I found this article on another site im posting it here.
Contributed by British Columbia Grower's Association:
In this first situation, we'll deal with the situation where a plant breeder finds a special individual or clone.
It's a natural thing to be curious and cross a couple of plants that catch your fancy. Grow them out and find a new variation that you like even better. We can preserve the new variation through cloning indefinately, but accidents happen and clones die. They can get viruses or can suffer clonal deprivation from somatic mutations over time. Plus it's harder to share clones with friends through the mail than seeds. So it's only natural that we would want to create seed backups of this special clone.
But before we start breeding this clone, we should try and figure what exactly it is we want from the seeds we are going to create. Do we want them to simply be able to reproduce individuals like the special clone? Simple backcrossing (cubing) will accomplish this. Or do we want to to create seeds that will be able to create more seeds like the special clone, a true breeding strain? These are very different in nature. You see, chances are that your special clone will be heterozygous for many of traits she phenotypically expresses. This just means that she will contain genetic information (genes) for two opposing triats, but you can only see one, the dominant one. However, her seeds will only get one or the other of the genes, so her offspring will express all the genetic information she has, including what you can't see within herself. If you want to create a true breeding strain, you need to preserve all the genes you can see, and remove all the genes that you cannot, but may show up in the offspring. Creating homozygosity. The only way to accomplish this is through selection and generational inbreeding (selecting the homozygous offspring to be parents for the next generation).
BackCrossing and Cubing
Backcrossing is where you breed an individual (your special clone) with it's progeny. Sick in our world, but plants seem to like it
1) Your first backcross is just a backcross.
2) Your second backcross where you take the progeny from the first backcross and cross back to the SAME parent (grandparent now) is often called SQUARING by plant breeders.
3) Your third backcross where you take the progency (squared) from the second backcross and cross back to the SAME parent (great grandparent now) is often called CUBING by plant breeders. You can continue the backcrossing but we just call this backcrossing. Cubing is in reference to the number three, as in 3 backcrosses
Cubing works on the basis of mathamatical probabilities with respect to gene frequencies. The more males you use with each cross, the better the chance that your reality matches the theory. In theory, with the first backcross, 75% of your genepool will match the genepool of the P1 parent being cubed. Squaring increases this to 87.5% and cubing increases it to 93.75%. You can arrive at these numbers by taking the average between the two parents making up the cross. For instance, you start by crossing the P1 mom (100%) with and unrelated male (0%) getting 100% + 0% divided by 2 = 50%. Therefore, the offspring of this first cross are loosly thought of as being 50% like the mom. Take these and do your first backcross and you get 100% (mom) + 50% divided by 2 = 75%. And this is where we get the 75% for the first backcross. Same thing applies as you do more backcrosses. As you will see later, you can apply this same probability math to specific genes or traits, and this can have a dramatic effect on your methodologyology and selection ways.
Your selection of the right males for each backcross are the crucial points for success with this technique. In each case, you could select males that contain the genes you want, or you could inadvertedly pick those individuals that carry the unwanted recessive genes. Or more likely, you could just pick individuals that are heterozygous for both genes like the P1 mom being backcrossed. The easiest way to deal with this is to start by only looking at one gene and one trait, like lets assume that flavour is determined by a single gene (in reality it's probably not). And do some punnet squares to show gene frequencies through 3 generations of backcrossing. Now lets assume that we found a special pineapple flavoured individual in our pine flavoured population that we wanted to keep. The gene causing the pineapple flavour could be dominant or recessive and the selection abilities and cubing outcome will be different in both cases.
a) pineapple flavour is dominant.
P = pineapple flavour and p = pine flavour
Therefore since each individual will have two flavour genes paired up, the possible genotypes are PP, Pp, and pp. Since P is dominant, PP and Pp will express pineapple flavour while pp will exhibit pine flavour, these are their phenotypes. Now since the pineapple is a new flavour, chances are that the special individual will be heterozygous, or more specifically, Pp. Therefore, the only possible parent combination is Pp X pp with the Pp being the parent to be cubed.
Figure 1. The F1 cross
Now most will find it tough to pick males with the gene for pineapple flavour since males don't produce female flowers. Therefore, they will select males randomly and blindly with respect to this trait. The ratio of P to p genes of the male F1 generation to be used in the first backcross will be 2:6. Another way to look at it is to say that the P gene fequency is 25%. This means that one out of four pollen grains will contain the gene for pineapple flavour. Here is how this plays out in the first backcross.
Figure 2. The B1 cross
Now it's this first backcross that first creates an individual that is homozygous (PP) for the pineapple flavour. However, again because of our limited selection abilities, we choose males randomly. From the random males we should expect three out of eight pollen grains to to contain the gene for pineapple flavour. The P1 female will still contribute one P gene for every p gene. I'll spare your computor's memory and and not post the table, feel free to do it yorself though on paper to be sure you understand what happening
The second backcross (Squaring) will produce the following:
3 PP 8 Pp 5 pp
Therefore, 68.75% will have pineapple flavour and 31.25% will have pine flavour. The frequency of the P gene has risen to 7/16 or 43.75%.
And finally, the third backcross (Cubing) will net the following genotypic ratios:
7PP 16Pp 9pp
Therefore, 71.875% will have pineapple flavour after cubing has been completed. Roughly 22% (7/32*100) of the cubed progeny will be true breeding for the pineapple flavour. The frequency of the P gene has risen to roughly 47% (30/64).
In conclusion, if the backcrossing continued indefinately with random selection of males and with large enough of a population size, the frequency of the P gene would max out at 50%. This means that the best that can be expected from cubing is 25% true breeding for pineapple flavour and 75% that will display the pineapple flavour. You would never be rid of the 25% that would maintain the pine flavour. This model would hold true when trying to cube any heterozygous trait.
b) Pineapple flavour is recessive
In this case, P is for the pine flavour and p is for pineapple flavour. Convention is that the capital letter signifies dominance. For the breeder to have noticed the interesting trait, the mom to be cubed would have to be homozygous for the pineapple flavour (pp). Depending where the male came from and whether it was related, it could be Pp or PP, with PP being more likely. It won't make much difference which in the outcome.
F1 cross is pretty basic, we'll skip the diagram. We simply cross the female (pp) with the male (PP) and get offspring that are all Pp. Since the pine flavour is recessive, none of the F1 offspring will have pineapple flavour (hint ). However, the frequency of the gene p will be 50%.
pp X PP = Pp + Pp + Pp + Pp
Since the F1 generation are all the same (Pp), the pollen it donates to the first backcross will contain a p gene for every P gene. The first backcross will be:
B1 = pp X Pp = Pp + Pp + pp + pp
As you can see, 50% of the offspring will be pineapple flavoured and the frequency of the p gene is 6/8 or 75%. This B1 generation will generate pollen containing 6 p genes for every 2 P genes.
Figure 3. The second backcross.
As you can see, the second backcross or squaring produces pineapple flavour in 75% of the offspring. And the p gene frequency within those offspring is roughly 88%. (Remember C88 ). Of the pollen grains from this squaring, 14 out of 16 will carry the p gene for pineapple flavouring. When they are backcrossed to the P1 mom for the third time, they net the following cubed progeny:
Figure 4. The third backcross
After cubing of a homozygous gene pair, we end up with roughly 88% of them displaying the desired trait (pineapple flavour in this case) and also being true breeding for that same trait. The frequency of this desired gene will be roughly 94%. If the backcrossing was to continue indefinately, the gene frequency would continue to approach 100% but never entirely get there.
It should be noted that the above examples assume no selective pressure and large enough population sizes to ensure random matings. As the number of males used in each generation decreases, the greater the selective pressure whether intended or not. The significance of a breeding population size and selective pressure is much greater when the traits to be cubed are heterozygous. And most elevatedly, the above examples only take into account for a single gene pair.
In reality, most of the traits we select for like potency are influenced by several traits. Then the math gets more complicated if you want to figure out the success rate of a cubing project. Relatively speaking, you multiply the probabilities of achieving each trait against each other. For example, if your pineapple trait was influenced by 2 seperate recessive genes, then you would multiply 87.5% * 87.5% (.875 * .875 *100) and get 76.6%. This means that 76.6% of the offspring would be pineapple flavoured. Now lets say the pineapple trait is influenced by 2 recessive traits and and a heterozygous dominant one. We would multiply 87.5% by 87.5% by 71.9% (.875*.875*.719*100) and get 55%. Just by increasing to three genes, we have decreased the number of cubed offspring having pineapple flavouring down to 55%. Therefore, cubing is a good technique where you want to increase the frequency of a few genes (this is an elevated point to remember ), but as the project increases, the chance of success decreases .... at least without some level of selective pressure.
Applying the pressure
The best way to significantly increase your chances of success is to apply intended selective pressure and eliminate unintentional selective pressure. Try to find clearcut and efficient ways to isolate and select for and against certain traits. Find ways to be sure your males are passing along the intended traits and remove all males that do not. This includes ALL traits that may be selected for. Some traits you will be able to observe directly in the males. Other traits like flowering duration you may not. If you are selecting for a trait you can't directly observe, you want to do some progeny tests and determine which males pass on the most desireable genes. I'll explain more on progeny tests later.
It's elevated that when chosing your best males to ignore the superficial traits having nothing to do with the real traits your looking for. You see, cannabis has several thousand genes residing on just 10 chromosome pairs or 20 individual chromosomes. Therefore each chomosome contains hundred of genes. Each gene residing on the same chromosome is said to be linked to each other. Relatively speaking, they travel as a group . If you select for one of them, you are actually selecting for all of the traits on the chromosome. There is an exception to this rule refferred to as breaking linked genes via crossing over, but for simplicity sake, we will ignore that for now. Getting back to selection, you could decide to select for a trait such as you like the spikey look of the leaves while really being interested in fixing the grapefruit flavour. But as it may happen, both traits may be on the same chromosome pair but opposite chromosomes. If so, as long as you select the plants with spikey leaves, you will never get the grapefruit flavour you really want. It's good to keep in mind that each time you select for a triat, you are selecting against several hundred genes This is why most serious breeders learn to take small methodologyical steps and work on one or two traits at a time. Especially with inbreeding projects such as selfing and backcrossing.
Now lets see what kind of improvements we can make in the first example of trying to cube a heterozygous dominant trait using some selective pressure. Lets say that with each generation, we are able to remove the individuals recessive for the pine flavour (pp), but can't remove the heterozygous ones (Pp). If you recall, our P1 mom had the genotype (Pp) in that model and the F1 cross yielded (Pp + Pp + pp + pp) as possible offspring combinations. We remove the two (pp) individuals leaving us with only Pp. Therefore our first backcross will be:
Pp * Pp = PP + Pp + Pp + pp
Again we remove the pp individual leaving us with PP + 2Pp. Going into the second backcross we have increased our P gene frequency from 37.5% up to 66.7%. This means that going into the second backcross 4 of every six pollen grains will carry the P gene. The outcome is as follows
As you can see, after selecting against the homozygous recessives for 2 backcrosses, we have increased our P gene frequency to 58% from 44% in our squared population. If we again remove the homozygous recessives, our gene frequency increases to 70% (14/20) going into the third backcross, meaning that 7 out of 10 pollen grains will carry the P gene. Again, I'll spare your PC's memory and just give your the results of the third backcross.
B3 cross = 7 PP + 10 Pp + 3 pp
This translates to mean that 95% of the progeny will taste like pineapple after cubing a heterozygous dominant strain if the homozygous pine tasting ones are removed prior to to each backcross. This is an improvent from 72% when no selection occurred. The frequency of individuals true breeding for the pineapple flavour rose to 35%. But more elevatedly, the P gene frequency improves to 60%. This will be an elevated consideration when we discuss progeny testing .
But for now lets recap the percentage of individuals true breeding for the pineapple taste in each of the models. In the case where the pineapple flavour trait is heterozygous dominant and no selective pressure is used, cubing produced 22% true breeding individuals. By selecting against the homozygous pine recessive, we were able to increase this too 35%. And finally, when cubing a homozygous recessive gene, we are able to achieve a cubed population that is 87.5% true breeding for the pineapple flavour. And as I pointed out earlier, these numbers only apply to single gene traits. Lets say the pineapple flavour is coded by two seperate genes, one dominant and one recessive, and you are able to select against the homozygous recessive pine flavour while selecting for the dominant pineapple flavour gene. Your cubed population would then contain 87.5% * 35% (.875 * .35 * 100) = 30% true breeding individuals. As you can see, as long as the cubed source is heterozygous, it doesn't matter how many backcrosses you do, you will never achieve a true breeding strain.
Contributed by British Columbia Grower's Association:
In this first situation, we'll deal with the situation where a plant breeder finds a special individual or clone.
It's a natural thing to be curious and cross a couple of plants that catch your fancy. Grow them out and find a new variation that you like even better. We can preserve the new variation through cloning indefinately, but accidents happen and clones die. They can get viruses or can suffer clonal deprivation from somatic mutations over time. Plus it's harder to share clones with friends through the mail than seeds. So it's only natural that we would want to create seed backups of this special clone.
But before we start breeding this clone, we should try and figure what exactly it is we want from the seeds we are going to create. Do we want them to simply be able to reproduce individuals like the special clone? Simple backcrossing (cubing) will accomplish this. Or do we want to to create seeds that will be able to create more seeds like the special clone, a true breeding strain? These are very different in nature. You see, chances are that your special clone will be heterozygous for many of traits she phenotypically expresses. This just means that she will contain genetic information (genes) for two opposing triats, but you can only see one, the dominant one. However, her seeds will only get one or the other of the genes, so her offspring will express all the genetic information she has, including what you can't see within herself. If you want to create a true breeding strain, you need to preserve all the genes you can see, and remove all the genes that you cannot, but may show up in the offspring. Creating homozygosity. The only way to accomplish this is through selection and generational inbreeding (selecting the homozygous offspring to be parents for the next generation).
BackCrossing and Cubing
Backcrossing is where you breed an individual (your special clone) with it's progeny. Sick in our world, but plants seem to like it
1) Your first backcross is just a backcross.
2) Your second backcross where you take the progeny from the first backcross and cross back to the SAME parent (grandparent now) is often called SQUARING by plant breeders.
3) Your third backcross where you take the progency (squared) from the second backcross and cross back to the SAME parent (great grandparent now) is often called CUBING by plant breeders. You can continue the backcrossing but we just call this backcrossing. Cubing is in reference to the number three, as in 3 backcrosses
Cubing works on the basis of mathamatical probabilities with respect to gene frequencies. The more males you use with each cross, the better the chance that your reality matches the theory. In theory, with the first backcross, 75% of your genepool will match the genepool of the P1 parent being cubed. Squaring increases this to 87.5% and cubing increases it to 93.75%. You can arrive at these numbers by taking the average between the two parents making up the cross. For instance, you start by crossing the P1 mom (100%) with and unrelated male (0%) getting 100% + 0% divided by 2 = 50%. Therefore, the offspring of this first cross are loosly thought of as being 50% like the mom. Take these and do your first backcross and you get 100% (mom) + 50% divided by 2 = 75%. And this is where we get the 75% for the first backcross. Same thing applies as you do more backcrosses. As you will see later, you can apply this same probability math to specific genes or traits, and this can have a dramatic effect on your methodologyology and selection ways.
Your selection of the right males for each backcross are the crucial points for success with this technique. In each case, you could select males that contain the genes you want, or you could inadvertedly pick those individuals that carry the unwanted recessive genes. Or more likely, you could just pick individuals that are heterozygous for both genes like the P1 mom being backcrossed. The easiest way to deal with this is to start by only looking at one gene and one trait, like lets assume that flavour is determined by a single gene (in reality it's probably not). And do some punnet squares to show gene frequencies through 3 generations of backcrossing. Now lets assume that we found a special pineapple flavoured individual in our pine flavoured population that we wanted to keep. The gene causing the pineapple flavour could be dominant or recessive and the selection abilities and cubing outcome will be different in both cases.
a) pineapple flavour is dominant.
P = pineapple flavour and p = pine flavour
Therefore since each individual will have two flavour genes paired up, the possible genotypes are PP, Pp, and pp. Since P is dominant, PP and Pp will express pineapple flavour while pp will exhibit pine flavour, these are their phenotypes. Now since the pineapple is a new flavour, chances are that the special individual will be heterozygous, or more specifically, Pp. Therefore, the only possible parent combination is Pp X pp with the Pp being the parent to be cubed.
Figure 1. The F1 cross
Now most will find it tough to pick males with the gene for pineapple flavour since males don't produce female flowers. Therefore, they will select males randomly and blindly with respect to this trait. The ratio of P to p genes of the male F1 generation to be used in the first backcross will be 2:6. Another way to look at it is to say that the P gene fequency is 25%. This means that one out of four pollen grains will contain the gene for pineapple flavour. Here is how this plays out in the first backcross.
Figure 2. The B1 cross
Now it's this first backcross that first creates an individual that is homozygous (PP) for the pineapple flavour. However, again because of our limited selection abilities, we choose males randomly. From the random males we should expect three out of eight pollen grains to to contain the gene for pineapple flavour. The P1 female will still contribute one P gene for every p gene. I'll spare your computor's memory and and not post the table, feel free to do it yorself though on paper to be sure you understand what happening
The second backcross (Squaring) will produce the following:
3 PP 8 Pp 5 pp
Therefore, 68.75% will have pineapple flavour and 31.25% will have pine flavour. The frequency of the P gene has risen to 7/16 or 43.75%.
And finally, the third backcross (Cubing) will net the following genotypic ratios:
7PP 16Pp 9pp
Therefore, 71.875% will have pineapple flavour after cubing has been completed. Roughly 22% (7/32*100) of the cubed progeny will be true breeding for the pineapple flavour. The frequency of the P gene has risen to roughly 47% (30/64).
In conclusion, if the backcrossing continued indefinately with random selection of males and with large enough of a population size, the frequency of the P gene would max out at 50%. This means that the best that can be expected from cubing is 25% true breeding for pineapple flavour and 75% that will display the pineapple flavour. You would never be rid of the 25% that would maintain the pine flavour. This model would hold true when trying to cube any heterozygous trait.
b) Pineapple flavour is recessive
In this case, P is for the pine flavour and p is for pineapple flavour. Convention is that the capital letter signifies dominance. For the breeder to have noticed the interesting trait, the mom to be cubed would have to be homozygous for the pineapple flavour (pp). Depending where the male came from and whether it was related, it could be Pp or PP, with PP being more likely. It won't make much difference which in the outcome.
F1 cross is pretty basic, we'll skip the diagram. We simply cross the female (pp) with the male (PP) and get offspring that are all Pp. Since the pine flavour is recessive, none of the F1 offspring will have pineapple flavour (hint ). However, the frequency of the gene p will be 50%.
pp X PP = Pp + Pp + Pp + Pp
Since the F1 generation are all the same (Pp), the pollen it donates to the first backcross will contain a p gene for every P gene. The first backcross will be:
B1 = pp X Pp = Pp + Pp + pp + pp
As you can see, 50% of the offspring will be pineapple flavoured and the frequency of the p gene is 6/8 or 75%. This B1 generation will generate pollen containing 6 p genes for every 2 P genes.
Figure 3. The second backcross.
As you can see, the second backcross or squaring produces pineapple flavour in 75% of the offspring. And the p gene frequency within those offspring is roughly 88%. (Remember C88 ). Of the pollen grains from this squaring, 14 out of 16 will carry the p gene for pineapple flavouring. When they are backcrossed to the P1 mom for the third time, they net the following cubed progeny:
Figure 4. The third backcross
After cubing of a homozygous gene pair, we end up with roughly 88% of them displaying the desired trait (pineapple flavour in this case) and also being true breeding for that same trait. The frequency of this desired gene will be roughly 94%. If the backcrossing was to continue indefinately, the gene frequency would continue to approach 100% but never entirely get there.
It should be noted that the above examples assume no selective pressure and large enough population sizes to ensure random matings. As the number of males used in each generation decreases, the greater the selective pressure whether intended or not. The significance of a breeding population size and selective pressure is much greater when the traits to be cubed are heterozygous. And most elevatedly, the above examples only take into account for a single gene pair.
In reality, most of the traits we select for like potency are influenced by several traits. Then the math gets more complicated if you want to figure out the success rate of a cubing project. Relatively speaking, you multiply the probabilities of achieving each trait against each other. For example, if your pineapple trait was influenced by 2 seperate recessive genes, then you would multiply 87.5% * 87.5% (.875 * .875 *100) and get 76.6%. This means that 76.6% of the offspring would be pineapple flavoured. Now lets say the pineapple trait is influenced by 2 recessive traits and and a heterozygous dominant one. We would multiply 87.5% by 87.5% by 71.9% (.875*.875*.719*100) and get 55%. Just by increasing to three genes, we have decreased the number of cubed offspring having pineapple flavouring down to 55%. Therefore, cubing is a good technique where you want to increase the frequency of a few genes (this is an elevated point to remember ), but as the project increases, the chance of success decreases .... at least without some level of selective pressure.
Applying the pressure
The best way to significantly increase your chances of success is to apply intended selective pressure and eliminate unintentional selective pressure. Try to find clearcut and efficient ways to isolate and select for and against certain traits. Find ways to be sure your males are passing along the intended traits and remove all males that do not. This includes ALL traits that may be selected for. Some traits you will be able to observe directly in the males. Other traits like flowering duration you may not. If you are selecting for a trait you can't directly observe, you want to do some progeny tests and determine which males pass on the most desireable genes. I'll explain more on progeny tests later.
It's elevated that when chosing your best males to ignore the superficial traits having nothing to do with the real traits your looking for. You see, cannabis has several thousand genes residing on just 10 chromosome pairs or 20 individual chromosomes. Therefore each chomosome contains hundred of genes. Each gene residing on the same chromosome is said to be linked to each other. Relatively speaking, they travel as a group . If you select for one of them, you are actually selecting for all of the traits on the chromosome. There is an exception to this rule refferred to as breaking linked genes via crossing over, but for simplicity sake, we will ignore that for now. Getting back to selection, you could decide to select for a trait such as you like the spikey look of the leaves while really being interested in fixing the grapefruit flavour. But as it may happen, both traits may be on the same chromosome pair but opposite chromosomes. If so, as long as you select the plants with spikey leaves, you will never get the grapefruit flavour you really want. It's good to keep in mind that each time you select for a triat, you are selecting against several hundred genes This is why most serious breeders learn to take small methodologyical steps and work on one or two traits at a time. Especially with inbreeding projects such as selfing and backcrossing.
Now lets see what kind of improvements we can make in the first example of trying to cube a heterozygous dominant trait using some selective pressure. Lets say that with each generation, we are able to remove the individuals recessive for the pine flavour (pp), but can't remove the heterozygous ones (Pp). If you recall, our P1 mom had the genotype (Pp) in that model and the F1 cross yielded (Pp + Pp + pp + pp) as possible offspring combinations. We remove the two (pp) individuals leaving us with only Pp. Therefore our first backcross will be:
Pp * Pp = PP + Pp + Pp + pp
Again we remove the pp individual leaving us with PP + 2Pp. Going into the second backcross we have increased our P gene frequency from 37.5% up to 66.7%. This means that going into the second backcross 4 of every six pollen grains will carry the P gene. The outcome is as follows
As you can see, after selecting against the homozygous recessives for 2 backcrosses, we have increased our P gene frequency to 58% from 44% in our squared population. If we again remove the homozygous recessives, our gene frequency increases to 70% (14/20) going into the third backcross, meaning that 7 out of 10 pollen grains will carry the P gene. Again, I'll spare your PC's memory and just give your the results of the third backcross.
B3 cross = 7 PP + 10 Pp + 3 pp
This translates to mean that 95% of the progeny will taste like pineapple after cubing a heterozygous dominant strain if the homozygous pine tasting ones are removed prior to to each backcross. This is an improvent from 72% when no selection occurred. The frequency of individuals true breeding for the pineapple flavour rose to 35%. But more elevatedly, the P gene frequency improves to 60%. This will be an elevated consideration when we discuss progeny testing .
But for now lets recap the percentage of individuals true breeding for the pineapple taste in each of the models. In the case where the pineapple flavour trait is heterozygous dominant and no selective pressure is used, cubing produced 22% true breeding individuals. By selecting against the homozygous pine recessive, we were able to increase this too 35%. And finally, when cubing a homozygous recessive gene, we are able to achieve a cubed population that is 87.5% true breeding for the pineapple flavour. And as I pointed out earlier, these numbers only apply to single gene traits. Lets say the pineapple flavour is coded by two seperate genes, one dominant and one recessive, and you are able to select against the homozygous recessive pine flavour while selecting for the dominant pineapple flavour gene. Your cubed population would then contain 87.5% * 35% (.875 * .35 * 100) = 30% true breeding individuals. As you can see, as long as the cubed source is heterozygous, it doesn't matter how many backcrosses you do, you will never achieve a true breeding strain.
