Two applications of relative contour maps are shown in Figures 14 and 15. Figure 14 displays age-specific mortality rates for Italian males relative t o their levels in 1925, a year roughly halfway through the period studied. T h e m a p clearly reveals the great progress that has been made in reducing mortality a t the youngest ages compared with the slow progress a t the oldest ages. T h e map also puts the devas- tation of World War I into perspective: World War I essentially erased a half cen- tury of progress, but the setback was temporary and pre-World War I mortality rates a t most ages were achieved and surpassed within a decade or so.
Figure 15 presents age-specific birth rates for US females relative to their level in the final year, 1980. T h e map highlights the dramatic reduction in birth rates above age 35, compared with the less radical (relative) changes a t younger ages.
2000 2020 Year
Figure 19. Population of Sophia, Bulgaria, with contour lines from 9000 to 121000 at in- tervals of 8000, and from age 0 to 85, projected from 1975 to 2049.
Even the baby boom pales in significance when viewed from this perspective.
Instead of dividing a demographic array by the age-specific statistics for a particular year, the array could be divided by the period-specific statistics for a par- ticular age. For example, Figure 1 6 shows Italian male mortality rates a t various ages relative to the infant mortality rate in the appropriate year. The falling con- tours on the top half of the map emphasize a trend that was less apparent in the original Figure I(b), namely that progress against mortality at older ages has been slower than that a t younger ages. In 1870 mortality rates at age 65 were roughly one fifth the level of infant mortality; a century later, mortality rates at age 65 were about one quarter higher than the prevailing infant rates.
Demographic statistics can also be expressed relative to some composite age- specific or period-specific measure. Figures 1 7 and 1 8 provide two examples. To produce Figure 17, Belgian age-specific female population levels (from Veys, 1983) were divided by the total Belgian female population in each year. Thus, the map
1900 1920 1940 1960 Year
Figure 17. Age-distribution of Belgian female population, with contour lines selectively placed from 0.00005 to 0.027, and from age 0 to 99 and year 1892 to 1977.
gives contours of the age distribution of t h e population, i.e., the percentage of the population in each year t h a t are at various ages. T h e diagonal traces of the small cohorts born during World Wars I and I1 are apparent, as is the general trend of t h e age composition of the population to shift upward t o older ages. As a propor- tion of the population, 70-year-olds were as important in 1970 as 40-year-olds were in 1892.
Figure 18, which is based on US fertility d a t a , is similar in nature except t h a t the contours pertain t o cumulative levels u p through age 49 relative to t h e total level over all ages. T h e map can be interpreted as showing t h e proportion of all births in a given year t h a t occurred t o women of some age or less-in a synthetic population in which there were equal numbers of women a t each age. T h e general trend is downward, especially a t older ages: a greater cumulative proportion of children is being born each year t o younger women. This trend runs through the periods of baby boom a n d bust.
1920 1940 1960 1980 Year
Figure 18. Cumulative distribution of US births by age of mother and year, with contour lines selectively placed from 0.1 to 0.999, and from age 14 to 49 and year 1917 to 1980.
i g i o 1930
Year of birth
Figure 19. Cumulative distribution of US births by age and year of birth of mother, with contour lines selectively placed from 0.1 to 0.999, and from age 14 to 39 and year o l birth 1903 to 1941.
Finally, it may sometimes be useful to examine Lexis maps based on statistics approximate because seventh and higher birth orders are omitted. In other words, the maps decompose total fertility into the contribution made a t different parities.
This decomposition indicates that the absolute fluctuations in numbers of first and second children were more significant, in creating the waves of baby booms and rates accounted for roughly two thirds of the tol.al change.
One aspect of the recent baby boom thal is strikingly revealed by the maps in tinue to decline. In general, the maps provide further eviderlce of the importance of age and period effects, but sr~bstantial cohort efiects are not appareril..
T h e six small rnultiples shown in Figure 20 are included on lhe computer diskette (see page 3 ) , together with a program that displays the rriaps in sequence, either slowly or quickly, as a kirid of derriographic movie. 'I'he movie is not, only visually striking, but also informative. In particular, movement in the cohort direc- tion is apparent, as it should be since a woman cannot have her third child until after she has had her second child.
Figure 21 presents another illustration of the use of small multiples, this time or to irregularities in the available mortality data.
Figure 22 displays relative mortality rates for males and females in England (1985) present similar tables. These analysts ascribe the diagonal contours in their tables to cohort effects.
T h e maps in Figure 22 provide a richer, more detailed picture of the various local and global patterns in the changes in mortality rates, in vertical, horizontal, and diagonal directions. Some diagonal trends are evident, especially for females in England and Wales [ F i g u r e 2 l ( f ) ] , but it is also evident that age and period effects play a substantial role in the evolution of mortality. The light rectangles in the lower right corners of all six maps show the rapid progress in reducing mortality at younger ages since World War 11; the darkness of the remaining three quadrants of the maps displays the slow rate of progress a t older ages and during earlier years. Italy, are probably largely attributable to these differences in d a t a richness.
In the analyses of Kermack et al. ( 1 9 3 4 ) , Preston and van der Walle ( 1 9 7 8 ) , ing pattern of mortality before the middle of the nineteenth century and the general pattern of progress against mortality subsequently. The pattern is clearly more complex than a pure cohort-effect model would suggest.
1870 1890 1910 1930 1950 1970 1870 1890 1910 1930 1950 1970
Year Year
Figure 22 ( c o n t i n u e d )
Year Year
Figure 29. Swedish mortality rates relative t o age-specific levels from 1778 to 1799, with contour lines frorn 0.05 t o 1.137 at multiples of 1.15, smoothed on a 5 x 5 square, and from age 0 to 79 and year 1778 to 1981: ( a ) male; ( b ) female.
A direct way of considering the hypothesis t h a t "a cohort carries its mortality and vertical directions. Interpretation of these and similar surfaces should also be tempered by the realization that diagonal patterns can emerge not only as a result of cohort effects, but also as the result of the interaction of period and age effects.