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The Gompertz Equation And Its Relationship To Mortality, The Biology Of Life Span, Mortality In The Twentieth And Twenty-first Centuries

Genes are the ultimate time travelers. They transcend the bounds of time by hitching a ride in sexually reproducing species such as humans, but then discard the human body later in life as if it was a used car that had passed its warranty period. Once immortality became a fundamental property of deoxyribonucleic acid (DNA), at some time in the distant history of life on earth, the carriers of these genetic codebooks for constructing living organisms, including humans and other sexually reproducing species, became disposable. The timing with which death occurs—both for individuals, as measured by their lifespan, and collectively for populations, as measured by life expectancy—defines the concept of mortality.

Although it is not possible to know with certainty when any single individual will die, it is known with surprising accuracy when death occurs for members of a population when viewed as a group. In humans and a large number of other species, scientists have demonstrated that the risk of death is highest just after birth, declines to its lowest point near the time of sexual maturation (puberty), and then increases exponentially until extreme old age.

Why is this age pattern of death so common among sexually reproducing species? Early in life, death rates are high because newborns are subject to mortality risks from infectious and parasitic diseases, predation, and congenital malformations. Puberty is the time of lowest mortality because, from an evolutionary perspective, this is the moment at which the investment in the next generation has reached its maximum. This implies that the body design of humans and other living things are constructed with the ultimate goal of reproduction in mind (e.g., the passage of genes from one generation to the next), so this time of life is the most highly protected of all times in the life span. Following puberty, the risk of death from intrinsic (aging-related) causes increases exponentially because of a combination of wear and tear to the physical components of the body; accumulated damage to DNA, cells, tissues, and organs, highly efficient but nevertheless imperfect maintenance and repair mechanisms; and because of the presence of lethal inherited genes that "leak" into the gene pool of every generation.

Scientists have demonstrated that the rate of increase in the death rate following puberty is often calibrated to the length of each species' reproductive window, which is the average duration of time that elapses between puberty and menopause. In other words, animals like mice that experience puberty within weeks after birth tend to age much more rapidly and live considerably shorter lives than sea turtles, which do not experience puberty until about fifty years after birth. As a result of these differences in the rate of aging across species, one day in the life of a human is, in terms of percentage of life span, equivalent to about one week in the life of a dog and one month in the life of a mouse.

Death is an event that can and does happen at every conceivable age in a genetically diverse population. The death rate (also referred to as the mortality rate) for a population may be calculated in its simplest form as the number of deaths that occur in a given year divided by the population at risk of death, the product of which is then multiplied by a standard number (such as one thousand) to give the statistic more intuitive meaning. For example, in the United States in 1995 there were 2.3 million deaths and 262.8 million people alive in the middle of that year. This means that the crude death rate for the United States in 1995 was 8.8 deaths per thousand people [(2.3 / 262.8) × 1,000 = 8.8]. Death rates may also be calculated for people of various age groups or by single-year-of-age, and are often used to estimate the life expectancy of a population.

The various ages at which death occurs provides useful information about the longevity attributes of a population. For example, if one were to imagine a hypothetical group or cohort of one hundred thousand babies born in any given calendar year, and one applied to those babies throughout their lives the death rates that prevailed at every age in that year, it would be possible to plot on a graph the hypothetical ages at which all of the babies would have died. This is known as the distribution of death for a population. Although the distribution of death in 1900 was characterized by high mortality early in life, for those who lived beyond the perilous early years, the modal age at death for females was about 73 years of age (see Figure 1). A comparable distribution of death was observed for males in that year.

The opposite of the distribution of death is a plot of the number of people that are expected to survive from one year to the next. This is known as a survival curve. The survival curve is another useful tool for examining age patterns of death and survival in a population because it provides summary statistics that are easy to interpret and understand. For example, from the survival curve for U.S. females born in 1900 it may be determined that, based on the death rates that prevailed in that year, 58 percent would have been expected to survive to the age of fifty (see Figure 2). By contrast, an estimated 95 percent of the female babies born in the United States in the year 2000 are expected to survive to at least their fiftieth birthday. This demonstrates the dramatic improvements in survival that occurred at younger ages during the twentieth century. In 1900 in the United States the survival curve for Figure 1 Deaths/Age SOURCE: Author females illustrates that the median age at death (the age at which 50 percent of the babies born in that year will still be alive) was fifty-eight years of age. By the year 2000 the median age at death for females in the United States was eighty-three years. As shown in Figure 2, based on death rates observed in the U.S. in 2000, an estimated 86 percent of all the female babies born will survive at least to their sixty-fifth birthday—a dramatic improvement that occurred during the twentieth century. Both curves provide actuaries, demographers, and other scientists with valuable information that can be used to compare the same population across time, or different populations during the same time period.

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