Meiosis & Sexual Reproduction

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1. First, define Meiosis.

Meiosis is the process of cell division in sexually reproducing organisms that reduces the number of chromosomes in reproductive cells from diploid to haploid, leading to the production of gametes in animals and spores in plants. http://www.thefreedictionary.com/meiosis
During meiosis, the genes of each parent are "shuffled" such that each gamete, while possessing half of the parental genotype, carries a unique combination of parental genes. This "shuffling" arises by recombination which includes two components; independent assortment and crossing-over. As a consequence, sexual reproduction is capable of generating a wide variance of phenotypes, even in the absence of mutation. Asexual reproduction can be vegetative or parthenogenetic apomixis. In parthenogenesis, a single cell can give rise to a new diploid individual. In apomixis, meiosis is suppressed so that offspring develop from a single diploid cell produced by their parent. In some organisms, females can give rise to only female offspring, but the offspring are produced by meiosis. This is sexual reproduction, even though no males are involved. In the absence of mutation, asexual offspring are genetically identical to their parent (1)
See other definitions below.

2. Then, define and discuss the "cost of meiosis" (Be sure to list at least 2 references in a References section.
There is a "cost of meiosis". Imagine an asexual population of females. In this population a mutation arises that causes meiosis. Initially, this allele will be found only in heterozygous individuals. Therefore a female will pass on this gene for meiosis to only half her offspring while asexual females will pass on the allele for asexual reproduction to all her offspring. Assuming that the mean number of offspring is the same regardless of the parental genotype, the rate of increase for the allele causing meiosis is only half that of the allele for asexual reproduction. Under these conditions, the allele for meiosis should not persist. http://www.life.uiuc.edu/ib/405/lectures/SexRec.pdf.

3. Second, speculate on why sexual reproduction has evolved.

This question is straightforward, as it is asking for your opinion, as to why you think sexual reproduction has evolved. Often the question, what is the purpose of sex? provides ideas of why sexual reproduction has evolved.
Let's look at a couple of examples that you can consider:

Example 1:
According to evolution theory, it was difficult to explain why it evolved, mainly because asexual was thought to be less risk of a risk to the organisms and to the species, so it is perplexing why sexual reproduction evolved at all. Indeed sexual reproduction increased the risk by 50%. Additionally, it was believed that sexual reproduction might "speed up" evolution. However, theorists soon realized that, from an evolutionary viewpoint, an organism's "fitness" was damaged, not improved, as a result of sexual reproduction. Graham Bell pointed out:
Sex...does not merely reduce fitness, but halves it. If a reduction in fitness of a fraction of one percent can cripple a genotype, what will be the consequence of ...