What is the relationship between crossing over and linked genes?

[iScience]

in a table with a in all of the table with the genotypes I'm being presented with (for linkages), like this one..

http://i.imgur.com/MQ7p2bI.jpg

the parent genotype (original genotype) is always statistically the highest. i don't understand, i thought crossing over always happened in prophase I, this data would suggest otherwise wouldn't it? if the offspring statistics match that of the parent's genotype, then it's not likely that crossing over happens many many times and then eventually comes back to to the original; it's more likely that the offspring genotypes just haven't changed at all which would imply no crossing over, but why? again, i thought all chromosomes underwent crossing over in Prophase I.

and what makes the middle gene so probablistically low when it is the only one from another chromosome? the fact that it had to undergo crossing over twice? why is this so unlikely?

also, what is the difference between complete linkage and partial linkage?

http://i.imgur.com/6lqfhlG.png

my understanding is that complete linkage is when there is a zero probability of a cross over. how can this ever be true if two genes are on one chromosome? even if the two genes are right next to each other, how can this be true?

 

[atyy]

Crossing over is a random event. http://www.ncbi.nlm.nih.gov/books/NBK21827/ (Linkage maps)

"The basic idea here is quite simple. Imagine two specific genes positioned a certain fixed distance apart. Now imagine random crossing-over along the paired homologs. In some meiotic divisions, nonsister chromatids cross over by chance in the chromosomal region between these genes; from these meioses, recombinants are produced. In other meiotic divisions, there are no crossovers between these genes; no recombinants result from these meioses. Sturtevant postulated a rough proportionality: the greater the distance between the linked genes, the greater the chance that nonsister chromatids would cross over in the region between the genes and, hence, the greater the proportion of recombinants that would be produced."