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Abstract Much attention has been paid to the ways that people’s home energy use, travel, food choices and other routine activities affect their emissions of carbon dioxide and, ultimately, their contributions to global warming. However, the reproductive choices of an individual are rarely incorporated into calculations of his personal impact on the environment. Here we estimate the extra emissions of fossil carbon dioxide that an average individual causes when he or she chooses to have children. The summed emissions of a person’s descendants, weighted by their relatedness to him, may far exceed the lifetime emissions produced by the original parent. Under current conditions in the United States, for example, each child adds about 9441 metric tons of carbon dioxide to the carbon legacy of an average female, which is 5.7 times her lifetime emissions. A person’s reproductive choices must be considered along with his day-to-day activities when assessing his ultimate impact on the global environment.


Introduction
Much attention has been paid to the ways that people's home energy use, travel, food choices and other routine activities affect their personal emissions of carbon dioxide and, ultimately, their potential contributions to global warming (O'Neill and Chen, 2002;Bastianoni et al., 2004;Bin and Dowlatabadi, 2005;Vandenbergh and Steinemann, 2007;Wei et al., 2007). For example, a variety of ''carbon calculators'' allows individuals to estimate their lifetime emissions of greenhouse gases (U.S. Environmental Protection Agency, 2007).
While population growth is obviously a key component of projections of carbon emissions at a global level (Dyson, 2005;Harte, 2007;IPCC, 2007), there has been relatively little emphasis on the environmental consequences of the reproductive choices of an individual person. Obviously, the choice to reproduce contributes to future environmental impacts. There are the immediate effects caused by each offspring over his or her lifetime (Hall et al., 1994), but, should the offspring reproduce, additional impacts could potentially accrue over many future generations. Some authors have discussed the ''externalities'' of childbearing (i.e., the consequences of an individual's reproduction that are borne by society, rather than the individual himself), focusing on the costs of abatement of the impacts caused by the individual's descendants (Cline, 1992;O'Neill et al., 2001). For example, O'Neill and Wexler (2000) consider emission scenarios that lead to particular stabilization concentrations of CO 2 , and they model the abatement costs incurred by the addition of a single individual (and his or her descendants) to the population.
We explore the effects of an individual's reproductive behavior by tracing a single female's genetic contribution to future generations and weighting her descendants' impacts by their relatedness to her. We apply this approach to emissions of fossil carbon dioxide with the goal of quantifying the carbon legacy of an individual and examining how it is affected by the individual's reproductive choices.

The carbon legacy of an individual
Our basic premise is that a person is responsible for the carbon emissions of his descendants, weighted by their relatedness to him. For a descendant that is n generations removed from the focal individual, the weight is ð1=2Þ n . So, for example, a mother and father are each responsible for one half of the emissions of their offspring, and 1/4 of the emissions of their grandchildren. Fig. 1 illustrates this simple idea.
We will refer to the weights that indicate the relatedness of a descendant to the initial parent as ''genetic units''. The fractional genetic unit represented by a particular descendant can be thought of as the proportion of the ancestor's genes (or alleles) that are shared with the descendant, or the ''percentage of blood'' that the two have in common (Lush, 1994).
At any calendar date, the persistence of a lineage can be quantified as the number of genetic units represented by members of the lineage who are alive at that time. If we integrate the number of genetic units over time, we obtain an estimate of the total Global Environmental Change 19 (2009) 14-20 Much attention has been paid to the ways that people's home energy use, travel, food choices and other routine activities affect their emissions of carbon dioxide and, ultimately, their contributions to global warming. However, the reproductive choices of an individual are rarely incorporated into calculations of his personal impact on the environment. Here we estimate the extra emissions of fossil carbon dioxide that an average individual causes when he or she chooses to have children. The summed emissions of a person's descendants, weighted by their relatedness to him, may far exceed the lifetime emissions produced by the original parent. Under current conditions in the United States, for example, each child adds about 9441 metric tons of carbon dioxide to the carbon legacy of an average female, which is 5.7 times her lifetime emissions. A person's reproductive choices must be considered along with his day-today activities when assessing his ultimate impact on the global environment.
number of person years that are traceable to the original parent (see Fig. 2). If we integrate the product of the number of genetic units and the per-capita rate of carbon emissions over time, we obtain an estimate of the total emissions attributable to the ancestor, or her carbon legacy.
Our goal is to quantify the consequences of the childbearing decisions of an individual. The appeal of our weighting scheme is that it provides an accounting of the extent to which a parent's genetic material propagates through subsequent generations, and it allows the emissions of any individual to be unambiguously traced back and ''assigned'' to ancestors from any preceding generation. For example, the responsibility for the rightmost male in the bottom line of Fig. 1 lies, in 1/4 portions, with his maternal and paternal grandparents (only one of which, the maternal grandmother, is shown in the figure).
Depending on one's view of whether, and how, future environmental impacts of an individual's descendants should be discounted, other weighting schemes are possible. O' Neill and Wexler (2000), for example, quantify the expected effect of one additional birth by following his or her descendants, but without adjusting for relatedness (see their Equation A22).

Approaches to estimating the carbon legacy
We calculated trajectories of genetic units vs. time for genetic lineages of in each of the 11 most populous countries in the world, listed in Table 1. We used two approaches, one based on a simple analytical model and one involving numerical simulation.

Analytical model
We first develop a simple model of the propagation of family trees that provides a conceptual basis for the simulations that we used to generate the numerical results presented here. The model is developed fully in Appendix A.1; an abbreviated explanation follows.
We start with a single female born at time t 0 ¼ 0 (generation 0), and assume that all reproduction occurs in pulses at times t 1 , t 2 , t 3 , where t k À t kÀ1 ¼ t 1 is the generation time, i.e., the mean of the ages at which females give birth. If we assume that males and females are born at the same rate (see Appendix A.1.1), then the expected number of children produced per female at time t k is 2 Á Rðt k Þ, where Rðt k Þ is the net reproductive rate, i.e., the average number of daughters a woman would be expected to have if she were subject to the fertility and mortality rates prevailing in the population. We assume that all members of the family tree, male and female, pair with members of the opposite sex from outside the tree, so that the reproductive rate of 2 Á Rðt k Þ is applied to males as well as females within the tree. As explained earlier, an individual of generation k, born at time t k , represents ð1=2Þ k genetic units, reflecting his relatedness to the ancestral female.
We assume further that the survival of all individuals follows a distribution characterized by the survivor function, SðtÞ, defined as the probability that an individual lives to at least age t. It can then be shown (Appendix A.1) that the expected number of genetic units alive at time t k is where E½Bðt 0 Þ is the expected number of births at time t 0 , equal to one (the ancestral female). Following the pulse of births at time t k , mortality erodes the number of individuals, and genetic units, until the next pulse of

Table 1
Average person years associated with lineages in the world's eleven most populous countries, using medium-variant fertility projections. The initial parent contributes the number of years constituting his life expectancy. The last column is an estimate of the person years added to the ancestor's legacy for each child that he has, assuming his descendants survive and reproduce at the rates prevailing in the country.  reproduction, at time t kþ1 . Appendix A.1 gives expressions for a piecewise-linear model of this jagged trajectory of E½GðtÞ vs t.
The area under a plot of E½GðtÞ vs. t gives an estimate of the total person years attributable to the ancestral female. If HðtÞ is the percapita rate of carbon emissions at time t (mass per person per year), the area under a plot of E½GðtÞ Á HðtÞ vs. t provides an estimate of the total carbon emissions for which the ancestor is responsible.

Simulations
The simulations expand on the analytical model by allowing the births and deaths of individuals to be stochastic, i.e., to occur at other than set time points. This allows more realistic modeling of carbon legacies and gives an idea of how variable those legacies are among individuals.
Following lineages that include both males and females is computationally prohibitive. It turns out that the number of genetic units (of both sexes) attributable to an ancestral female is, on average, simply the number of females comprising an unbroken lineage of females descending from the ancestor (see Appendix A.2 for details). If we integrate the number of living females over time, we obtain an estimate of the total number of person years, male and female, that are traceable to the ancestral female.
Lineages were simulated with the following steps, implemented as a recursive algorithm in R (R Development Core Team, 2005): 1. Each lineage starts with a single female whose death time is chosen randomly, based on life tables for her home country (World Health Organization, 2007). A potential number of children is generated randomly from a Poisson distribution having a mean equal to the total fertility. Age-specific fertility schedules for the country (United Nations Population Division, 2007) are then used to generate the birth times and sexes of the potential children. Finally, these birth times are compared to the female's death time to determine how many (if any) births are actually attributed to her. 2. If there are female offspring, each daughter's lifetime and reproduction are simulated as done for the original female. 3. This continues until the lineage dies out, i.e., until all of the females having a direct path of female progenitors tracing back to the ancestor have perished. Some lineages persist indefinitely, in which case a pre-specified time limit terminates the simulation. 4. Each lineage is summarized as a trajectory of genetic units vs.
time. As explained earlier, the number of genetic units at a particular time is estimated as the number of descendants alive at that time, assuming we are following females only.
Integration of the number of genetic units over time gives the person years attributable to the ancestor. If the number of genetic units at each time is multiplied by the prevailing percapita rate of CO 2 emissions, the integral of that quantity vs. time gives an estimate of the total CO 2 emissions attributable to the ancestral female.
Each set of simulations followed 10,000 female-only lineages subject to particular schedules of fertility and per-capita rates of carbon emissions, described in the next section.

Demographic and carbon-emission scenarios
The United Nations' ''medium variant'' projections of total fertility were used throughout (United Nations Population Division, 2007). These projections assume a convergence of fertility in all countries to 1.85 children per woman by 2050.
In 2005, world emissions of CO 2 from the combustion of fossil fuels were 28.1 billion metric tons, or 4.31 metric tons (t) per person per year, assuming a global population of 6.51 billion (Energy Information Administration, 2008). Three scenarios of future carbon emissions were considered for the 11 countries focused on in this paper: 1. Optimistic: Each country's per capita emission rate changes linearly from its 2005 value to a global target of 0.5 t CO 2 per person per year by 2100, and emissions continue at that rate indefinitely. A set of aggressive emission-reduction scenarios summarized by the IPCC (2007; Category III in Fig. 3.17) Fig. 3.8) was 60 Gt CO 2 per year in 2100. Assuming a world population of 9.1 billion in 2100, this translates into a roughly 50% increase in the global per capita emission rate between 2000 and 2100.
For Bangladesh, with an extremely low per capita emission rate in 2005 (0.27 t person À1 year À1 ), the optimistic limit was set at 0.27 and the pessimistic limit at 0.5 t person À1 year À1 . and medium-variant fertility in the United States. As in the example of the U.S., any country having net reproductive rate exceeding one daughter per woman (roughly corresponding to fertility exceeding two) will have lineages with exponentially increasing person years, unless fertility decreases in the future. Even under the medium-fertility variant, with fertility decreasing to 1.85 children per woman by 2025, the average lineage still has nearly one genetic unit alive four centuries after the birth of the ancestral individual (Fig. 3).

Genetic units and person years
As shown in Fig. 4, the distributions of both the duration and number of person years associated with simulated lineages can be extremely skewed. For the United States, under the scenario of medium-variant fertility, the median duration of female-only lineages is 111 years, and the mean is 168 years. The median number of person years per lineage (171) is less than 20% of the mean (921). Fig. 5 shows trajectories of person years vs. time in the United States, for ancestral females that are constrained to have exactly 0, 1, 2 or 3 children, with all descendants then reproducing according to the medium-variant fertility scenario. A female bearing no children contributes, on average, a number of person years equal to the life expectancy of females in that country -this is the area under the curve corresponding to no children. Each child adds to the total person years attributable to the original female, manifested in increasing heights and skewness of the trajectories in Fig. 5. Table 1 summarizes demographic characteristics of family trees simulated for the world's 11 most populous countries, including the United States, assuming that the initial parent has exactly one child. That child, and all of his descendants, then reproduce according to the medium-variant fertility schedule for the home country. The single child adds from 136 (Nigeria) to 470 (U.S.) person years to the ancestor's legacy. The ratios of the additional person years to the life expectancy of the ancestor (fourth divided by third columns) range from 2.5 (Japan) to 5.9 (United States).      From the point of view of this paper, which focuses on the consequences of an individual's reproductive behavior, it is useful to compare the carbon emissions added per child, rather than the emissions of females having the average number of children, among the different countries. Table 2 summarizes this metric for the 11 countries, assuming medium-variant fertility projections. Under the constant-emission scenario, the average emissions added by having a single child range from 56 t (Bangladesh) to 9441 t (United States). The ratios of the added emissions per child to the ancestor's expected emissions range from 2.4 (Japan) to 5.7 (United States). Table 3 compares the emissions attributable to an individual's reproduction to the emissions that are avoidable through changes in household activities and transportation during the individual's lifetime. Clearly, the potential savings from reduced reproduction are huge compared to the savings that can be achieved by changes in lifestyle. For example, a woman in the United States who adopted the six non-reproductive changes in Table 3 would save about 486 tons of CO 2 emissions during her lifetime, but, if she were to have two children, this would eventually add nearly 40 times that amount of CO 2 (18,882 t) to the earth's atmosphere.

General discussion
This is not to say that lifestyle changes are unimportant; in fact, they are essential, since immediate reductions in emissions worldwide are needed to limit the damaging effects of climate change that are already being documented (Kerr, 2007;Moriarty and Honnery, 2008). The amplifying effect of an individual's reproduction documented here implies that such lifestyle changes must propagate through future generations in order to be fully effective, and that enormous future benefits can be gained by immediate changes in reproductive behavior.
It is important to remember that these analyses focus on the carbon legacies of individuals, not populations. For example, under the constant-emission scenario, an extra child born to a woman in the United States ultimately increases her carbon legacy by an amount (9441 metric tons) that is nearly seven times the analagous quantity for a woman in China (1384 tons), but, because of China's enormous population size, its total carbon emissions currently exceed those of the United States (Netherlands Environmental Assessment Agency, 2008).
Clearly, an individual's reproductive choices can have a dramatic effect on the total carbon emissions ultimately attributable to his or her genetic lineage. Understanding the ways that an individual's daily activities influence emissions and explain the huge disparities in per capita emissions among countries (Table 1) is obviously essential, but ignoring the consequences of reproduction can lead to serious underestimation of an individual's long-term impact on the global environment.

Acknowledgments
We are grateful to three anonymous reviewers who identified a key shortcoming of an earlier version of our paper and offered many constructive suggestions for improvements. M.S. was supported by NASA through contract 1206715 administered by the Jet Propulsion Laboratory.

. General assumptions
We start with a single female born at time t 0 ¼ 0, and assume that all reproduction occurs in pulses at multiples of the generation time, t 1 (the mean of the ages at which females give birth), so that the members of generation k are born at time t k and t k À t kÀ1 ¼ t 1 . In the tree of relatives descending from the ancestral female, assume that each descendant pairs with a person from outside the tree. We express reproduction in terms of RðtÞ, the net reproductive rate at calendar time t, i.e., the average number of daughters produced per woman, assuming she is subject to the prevailing fertility and mortality rates. Since each male in the tree is paired with a female from outside the tree, RðtÞ in this context can be thought of as the average number of daughters per member of the tree, male or female.
Because data on age-specific fertility obviously pertain to females, we use data on survivorship and life expectancy for females only. We assume a 1:1 sex ratio at birth, even though there is in fact a slight excess of male births worldwide (James, 1987). Error introduced by this assumption is small when compared to the uncertainty in estimates of other key demographic parameters and considered in the context of the simplified models used in our analyses.

A.1.2. Births
Assume that the only births in generation k are to parents born in generation k À 1. Let Y ki denote the random variable for the number of children (of both sexes) born to parent i in generation k. The expected value of Y ki is 2 Á Rðt k Þ. Let Bðt k Þ denote the number of births in generation k. We have Bðt 0 Þ ¼ 1 (the ancestral female), and The conditional expected value is This in turn has expectation E½Bðt k Þ ¼ 2Rðt k Þ Á E½Bðt kÀ1 Þ for k ! 1: Expanding this recursive relationship, we obtain Rðt i Þ for k ! 1: (2)

A.1.3. Survival
To calculate Nðt k Þ, the total number of individuals alive at time t k , we need to model the survival of individuals born at times t kÀ1 ; t kÀ2 ; . . . Let N ki be the number of individuals born at t i who survive to time t k (k > i). Then N ki can be thought of as the number of ''successes'' (survival to time t k ) out of Bðt i Þ ''trials'' (individuals born at time t i ). Given a particular value of Bðt i Þ, N ki has a binomial distribution with probability Sðt k À t i Þ, where SðtÞ is the survivor function at t, i.e., the probability that an individual survives to at least age t: ½N ki j Bðt i Þ ¼ bðt i Þ $ Binomial ½bðt i Þ; Sðt k À t i Þ so that E½N ki j Bðt i Þ ¼ bðt i Þ ¼ bðt i Þ Á Sðt k À t i Þ and E½N ki ¼ E½Bðt i Þ Á Sðt k À t i Þ: Then Rðt j Þ 0 @ 1 A Sðt k À t i Þ; (4) using Eq. (2).

A.1.4. Genetic units and carbon emissions
Since each member of generation i represents ð1=2Þ i genetic units, the expected number of genetic units alive at time t k is Eq. (5) gives the expected number of genetic units alive immediately after the pulse of births at time t k . Just before t k , we have where E½Bðt k Þ is obtained from Eq. (2). This yields a jagged trajectory of E½GðtÞvs. t, reflecting discrete pulses of reproduction followed by periods of gradual mortality. If we integrate under a piecewise linear plot of E½GðtÞ vs t, for t ¼ t 0 ; t À 1 ; t 1 ; t À 2 ; t 2 ; . . ., we obtain an estimate of the total person years attributable to the ancestral individual. If we integrate under a plot of E½GðtÞ Á HðtÞ, where HðtÞ is the per-capita rate of carbon emissions at time t (mass per person per year), we obtain an estimate of the total carbon emissions for which the ancestor is ''responsible''.
This analytical model gives numerical results that are very close to those obtained from the simulations. For example, for the constantemission values presented in Fig. 7, the mean absolute deviation of the model predictions from the simulation-based results is 1.9% (range 0.3-6.4%).
A.2. Female-only lineages: a shortcut for the simulations Suppose we follow only female descendants, denoting the number of females at time t k as N f ðt k Þ. The expected number of daughters per female is the net reproductive rate, Rðt k Þ. Following the same logic that led to Eq. (4), but replacing 2Rðt j Þ by Rðt j Þ, we can write: which is identical to the expression in Eq. (5) for E½Gðt k Þ, the expected number of genetic units alive at t k . Consequently, in simulations we can greatly reduce the number of computations by following female-only lineages, yet still obtain an unbiased estimate of the number of genetic units of both sexes that are alive at any time.