Electronic Supplementary Materials (ESM) for Kramer (2013) DOI 10.1007/s12110-013-9189-5
Why What Juveniles Do Matters in the Evolution of Cooperative Breeding
The following materials describe methods for building the age-specific production and consumption schedules used in the iterative models. An intermediate baseline production and consumption schedule was constructed from ethnographic time allocation data.Since only summary-level data for broad age categories are available for most data published on children=s work and ethnographic populations do not represent the full range of crossover points desired in this analysis, the early and late production scheduleswere derived byadjusting the intermediate schedule as described below. Computations and analyses were performed in SAS version 9.3 (2002-2003 SAS Institute, Inc., Cary, NC).
A. Constructing baseline intermediate schedules
1. Data Source and Study Population
Detailed information on time budgets, return rates, body size, and energy expenditure is used to compute age-specific production and consumption. These behavioral observations were collected among a group of Maya subsistence agriculturalists. Maya children live in self-supporting households that typically produce what they consume, consume what they produce, and do not store resources beyond subsistence needs. At the time of the study, they had negligible access to the labor-market economy, health care, or schooling.The year-long study included 69 children ages 0–20 and more than 10,500 scan samples collected on those children.Scan sampling has several advantages for estimating how people allocate their time (Dunbar 1976; Hames 1992; Reynolds 1991).Rather than reconstructing a participant=s time use from recall or interview data, the observer records firsthand the child=s activity at specified time intervals, in this case every 15 minutes during a 3- to 4-hour block of time, every several weeks over the course of a year (Kramer 2005).
Fig.ESM-1 comparesthe available cross-cultural data with the average work load for a 6- to 14-year-old in the intermediate (age 15) net production schedule (Table 1).Values used for the baseline fall close to the mean for the cross-cultural sample of children=s labor in today=s traditional societies. Because methodologies and age groupingsdiffer among the empirical studies, and some of the cross-cultural variation is likely attributable to methodological vagaries, this figure is intended only for general comparison. For example, the intermediate production schedule is based on weighted hours (an hour of child labor is discounted by difference in return rates and energy expenditure to be equivalent to an hour of adult labor; described below), while the cross-cultural data are reported as raw hours.
2. Using Time as the Measure of Production and Consumption
Although production and consumption could be constructed from independent measures (for example, production as time and consumption as calories), these functions must be expressed in the same metric to calculate net balance.These functions have been published for a number of traditional societies using both calories (Kaplan 1994; Kaplan et al. 2000) and time (Kramer 2005; Lee and Kramer 2002; Sullivan Robinson et al. 2008) as the common unit of measure.In the models developed here, time (weighted hours of work per day) is used as the most comprehensive assessment of investments in children.For example, a 10-year-old boy consumes food that others provide him, but he also consumes some portion of the time his mother spendshauling water, fetching firewood, or collecting grass to construct a shelter.Whereas food production has an obvious caloric output, numerous other processing and procurement tasks have no readily measurable caloric equivalent. Sensitivity analyses using calories show similar age trends to models constructed with time, but with greater deficits at younger ages since young children tend to allocate time to camp and home-based support tasks rather than to food acquisition activities (Fig.ESM-2).
3. Converting Time Allocation Data to a Measure of Production and Consumption
The procedure to convert time allocation data into measures of production and consumption so these values are comparable across individuals of different sex and ages was as follows.
Weighted Production.Each child in the sample spends a certain number of observed hours each day in productive work, which includes time spent foraging, doing garden work, hunting, hauling water, collecting firework, processing and preparing food, cooking, sewing, weaving, collecting building materials and other raw resources, and the like.Two adjustments are made to the simple count of hours children work each day so an hour of a child=s work is comparable to an hour of adult work.
The first adjustment accounts for age differences in the value of time because some activities are more strenuous and require greater caloric expenditure than others.For example, if a child spends 5 hra day in a hammock rocking his baby brother and his mother spends 4 hr chopping firewood, a simple count of hours would lead to the conclusion that the child works more than the mother.Because young children are strength-limited, they tend to spend time in energetically less expensive tasks, while older, stronger individuals spend time in more difficult and energetically costly activities.If two tasks take the same amount of time, but one requires more energy, then its product is more highly valued at the margin than the product of the other task.Consequently, time spent in more calorically expensive tasks is commonly weighted more heavily than time spent in less expensive tasks. Here these weights are derived from a constant calorie cost per hour of time and the energy requirement to perform a particular task (Lee and Kramer 2002).Standard coefficients for energy expenditure (kcal/minute) are taken from experimental studies that calibrate respiratory exchange while a wide range of activities common in traditional societies is performed (Montgomery and Johnson 1977; National Research Council 1989; Ulijaszek 1995). These coefficients represent multiples of basal metabolic rate for kcal expended per minute of activity.An individual=s time spent working is weighted by energy expenditure as follows (Eq. ESM-1):
Pi(ee) = {hours spent in light work * 1+ k[(REE/24)*2.5]} +
{hours spent in moderate work * 1+ k[(REE /24) * 5.0]}
where k = the constant 0.00187, a coefficient that relates the price of a calorie to the value of an hour=s work (Lee and Kramer 2002);REEis resting energy expenditure based on an individual=s height and weight;the coefficients 2.5 and 5.0 refer to the kcal per minute expended while performing at a light and moderate activity level, respectively. Weighted hours for each individual in the sample are given in Table ESM-2, column b.
The second adjustment accounts for age differences in efficiency.For example, if a mother and child spend an hour chopping firewood, the adult may produce 10k of wood per hour, while the child yields 2k.Because children produce less output per unit time than adults, real-time hours can overvalue children=s labor.In other words, children could work all day but, because they are not very efficient, save mothers only a couple of hours of her time.For their work effort to be comparable, children=s real time is discounted by their efficiency relative to a prime-aged adult=s.These weights are based on observed differences in return rates and computed by dividing a child=s return rate (rrij) by a prime-aged adult=s (rrAj) for a variety of tasks. Weights vary between zero and unity.On the basis of these measurements, an hour of productive work for children aged 0–10 is weighted at 0.5; for male children aged 10–20 an hour is weighted at 0.76; and for female children aged 10–20 an hour is weighted at 0.72 for tasks that have a strength component and 0.76 for tasks that are non-strength-based (Lee and Kramer 2002). These efficiency weights (ew) are given in Table ESM-2, column c.
An individual=s production score combines these two adjustments (Table ESM-2, column d) and is given by (Eq. ESM-2):
Pi = Piee * ew
wherePiee is an individual=s productive time weighted by energy expenditure, andew is the age- and sex-specific efficiency weight, as described above.
Comparing weighted and unweighted hours. Weighting hours permits work effort to be compared across age and sex, and it compensates for the problem that the simple count of hours can overvalue children=s labor.Weighting affects children=s production in the following ways.It discounts children=s work effort relative to an adult=s, and it discounts the work of younger children, who perform easier, less energetically demanding work tasks, relative to older children, who perform more energetically demanding tasks and have higher return rates.The change from unweighted, real-time hours to weighted hours is shown in Table ESM-2, columns a and d. Compared with counting hour-for-hour, weighting gives a more conservative estimate of children's contributions, which lowers the estimate of net balance.
Consumption.The calculation for age-specific consumption incorporates children’s consumption of food as well as nonfood resources and other services—shelter, clothing, cleaning, tools and other technology—on which humans depend.Based on the Maya time allocation data, 80% of working time is spent in food-related activities—producing food, processing it, preparing and cooking it, transporting goods, fetching wood and water, tending animals and beehives, and the like.The other 20% of working time is spent in domestic tasks, collecting and processing raw materials to make tools, building shelters, making clothing, weaving, etc.Given this breakdown, 80% of an individual=s consumption is estimated as proportional to his or her body size, and 20% is proportional to his or her family size (see caveats below).Consumption is expressed in hours by relating these proportional allocations to total family production.
The share of an individual=s consumption that is related to food is computed by dividing the sum of total daily energy requirements for each family member by the individual=s total daily energy requirements (TEEi).TEEi is generated by multiplying an individual=s resting energy expenditure (REEi) by his or her observed physical activity level (PALi).REEi is a function of height, weight, and sex, using values that are taken from standard tables (National Research Council 1989).PALi is calculated for each individual based on his or her observed time allocation budget and how he or she allocates time to various activities over a 24-hr period.For example, from the time allocation data we know that a 14-year-old girl spends 10 hr a day sleeping and resting, 4 hr in child care, 6 hr playing and in leisure, and 2 hr doing light domestic work and 2 hr collecting firewood.Her 24-hr PAL = 1.77 (Eq. ESM-3).Multiplied by REEi this gives an estimate of her total daily caloric expenditure, or TEEi.
PALi= 10(1.0) + 4(1.5) + 6(1.9) + 2(2.5) + 2(5.0) / 24 hr
= 1.77
where 1.0, 1.5, 1.9, 2.5, and 5.0 represent calorie consumption per minute of activity at various activity levels (Montgomery and Johnson 1977; National Research Council 1989; Ulijaszek 1995).
An individual=s consumption score is given by (Eq. ESM-4):
Ci = Ph * {[0.8 * (TEEi / TEEh)] + (0.2 / number of other children)}
wherePh is the total time a family spends in productive work;TEEi is an individual=s total daily caloric expenditure, calculated asREEi* PALi(resting energy expenditure multiplied by observed activity level);and TEEh is the sum of total daily energy expenditure for all family members.
4. Caveats and considerations
The benefit of using timeis that it incorporates nonfood investments in children. This also presents a methodological challenge.We do not knowprecisely how non-food-related activities are consumed by family members.Many domestic tasks, such as the time spent washing clothes or weaving a hammock, are generally expected to be consumed in proportion to the number of individuals who share its product.For other tasks, that proportion may be less certain or measurable.For example, how much of the time spent building a house or shelter does any one child consume? Some individuals may consume more and some less than a per-capita share of these tasks, and the consumption of non-food-related activities may vary among individuals more than is accounted for here.
Non-depreciable care (Clutton-Brock 1991) may be another consideration in some ethnographic contexts.Some tasks have the same time expenditure, no matter how many children share their parent=s investment—time spent being vigilant at the nest or travel time to a foraging location, for example.My original analysis (Kramer 1998) was designed to distinguish the Maya time allocation data in this way.However, sensitivity tests showed that the time allocated to most tasks that were sufficiently common was positively correlated with family size (one exception being house sweeping).In the Maya case, exceptions occurred too infrequently to warrant further weighting in terms of non-depreciable and depreciable care.That said, one of the advantages of the model developed here is that adjustments for specific ethnographic contexts can be readily incorporated.
PAL is widely used to compare activity levels cross-culturally (Dufour and Piperata 2008; Jenike 2001; Leonard 2003; Leonard and Roberson 1992). Although there are more precise ways to measure overall energy expenditure, the factorial method is advantageous because it retains individual information about task-specific time allocation.There is discussion in the sports and medicine literature about whether energy expenditure should be further refined for children=s activities.The FAO/WHO/UNU(World Health Organization 1985) recommend using standard adult multiples of REE for different activity levels, but other studies have found that adults have lower rates of energy expenditure(calories/time, and especially when expressed as calories/kg/time) than children when performing certain activities, such as walking and running (Sallis et al. 1991).A recent meta-analysis of existing methods to calculate children=s total energy expenditure found that combining children=s resting metabolic rates with standard adult multiples for activity levels is the best estimate of children=s total energy expenditure, except for the specific activities of sustained running or walking (Ridley and Olds 2008).If an adjustment were made for these activities, it would raise consumption relative to production.However, because these activities are relatively rare, this adjustment is not expected to have much influence on Ci values or net balances.
Finally, it should be noted that the Maya are of relatively short stature and consequently may have lower total energy expenditure than taller children (Wilson2012). If children in the past were appreciably larger, the age-specific consumption values may be under-represented.
B. Constructing the Early and Late Schedules
Under the intermediate production schedule, children become net producers at age 15.The early production schedule is derived by doubling the intermediate values between ages 2 and 10 when production plateaus at 7.12 hr per day. Under these assumptions, net production occurs at age 7, which isseveral years younger than the earliest documented crossover point in an ethnographic population (Cain 1977).However, few data are available on the actual range of variation in modern traditional populations. Juvenile independence at age 7 is evolutionarily conservative because it does not include a schedule where independence occurs at weaning, or about age 5 in chimpanzees (Kaplan et al. 2000).Although chimpanzee juveniles are independent of their mothers by weaning, they often forage in close proximity to them for several more years.
The late production values are calculated at 50% of the intermediate schedule for children ages 3–10 and at 75% for children aged 11–20.Under these assumptions, children become net producers at age 21. This age profile of work is equivalent if calculations are estimated for the !Kung, who are at the lowest end of variation for modern populations.
In all three schedules, production asymptotes at 7.12 hr per day.Adult production levels are constant in all models to highlight the effects that juvenile production has on net balance rather than ecological differences that might determine the amount of time spent in subsistence activities. Likewise, the consumption schedule is the same in all model calculations.
Table ESM-1 Minimum net balance (production of all children minus their consumption expressed indaily hours) stratified by age at net production (early, intermediate, late), birth interval (6,5,4,3) and dispersal age (14,16,18,20). Values represent the lowest net balance that a mother experiences in any year over the course of her reproductive career.Values are taken from models shown in Fig. 1 and are the values given in Fig. 2.
Min Net BalanceEarly / 14 / 16 / 18 / 20
6 / −2.33 / −2.33 / −2.33 / −2.33
5 / −2.74 / −2.74 / −2.74 / −2.74
4 / −3.31 / −3.31 / −3.31 / −3.31
3 / −4.10 / −4.10 / −4.10 / −4.10
Inter / 14 / 16 / 18 / 20
6 / −4.47 / −4.47 / −4.47 / −4.47
5 / −5.05 / −5.08 / −5.08 / −5.08
4 / −6.28 / −6.28 / −6.28 / −6.28
3 / −8.10 / −8.13 / −8.13 / −8.13
Late / 14 / 16 / 18 / 20
6 / −6.64 / −6.64 / −7.29 / −7.31
5 / −7.32 / −8.65 / −8.65 / −8.65
4 / −9.33 / −10.19 / −10.30 / −10.30
3 / −11.84 / −13.07 / −13.89 / −13.89
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Table ESM-2 Individual production scores for the intermediate schedule showing unweighted (column a) and weighted (column d) hours. Column a gives the sum of real-time hours that an individual spends on average each day in productive work.Column b is real-time hours weighted by energy expenditure (see Eq.ESM-1).Column c is an individual=s efficiency weight, or the amount that their hours are discounted (see description of age difference in efficiency above).Column d (column b * column c) is the individual=s production score (Pi ).
(a) / (b) / (c) / (d)Piee / Pi
Case / Age / Sex / Unweighted
Hours / EE Weighted
Hours / Efficiency
Weights / Fully Weighted
Hours
1 / 0 / 1 / 0.000 / 0.000 / 0.500 / 0.000
2 / 0 / 2 / 0.000 / 0.000 / 0.500 / 0.000
3 / 1 / 2 / 0.000 / 0.000 / 0.500 / 0.000
4 / 1 / 2 / 0.000 / 0.000 / 0.500 / 0.000
5 / 1 / 2 / 0.000 / 0.000 / 0.500 / 0.000
6 / 1 / 2 / 0.000 / 0.000 / 0.500 / 0.000
7 / 1 / 2 / 0.000 / 0.000 / 0.500 / 0.000
8 / 1 / 2 / 0.000 / 0.000 / 0.500 / 0.000
9 / 2 / 1 / 0.081 / 0.092 / 0.500 / 0.046
10 / 2 / 2 / 0.542 / 0.604 / 0.500 / 0.302
11 / 2 / 2 / 0.000 / 0.000 / 0.500 / 0.000
12 / 3 / 1 / 0.229 / 0.286 / 0.500 / 0.143
13 / 3 / 2 / 0.171 / 0.211 / 0.500 / 0.105
14 / 3 / 1 / 0.073 / 0.083 / 0.500 / 0.042
15 / 3 / 1 / 0.073 / 0.084 / 0.500 / 0.042
16 / 3 / 2 / 0.168 / 0.193 / 0.500 / 0.096
17 / 4 / 2 / 0.981 / 1.192 / 0.500 / 0.596
18 / 4 / 2 / 0.633 / 0.766 / 0.500 / 0.383
19 / 4 / 2 / 1.347 / 1.584 / 0.500 / 0.792
20 / 4 / 1 / 0.248 / 0.315 / 0.500 / 0.158
21 / 4 / 1 / 0.583 / 0.686 / 0.500 / 0.343
22 / 5 / 2 / 1.290 / 1.596 / 0.500 / 0.798
23 / 5 / 1 / 0.516 / 0.620 / 0.500 / 0.310
24 / 5 / 1 / 0.073 / 0.085 / 0.500 / 0.043
25 / 5 / 1 / 0.588 / 0.706 / 0.500 / 0.353
26 / 6 / 2 / 1.674 / 2.135 / 0.500 / 1.068
27 / 6 / 1 / 1.583 / 2.082 / 0.500 / 1.041
28 / 6 / 2 / 1.231 / 1.504 / 0.500 / 0.752
29 / 6 / 2 / 1.833 / 2.284 / 0.500 / 1.142
30 / 6 / 1 / 0.568 / 0.724 / 0.500 / 0.362
31 / 7 / 1 / 0.000 / 0.000 / 0.500 / 0.000
32 / 7 / 2 / 3.395 / 4.043 / 0.500 / 2.021
33 / 8 / 1 / 2.301 / 2.983 / 0.500 / 1.492
34 / 8 / 2 / 3.590 / 4.414 / 0.500 / 2.207
35 / 8 / 2 / 2.063 / 2.426 / 0.500 / 1.213
36 / 8 / 1 / 1.737 / 2.223 / 0.500 / 1.111
37 / 8 / 2 / 1.176 / 1.421 / 0.500 / 0.710
38 / 9 / 1 / 2.312 / 2.801 / 0.500 / 1.400
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