (>= 3) are in green. Profiles from invalid solutions (< 3) are in red. Note the change in scale above and below zero.
A more complete solution is:

$$\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}} \ge 3$$

Ramanujan's puzzle remains of interest to many and seems to inspire ongoing conversations in various online forums. I have come across a few discussions where people mention calculating subsequent radicals for different starting values, the method at the root of my proof, but I've never come across anyone discussing an actual proof. Ramanujan's solution to his puzzle held for 115 years, but I've now proven his solution to be incomplete. I wonder how long it will take for my proof to start appearing in some of those forum discussions.

Unfortunately, my solution remains incomplete. As of yet, I do not have a proof to back up my intuition that all values less than three are invalid solutions. The method of proof I used here is not simply applied to show values less than 3 are invalid solutions, but I am pondering on methods of doing so.

Stay tuned for further developments.

References

## Tuesday, August 9, 2016

### Mathematical Recreations : Ramanujan's Nested Radical 2

I've previously discussed an interesting math problem posed by Srinivasa Ramanujan way back in 1911.

In that discussion I suggested there were probably multiple valid solutions to his puzzle, not just the solution he published (three). I even went a bit further to suggest there was an infinite number of valid solutions.

I still don't have a nice proof, but I have done some further calculations to help illustrate my thoughts. The following figure shows plots of subsequent radical values when initial values are set to various numbers. Initial values of [0, 1, 2, 2.9, 2.99, 2.999, 2.9999, 2.99999, 2.999999, 2.9999999, 2.99999999, 2.999999999, 2.9999999999, 2.99999999999, 2.999999999999, 2.9999999999999] result in the series of descending curves. Initial values of [3.1, 3.01, 3.001, 3.0001, 3.00001, 3.000001, 3.0000001, 3.00000001, 3.000000001, 3.0000000001, 3.00000000001, 3.000000000001, 3.0000000000001] result in the series of ascending curves.  The closer these values are to 3, the further to the right in the figure they diverge from the single straight line resulting from an initial value of [3].

 The top shows positive values. The bottom shows negative values.

The calculated profile for every initial value below three drops down to just below zero and then rises towards an asymptote at zero. It surprised me that the fall of the profiles is slowed before they reach zero, as well as the behavior below zero, but neither result lead me to think there is a problem with intuitions about the problem. This more complicated behavior leads me to think that a proof showing every value less than three is invalid might be a bit difficult.

The behavior of the profiles starting above three are simple enough that I suspect there is a relatively simple proof of their general behavior. That is to say, I think it will be a relatively simple task to prove any values greater than three are valid solutions to Ramanujan's Nested Radical.

Stay tuned for further developments.

References

## Tuesday, August 2, 2016

### Interaction Networks

I took a course titled, "Mathematical Ecology" in undergrad at the University of Texas. The course was taught by Dr. Eric Pianka and it was the worst classes I ever took. Well, no, not really. It was a distressing class, though. I studied like mad and got Ds on every mid-term. I didn't realize until the night before the final how I was approaching the class wrong. Most points in each midterm were assigned on the basis of questions about a single mathematical model described in the course section (and not all the other little info-bits that I had been focusing on). I stayed awake all night, studying only the mathematical models discussed all semester. I ended up getting a B as my final grade for the semester.

I never did pick up the graded exam, but my course grade told I ended up blowing the exam out of the water. Now, this alone might not have been enough to get the grade I got. I suspect the professor acknowledged my --eventual-- mastery of the semester's most important material by making my final exam score have a bigger impact in the overall grade than it was originally designed to be. Thanks very much for that, Dr. Pianka.

 Figure 1a. Positive interactions.
One particular lesson started with an observation of life out in the open ocean, well away from shore or reef systems at least. Out in the open ocean, there is a large amount of biomass present in tiny plankton and in large fish, but relatively little in small fish. The plankton feeds the small fish and then the small fish feed the large fish. Another way to say this is that plankton biomass has a positive influence on small fish biomass and small fish biomass has a positive influence on large fish biomass. We can represent each positive interaction with a pointed arrow. One positive influence and a second positive influence together forms an overall positive influence (Figure 1a). This can be translated into an equation as: (I1 * I2) = If.

 Figure 1b. Negative interactions.
We can think about these steps in the opposite direction. Large fish biomass has a negative influence on the amount of small fish biomass, which has a negative influence on the amount of plankton biomass. We can represent each negative interaction with a flat-arrow, going the opposite direction of the earlier pointed arrows. One negative influence and a second negative influence together also forms an overall positive influence (Figure 1b). This can be translated into an equation as: (-I1 * -I2) = If.

 Figure 1c. Fishy feedback.
Plankton biomass has a positive influence on large fish biomass and large fish biomass has a positive influence on plankton biomass. All together (Figure 1c), we have a positive feedback loop that explains why there is more biomass in plankton and large fish than there is in small fish. On average, the ecosystem only produces enough small fish to be consumed by the large fish. Any more small fish would result in the growth of the population of large fish. Any less small fish would result in a reduction in the population of large fish.

This sort of analysis won't let you know what levels the elements of the system being modeled will stabilize at, or if it will even stabilize at all, but it can quickly give you an overview of the likely overall behavior of the system.

 Figure 2a. Otters in the Kelp forest.
Another scenario with the same dynamics is the relationship between Kelp, Sea Urchins, and Sea Otters (Figure 2a). This relationship is discussed in some detail in a recent episode of Science Friday. Otters help maintain the kelp forest by limiting the numbers of the major herbivore (urchins) which would otherwise obliterate the kelp.

 Figure 2b. Orca in the Kelp forest.
We can add Orca, a major predator of sea otters, into the model (Figure 2b). Because Sea Otters aren't the dominant food source for Orca, I haven't added a positive arrow between Sea Otters and Orca. The model allows us to see that Orca have a negative influence on Kelp forests. Humans hunting otters for their fur would have a greater impact than the Orca because the humans are looking specifically for the Sea Otter (no matter how scarce), while the Orca will switch to other prey if Sea Otters become scarce.

A more complicated system also discussed in the episode of Science Friday describes how the introduction of a vaccine against the Rinderpest virus could have an impact on the population of Giraffes on the Serengeti. Rinderpest is a virus of cattle which kills Wildebeest. Wildebeest eat large amounts of grass, so when Wildebeest are killed off, more grass will grow. More grass means the ecosystem is more susceptible to fires, which kill Acacia seedlings. Since adult Acacia trees feed Giraffes, more fires means less food for Giraffes. Altogether, the model presented in Figure 3 shows that the introduction of the Rinderpest vaccine would result in an increased population of Giraffes. Unfortunately, this analysis wasn't done in advance of vaccine introduction. Instead it was developed in an attempt to understand why the population of Giraffes increased after the introduction.

 Figure 3. Impact of Rinderpest vaccine on Serengeti Giraffes.

 Figure 4a. Opaque-white switching in C. albicans.
The same logic can be used to analyze networks of interactions outside ecological modeling. Figure 4a describes the genetic regulatory network responsible for white-opaque switching in Candida albicans, a sometimes pathogenic yeast commensal of the human gut. Opaque-white switching refers to a transition of the yeast between a reproductive and vegetative developmental state. The opaque/white labels refer to how colonies of the cells in each developmental state appear when growing on media in a petri dish. My Figure 4a is updated a figure from the original paper describing this interaction network so it has colors consistent with my other figures here. The relationships illustrated in the figure had been constructed by involved experiments examining interactions between each of the genes involved in the process.

The diagram was presented by a speaker at a yeast research conference I attended. The speaker then went through an involved discussion of all the experiments they did to explain why the network resulted in the final observed behavior of switching between the white and opaque developmental states. As the presentation went on and on, I found myself getting more and more irritated. I was expecting a couple slides describing the interactions, then a continuation on to the real meat of the presentation. It was quickly clear to me why this network would result in the observed switching behavior because I was analyzing it using the techniques discussed earlier in this posting. The final conclusion of the presentation was the result I understood at the beginning of the presentation. I felt very frustrated.

After the presentation, I tried to convey my frustration to my graduate advisor. Unfortunately, I didn't know how to explain how I was processing the interaction network that had been shown. It turns out that most biologists don't have the mathematical background that I had taken for granted in my own research.

 Figure 4b. Simplification step 1.
I knew how the overall network behaved because I was able to quickly simplify the network. In the left half of the network (in Figure 4a), the positive interaction between WOR1 and CZF1 and the negative interaction between CZF1 and EFG1 together have an overall negative interaction. There is already a negative interaction between WOR1 and EFG1, so this side chain would act to amplify the effect. For our purposes, this means we can simplify the network by removing this side chain (Figure 4b).

 Figure 4c. Simplification step 2.
The interactions between WOR1 and WOR2 represents a feedback loop which stabilizes them in an active state. The negative interaction between EFG1 and WOR2, paired with the positive feedback loop, means that the right half of the figure has an overall negative influence between EFG1 and WOR1. Again, we can simplify the network by drawing a single negative interaction on the right (Figure 4c).

Two elements in the network with negative interactions between them represent a bistable switch. If either WOR1 or EFG1 gets the upper hand, it then suppresses the other. Only one will ever be active at one time. The final element of the network which remains is the influence of the a1/α2 ratio, which acts as an outside control element on the switch. There are other elements impacting the activity of EFG1 which aren't described in this network, but they will also act as external control elements. Together, these outside influences determine the state of the switch and when it can change from one state to the other.

The relationship between WOR1 and EFG1 was very quickly apparent to me at the start of the presentation, but then the presentation kept going on and on in some detail trying to explain the overall behavior. A the time of the conference, my frustration then was in why the presenter wasted so much of our time, as well as in my inability to explain this concept to my graduate advisor.

Now, however, my frustration with this memory has more to do with my irritation at researchers not collaborating with mathematicians (or at least mathematically-inclined researchers) during their work. Having some basic level of literacy at math, computer programming, statistics, or any other specialized field can help you in many ways. You don't need to be an expert in these subjects because even a limited grasp of them will help you to know when it is a good idea to call in someone with the specialized knowledge that you lack.

Dr. Pianka's course is the one I have most often thought of over the years. Specific lessons I learned in his course routinely come to mind and help guide how I interpret material seen in my scientific career so far. I expect the course will continue to inform my future biology research endeavors. Thank you again, Dr. Pianka.

References

## Tuesday, July 26, 2016

### Artistry of the Insect Kind

I've been posting a lot about mimicry lately, so I figured I would post about a few interesting insects I've come across that appear to take mimicry to another level. They mimic things in the way an artist would - by painting them on a canvas. Of course, the insects aren't really painting anything. Instead, they're growing the images using some complicated developmental processes.

 Goniurellia tridens
Goniurellia tridens is a species of small fly which appears to have ants/spiders/somethings on its wings. The group of flies to which this species belongs have many examples with marked/patterned wings, but usually the patterns are simpler. Generally the flies use their patterned wings in courtship displays, dancing with their wings held to the side (like in this photo) while they shift and flap one wing after the other.

It is easy to imagine them using the patterns on their wings to discourage ants/spiders/etc. from attacking them, but it isn't clear if they do this behavior. It would seem to be far less risky to simply take to the air and fly away when faced with a predator. There are quite a few jumping spiders that would be able to leap and grab them out of the air. (As well, they have an impressive visual system that would let them see the images as ants/spiders/etc. in a way similar to how we do.) If such a spider were to jump at one of the high-contrast  "prey" images instead of the fly itself, the fly might gain time to escape. A jumping spider might also see the patterns as a pair of predatory ants and choose to be elsewhere. I would love to see some video footage of how this fly responds to predators as this would help clarify if any of the above hypotheticals have any basis in reality.

 Siamusotima aranea
Or next mimic is the moth, Siamusotima aranea, that appears to have a bunch of spidery legs painted on its wings. This image, again, would be most useful against a predator with acute eyesight like a jumping spider. The photo at right provides some additional evidence. Moths typically rest flat to the surface, with their wings held close. In this image the moth is holding its abdomen raised from the surface and extending its wings, effectively displaying its image in a way not associated with typical moth behavior.

Other moths (like Callimorpha dominula) will actively flash their bright hind-wings to discourage predators (or photographers) who are expressing too much interest, so it is reasonable to interpret the behavior of S. aranea in this photo as being an active display to discourage predation.

Another moth, Macrocilix maia, appears to be a very good mimic of something different - bird poop and flies. The moth even has behavior to back this hypothesis up, often choosing to rest adjacent to real bird poop. Since it rests flat to a surface, like most moths, the image isn't one presented to an predator coming along the surface. Instead the image is presented continuously to the air above, where birds are using their acute color vision to hunt for insects.

It can take some experimentation to determine if an animal is really using its patterns as mimicry. We can make a hypothesis about what their wing patterns are used for and then test the hypothesis using the "natural experiment" of the moths' behavior. If their behavior is consistent with the mimicry hypothesis, then the experiment has a positive result and we can more strongly state their wing patterns are a form of mimicry. In the moth examples above, each species definitely has behavioral traits that align with the mimicry hypothesis.

In the fly example, I haven't been able to find enough information about their behavior to be able to interpret it as a natural experiment. It could be that female flies like male flies with wing-men, so to speak. (This would be consistent with the the use of wing markings in courtship displays seen generally in the group.) It could be that we humans are seeing a pattern in the image that is essentially random with respect to predation. I definitely like the anti-predation model, but without some form of experiment, we really don't have enough information to determine which hypothesis is better aligned with reality.

References:

## Tuesday, July 19, 2016

### More Crop Mimics

I've previously posted about a form of mimicry in plants (called Vavilovian mimicry) where one [or several] wild species end up mimicking a crop species due to the selection pressures in crop fields. Since then, I've come across a few other species that are useful examples for the topic.

 Wheat (top) vs. Darnel (bottom). [from link]
Darnel (Lolium temulentum) is a  mimic of wheat. It looks almost identical to wheat plants right up until the seed heads form (see at right). The seeds themselves are large and are indistinguishable from those of wheat after threshing. The seeds are also highly poisonous, leading to the common name of "Poison Darnel". When wheat contaminated with sufficient Darnel is milled into flour, the resulting bitter taste reduces its value.

Darnel control efforts have limited success and the plant is found essentially everywhere wheat is grown. Even though the toxic character of this species (when infected) means it will likely never be developed into a primary crop, it is still a nice example of Vavilovian mimicry.

Another common weed in wheat fields is Small Canary Grass (Phalaris minor). It also produces large seeds that would probably get sorted with wheat seeds at the end of the season and its seedlings look very much like those of wheat.

As a general rule, any random grass species is going to be a much better mimic of the grass we call wheat than any other random type of weed would be. Of the five weed mimics of wheat that I've come across (below), all are grasses and three have become major crops in their own right.

Rice crops are often plagued by weedy forms called "Red Rice" due to the red color of their seeds. They are generally less productive than the main cultivated varieties, so farmers try to keep it out of their paddies. Red-Rice happens to be the same species as the cultivated types. It evolved from (or alongside) cultivated rice so it really isn't a case of Vavilovian mimicry, even though it is a useful example in the discussion of crop weed mimics.

References

## Tuesday, July 12, 2016

### Ant Mimicry

Ants are often unpalatable to insect-eating birds due to the formic acid present in their abdomens, so they're often avoided in favor of other prey items. Any potential prey item that happens to look like an ant will have a better chance to live another day than one that doesn't. This selective pressure seems to have led many unrelated arthropods to take on body forms (and behavior) that mimic those of ants.

There are a large number of ant mimic spiders, that often look remarkably like the ant species they're associated with. Because they look like the ants, they are free to go about their business hunting the ants without intervention by birds. The ant mimic mantis probably gains the same freedom to hunt near ant colonies, though I haven't read anything specific about its life-style.

Though I have seen ant mimics in real life (spiders and the occasional beetle), I don't have any of my own photos for illustration. Because they mimic the behavior of ants (in addition to the look), they tend not to stay still for my camera. I've never really gotten a good photo of an ant either, for the same reason.

The photos that follow here were found around the web and I have no legal claim to them, though I feel their educational use here should provide me some protection as fair-use under US copyright law.

 Spider
 Macroxiphus sp cricket.
 Dulichus inflatus (Hemiptera)
 Euderces beetle.
 Asian Ant Mantis (Odontomantis planiceps)
References: