  In the type of population ecology that was discussed earlier (in  Section 2),  populations were characterized by their state variables, parameters such as size or density describing the population as a whole and—with two exceptions—ignoring individual differences. The exceptions are age and stage; the age or stage structure of populations (the fraction of individuals in each age or developmental stage class) is sometimes incorporated in the traditional models of population ecology. Since about 1980, that situation began to change when the so-called “individual-based models” (IBMs), which incorporate individual differences, began to be explored  systematically.[87]  IBMs represent a population as a collection of individuals with variable properties such as size, growth-rate, biomass, and so on. The interactions between individuals are incorporated into the model. Since, because of their sheer complexity, such models are typically impossible to study analytically, they are studied by simulation on a computer. The wealth of detail that can be incorporated into IBMs allows specific predictions to be made. Part of the attraction of IBMs has been their relatively greater predictive success compared to other types of ecological  models.[88]