Author Topic: Calculus for plant breeding  (Read 405 times)

William S.

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Calculus for plant breeding
« on: 2019-10-15, 09:31:19 PM »
Does anyone know of the top of their heads any practical applications for calculus in plant breeding?
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spacecase0

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Re: Calculus for plant breeding
« Reply #1 on: 2019-10-29, 10:47:07 PM »
I learned calculus from someone that loved math, he shared every possible use for it.
I know how it is used in farming plants and animals
but never a mention of plant breeding
if there is an application for it, I bet it is a new one.

Nicollas

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Re: Calculus for plant breeding
« Reply #2 on: 2019-10-29, 11:17:30 PM »
For example how many plants do you have to grow to have X% of chances to recover a certain combination of genes (e.g. 3 recessives) knowing the parents. Conversly, how lany chances if one grows Y plants.


William S.

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Re: Calculus for plant breeding
« Reply #3 on: 2019-10-30, 09:48:23 AM »
For example how many plants do you have to grow to have X% of chances to recover a certain combination of genes (e.g. 3 recessives) knowing the parents. Conversly, how lany chances if one grows Y plants.

Is that probability?
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William S.

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Re: Calculus for plant breeding
« Reply #4 on: 2019-10-30, 09:54:25 AM »
I learned calculus from someone that loved math, he shared every possible use for it.
I know how it is used in farming plants and animals
but never a mention of plant breeding
if there is an application for it, I bet it is a new one.

I am retaking basic calculus after twenty years. I didn't do well the first time. However I did recall with a bit of googling last night that the applied calculus for biology majors had quite a bit about using exponential functions to model animal or plant population growth with respect to r and k selection.

It does seem to me like there should be some application of differentials at least to gene frequencies as populations grow and contract.
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Ocimum

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Re: Calculus for plant breeding
« Reply #5 on: 2019-10-30, 11:07:20 AM »
William S.

Bos & Caligari 2008 Selection Methods in Plant Breeding
Quote
Yield is a trait affected by many loci. Each chromosome arm may be
assumed to contain at least one relevant locus. Then grain yield of bread
wheat is controlled by at least 42 more-or-less independently segregating
loci (Chapter 1). If two wheat varieties, which have a different homozygous
genotype with regard to 25 of such loci, are crossed, the probability that a
plant of the F2 generation has genotype BB or Bb for each of the 25 loci
amounts to
( 3/4 )^25 = 0.00075
Thus it is expected that 1 out of 1329 plants of the F2 has the complex
genotype B1 B2 . . . B25, where indicates the presence at the considered
locus of either allele b or B. The probability that a plant of the F2 generation
has a different genotype is 0.99925.
The probability that a plant has genotype BB or Bb for each of the 25 loci
amounts in the F3 to
( 5/8 )^25 = 0.0000079
Then 1 out of 126,765 plants of the F3 is expected to have genotype B1
B2 . . . B25. In the F4 ...
Is this what you are looking for?
@Joseph, or any other admin: as far as I know, short extracts of publications are allowed, as long as the source is cited. Is this also allowed for forums? If not, please delete this message.

William S.

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Re: Calculus for plant breeding
« Reply #6 on: 2019-10-30, 05:29:27 PM »
Found a book, its a bit expensive, and is plant physiology. However there exists a book called Calculus in Plant Science.
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Joseph Lofthouse

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Re: Calculus for plant breeding
« Reply #7 on: 2019-10-31, 12:16:23 PM »
@Joseph, or any other admin: as far as I know, short extracts of publications are allowed, as long as the source is cited. Is this also allowed for forums? If not, please delete this message.

We allow short quotes with proper attribution.

William S.

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Re: Calculus for plant breeding
« Reply #8 on: 2019-11-30, 04:17:11 PM »
So in my own personal calculus journey I took applied calculus ~20 years ago and am currently about to start the final week of an equivalent course I am retaking because I didn't really do that well at it twenty years ago. The trajectory of the result is suboptimal and I suspect a B or C grade may be the result but the real pain is that I am not going to quite obtain mastery, though another 5 weeks or so of self study might rectify the difference.
     This question I asked here is central to the question of if I should devote more time to studying calculus. So far what I have found is that calculus may not be important to the mathematics of plant breeding. However it may be important to plant ecology, it may have applications in statistics, and it may have applications in plant physiology such as water potential. All of which can be applied back to plant breeding.
     For instance several of us are growing domestic hybrids, Solanum penellii, and interspecies hybrids between the two. It seems to me that we've thus created three populations for comparison. If we want to know if a subset or selection of the interspecies hybrids retain some of the superpowers of Solanum penellii we may be able to make some comparisons using calculus. My calculus text has a section on probability distributions and there is an example regarding comparing normal curves (this would be integrals). So if we collect data in regards to growth rate, reproductive output, water potential, or ? we might be able to compare the statistical distribution of those data using integrals, and find individuals within the hybrid population that have the traits we are seeking. So maybe not important to the actual breeding, but could inform our understanding of which individuals or subpopulations to move forward with IF we are strictly trying to retain some superpower such as extreme drought tolerance.

Notably our populations of the species tomatoes seem to be rapidly adapting to our gardens. In so doing are they losing their super powers? Possibly statistical analysis using integral calculus could give us answers.

Though some of you out there may already have a much higher degree of calculus mastery than I have ever obtained. Does any of this seem reasonable?

Calculus can be thought of as the mathematics of change with differentials being instantaneous change and integrals accumulated change. Can that be used to compare plant populations within a meta population I.E. the 14 species tomato complex?

A quick search for comparative physiology of tomato species found this summary of a paywall blocked paper https://www.tandfonline.com/doi/abs/10.1080/14620316.1994.11516495 on comparative salt responses on domestic, penellii, and the hybrids.
« Last Edit: 2019-11-30, 04:21:58 PM by William S. »
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Ocimum

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Re: Calculus for plant breeding
« Reply #9 on: 2019-11-30, 09:33:26 PM »
When using these types of calculus, we usually don't take into account epigenetic effects, which also have an influence on environmental tolerance.