and values is: {| border="0" cellpadding="0" cellspacing="0" width="100%" |- | align="left" | | align="right" | |} The notation will also be used when convenient. Suppose there is a population of organisms all of which have a genetic characteristic described by some real number. For example, high values of the number represent an increased visual acuity over some other organism with a lower value of the characteristic. Groups can be defined in the population which are characterized by having the same value of the characteristic. Let subscript identify the group with characteristic and let be the number of organisms in that group. The total number of organisms is then where: The average value of the characteristic is defined as: {| border="0" cellpadding="0" cellspacing="0" width="100%" |- | align="left" | | align="right" | |} Assume that the population grows and the number of persons in each group grows. in the next generation is represented by . The so-called fitness of group is defined to be the ratio of the number of its individuals in the next generation to the number of its individuals in the previous generation. That is, {| border="0" cellpadding="0" cellspacing="0" width="100%" |- | align="left" | | align="right" | |} As a result, a group's "greater fitness" equates to its members producing more offspring per individual in the following generation. Similarly, n' stands for the total number of people in all groups, which may be written as: Furthermore, the average fitness of the population can be shown to be the growth rate of the population as a whole, as in: {| border="0" cellpadding="0" cellspacing="0" width="100%" |- | align="left" | | align="right" | |} Although the overall population may increase, the proportion of people in each category may alter. If one group is more physically fit than another, the higher-fitness group will have a greater rise in representation in the following generation than the lower-fitness group. The average fitness indicates how the population increases, and individuals with below-average fitness will see their proportions drop, while those with above-average fitness will see their proportions increase. In addition to the number of people in each group shifting over time, characteristic values within a single group may fluctuate slightly from generation to generation (e.g., due to mutation). Together, these two forces will lead the characteristic's average value to rise across the board. {| border="0" cellpadding="0" cellspacing="0" width="100%" |- | align="left" | | align="right" | |}