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In biology, fitness may be thought of as the ability of an organism to ensure its genes are passed on to future generations. Since children are the primary means of passing on genetics fitness usually comes down to a measure of how many offspring an organism can produce that will reach reproductive maturity and manage to produce genetically fit offspring of their own.[1] Though there are some other means of passing on genetics, such as assisting closely related individuals in producing children, that can also contribute to overall genetic fitness.[2]
Evolution is often summarized (read as: oversimplified) as "Survival of the Fittest." In more expanded terms, this means that evolution favors mutations or adaptations which increase the fitness of their host organism. For the most part, that makes sense to people. The misconceptions start to leak in when people forget that fitness is defined solely as an organisms ability to pass on their genetics and instead use their own layman idea of what would make an animal fit. Fitness does not require an organism to be bigger, stronger, faster, smarter, or longer lived then another organism. An extreme example would be the following: suppose Organism A has a gene which makes it reproduce five times more viable offspring but makes it die at a very young age. Organism B, on the other hand, has a competing allele which makes the organism survive five times longer but produce far fewer viable offspring. Which one is more fit? The answer, as long as we keep things simple, is A. It may not live as long, but it produces way more copies of its gene, which in turn produce way more copies until Organism B is just a tiny minority. To give another example whenever a larger herbivore species successfully migrates to a smaller island it usually evolves to be smaller, slower, and weaker then its ancestors.[3] These traits are no longer needed on an island that lacks predators[note 1] and thus are traded away so the creature can dedicate more resources to its primary goal of making more babies.
Another related misconception about fitness is that it can be termed simply in the number of offspring. However the number of offspring only counts if those offspring successfully grow up and produce offspring of their own, having hundreds of offspring who all die young or fail to reproduce is less fit then having a single child that grows up to produce children of its own. This is why both R and K select strategies, which roughly is the difference between having lots of offspring and dedicating little effort to caring for them, and having a few offspring you dedicate extensive energy into raising, are both viable strategies. R species may have hundreds of children, but most of their children die young. In the end both R and K species will have roughly the same number off offspring per parent live long enough to achieve reproductive success per generation.
To further complicate things fitness is defined only by the ability to spread one's genetics. Usually this is done by having viable offspring, but this can also be done by supporting closely related individuals in having offspring of their own. So for example let's say some organism named Alice can have one child of it's own, or can instead aid each of her three siblings in raising their children, allowing each sibling to be able to have another child of their own. Given these two options our organism Alice is more fit by giving up on having children of her own and instead dedicating her energy to aiding her siblings in raising their children. This is because each of Alice's siblings carry half of Alice's DNA, assuming they share the same biological parents, which in turn means that children of Alice's siblings will also have half as much of Alice's DNA then her own child would posses. Ultimately helping to ensure an additional three nieces or nephews are born will result in spreading 1.5 times as much of Alice's DNA then her own child would have been expected to spread. Evolutionary fitness through aiding generically related relatives is the primary driver of the evolution of eusocial insects. Only one queen out of hundreds may be allowed to reproduce in such a setup, but if all the workers of a hive are related to that queen they can still be evolutionary fit without having children by helping their mother to spread the DNA they share with their mother.
Note here that we're not talking about the actual factors which may increase or decrease fitness. Rather, the focus here is on factors which may affect our evaluation of a gene in terms of fitness. These can come in a variety of forms, but the salient point is that looking only at the number of offspring produced is often overly simplistic. One must also look at the health of each of these offspring and their reproductive success.
The term "heterozygote advantage" applies to a gene which imparts some sort of advantage when present in only one copy (that is, when the organism is heterozygous). The most common example involves the gene for sickle-cell anemia. When a person is homozygous-dominant for this trait, their red blood cells are normal; when they are homozygous-recessive, they are prone to sickle-cell anemia. However, sickle-cell heterozygous humans have increased immunity to malaria. So, it's adaptive, but not in double doses.
In terms of individual selection, this concept does not have many implications, but the ramifications of heterozygote advantage in terms of gene selection can be fairly complex. A gene "wishes" to create copies of itself, not copies of its competing allele. However, in the case of heterozygote advantage it is actually beneficial for the gene to cooperate with its competitor, contrary to what simple gene-selection theory might predict.
Some of the problems of thinking of fitness can be solved if we break away from the idea of an individual and start thinking from the point of view of the gene, as first suggested by Prof. Dr. Richard Dawkins in The Selfish Gene.[4] The gene "wants" only to produce more copies of itself, and so it could be considered successful if it contributes to the creation of a body which passes on more copies of that gene. It could go about this a variety of ways, from the creation of a number of low-quality bodies or the creation of a few high-quality bodies. The quality doesn't matter; what matters is how many copies of the gene the new body can pass on. That's fitness.