Leslie Matrices are tables used for population projection.A transition matrix is a table with rows and columns
 showing the expected number of people
 who
 END up in the state with the label on the ROW
 per person
 at the START in the state with the label on the COLUMN.ALeslie matrix is a special case of a transition matrix in which
 the states correspond to age groups.We begin by defining a transition matrix.Although the
 choice of assumptions about the future course of fertility, mortal
ity, marriage, divorce, and immigration is fraught with problems,
 the methods for using those assumptions to calculate future popu
lation sizes and age distributions are very well-developed and sat
isfactory.Much of the mathematics of projection was developed treating
 time and age as continuous variables, but projections on comput
ers generally are done with populations split into age groups and
 with discrete steps of time.The choice of credible assump
tions about vital rates is as much a part of the art and science of
 projection as are the formulas we use to implement the calcula
tions.Sophisticated projections treat a population classified by many
 characteristics including race, ethnicity, marital status, income,
 education, and locality as well as sex and age.Current thinking about plausible assumptions for predicting
 populations around the world is presented in a recent book called
 Beyond Six Billion edited by Bongaarts and Bulatao (2000).Of
f
 icial presentations of projections are often filled with disclaimers
 cautioning the reader that projections are not predictions.It largely failed to predict the continuing
 trend toward lower mortality in industrialized countries.But the basic ideas
 are well-illustrated by simpler projections which focus on a single
 sex and on all races and ethnicities together and which subdivide
 the population only by age.When demographers
 project a distribution of marital status, parity, educational level,
 or other variables into the future, they use general transition ma
trices.TRANSITION MATRICES
 111
 The kind of calculations we shall be doing are closely related
 to the subject of Markov chains in probability theory.Generally
 speaking, however, we shall be projecting expected numbers of
 people rather than probabilities, and that makes the demographic
 theory slightly different from the theory of Markov chains.They
 do not tell us what the world will be like but only what the world
 would be like if a particular set of stated assumptions about future
 vital rates turned out to be true.Here we study the discrete versions of
 projection, which use matrices and project populations one step
 at a time.are called "Leslie
 matrices". It was P. H. Leslie who published a description of their
 use in 1945. The same theory was developed a few years earlier
 by H. Bernardelli and by E. G. Lewis, but their work did not
 become widely known until Leslie published his. Leslie matrices
 are a special case of "transition matrices".Such disclaimers, however, are disingenuous.5.1.