No, independent assortment occurs after crossing over. Crossing over occurs in prophase I while independent assortment occurs in metaphase I and anaphase I.
During prophase I, a process called synapsis occurs. That is, homologous chromosomes (one from your mother and one from your father) come together and bind together, forming a tetrad. This binding is due to crossing over, which is when the genetic material on the maternal chromosome and the paternal chromosome exchange places. The maternal chromosome gives some of its genes to the paternal chromosome, and the paternal chromosome gives some of its genes to the maternal chromosome. Crossing over increases genetic variety by creating a new chromosome with a new combination of genes. During metaphase I, the tetrads line up at the equator of the cell. During anaphase one, the tetrads are broken apart and each homologous chromosome that made each tetrad up is pulled toward one end of the cell. Look at the image below, where the blue represents paternal chromosomes and the red represents maternal chromosomes.  Independent assortment describes the phenomenon where the paternal and maternal chromosomes can be lined up randomly at the equator. There are many combinations. For example,
This random alignment at the equator makes it so that during anaphase, random proportions of maternal and paternal chromosomes get assorted into each of the resulting daughter cells. Some cells could get more maternal chromosomes and the other would get more paternal chromosomes, and vice versa. On the other hand, they could get similar amounts. Independent assortment increases genetic variation by allowing daughter cells to each randomly receive a different proportion of paternal and maternal chromosomes. In conclusion, crossing over and independent assortment (sometimes called random assortment) are different independent processes that both lead to an increase in genetic diversity. References Figure 2: Examples of polytene chromosomes Pairing of homologous chromatids results in hundreds to thousands of individual chromatid copies aligned tightly in parallel to produce giant, "polytene" chromosomes. Although he did not know it, Walther Flemming actually observed spermatozoa undergoing meiosis in 1882, but he mistook this process for mitosis. Nonetheless, Flemming did notice that, unlike during regular cell division, chromosomes occurred in pairs during spermatozoan development. This observation, followed in 1902 by Sutton's meticulous measurement of chromosomes in grasshopper sperm cell development, provided definitive clues that cell division in gametes was not just regular mitosis. Sutton demonstrated that the number of chromosomes was reduced in spermatozoan cell division, a process referred to as reductive division. As a result of this process, each gamete that Sutton observed had one-half the genetic information of the original cell. A few years later, researchers J. B. Farmer and J. E. S. Moore reported that this process—otherwise known as meiosis—is the fundamental means by which animals and plants produce gametes (Farmer & Moore, 1905).The greatest impact of Sutton's work has far more to do with providing evidence for Mendel's principle of independent assortment than anything else. Specifically, Sutton saw that the position of each chromosome at the midline during metaphase was random, and that there was never a consistent maternal or paternal side of the cell division. Therefore, each chromosome was independent of the other. Thus, when the parent cell separated into gametes, the set of chromosomes in each daughter cell could contain a mixture of the parental traits, but not necessarily the same mixture as in other daughter cells. To illustrate this concept, consider the variety derived from just three hypothetical chromosome pairs, as shown in the following example (Hirsch, 1963). Each pair consists of two homologues: one maternal and one paternal. Here, capital letters represent the maternal chromosome, and lowercase letters represent the paternal chromosome:
When these chromosome pairs are reshuffled through independent assortment, they can produce eight possible combinations in the resulting gametes:
A mathematical calculation based on the number of chromosomes in an organism will also provide the number of possible combinations of chromosomes for each gamete. In particular, Sutton pointed out that the independence of each chromosome during meiosis means that there are 2n possible combinations of chromosomes in gametes, with "n" being the number of chromosomes per gamete. Thus, in the previous example of three chromosome pairs, the calculation is 23, which equals 8. Furthermore, when you consider all the possible pairings of male and female gametes, the variation in zygotes is (2n)2, which results in some fairly large numbers. But what about chromosome reassortment in humans? Humans have 23 pairs of chromosomes. That means that one person could produce 223 different gametes. In addition, when you calculate the possible combinations that emerge from the pairing of an egg and a sperm, the result is (223)2 possible combinations. However, some of these combinations produce the same genotype (for example, several gametes can produce a heterozygous individual). As a result, the chances that two siblings will have the same combination of chromosomes (assuming no recombination) is about (3/8)23, or one in 6.27 billion. Of course, there are more than 23 segregating units (Hirsch, 2004). While calculations of the random assortment of chromosomes and the mixture of different gametes are impressive, random assortment is not the only source of variation that comes from meiosis. In fact, these calculations are ideal numbers based on chromosomes that actually stay intact throughout the meiotic process. In reality, crossing-over between chromatids during prophase I of meiosis mixes up pieces of chromosomes between homologue pairs, a phenomenon called recombination. Because recombination occurs every time gametes are formed, we can expect that it will always add to the possible genotypes predicted from the 2n calculation. In addition, the variety of gametes becomes even more unpredictable and complex when we consider the contribution of gene linkage. Some genes will always cosegregate into gametes if they are tightly linked, and they will therefore show a very low recombination rate. While linkage is a force that tends to reduce independent assortment of certain traits, recombination increases this assortment. In fact, recombination leads to an overall increase in the number of units that assort independently, and this increases variation. While in mitosis, genes are generally transferred faithfully from one cellular generation to the next; in meiosis and subsequent sexual reproduction, genes get mixed up. Sexual reproduction actually expands the variety created by meiosis, because it combines the different varieties of parental genotypes. Thus, because of independent assortment, recombination, and sexual reproduction, there are trillions of possible genotypes in the human species.
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What are the outcomes from independent assortment and crossing over?
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