When we compare two different types of organisms we often find traits that are similar. On the basis of evolutionary theory, these traits can arise through either of two processes: the trait could have been present in the ancestral population that gave rise to the two species or the two species could have developed their version of the trait independently. In this latter case, the trait was not present in the last common ancestor shared by the organism. Where a trait was present in the ancestral species it is said to be a homologous trait. If the trait was not present in the ancestral species but appeared independently within the two lineages, it is known as an analogous trait that arose through evolutionary convergence.
For example, consider the trait of vitamin C dependence, found in Haplorrhini primates and discussed above. Based on a number of lines of evidence, we conclude that the ancestor of all Haplorrhini primates was vitamin C dependent and that vitamin C dependence in Haplorrhini primates is a homologous trait. On the other hand, Guinea pigs (Cavia porcellus), which are in the order Rodentia, are also vitamin C dependent, but other rodents are not. It is estimated that the common ancestor of primates and rodents lived more than ~80 million years ago, that is, well before the common ancestor of the Halporrhini. Given that other rodentia are vitamin C independent, we can assume that the common ancestor of the rodent/primate lineages was itself vitamin C independent. We conclude that vitamin C dependence in Guinea pigs and Halporrhini are analogous traits.
As we look at traits, we have to look carefully, structurally, and more and more frequently in the 21st century, molecularly (genotypically) to determine whether they are homologous or analogous - the result of evolutionary convergence. Consider the flying vertebrates. The physics of flight (and many other behaviors that organisms perform) are constant. Organisms of similar size face the same aerodynamic and thermodynamic constraints. In general there are only a limited number of physically workable solutions to deal with these constraints. Under these conditions different populations that are in a position to exploit the benefits of flight will, through the process of variation and selection, end up with structurally similar solutions. This process is known as convergent evolution. Convergent evolution occurs when only certain solutions to a particular problem are evolutionarily accessible.
Consider the wing of a pterodactyl, which is an extinct flying reptile, a bird, and a bat, a flying mammal. These organisms are all tetrapod (four legged) vertebrates – their common ancestor had a structurally similar forelimb, so their forelimbs are clearly homologous. Therefore evolutionary processes (using the forelimb for flight) began from a structurally similar starting point. But most tetrapod vertebrates do not fly, and forelimbs have become adapted to many different functions. An analysis of tetrapod vertebrate wings indicates that each took a distinctly different approach to generating wings. In the pterodactyl, the wing membrane is supported by the 5th finger of the forelimb, in the bird by the 2nd finger, and in the bat, by the 3rd, 4th and 5th fingers [←]. The wings of pterodactyls, birds, and bats are clearly analogous structures, while their forelimbs are homologous.
As another example of evolutionary convergence consider teeth. The use of a dagger is an effective solution to the problem of killing another organism. Variations of this solution have been discovered or invented independently many times; morphologically similar dagger-like teeth have evolving independently (that is, from ancestors without such teeth) in a wide range of evolutionarily distinct lineages. Consider, for example, the placental mammal Smilodon and the marsupial mammal Thyacosmilus [→]; both have similarly-shaped highly elongated canine teeth. Marsupial and placental mammals diverged from a common ancestor ~160 million years ago and this ancestor, like most mammals, appears to have lacked such dagger-like teeth. While teeth are a homologous feature of Smilodon and Thyacosmilus, elongated dagger-like teeth are analogous structures that resulted from the convergent evolution.