Where to start…
I guess I’ll start with the definitions:

N (Haploid)- Describes a nucleus, cell or organism possessing a single set of unpaired chromosomes. Gametes are haploid.

Polyploidy- cells or organisms contain more than one copy (ploidy) of their chromosomes. Polyploidy occurs in animals but is especially common among flowering plants, including both wild and cultivated species.

Gametes-Specialized haploid cells produced by meiosis and involved in sexual reproduction.
Male gametes are usually small and motile (spermatozoa), whereas female gametes (oocytes) are larger and nonmotile.

2N (Diploid)- A cell with a full set of genetic material, consisting of chromosomes in homologous-(corresponding in structure, position, origin, etc.) pairs and thus having two copies of each autosomal genetic locus- (The position of a gene or chromosome segment on a chromosome. Alleles are located at identical loci on homologous chromosomes). A diploid cell has one chromosome from each parental set.
Most animal cells have a diploid set of chromosomes. The diploid human genome has 46 chromosomes. The gametes (eggs and sperm) contain a single set of chromosomes (haploid).

4N (Tetraploid)- Having four times the haploid number of chromosomes in the cell nucleus.

3N (Triploid)- Having three times the haploid number of chromosomes in the cell nucleus.

Colchicine- A poisonous, pale-yellow alkaloid, C<sub>22</sub>H<sub>25</sub>NO<sub>6</sub><sub></sub> (N-[(7S)-5,6,7,9-tetrahydro-1,2,3,10-tetramethoxy-9-oxobenzo[a]heptalen-7-yl)acetamide]), is obtained from the autumn crocus and used in plant breeding to induce chromosome doubling and also in medicine to treat gout.
The alkaloid extracted from plants of the genus Colchicum and especially from the corms of the autumn crocus, Colchicum autumnale (meadow saffron). The metabolic effect of colchicine is not known, but it is thought that it may decrease production of lactic acid and prevent accumulation of uric acid crystals in the body, making it useful in the treatment of gout. Colchicine and derivatives such as demecolcine inhibit mitosis, or cell division. As a mitotic poison, it inhibits rapidly proliferating cells and has been used in cancer therapy and as an immunosuppressive drug. Colchicine has also been used to visualize chromosomes photomicrographically and to induce mutations experimentally. In laboratory setting colchicine is also used for inducing polyploidy in plant cells during cellular division.


There are several mechanisms by which polyploids arise. Three examples are somatic doubling, gametic nonreduction and triploid bridges. Somatic doubling occurs at the zygotic, embryonic, or meristematic stages of a plant’s life cycle. Polyploid offspring can be generated from the production of polyploid tissues. Although many examples of polyploidy via somatic doubling have been reported, this mechanism now seems less common than gametic nonreduction, or the production of unreduced gametes, as a means of polyploid formation in natural populations (Harlan and deWet, 1975). Unreduced gametes have been reported in a number of species, most notably those that also produce polyploids (Ramsey and Schemske, 1998). Both auto- and allopolyploids can arise in one step after unreduced gamete formation by the union of two unreduced gametes from the same plant.
Alternatively, the production of either an auto- or allotetraploid may involve a ‘triploid bridges”. Tetraploids are formed by triploid intermediates formed within a diploid population by backcrossing to diploids or by self fertilization of the triploid. This two-step method has been considered a significant pathway to polyploid formation (Harlan and deWet, 1975), but some (Bretagnolle and Thompson, 1995) suggest that the one-step process involving the union of two unreduced gametes may be more common. Ramsey and Schemske (1998) concluded that the triploid intermediates may be more significant in the formation of tetraploids since triploids could be more reproductively viable than originally thought.

The Advantages of Polyploidy
The main advantage of polyploidy is the production of heterozygotes. Typically the diploid Mendelian cross of AA and A’A’ would produce a 1:2:1 genotypic ratio (1 homozygous AA, 2 heterozygous AA’ and, 1 homozygous A’) of progeny. However, in a polyploid species the frequency of heterozygotes are much greater. A tetraploid, for example, cross of AAAA and A’A’A’A’ would result in a genotypic ratio of 1:32:1 (Stebbins, 1947). Heterozygotes offer many advantages including buffering effects, protection from inbreeding depression, and the unidirectional introgression phenomenon (Soltis and Soltis, 1995).
Buffering Effects
Tetrasomic inheritance has a buffering effect on intermediate genotypes, an effect of great adaptive value to a population (Stebbins, 1950). This production of nearly all heterozygous ferns is an advantage because it makes the appearance of deleterious homozygous alleles rare because of the masking effect of additional genomes (Soltis and Soltis, 2000).
Two closely related tetraploid species, for example, that hybridize have five possible genotypic progeny: (aaaa), (aaaa'), (aaa'a'), (aa'a'a'), and (a'a'a'a'). Therefore, it can be expected that those with more "a" alleles would be well suited for an area where that allele thrived. Likewise it can be expected that a greater composition of the a' allele would be best suited for areas where a' thrived. This combination of recombination, natural selection, and genetic segregation is capable of producing an entire spectrum of genotypic populations that would be compatible with any region of intermediate environmental conditions (Stebbins, 1971).
Inbreeding
An isolated plant is forced to undergo self-fertilization or selfing. In this situation the frequency of deleterious homozygous alleles increases leading to an overall reduction in the colony’s overall fitness. This inbreeding depression is defined as a reduction in fitness and vigor of individuals as a result of increased homozygosity through inbreeding in a normally out-breeding population. For example, an isolated colony of diploid plants would experience an increase in the number of deleterious homozygous alleles and have increased progression towards fixation or even loss of certain alleles. Studies have found that ferns actually have increased production of normal sporophytes when they are isolated and forced into self fertilization (Soltis and Soltis, 2000).
When considering a single allele at a single locus, the effects of inbreeding depression do not appear to a problem of great importance. The problem is escalated when all the loci are taking into consideration (Lynch, 1995). For example, examinations of lower organisms and other plants estimate about 100 deleterious alleles to be present in individuals when all genetic loci are examined. Individually these alleles produce only a small reduction in fitness ( 2%) when homozygous. However, the combination of all 100 homozygous loci accumulated through inbreeding could potentially reduce the fitness of the organism on the order of 200%! This is enough to "kill" the individual two times over (Lynch, 1995)
Despite the disadvantages of inbreeding, polyploid ferns have grown to favor selfing as a form of reproduction since polyploid protections against inbreeding depression. Two studies of inbreeding depression in diploid and tetraploid ferns show this tendency. In Phegopteris 30-60% of all selfed gametophytes from the diploid race produced normal sporophytes. However 100% of the selfed gametophytes of the tetraploid race formed sporophytes. Another example of selfing preference is present in Lepiosorus. Here, only 4% of the selfed diploid race produced normal sporophytes when nearly 100% of the selfed tetraploid race produced normal sporophytes (Soltis and Soltis, 1995).
Unidirectional introgression
Unidirectional introgression is an important advantage in that the tendency occurs to assist chromosomal segregation in helping ferns(or orchids) colonize into new areas. A combination of hybridization and natural selection on the backcrossed and better suited progeny, produces a tendency for the diploids to form tetraploids or other higher number systems. When triploids occur from this diploid–tetraploid cross, many are incompatible as a triploid hybrids. Therefore there is a tendency for these variants to form tetraploids (Sebbins, 1971).


Further reading.

http://members.cox.net/lmlauman/osp/...hicine1_4.html
http://www.carnivorousplants.org/cpn...lt291Colch.htm
http://www.hort.purdue.edu/newcrop/ncnu02/v5-458.html
http://www.bedfordorchids.com/ploidy.htm(A simpler explanation found here.)

hope this helps.