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Thursday, January 22, 2015

Hybrid Sterility and Speciation

1. Burbank's Fragaria x Rubus.
Luther Burbank (1849-1926) was a widely renown botanist and scientist. He bred numerous interesting plants. He liked to attempt wide crosses; crosses between distantly related species. One of the more unexpected crosses he attempted was the cross between a strawberry (Fragaria spp.) and a raspberry (Rubus spp.) (fig. 1). To the then (and now) commonly held Victorian ideal of plant species, this cross shouldn't have had a chance at all of working. However, the cross appeared to succeeded and fruit developed. The plants that developed from the seeds grew with a combination of characters from the parents, thus showing their hybrid nature. The hybrids flowered abundantly in the second year, but no fruit was ever produced. Burbank found that at most a few seedless drupelets (fruit segments like in a raspberry) would form and so he abandoned the project.

There is a lot that Luther Burbank didn't know about plants. His exuberance for performing crosses and doing selections let him produce some wondrous results, but his lack of knowledge was a limitation.


Chromosomes were discovered in the 1880s, but the process of meiosis wasn't made clear until 1905-1911. The dates suggest it is possible that Burbank was aware of meiosis, even if he wasn't aware of the consequences for his work. Fortunately, such knowledge is now widespread and biologists are well aware of the consequences.

2. Meiosis and failures of meiosis.
Strawberries and raspberries show a diversity of genome sizes, but they all have a basic chromosome count of 7. They species range from diploid with 14 chromosomes to decaploid with 70 chromosomes. An even number of chromosomes is found in all cases, as this is required for the formation of gametes (fig. 2A).

If two species with different chromosome counts are crossed, the resulting hybrid can have an uneven number of chromosomes and will be generally unable to generate gametes (fig. 2B). (Example: 2n x 4n => 3n; this is how seedless watermelons are made.)

If two species with the same number of chromosomes are crossed, but the chromosomes are too unrelated, the resulting hybrid will also fail to generate gametes (fig. 2C). In this case the hybrid will have an even number of chromosomes, but they won't line up during meiosis and the result will be a haploid with an increased basic chromosome count. This can be caused by a high level of structural rearrangements in the chromosomes of strawberries vs. raspberries, even if the genes are otherwise compatible.

Because Burbank performed the cross with whatever strawberry and raspberry plants were convenient and the cytogenetics of the parent plants wasn't examined, either of the above scenarios could be responsible for the hybrid infertility that he saw.


I have one raspberry (Rubus occidentalis, isolated in my yard in Minnesota) and one strawberry (Fragaria vesca, isolated in central Wisconsin) in my collection and I think I will set about crossing them during this year. Both species have been examined in detail and happen to be diploid with 14 chromosomes, so the first incompatibility mechanism isn't a concern.

3. Meiosis after allotetraploidy.
The second incompatibility mechanism can be overcome by inducing tetraploidy in the hybrid. This would be done using Colchicine or Oryzalin, herbicideal compounds that interfere with cell division and result in a doubling of the number of chromosomes in treated tissue. Induction of tetraploidy generally produces one branch that has larger fruit, thicker stems, and other visible features to distinguish it from the original diploid parts of the plant. Because this tetraploid would contain two full copies of genomes from different species, it would be referred to as an allotetraploid.

4. Tragopogon spp. hybrids.
This process has been observed to happen naturally. Three species of Tragopogon (T. dubius, T. porrifolius, and T. pratensis) were introduced into the Pacific northwest region of the USA in the early 1900s from Europe. By the 1950s, scientists realized there were two new species of Tragopogon to be found in the region (T. mirus and T. miscellus). The new species were fertile allotetraploid hybrids between pairs of the introduced species. The hybrid species have even been recreated in the lab. In this case, it appears the allotetraploids came about because the parent species occasionally produce aberrantly diploid gametes which merged to form the fertile allotetraploid. The precise pathway is different than what I expect would be going on with the strawberry/raspberry cross, but it is a wonderful case-study for hybrid speciation.

If everything works out, it will be a few years before I have a fertile strawberry/raspberry cross. I wonder what the fruit would taste like? I'll keep you informed as it goes.

References:
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Tuesday, January 13, 2015

Astrobiology : Mars & Isotopic Analysis

Two stable isotopes of carbon are found, carbon-12 (12C) and carbon-13 (13C). Carbon-12 is the vast majority, at 98.89% abundance. Individual samples of carbon from different sources can vary strongly from the general abundance ratio, depending on where they came from.

The reactions of biology tend to prefer the lighter form of carbon, so over time biological sources of carbon tend to become relatively enriched in carbon-12 vs. carbon-13. A consequence of this is that carbon samples from a living source are distinct from carbon samples from a geological source.

We've examined the carbon ratios from many sources here on Earth. We've now also examined the carbon ratios from a few sources on Mars. A study was published in the December 2014 edition of Meteoritics & Planetary Science that discussed the examination of carbon ratios in a recently recovered Martian meteorite called Tissint.


There are significant differences in the carbon pattern between Earth and Mars. I put together the above figure from one in references #1 and #2, to better compare the known carbon ratio differences by sample type.

The carbon ratios found in carbonates on Mars suggest they are of inorganic origin. Those from freshwater or marine sources on Earth have ratios consistent with their known biological origin.

The red data-points are from organic material found in Tissint. They compare very well to the blue data-points from coal here on earth. On both planets, atmospheric carbon is relatively reduced in carbon-12 compared to the organic material. This is pretty good evidence that the organics in the meteorite came from some living thing, just as the organics in coal did.

The carbon could still have come from contamination here on Earth, after the meteorite landed. To test for this, the researchers examined the isotopic ratios of the hydrogen in the sample. Mars is enriched in deuterium relative to Earth and this same enrichment was found in the examined organic material.

This research happens to be the best direct evidence so far for the existence of life on Mars (at some point in the past). This still isn't entirely conclusive physical evidence. For that we will have to go to Mars and either find an unambiguous macro-fossil, or culture some micro-organism from one of the brine-water seeps we've been looking at from space.

I've been convinced that there was in the past (and is most likely today) living organisms on Mars, from theoretical considerations about how life works, and how it must have spread in the early solar system. However, I wasn't really expecting to see any convincing physical evidence any time soon.


References:
  1. Tissent Carbon ratios: onlinelibrary.wiley.com/doi/10.1111/maps.12389/full
  2. Earth Carbon ratio: www4.nau.edu/meteorite/meteorite/book-glossaryc.html 
  3. Mars Carbon ratio: www.astrowatch.net/2014/12/scientists-find-new-evidence-for-life.html
  4. Organics on Mars: www.sciencedaily.com/releases/2014/12/141216144137.htm
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Thursday, January 8, 2015

Weedy plant domestication

Most of our garden vegetables and crop plants started out as weedy plants.   Part of the evolutionary syndrome of being a 'weedy' species is being r-selected ("r" for reproduction), meaning the species invests in producing as many offspring as possible instead of defending any one life that much. The opposite reproductive strategy is referred to as K-selected ("K" for… well, I have no idea), meaning a species invests a great deal in each offspring to help ensure they have a high chance of survival.

In the context of plants, this means that weedy plants tend to not be spiny, tough, or poisonous... In short, weedy plants tend to be more edible for a non-specialist vegetarian like us humans.

Since I was a child, I've liked the idea of domesticating weedy plants. I have several projects in mind, but have only taken the earliest steps of gathering seeds for some plants I find interesting (Arctium lappa, Carduus nutans, Lepdium virginicum, Leucanthemum vulgar, Malvaviscus drummondii, Oenothera biennis, Thlaspi arvense).

The internet is a wonderful thing in that it lets one find others who have similar interests, no matter how esoteric.

The left half of the image is a botanical plate for Plantago major. It is a common yard side weed native to Europe and Asia. It is easily confused with the related native species Plantago rugelii, which is equally weedy and much more common.

The right half of the image is the result of a project by a plant breeder over at Arrowhead Alpines.   The variety is named "Purple Perversion".   If you order the plant, it will probably spread its genes widely - contaminating the Plantago population already growing in your yard with genetics for interesting colors and textures. (Some other varieties can be found at Plant World Seeds.)

Plantago species have edible leaves that are rich in B vitamins, which gives them a savory taste reminiscent of mushrooms. Some further selection, perhaps with mutation breeding, could transition this plant from a yard weed to a prime garden vegetable. As a domestication project, this plant is already partly done, so I could imagine making significant progress with it.

References:
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Tuesday, December 30, 2014

Mathematical Recreations : Ramanujan's Nested Radical

Srinivasa Ramanujan posed the following puzzle to the Journal of Indian Mathematical Society in April 1911.

What is the value of the following?
\( \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}} \)

He waited over six months, and when nobody replied he gave his solution. The result he provided was 3.


The algebraic solution provided by Ramunujan:

Consider the identity 
\( (x+n)^2 = n^2 + 2nx + x^2 = n^2 + x[(x+n)+n] \)
Take square roots to get
\( [x+n] = \sqrt{n^2+x[(x+n)+n]} \)
Now inside the brackets you have (something + n), so you can
substitute in the same equation with (x+n) replacing (x) to get
\( x+n = \sqrt{n^2+x\sqrt{n^2+(x+n)[(x+2n)+n]}} \)
and repeat the process to get
\( x+n = \sqrt{n^2 + x\sqrt{n^2+(x+n)\sqrt{n^2+(x+2n)\sqrt{\cdots}}}} \)
If you now set n = 1, x = 2 you get
\( 3 = \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}} \)


An alternate way of calculating the equation reveals some interesting behavior.

\( 3 = \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}} \)
\( 3^2 = 1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}} \)
\( 3^2-1= 2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}} \)
\( \frac{3^2-1}{2}= \sqrt{1+3\sqrt{1+4\sqrt{\cdots}}} \)
\( 4 = \sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{\cdots}}}} \)
\( \vdots \)
\( n = \sqrt{1+(n-1)\sqrt{1+(n)\sqrt{1+(n+1)\sqrt{\cdots}}}} \)

The value of each sequential nested radical forms a series...

\( 3, 4, 5, 6, \cdots, \infty \)

...which is perfectly valid. If 3 was not a valid answer to the equation, then this calculation would have revealed a contradiction. Proof by contradiction is one of my favorite methods of proving.

So, what happens if we start with a different starting assumption?

\( 4 = \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}} \)
\( \frac{3\cdot5}{2} = \sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{\cdots}}}} \)
\( \frac{13\cdot17}{2^{2}3} = \sqrt{1+4\sqrt{1+5\sqrt{1+6\sqrt{\cdots}}}} \)
\( \frac{11\cdot19\cdot223}{2^{6}3^{2}} = \sqrt{1+5\sqrt{1+6\sqrt{1+7\sqrt{\cdots}}}} \)
\( \frac{17\cdot27902701}{2^{12}3^{4}} = \sqrt{1+6\sqrt{1+7\sqrt{1+8\sqrt{\cdots}}}} \) 
\( \vdots \)

The value of each sequential radical forms another series.

\( 4, 7.5, 18.41\bar6, 84.543402\bar7, 1429.71739065, \cdots, \infty \)

It is harder to predict subsequent entries of the series than for the original series, but no less valid. I've put some effort into constructing an algebraic function that also produces this series, but have set aside the challenge for now.


So, let's try another starting assumption.

\( 2 = \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}} \)

The value of each sequential radical forms a third series...

\( 2, 1.5, 0.41\bar6, -0.206597\bar2, -0.191463517554, \cdots, -\infty \)

...which is not valid under the convention that a radical can't have a negative value.


Generalizing this computation method, Ramanujan's Nested Radical has an infinite number of valid answers...

\( 3 \ge \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}} \)

Every starting value greater than 3 results in a series of radical values that increase at more than 1 per step and increase to positive infinity. Every starting value less than 3 results in a series of radical values that increases at less than 1 per step and eventually turns negative. I don't yet know how to prove this general statement, but the pattern holds. The system behaves very simply when the starting value is 3, more than 3, or less than 3.


Ramanujan's solution to his puzzle is correct, but it is also incomplete.

The algebraic method is unable to find the full solution to the equation. Algebra doesn't effectively deal with infinites, so it shouldn't entirely be a surprise that an algebraic intuition might make some faulty (or at least incomplete) inferences when infinity is involved. This is interesting because it hints at the limits of algebra as a way of knowing truth. The Gödel Incompleteness Theorems discuss something similar to this and are worth reading more about.

How does this connect with biology?

One detail of my training to be a scientist is learning to look for untested assumptions in arguments that are presented to me. This was never explicitly stated in any of my graduate coursework, but it has been important to do well in the academic environment I experienced in getting my PhD. When I find such an assumption, I see it as a puzzle to be explored. Am I seeing something real? What inferences is the presenter drawing from the assumption? Why is what I'm seeing not already addressed?

What assumptions have you made today?

References:
  1. Ramanujan: www.thefamouspeople.com/profiles/srinivasa-ramanujan-503.php
  2. Algebraic solve: mathforum.org/library/drmath/view/52674.html
  3. Numerical solve: www.johndcook.com/blog/2013/09/13/ramanujans-nested-radical/ 
  4. Proof by contradiction: en.wikipedia.org/wiki/Proof_by_contradiction
  5. Incompleteness theorems: en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
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Saturday, December 27, 2014

Mystery Plant ID Found!

1. omnilexica.com/?q=silphium
A little over a year ago, I was involved in a wedding party and we were walking through a park to a site for some of the arranged photographs. Along the walk, we crossed a stream and there I came across an interesting plant.

The plant was done flowering, but the seed heads retained a nice green color and had the lovely geometry seen in image #1. I picked a sample of the plant, using the pocket-knife I almost always carry (largely for such purposes as this).

Neither myself, my mother, nor my aunt were able to identify the plant. Now this was getting interesting, as my mother and aunt have a long history of gardening and interest in wildflowers. My aunt noted the material had the scent of sunflowers, but this only helped identify it to the family level, which the structure itself had already provided. I tucked the sample into my pocket, hoping to keep it intact until I could identify it at some later time. On returning home, I consulted the field guides I owned. I had no luck, since they all seem to focus on the most charismatic aspect of the wildflowers…  usually, the flowers themselves.

As the plant material dried, I realized that I had collected very mature looking seeds of this unknown plant. I cleaned the seeds and stored them in a vial, hoping to identify them when I later had the chance to grow plants from them. Part of the motivation was also because I thought that the green seed heads would make a nice display in a vase, so I could use the plant as part of my home flower cutting garden.
2. diggingdog.com/pages2/plantpages.php/P-1403

…a year passes…

I am in the final stages of completing my PhD thesis and found my mind wandering. I was reading about the efforts to breed perennial versions of annual crops and to domesticate new perennial crops from wild plants. While looking through a document on the efforts to generate perennial seed crops, I saw a dried plant specimen of Silphium integrifolium (Deam's Rosinweed) and it struck a memory. A quick web-search later and I found an image of exactly what I discovered on the creekside. However, there are several potential species in the genus Silphium that live in the area and have the memorable seed heads, so it will still take growing the seeds I saved to identify the plant down to the species level.

The plant was being studied for its domestication potential as a new seed crop. I still think it would be a worthwhile project to domesticate it as green material for florist use. Domestication of a single plant species can easily go in multiple directions at once, as the plethora of cabbage/broccoli/etc. plants indicate.

Now that I know what the plant looks like and that it will produce some really nice flowers (image #2), I can better plan for where the plant will go in my garden next year.

References:
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Tuesday, December 23, 2014

GMO labeling : The right to know what is in our food.

Sometimes biology intersects with political-charged topics that engage large-numbers of people. In the USA, there has been recent activity around the labeling of foods made from genetically modified organisms (GMOs). The following video epitomizes one viewpoint on the subject.

http://www.upworthy.com/a-14-year-old-explains-food-labeling-in-language-even-condescending-tv-hosts-should-get-3?c=reccon3


One of the major arguments presented in the video is that people have the right to know what is in our food. Because of this, GMO foods should be labeled.

I think this is a wonderful idea!

 However… there's a big problem. People think they know what is in regular crops, while they think they don't know what is in GMO crops. Can you list the compounds found in the last organic heirloom tomato that you ate? Do you know what is in "natural" corn? How about the poisons found in the various types of beans that people eat? How about the poisons sprayed on any crops (even organic) that you might find in the store? The reality is that people, in general, have no idea what is in any of the food they eat.

A second problem I have is that the GMO-labeling ideas being pushed will do nothing to assist people in knowing what is in their food. If you're eating a tomato which included a gene from a fish and the label only says the tomato has been altered with a certain form of technology, then the label does nothing at all to inform you about what you're eating.

We do already have an established method for indicating the presence of small amounts of diverse substances in our food that can be utilized for labeling GMOs: the ingredients list. If your tomato product also includes some fish genes, then the ingredients list for the tomato should include the fish (and any bacterial) genes that are found in it. Finding an ingredients label on a single tomato will discourage those who aren't interested in purchasing GMOs, but will allow those who are interested in learning what is in their food to be able to easily educate themselves.

So far, no organization is pushing for such an educational labeling idea. The people pushing for GMO-labeling don't want honest and educational labeling. They're pushing for labels to inspire fear, uncertainty, and doubt (FUD) about GMOs.

I think such a labeling system should also be extended to indicate what chemicals were sprayed on the fruit and thus are likely to remain on the fruit. This issue doesn't involve GMOs, but these chemicals are something we do know with certainty are poisons...  and yet there is no push for this information on labels.


I am a biologist, so I realize my perceptions of this subject are likely to be distinct from those of most people.

I agree with the reasons stated for GMO labeling, but I am totally against every GMO-labeling proposal I have so far heard being discussed because they don't help attain the goal of the stated reasons.
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Monday, December 15, 2014

Hybrid sunflower roots.

1. Plant 3, roots & tuber.
A few weeks ago, we had a solid freeze and the sunflower season came to an end. I dropped by the old place and dug up my sunflowers to see if any of the F1s had developed tubers. The largest hybrid (plant 3) produced one skinny tuber, while the smaller two plants appeared to produce no tubers at all. This was a disappointment, but a more detailed examination of the remaining plant material led to some positive surprises.

2. Plant 1, seeds.
The first plant looked very much like the Helianthus tuberosus mother, but with more red pigment on the stems. I had assumed this was the result of some recombination of maternal alleles and was at best a control to compare the hybrid plants against. When I looked at the remaining two dried flowers on this plant and found them to be full of seeds (image #2), I realized this plant is likely to also be a hybrid.
3. Plant 3, root bud.

The plant that grew the tuber in image #1 also produced a second type of perennial structure, a new bud growing from the old root crown (image #3). This is a structure that isn't seen in either parent species. This feature has been observed before in crosses of this type, however, so I should have expected the possibility.

4. Plant 2, roots.
The other two plants had mildly-swollen roots (images #4 & #5) that have appeared alive when I checked on them. I don't know if they will show new growth in the spring, or if the roots will at some point finally start to rot.
5. Plant 1, roots.

I'm storing the tuber and all the root structures in a dedicated small cube-fridge over the winter. This should keep them safe from the mice that wander through my basement and allow me to grow at least one of them again next year alongside additional F1s from the ~70 seeds that remain from the first cross.

References:
  1. H. annuss x H. tuberosus : bulbnrose.x10.mx/Heredity/sunflowerXchoke/sunflowerXchoke.html
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