2.2.1 Gross Human N and P Flows
 Human urban gross N and P flows consist of N and P in human excreta and detergent P. N in human excreta was estimated based on protein consumption. FAO provides country data on retail stage per capita protein consumption for most countries for the period 1961-2000 [FAO, 2012] and estimates for the 1930s and 1950s for ~15% of all countries [FAO, 1949, 1951, 1955, 1957, 1958, 1963]. These data were supplemented with various data sources [Boomgaard and Van Zanden, 1990; CBS, 2001; FAO/WHO, 1965; Grigg, 1995; Schmid Neset, 2004; Segura, 2005; State Statistical Bureau, 1986; USDA, 2012] (SI 2). To create a full data set for the twentieth century, we assumed that periods without data could be linearly interpolated between the nearest years with data. Protein consumption in the first decades of the twentieth century was close to midcentury protein consumption for most countries with data [Boomgaard and Van Zanden, 1990; Schmid Neset, 2004; Segura, 2005]. For countries lacking early twentieth century data, we therefore assumed that protein intake in 1900 was equal to that in the nearest year with available data for the country considered. For countries with no data for any year, protein intake was assumed to be equal to the population-weighted average for the corresponding world region (SI Figure 4).
 The data collected represent consumption at the retail stage and need to be corrected for retail and household losses to obtain the actual protein consumption and excretion. Retail and household losses of protein were estimated at a regional scale based on SIK/FAO , and values in 1900 were assumed to equal the lowest regional loss percentage of 2010 (SI 3). This agrees with literature for the U.K. [Cathcart and Murray, 1939] and the general pattern of increasing household and retail food waste losses as incomes grow [SIK/FAO, 2011]. The country average per capita protein consumption was directly applied to urban inhabitants, which is in agreement with observed small differences between rural and urban protein consumption [Liu et al., 2009; Liu, 2005; Qiao et al., 2011; Shehu et al., 2010].
 We used an N content in protein of 0.16 [Block and Bolling, 1946]. P consumption was obtained from N consumption using a N:P ratio of 10:1 (mass basis) (SI 4). This is based on a near complete twentieth century N and P consumption data set for the United States [USDA, 2012] and supported by a rather fixed N:P ratio in dietary intakes surveys in the range of 10.6:1 (adults) [Sette et al., 2011] to 11.1:1 (adolescent males) [Turan et al., 2009] and other estimates [Billen et al., 2009].
 Excretion occurs in the form of urine (80% of intake for N, 62% for P) and feces (17% for N, 35% for P); 3% of N and P intake is lost via sweat, hair, and blood [Calloway and Margen, 1971; Chittenden, 1904; Kimura et al., 2005; Langergraber and Muellegger, 2005; Oddoye and Margen, 1979; Schmid Neset et al., 2006; Takahashi et al., 1985].
 P-based detergent use for the period 1970–2000 was taken from the study by Van Drecht et al. . Assuming that the use of P-based detergents started in 1950, for all countries a linear interpolation was made between 1950 and 1970. This is based on the start of large-scale introduction of laundry machines around the 1950s in many industrialized countries [Billen et al., 1999; Han et al., 2011; Hukka et al., 2010].
2.2.2 Fate of Human N and P Waste
 All food losses and all losses through non-feces and non-urine pathways were assumed to end up in the “other” sink (Figure 1a). The fate of N and P in human excreta depends on the presence of a sewer connection (SI Figure 6); P-based detergents were assumed to be used exclusively by households with a sewer connection [Van Drecht et al., 2009]. The fraction of inhabitants with a sewer connection often increased rapidly when cities started to construct sewer networks. Well-documented examples include the city of Wagga Wagga (Australia) (1930–1970 exponential increase) [Burn et al., 1999], Helsinki (Finland) (1950–1980 steep increase) [Laakkonen and Lehtonen, 1999], and Paris (France) (32% connection in 1900 and 70% in 1914) [Barles, 2007; Barles and Lestel, 2007].
 For the period between 1970 and 2000, sewer connection data from Van Drecht et al.  were used. Since quantitative global country data on sewer connection and timing of rapid sewer construction during the period 1900–1970 are scant, sewage systems in industrialized countries were assumed to be constructed on a large scale from the year 1870 onward. This agrees with the development in many cities worldwide [Mokyr, 1998] such as Paris [Barles, 2007; Barles and Lestel, 2007], London, San Francisco/United States [Burian et al., 2000; Schultz and McShane, 1978; Smith, 2007], and multiple cities in the Netherlands [Lohuizen, 2006; Van Zon, 1986]. The separation between developing countries and industrialized countries was made based on the study by Ott et al. . For developing countries, we assumed that construction of sewage systems in cities began 50 years later (1920) based on historical estimates for sub-Saharan Africa [Nilsson, 2006; Nyenje et al., 2010] and Egypt [Roberts and Flaxman, 1985]. For the periods 1870–1970 (industrialized) and 1920–1970 (developing), we assumed a linear increase in the fraction of the urban population connected to a sewer. At present, large variations in human sewer connection exist between countries [WHO/UNICEF, 2000], with lower (but increasing) degree of sewer connection in developing countries (SI Figure 6). The definition of urban population was extended in those cases where urban population was smaller than the number of people with a sewer connection to incorporate all sewer connected persons in the model.
 Sanitation coverage is generally much further developed in urban than in rural areas. For example, rural human excreta collected in (primitive) tanks are often dumped in surface water without treatment [UNEP, 2010], open defecation is still common in rural areas of the world such as in some African countries [Erni et al., 2010], and open drainage systems discharge excreta from both animals and humans to surface water in many densely populated regions of the world. Estimated sewer leakage, biological degradation, nutrient particle settlement, and volatilization processes are 10% for both N and P [Nyenje et al., 2010; Rutsch, 2006; Wakida and Lerner, 2005] (SI 5).
 In the model, three treatment classes were distinguished based on the study by Van Drecht et al. , i.e., primary treatment (10% N and P removal), secondary treatment (35% N and 45% P removal), and tertiary treatment (80% N and 90% P removal). Treatment fractions were linearly interpolated to 1970 [Van Drecht et al., 2009], assuming large scale primary treatment to start in 1920 [Barles and Lestel, 2007; Gadegast et al., 2012; Melosi, 2000; Shuval, 1986] and secondary and tertiary treatment to start in 1950 [Brosnan and O'Shea, 1996; Cooper, 2001; Liu et al., 2008; Ogoshi et al., 2001; Schmid Neset et al., 2010] (SI 6). All nutrients removed were assumed to flow to the “other” sink because of the large variety in the handling of treatment sludge [Burian et al., 2000; Van Zon, 1986]. The remainder of nutrients (i.e. wastewater that is not treated at all or nutrients that are not removed) present in sewers was assumed to be discharged to surface water [UNEP, 2010; Van Drecht et al., 2009; Van Zon, 1986] (Figure 1a).
 Possible fates for nonsewered human N and P are surface water discharge, agriculture, or “other.” We assumed that 20% of N from human excreta from inhabitants lacking a sewage connection is lost as ammonia (“other”) (SI 5) [Huang et al., 2012; Kimura et al., 2005]. The collection of human excreta from urban areas for use in agriculture was common in the early twentieth century, most substantially in Europe, Asia, and North America [Barles, 2007; Liu et al., 2008; Noort, 1999; Shuval, 1986; Van Zon, 1986]. Only few quantitative studies are available on recycling practices in the early twentieth century. A good example is Paris, which has been reported to reuse most of its waste in sewage farms in the early twentieth century [Shuval, 1986].
 Agricultural recycling was quantified for 1900 based on four recycling classes: none (0% recycling), low (10%), medium (40%), and high (70%) (SI 7 and SI Figure 8). Countries or regions where recycling was important in 1900 include West Europe [Barles and Lestel, 2007; Svirejeva-Hopkins et al., 2011; Van Zon, 1986], China, India, and Japan [Drechsel et al., 2010; Shuval, 1986; WHO, 1989; Xue, 1961]. Countries with no or negligible recycling include, among others, Islamic countries and most African countries, where religious taboos limit handling and recycling of human excreta [Shuval, 1986]. Medium-recycling regions include the United States [Tzanakakis et al., 2006], Mexico, Central Europe, and South-East Asia [Shuval, 1986]. Low-recycling countries include those for which no literature on recycling was found and no taboos were expected but which are close to neighboring medium- or high-recycling countries (Canada, South America, and Russia).
 Over the course of the twentieth century, a decline in agricultural nutrient recycling resulted from (i) the introduction of the water closet in industrialized countries, thereby diluting wastewaters; (ii) the need for higher hygiene standards; (iii) the introduction of treatment facilities; and (iv) the application of cheap chemical fertilizers [Billen et al., 1995; Schmid Neset, 2005; Schmid Neset et al., 2010]. In the model, this development is mimicked by a linear decrease of the global fraction of recycled human waste from nonsewered populations between 1900 and 1950 to a value of 15% of the 1900 value. This trend is in agreement with qualitative information from various countries [Angelakisa and Durhamb, 2008; Cooper, 2001; Mokyr, 1998; Schladweiler, 2012; Tzanakakis et al., 2006; Van Zon, 1986] and data for Sweden [Schmid Neset, 2005].
 In the last few decades of the twentieth century, a renewed interest developed in the recycling of urban wastes including human excreta [IWMI and FAO, 2001; Shuval, 1986] in both industrialized [Angelakisa and Durhamb, 2008; Schmid Neset et al., 2010; Tzanakakis et al., 2006] and developing countries [Hayashi et al., 2012; Hofstedt, 2005]. Countries generally increased the amount of agricultural recycling to (i) reduce wastewater discharge, or use wastewater for irrigation in dry regions [Ogoshi et al., 2001; Olson, 1987]; (ii) avoid landfill and regular treatment costs; and (iii) close nutrient cycles for sustainable nutrient use and food production [Angelakisa and Durhamb, 2008; Bixio et al., 2005; IWMI and FAO, 2001; Tzanakakis et al., 2006]. In the model, this trend was described for countries with no recycling in 1950 by simulating an increase of the fraction of nonsewered human excreta being recycled to 20% in 1990 [Hayashi et al., 2012; Hofstedt, 2005; Liu et al., 2008] and no change between 1950 and 1990 for all other countries. For all countries, between 1990 and 2000, a linear increase by 20% of the 1990 value was incorporated in the model to simulate the most recent increase in recycling [IWMI and FAO, 2001].
 The remainder of the nonsewered human excreta ends in (i) surface water, representing the processes of surface runoff of wastes and dumping of collected excreta in open water as reported for both historical and present times [Noort, 1999; UNEP, 2010; Van Zon, 1986], and (ii) in “other”, representing leakage and seepage to soils, waste transport losses and losses through leaky cesspits, and tons and pit latrines [Jacks et al., 1999; Van Zon, 1986] (Figure 1a).