Alternatives to the Grandmother Hypothesis a Meta-Analysis of the Association Between Grandparental and Grandchild Survival in Patrilineal Populations

Hum Nat (2011) 22:201–222 DOI 10.1007/s12110-011-9114-8

Alternatives to the Grandmother Hypothesis A Meta-Analysis of the Association Between Grandparental and Grandchild Survival in Patrilineal Populations

Beverly I. Strassmann & Wendy M. Garrard

Published online: 3 June 2011 # Springer Science+Business Media, LLC 2011

Abstract We conducted a meta-analysis of 17 studies that tested for an association between grandparental survival and grandchild survival in patrilineal populations. Using two different methodologies, we found that the survival of the maternal grandmother and grandfather, but not the paternal grandmother and grandfather, was associated with decreased grandoffspring mortality. These results are consistent with the findings of psychological studies in developed countries (Coall and Hertwig Behavioral and Brain Sciences 33:1-59, 2010). When tested against the predictions of five hypotheses (confidence of paternity; grandmothering, kin proximity, grandparental senescence, and local resource competition), our meta-analysis results are most in line with the local resource competition hypothesis. In patrilineal and predominantly patrilocal societies, the grandparents who are most likely to live with the grandchildren have a less beneficial association than those who do not. We consider the extent to which these results may be influenced by the methodological limitations of the source studies, including the use of retrospective designs and inadequate controls for confounding variables such as wealth.

Keywords Grandmother . Grandparental investment . Child survival . Cooperative breeding . Kin competition . Local resource competition . Complementary filiation

A recent review by Sear and Mace (2008) collated a large amount of data on grandparental survival and grandchild survival in populations characterized by natural fertility and/or high child mortality. All but two of the populations were patrilineal. Among the studies that made at least a partial attempt to control for

B. I. Strassmann (*) Department of Anthropology, Institute for Social Research, University of Michigan, P.O. Box 48106, Ann Arbor, MI 48106, USA e-mail: [email protected]

B. I. Strassmann : W. M. Garrard Research Center for Group Dynamics, Institute for Social Research, University of Michigan, P.O. Box 48106, Ann Arbor, MI 48106, USA 202 Hum Nat (2011) 22:201–222 confounding variables, the maternal grandmother had a beneficial association in 7 of 11 (64%) studies, the paternal grandmother in 9 of 15 (60%) studies, the maternal grandfather in 2 of 10 (20%) studies, and the paternal grandfather in 2 of 10 (20%) studies (Sear and Mace 2008: Table 3). A potential problem was that, for any given study, a grandparent was scored as having a positive effect on grandchild survival if a positive association was found for any single age category, no matter how brief, even if the majority of age categories in the same study were not significant (Strassmann and Kurapati 2010). This procedure did not seem to adequately protect against chance associations, especially considering that most results were not significant and the findings for particular age groups were not predicted a priori. In a first attempt at replication, we looked up the same primary studies as Sear and Mace (2008) and made a table that included all findings, together with P values and effect sizes, regardless of whether or not a result was significant (Strassmann and Kurapati 2010). In our table, we used a consistent alpha of 0.05 across all studies even if a few of the primary authors used an alpha of 0.10.1 Here we return to the topic of grandparental associations with grandchild survival using a meta-analysis approach. In contrast with the results of Sear and Mace (see above), we found a significant positive association between grandparental survival and grandchild survival at alpha=0.05 for both the maternal grandmother (P=0.02) and the maternal grandfather (P=0.05) (K=7) but not for either paternal grandparent. Our results became even more significant when we used an analytic procedure that allowed us to include more studies (K=17). These findings agree with the matrilateral bias in grandparental investment and emotional closeness observed in studies conducted in developed countries (reviewed in Coall and Hertwig 2010). We caution, however, that wealth or genes for disease resistance may simultaneously improve the survival of grandparents and grandchildren. To exclude this possibility, it is necessary to control for variables other than grandparental investment that cause heterogeneity in grandchild survival (Nöel- Miller 2005). We discuss the extent to which the existing studies succeed or fail in this regard. We also articulate differences in the predictions made by five alternative hypotheses on grandparental investment: the grandmother hypothesis, the confidence of paternity hypothesis, the proximity hypothesis, the grandparental senescence hypothesis, and the local resource competition hypothesis.

The Confidence of Paternity Hypothesis (Alexander 1974; Gaulin and Schlegel 1980; Hartung 1981; Trivers 1972) predicts that parents invest less in children who are related through sons than through daughters. When paternity is uncertain, the mother’s mother (MM) has the greatest likelihood of being genetically related to a given grandchild, the father’s father (FF) has the least likelihood, and the risk for the father’s mother (FM) and mother’s father (MF) is intermediate, producing the expectation that the order of grandparental investment is MM > (FM & MF) > FF (Table 1) (Coall and Hertwig 2010; Euler and Weitzel 1996; Hawkes et al. 1998;

1 Coall and Hertwig (2010:49) questioned why we scored a particular result in Gibson and Mace (2005:475) as nonsignificant when the 95% confidence interval was 0.51–0.99. In clarification, the reported P-value was 0.06 and exceeded the cutoff of 0.05 (Strassmann and Kurapati 2010). Coall and Hertwig also questioned our scoring of the data in Beise (2005), yet the finding in question (maternal grandmothers) had a P-value >0.1, which we scored as nonsignficant. Hum Nat (2011) 22:201–222 203

Table 1 Predictions from five hypotheses about grandparental investment in patrilineal populations

Hypothesis Prediction

Confidence of Paternity MM > (FM & MF) > FF (or MM > MF > FM > FF) Grandmother MM & FM > MF & FF Proximity FM & FF > MM & MF Grandparental Senescence MM > (FM & MF) > FF Local Resource Competition MM & MF > FM & FF

MM=mother’s mother, FM=father’s mother, FF=father’s father, and MF=mother’s father. The inequal- ities indicate the relative predicted strengths of positive associations between grandparental survival and grandchild survival

Huber and Breedlove 2007; Pashos 2000; Smith 1987, 1988; see also Pollet et al. 2009). A nuance is that the MF is at risk for cuckoldry through infidelity on the part of his wife, whereas the FM is at risk for indirect cuckoldry through infidelity on the part of her son’s wife. The latter might be a more difficult risk for the grandparent to assess as it does not involve the grandparent’s own marriage. Thus, in cases where he trusts his wife, the MF might be more prone to invest than the FM, producing the expectation that: MM > MF > FM > FF (Table 1).

The Grandmother Hypothesis proposes that grandmaternal investment played an important role in the evolution of menopause (e.g., Shanley et al. 2007), lengthened the postmenopausal lifespan, and tightened the interbirth intervals of women compared with other primates (Hawkes et al. 1997, 1998). Further, it has been proposed that humans are a cooperatively breeding species in which help from grandmothers and other kin is a major factor in child rearing (Coall and Hertwig 2010; Hrdy 2009; Kramer 2005; Sear and Mace 2008). For example, Sear and Mace (2008:15) state that we are “evolved to rear children as part of an extended family enterprise.” Other authors put more emphasis on fathers and other adult males than on grandmothers (Gurven et al. 2006; Hill and Hurtado 2009; Kaplan et al. 2000; Lovejoy 1981). Proponents of the grandmother hypothesis downplay the role of grandfathers, perhaps because males are presumed to be more engaged in mating effort than nepotistic investment in grandchildren: for example, Sear and Mace (2008:10) concluded that “grandfathers are much less important to children.” Researchers usually emphasize the maternal grandmother (Hawkes et al. 1997, 1998; Lahdenpera et al. 2004; Sear and Mace 2008). Hawkes et al. (1998:1338) base this emphasis on the assumption of greater proximity between mothers and daughters than mothers and daughters-in-law: “When daughters mature, the assistance of aging mothers continues to enhance the benefits of proximity,” and “the grandmother hypothesis . . . favors co-residence between older mothers and their daughters.” Clearly, their assumption about daughters’ geographic closeness to the MM does not apply to patrilocal populations, where it is the FM who is the nearby grandmother. In patrilineal populations, the major reason given by Hawkes et al. for emphasizing the MM is no longer applicable. Further, Hawkes et al. (1998:1338) state: “any effects on the production of descendants through a son’s mate would be diluted by uncertain paternity.” This statement is equivalent to the confidence of paternity hypothesis 204 Hum Nat (2011) 22:201–222 articulated above. Thus, when applied to patrilineal populations, and when teased apart from the proximity and confidence of paternity hypotheses, the grandmother hypothesis predicts: MM & FM > MF & FF (Table 1). The proximity hypothesis states that residence pattern might influence grandparental investment (Euler and Weitzel 1996;GibsonandMace2005; Pashos 2000; Rossi and Rossi 1990; Sear and Mace 2008). Usually it is assumed that grandparents who live closest to the grandchildren will invest the most. In patrilocal populations, this hypothesis predicts that FM & FF > MM & MF, whereas in matrilocal populations the reverse might be anticipated (Table 1). The grandparental senescence hypothesis articulated here is an extension of the observation that the four grandparents of a given child are not equally likely to be alive (Euler and Weitzel 1996; Kemkes-Grottenthaler 2005;Searetal.2002). It predicts that the MM is the youngest and least senescent grandparent and the FF is the oldest and most senescent grandparent, with the MF and the FM being of intermediate physical health. Beneficial associations between grandparental survival and grandchild survival should follow suit, with less senescent grandparents being more helpful: MM > (MF & FM) > FF (Table 1). The grandparental senescence hypothesis builds on the observations that in most societies males marry at an older age than females, and the difference is especially great in polygynous societies (Pison 1986;Strassmann1997). Older males are more likely to reproduce than older females, and males senesce at a faster rate than females, becoming infirm and dying at younger ages. Prior to death an individual usually experiences a period of infirmity and dependence on others. Grandparents who are younger relative to their grandchildren are, on average, less likely to be a net drain on resources. The grandparental senescence hypothesis focuses on the dwindling capacity for older grandparents to be net producers.

The Local Resource Competition Hypothesis (see Borgerhoff Mulder 2007; Campbell and Lee 1996; Derosas 2002; Sear 2008; Sear and Mace 2008; Strassmann et al. 2006; Voland and Beise 2002) overlaps with the grandparental senescence hypothesis but emphasizes the competition that occurs among family members who belong to the same economic unit and who depend on the same resources (Strassmann et al. 2006). In three-generation families in patrilocal populations, the paternal grandfather is the patriarch and his inclusive fitness interests are not the same as those of a given grandchild. He may shunt resources toward mating effort or to other grandchildren at the expense of a particular grandchild. He may also grow infirm and cease to be a net producer, thereby competing for resources with his grandchildren. A given child might be better off if his own father is head of the family rather than either his paternal grandfather or, still worse, an even more remote relative such as a paternal great uncle. The paternal grandmother in such societies has less control over resources, but she too can become a net consumer whose continued survival has an adverse effect on grandchild survival through resource competition (Strassmann et al. 2006; Strassmann 2011). In patrilocal societies, maternal grandparents generally do not live in the same economic group as their grandchildren and do not compete with them even after they become elderly. Maternal grandparents may interact with their grandchildren less often than paternal grandparents, but they may still have opportunities to invest. Even when they do not have the means to invest positively, they at least have less Hum Nat (2011) 22:201–222 205 potential to be a negative influence. On balance, in patrilocal populations, the Local Resource Competition Hypothesis predicts that the survival of maternal grandparents is more positively associated with the survival of grandchildren than is the survival of paternal grandparents: MM & MF > FM & FF (Table 1). Children living matrilocally in a patrilocal population, or living patrilocally in a matrilocal population, are expected to be most adversely affected by the grandparent for whom they work and with whom they share resources. Kin competition can be strategically avoided by the practice of investing less in the philopatric sex (Clark 1978).

Methods

Data

We compiled a data set that included the studies that Sear and Mace (2008) identified in their Table 2a as having made at least a partial attempt to control for confounding variables. We updated Sear and Mace’s search so as to include published and unpublished studies available in March 2011 in the following electronic databases: Web of Science, Family & Society Studies Worldwide, Sociological Abstracts, Anthropology Plus, Africa-Wide Information, Social Service Abstracts, Dissertation Abstracts, and the general Google search engine. Our search used relevant English language key terms and their variants (e.g., child*, grandchild*, offspring, or grandoffspring, and grandparent*, grandmother, or grandfather, and survival or mortality). We also examined the references for each identified study and for literature reviews on our topic. Studies eligible for inclusion were not restricted by language and reported child mortality or survival rates in association with at least one specific category of grandparent (FM, FF, MM, and MF). Eligible studies focused on populations identified as predominantly natural or high fertility or that were still undergoing the demographic transition, as well as populations with high child mortality. To permit a coherent interpretation, we excluded one study (Hill and Hurtado 1996) in which maternal and paternal grandmothers were grouped together, and we excluded two studies that focused on strongly matrilineal, matrilocal populations [the Chewa of Malawi (Sear 2008)and the Khasi of India (Leonetti et al. 2005)]. The studies included in the meta-analysis all practiced patrilineal descent. The African and Asian populations practiced patrilocal residence and the European and North American populations practiced a combination of patrilocal, multilocal, and neolocal residence. Unfortunately, the source studies for the Euroamerican populations did not discuss postmarital residence in any depth. When authors reported data for grandchildren whose parents were both alive as well as for children whose mother or father had died, we used the data for children with two living parents, which was probably the more common situation in the studies that did not disaggregate their analyses in this way. Our goal was to improve comparability across studies. Our search produced one unpublished study (Strassmann 2011) and two Ph.D. dissertations (Nöel-Miller 2005;Walker1990) not analyzed by Sear and Mace (2008) that we included in our analysis. 0 u a 21)22:201 (2011) Nat Hum 206 Table 2 Features of the eligible studies (K=17, N≈252,320)

Population Reference Age range Time period N (approx.) RR (±95% Wealth Research Design Subsistence in months CI) estimatea Control

Africa Kipsigis, Kenya Borgerhoff Mulder 2007 0–60 1945–1990 785 Yes No Retrospective Agropastoralist Oromo, Ethiopia Gibson and Mace 2005 0–36 1993–2003 ≈ 1,500 Yes Yes Retrospective Agropastoralist West Kiang District, Gambia Sear et al. 2002 0–60 1950–1974 ≈ 1,100 Yes No Prospective Rice and groundnut farming Dogon, Mali Strassmann (2011)0–60 1998–2001 2,930 person-years Yes Yes Prospective Millet farming Gambia Nöel-Miller 2005 unspecified 1993 ≈ 129,000 No Yes Retrospective Variable Asia Liaoning Province, China Campbell and Lee 1996 24–180 1792–1867 9,867 No No Family Reconstitution Farming Uttar Pradesh, India Griffiths et al. 2001 1–8 1992–1993 4,477 person-years Yes No Retrospective Unstated Tokugawa, Japan Jamison et al. 2002 0–192 1671–1871 ≈ 17,700 person-years No No Family Reconstitution Rice farming Northeast India Ladusingh and Singh 2006 unclear 1998–1999 7,774 No Yes Retrospective Agriculture Bengali, India Leonetti et al. 2005 0–120 1980–2000 2,069 Yes No Retrospective Farming, unspecified crop Europe Venice, Italy Derosas 2002 0–120 1850–1869 >21,000 Yes Yes Family Reconstitution Urban Ludwigshafen, Germany Kemkes-Grottenhaler 2005 0–24 1700–1899 ≈ 870 No No Family Reconstitution Farming & artisanry Finland Lahdenpera et al. 2004 0–180 1702–1823 6,002 No No Family Reconstitution Agriculture, servant, priest, etc. Bejsce Parish, Poland Tymicki 2009 0–60 1737–1968 17,000 Yes No Family Reconstitution Farming, unspecified crop Krummhörn, Germany Voland and Beise 2002 0–60 1720–1874 3,095 No No Family Reconstitution Farm workers, small, rural craftsmen & tradesmen North America Colonial Quebec, Canada Beise 2005 0–60 1680–1750 26,449 Yes No Family Reconstitution Farming unspecified crop Mexican-Americans, Walker 1990 0–216 1905–1979 702 No Yes Retrospective Variable, salaried Laredo, Texas employment

a –

Yes = Studies included in the meta-analysis of effect sizes (Tables 3 and 4 and Fig. 1). No = Studies that did not report RR or information for calculating both RR and the 95% 222 confidence interval Hum Nat (2011) 22:201–222 207

Statistical Analysis

Meta-Analysis We chose relative risk (RR) as the metric for our meta-analysis since studies that reported RR took into account time-varying covariates and censoring (see Strassmann and Gillespie 2003; Wood 1994:81–102). Explanatory variables such as mother’s marital rank (sole wife, first wife, second wife, etc.) change over time, and they cannot be adequately controlled using cross-sectional data for a single time point. Censoring bias occurs in retrospective studies when researchers assess child survival status at the time of the interview instead of determining whether each child survived to a specific age, such as 5, 10, or 15 years. Children who were born closer to the time of the interview are more likely to be alive than children born earlier—in effect, their exposure to the risk of death is censored (truncated) and their survival is exaggerated. When source studies were missing both standard errors and confidence limits, we contacted the study authors to request measures of variability. We combined nonoverlapping age groups within the same study to create aggregate age groups (e.g., 0–60 months) using the inverse of the standard error to weight the age groups when pooling them. Prior to analysis, the natural log of the RR was calculated for each type of grandparent and for three grandchild age categories (All ages available in a particular study, 0–12 months, and 0–60 months). The meta-analysis was conducted on the log RR and its standard error based on a random effects model using the DerSimonian and Laird procedure with inverse variance weighting (Lipsey and Wilson 2000;Sterne2009). For reporting purposes, the log RR values used in the analyses were converted back into the original RR metric. The corresponding significance tests used 1 as the reference value for the null hypothesis (H0: RR=1 vs. HA:RR≠1). RR values greater than 1 indicated that the survival of the grandparent was associated with increased grandoffspring mortality, and values less than 1 indicated that the survival of the grandparent was associated with decreased grandoffspring mortality. The presence of heterogeneity beyond what would be expected due to sampling error was examined via the Q and I2 statistics. A significant Q value suggests the presence of variability in the distribution of studies not due to chance, and the I2 value reflects the degree of heterogeneity on a scale of 0 to 100. According to guidelines, I2 values around 15% reflect a low degree of heterogeneity; between 25% and 50%, a moderate degree; and ≥ 75%, a high degree (Higgins and Green 2009). Because the Q statistic is known to perform poorly when the number of studies is small, we expect the I2 value to be the best indicator of unexplained variability in our meta-analysis.

Modified Vote Counting Seventeen studies met the eligibility criteria for this review. Nine of the studies also provided adequate quantitative information for calculating a relative risk (RR) value. Eight studies met the eligibility criteria but could not be included in the meta-analysis because they reported results as odds ratios or logistic regression parameter estimates and lacked information on the baseline hazard rate (preventing the calculation of RR), or they lacked measures of variability (standard errors or confidence intervals). One of the eight studies reported only a survival distribution function with a log-rank test and did not state unambiguously that 208 Hum Nat (2011) 22:201–222 control variables were included in the pertinent analysis (Lahdenpera et al. 2004). Rather than exclude these eight studies from further consideration, we combined them with the nine studies from the meta-analysis in a parallel synthesis using a modified vote-counting procedure based on the sign test (Bushman 1994, Sutton et al. 2000). This increased our sample size to 17 and allowed us to evaluate whether the results we obtained for the nine studies in the meta-analysis might be biased by the exclusion of studies, including unpublished studies (the “file drawer problem”; Rosenthal 1979) which are conventionally assumed to have nonsignificant P-values. The criticism of vote counting pertains to analyses that count the number of studies that have statistically significant versus nonsignificant findings. In such analyses, nonsignificant P-values are taken as evidence that an effect is absent when, in reality, such effects might be driven by low statistical power (Borenstein et al. 2009). This criticism does not apply to the approach we used because we only considered the direction of the effect and not the P-value. Our approach followed the recommendations of Bushman (1994:194), who advised that effect size procedures be used for those studies that contain sufficient information to make estimates of effect size possible and that vote-counting procedures be used for the larger group of studies. In our modified vote-counting analysis, we scored each result in each study according to whether the survival of a given kind of grandparent was associated with increased or decreased survival for grandchildren (positive associations were scored as 1 and negative associations as 0). We used the direction of the estimate without regard to the significance level. Hence even associations that were nonsignificant based on P-values became either positive or negative using this technique. Whereas some studies had a single age category because they lumped children age 0 to 5 years (e.g., Borgerhoff Mulder 2007; Strassmann 2011) or even 0 to 16 years (Jamison et al. 2002), others used multiple age categories (e.g., Beise 2005), and the width of the age categories varied across studies. Researchers did not consistently subdivide their analyses by sex of child. The number of studies that broke the analysis down in a similar way was too small to permit separate analyses by age and gender. Instead we included all categories found in each publication, with each category getting a “vote.” We employed a generalized estimating equations model (Diggle et al. 2002)to account for the within-study correlation. The analysis was carried out in SAS software (version 9.2) using the GENMOD procedure and the binomial distribution. We calculated the predicted probabilities of a positive association for each kind of grandparent. The null hypothesis stated that the probability that a given kind of grandparent (MM, MF, FF, FM) had a positive association with grandchild survival was 0.5. The alternative hypothesis stated that the probability was either greater or less than 0.5 (for a 2-tailed test). The modified vote counting analysis was based on 17 publications that contributed 41 observations (categories across all studies). To shed further light on grandparental investment, especially in regard to the grandparental senescence hypothesis, we collected data on the survival of grandparents for the children in a prospective, cohort study of the Dogon of Mali. The cohort includes the total population of children age 0 to 5 years in nine Dogon villages in 1998 with the addition of all children born by August 2000 (N=1,700). Hum Nat (2011) 22:201–222 209

The data we present are for the year 2007, when the children were age 7 to 14 years. After deaths and urban migration, the sample had approximately 1,400 children for whom follow-up was possible that year.

Results

Meta-Analysis

Table 2 summarizes major features of the 17 studies included in this review, for nine of which it was possible to estimate RR. The grand study-level mean RR for grandoffspring mortality given survival of a particular grandparent type is shown in Table 3. Mean RR ranges from 0.89 to 0.97 across all age groups and types of grandparents (Fig. 1,Table3). Disaggregated data for the nine studies are shown in Table 4. On the paternal side, the survival of neither the FM (RR=0.95; 95% CI: 0.78 to 1.14; P=0.57; K=9) nor the FF (RR=0.95; 95%CI:0.82 to 1.10; P=0.57; K=7) was

Table 3 Mean RR of death for grandchildren if the grandparent is alive (reference category = dead) by grandchild age category (K≤9; N≤58,410)

Age category RR of grandchild mortality when grandparent is alive

Paternal Maternal

FM FF MM MF

All available ages in a given RR .95 .95 .91* .92* ≤ study ( 120 months) CI .78 to 1.14 .82 to 1.10 0.84 to .99 .85 to 1.00 Q 38.3* 11.7 3.0 6.0 I2 79% 49% 0% 0% K 9777 0 to 12 months RR .97 .94 .95 .89 CI .86 to 1.07 .79 to 1.11 .88 to 1.02 .75 to 1.05 Q 6.08 8.4* 0.2 9.3* I2 34% 65% 0% 68% K 5444 0 to 60 months RR .93 .93 .91* .94 CI .67 to 1.29 .76 to 1.12 .83 to .99 .86 to 1.03 Q 34.5* 9.6* 0.6 3.8 I2 88% 58% 0% 0% K 5555

RR = Relative Risk, CI = 95% confidence interval. Q and I2 are measures of heterogeneity. K = number of studies FM = father’s mother, FF = father’s father, MM = mother’s mother, MF = mother’s father *P≤0.05 210 Hum Nat (2011) 22:201–222

a Father's Mother b Father's Father 1 2 1 3 2 4 3 5 4 6 7 7 8 8 9 9 Overall Overall

.2 .5 1 1.5 2 3 .2 .5 1 1.5 2 3

c Mother's Mother d Mother's Father 1 1 2 2 3 3 4 4 7 7 8 8 9 9 Overall Overall

.2 .5 1 1.5 2 3 .2 .5 1 1.5 2 3 Lower mortality Higher mortality Lower mortality Higher mortality Fig. 1 Mean relative risk (RR) of death for grandchildren if the grandparent is alive (dead is the reference). Forest plots show the relative risk (RR) and 95% confidence intervals (CI) for each source study contributing an estimate for at least one type of grandparent in the meta-analysis. The dashed line indicates the grand mean RR, and its 95% CI corresponds to the angle brackets in the row labeled “Overall” (Table 2). Key to source studies: (1) Beise 2005; (2) Borgerhoff Mulder 2007; (3) Derosas 2002; (4) Gibson & Mace 2005; (5) Griffiths et al. 2001; (6) Leonetti et al. 2005; (7) Sear et al., 2002; (8) Strassmann 2011; (9) Tymicki 2009. Summary results for each source study are provided in Table 4

associated with increased or decreased risk of grandoffspring mortality since the confidence limits included 1. The moderate-to-high heterogeneity associated with the RR for FM (Q=38.3; P=0.00; I2=79%) and FF (Q=11.7; P=0.07; I2=49%) suggests that the between-study variability is influenced by non-chance factors other than mere sampling error. The heterogeneity is seen in the forest plots (Fig. 1a, b)by the relatively wide dispersion of the results around the overall mean RR values, including three studies reporting RR>1, for both FM and FF. Thus, the available evidence does not support a clear tendency toward either increased or decreased mortality given the survival of either paternal grandparents. A similar pattern of results was noted for the subset of studies that reported separate results for the age category 0–12 months for FM (K=5) and FF (K=4) and also for the subset of five studies for which it was possible to estimate RR between ages 0 and 60 months (Table 3). For both age categories, neither RR associated with a paternal grandparent was significantly different from 1, and both age categories were characterized by moderate-to-high heterogeneity for both FM and FF. On the maternal side, the survival of both the MM (RR=0.91; 95%CI:0.84 to 0.99; P=0.02; K=7) and the MF (RR=0.92; 95%CI:0.85 to 1.00; P=0.05; K=7) was associated with a statistically significant decreased risk of grandchild death. In addition, the between-study heterogeneity associated with the RR for MM (Q=3.0; Hum Nat (2011) 22:201–222 211

Table 4 Mean RR of death for grandchildren if the grandparent is alive (reference category = dead) by study (K≤9). All available ages in a given study are pooled

Reference RR of grandchild mortality when grandparent is alive

Paternal Maternal

FM FF MM MF

1. Beise 2005 RR .97 .97 .92 .98 CI .86 to 1.09 .85 to 1.10 .82 to 1.04 .87 to 1.10 2. Borgerhoff Mulder 2007 RR .35* .60* .74 1.05 CI .23 to .54 .39 to .92 .43 to 1.29 .65 to 1.71 3. Derosas 2002 RR .99 1.12 1.04 .91 CI .77 to 1.17 .85 to 1.49 .84 to 1.29 .72 to 1.15 4. Gibson and Mace 2005 RR .90 .93 .82 .87 CI .70 to 1.15 .71 to 1.22 .66 to 1.03 .70 to 1.07 5. Griffiths et al. 2001 RR 1.19 ––– CI .90 to 1.56 ––– 6. Leonetti et al. 2005 RR .85 ––– CI .60 to 1.20 ––– 7. Sear et al. 2002 RR 1.17 1.04 .89 .91 CI .76 to 1.79 .68 to 1.61 .56 to 1.40 .59 to 1.41 8. Strassmann 2011 RR 1.93** 1.54 .93 1.08 CI 1.31 to 2.83 .97 to 2.45 .65 to 1.33 .78 to 1.51 9. Tymicki 2009 RR .85 .82 .88 .76* CI .71 to 1.03 .65 to 1.02 .75 to 1.05 .61 to .93

RR = Relative Risk, CI = 95% confidence interval FM = father’s mother, FF = father’s father, MM = mother’s mother, MF = mother’s father *P<0.05 **P<0.001

P=0.98; I2=0%) and MF (Q=6.0; P=0.42; I2=0%) was not larger than would be expected by chance (or sampling error). The low heterogeneity for the maternal grandparents is apparent in the forest plots (Fig. 1c, d) for MM and MF, which display relatively low dispersion of the individual study RRs around the overall mean RRs. The consistency of between-study results is most evident for MM, for whom only one of seven studies reported a RR greater than 1. When the data are broken down by age category, sample sizes get extremely small. However, in the age category 0–60 months, the results remained significant for MM (RR=0.91; 95%CI:0.83 to 0.99; P=0.04; K=5) (Table 3). The heterogeneity values generally remained low for the two age categories (0–12 months and 0–60 months, with the exception of MF for the 0–12 month age group wherein the results suggested significant and moderate heterogeneity beyond what would be expected due to chance for these four studies (Q=9.3; P=0.03; I2=68%; K=4). We considered potential moderator variables that might influence the associations between grandparental survival and grandoffspring mortality (Table 2). The 212 Hum Nat (2011) 22:201–222 methodological moderator variables were research design (prospective, retrospective, or family reconstitution study) and whether a wealth covariate was used (yes or no). The moderator variables that referred to characteristics of the population were geographic location (Africa, Asia, Europe, and North America) and means of subsistence (agropastoral, farming, or urban-based). Given the small number of studies (K=9) that could be included in our meta-analysis of RR effect-sizes, it was not surprising that the results were not significant in all categories of these moderator variables. However, the overall pattern was consistent with the finding that the RR of grandoffspring mortality was lower in the presence of surviving maternal but not paternal grandparents. To check for bias, such as publication bias, we examined funnel plots for the RR associated with each type of grandparent in each study. The funnel plots, simple scatter plots of individual study results by their standard errors, revealed no consistent evidence of bias due to potentially missing studies that have large standard errors and small RR values around 1. In addition, we conducted a graphical analysis of the influence of individual studies on the overall RR associated with each type of grandparent. The results showed that if any one of the studies in the meta- analysis were omitted, the overall mean RR for each grandparent type would still lie within the confidence intervals of the primary analyses. Thus, the results of the funnel plots and influence analyses bolster our confidence that, despite the small number of studies, our results are not artifacts of these methodological issues.

Modified Vote-Counting Analysis

Figure 2 shows the estimated probabilities that a given kind of grandparent had a positive association with grandchild survival in the modified vote-counting analysis (K=17 studies overall, K=16 for FM, K=12 for FF, K=13 for MM, and K=11 for FF). Where the confidence limits do not include 0.50 there is a significant association between that kind of grandparent and grandchild survival. The estimated probabilities, confidence limits, and P-values are: FM=0.58 (95% CI:0.370 to 0.768; P=0.450), FF=0.53 (95%CI:0.297 to 0.744; P=0.836), MM=0.83(95%CI:0.704to0.911;P<0.0001), and MF=0.74 (95%CI:0.532 to 0.875; P=0.025). Consistent with the results for the effect-size meta-analysis, survival of the MM (P<0.0001) and the MF (P=0.025) was positively

Fig. 2 The estimated probability of a positive association (±95% confidence limits) between grandparental survival and grandchild survival. Data are for the 17 studies in the modified vote-counting analysis based on the sign test (Bushman 1994) and described in Table 2. MM=mother’smother, FM=father’smother, FF=father’s father, and MF=mother’sfather Hum Nat (2011) 22:201–222 213 associated with grandchild survival. No statistically significant association was found for the other two kinds of grandparent.

Discussion

Regardless of which methodology we used, the survival of the maternal but not the paternal grandparents was significantly positively associated with grandoffspring survival in patrilineal populations (K=17). In what follows, we consider how our results bear on the hypotheses about grandparental investment. These hypotheses are overlapping and are not intended to be mutually exclusive.

Confidence of Paternity Hypothesis

The finding that the survival of the maternal but not the paternal grandparents was significantly positively associated with grandoffspring survival is generally consistent with the confidence of paternity hypothesis. However, the data do not support the expectation that investment by the FM and MF should be equivalent, as we got a significant result only for the MF. The confidence of paternity hypothesis assumes a low, albeit unspecified, level of paternity certainty that is probably inappropriate for patrilineal, patrilocal populations (Pashos 2000). Men in patrilineal populations appear to have higher paternity certainty than do men in matrilineal populations, and it is unlikely that they would continue to transmit wealth patrilineally in the face of significant levels of cuckoldry (Alexander 1974; Flinn 1981; Gaulin and Schlegel 1980; Hartung 1976, 1981; Holden et al. 2003; see also Huber and Breedlove 2007). Among the Dogon, paternity certainty is as high as that found in contemporary populations that practice contraception (Strassmann et al. 2011; see Anderson 2006). Previous studies have also found the confidence of paternity hypothesis to be insufficient, on its own, for explaining differences in nepotism by grandparent type (Euler and Weitzel 1996; Pashos 2000; Pashos and McBurney 2008; but see Gibson and Mace 2005).

Grandmother Hypothesis

Our meta-analysis showed that the RR of grandoffspring mortality was 9% lower when the MM was still alive (RR=0.91; 95% CI: 0.84 to 0.99; P=0.02; K=7). Similarly, the modified vote-counting procedure showed that the probability that the survival of the MM had a positive association with grandchild survival was 0.83 (95% CI: 0.704 to 0.911), which was significantly (P<0.0001) different from the random expectation of 0.5. These results for the MM support the grandmother hypothesis. However, the absence of a significant result for the FM (RR=0.95; 95% CI: 0.78 to 1.14; P=0.57; K=9) in both analyses does not support a general grandmother hypothesis (one that includes both kinds of grandmother). Furthermore, the grandmother hypothesis does not predict the 8%-lower risk of grandoffspring mortality when the MF was alive (RR=0.92; 95% CI: 0.85 to 1.00; P=0.05; K=7). In the modified vote-counting procedure, the probability that the survival of the MF had a positive association with grandchild survival was 0.74 (P=0.025). 214 Hum Nat (2011) 22:201–222

In addition, the grandmother hypothesis is not consistent with the finding that the grandmother who is most likely to co-reside with grandoffspring is less positively associated with grandoffspring survival than the grandmother who lives elsewhere. As discussed above, Hawkes et al. (1998) emphasized the benefits of coresidence between daughters and their mothers. Our results show that coresidence is not essential (the MM appears to be beneficial even though she lives elsewhere) and that even when a grandmother lives in the same household (as is the case for the FM in patrilocal families), she is often not beneficial. On the other hand, a particular kind of grandfather—the MF—does appear to be beneficial. It is difficult to align these results with the grandmother hypothesis as articulated by Hawkes et al. (1998). The grandmother hypothesis would have been more strongly supported if both the FM and the MM were positively associated with grandoffspring survival (and if no association had been found for either kind of grandfather). For example, when Sear and Mace (2008) stated that 64% of studies found beneficial associations for the MM, 60% for the FM, and only 20% for the FF and MF, they viewed their data as strongly supportive of the grandmother hypothesis. Their percentages were based on a subjective form of vote counting in which nonsignificant associations in a given study were ignored. Our systematic meta-analysis provides strong evidence that the positive association holds only for the maternal and not the paternal grandmother. Moreover, the widespread notion that grandfathers are unimportant was not supported for the MF.

Proximity Hypothesis

Most of the populations in our meta-analysis were patrilocal, yet there was no significant beneficial association for survival of the paternal grandparents and grandoffspring survival. Instead, the opposite was found: namely, a beneficial association for the maternal grandparents. This result directly contradicts the proximity hypothesis. Previous studies have also found that residential proximity does not explain differential grandparental solicitude (Euler and Weitzel 1996, see also Gibson and Mace 2005). For example, in the Gambia, Noel-Miller (2005:199) found that the coresidence of a grandparent and grandchild did not improve the grandchild’s survival chances. In Puerto Rico, Scelza (2011) concluded that geographic proximity between a woman and her mother was crucial for infant health—but only so long as it occurred in conjunction with the mother’s social support.

Grandparental Senescence Hypothesis

Strictly based on the age differences between the four kinds of grandparent, and the difference in rates of senescence between males and females, one would expect that a child is most likely to have a living MM and least likely to have a living FF, with the probabilities of the other two kinds of grandparent being intermediate. As shown in Fig. 3, this expectation is supported by data for Dogon children age 7 to 14 years in Mali. When analyzed statistically, the odds of death for a given grandparent type were lowest for the MM and highest for the FF. All comparisons between grandparent types were highly significant (P<0.001) except for the comparison Hum Nat (2011) 22:201–222 215

Survival of Parents and Grandparents by Child's Age 100 90 80 Age (years) 70 7 - 8 60 9 - 10 50 11 - 12 40 13 - 14 30

Percentage of Kids 20 10 0 mom dad fm ff mm mf Fig. 3 Survival of parents and grandparents by child’s age in 2007. The data are for the children in a prospective cohort study of the Dogon of Mali [mother (N=1,420), father (N=1,030), mother’smother (N=1,403), mother’sfather(N=1,394), father’smother(N=1,413), father’sfather(N=1,449)] between mother’s father and father’s mother (P=0.086). Under the grandparental senescence hypothesis, the relative survival of the four kinds of grandparent is also a good indication of their relative health and their probability of investment, producing the expectation that the order of investment is: MM > (FM&MF) > FF. The finding that the MM had a significant positive association with grandchild survival (and the smallest P-value) is consistent with this hypothesis, but it is not clear why we should find a significant association for the MF and not for the FM. In a previous study in Germany, age differences between the four kinds of grandparent were not found to correspond to differences in nepotism by grandparent type (Euler and Weitzel 1996). In that study, the mean age of the MM was 59.3 years and of the FF was 63.0 years, with the other two kinds of grandparent being of intermediate age. Several of the populations included in our meta-analysis are polygynous and can be expected to have had much greater age differences between grandparents (and poorer health care) than in the German study. Further data are needed on the relative health of the four kinds of grandparent in patrilineal populations.

Local Resource Competition Hypothesis

One interpretation of our results is that they show covert matriliny (preferential investment in daughters’ children over sons’ children) in populations that are otherwise patrilineal. In all subsistence-based populations in our data set, however, land and livestock were inherited patrilineally. Given that these are the most critical resources for reproduction in farming and agropastoralist populations, one would need to posit a dual strategy of passing resources to sons but favoring the rearing of daughters’ children. Such a strategy is compatible with local resource competition— avoiding overproduction of offspring who will compete against kin (Clark 1978). The children of daughters marry out of the patrilineage and are dispersed among the different families of the daughters’ husbands. Paternal grandsons, by contrast, stay 216 Hum Nat (2011) 22:201–222 home to compete against each other, so it does not make sense to rear too many. The results of our meta-analysis are in line with this hypothesis, which predicts that in patrilocal populations, the continued survival of maternal grandparents is, on balance, more beneficial than that of paternal grandparents: (MM & MF) > (FM & FF). Among the Dogon of Mali, a living FM was associated with a twofold increased risk of grandchild mortality by age 5 years, and culturally the lack of perceived benefit from the FM is captured by the norm that she must return to her natal patrilineage as soon as the mourning period for her husband is over (Strassmann et al. 2006;Strassmann2011). A living FF was also associated with decreased grandchild survival, but this result was not quite significant in statistical models. The detrimental association with grandoffspring survival was greatest for older paternal grandmothers who were more likely to be a net drain on resources (Strassmann et al. 2006; Strassmann 2011). Although there was no significant interaction of the form “sex of grandchild by FM survival status,” there was a significant interaction in data on growth. Boys were significantly more stunted than girls if the FM was alive (rather than dead) (Strassmann et al. 2006;Strassmann2011). Similarly, in Tokugawa Japan, the presence of the FM was associated with increased odds of death for boys but not girls (Jamison et al. 2002). The Dogon and the Japanese are patrilineal. Among the matrilineal Chewa of Malawi, the survival of female maternal kin (grandmothers and aunts) was negatively associated with grandchild survival (with girls tending—albeit nonsignificantly—to be more adversely affected) (Sear 2008). The original formulation of the local resource competition hypothesis emphasized sex-biased investment as a strategy for avoidance of kin competition in a prosimian primate (Clark 1978). Humans are extremely diverse, and it is difficult to make generalizations about such a broad category as “patrilineal.” Some populations may favor daughters in certain contexts, whereas others favor sons, the latter type being especially common in Asia (Hrdy 1999:323). In India, son preference might reflect the difficulty of providing dowries for daughters as females compete against each other for the resources needed to contract hypergynous marriages (Dickemann 1979). We would not expect a universal tendency for one sex to be favored over the other in all socioecological contexts. However, we do posit that kin competition is a universal aspect of human family systems. Competition starts in utero with genomic imprinting—maternal genes “prefer” to allocate resources strategically between present and future offspring; sibling rivalry extends this competition throughout childhood (Haig 1993). Upon reproductive maturity, kin compete for the resources required for mating and parental effort (e.g., Borgerhoff Mulder 1998; Mace 1996). Finally, in old age, net producers eventually become net consumers who compete with other family members for food and shelter. Early research in human social behavior recognized that humans both cooperate and compete with their kin (Alexander 1974, 1979). Identifying the human species as a whole as “cooperatively breeding” is not terribly useful for understanding the interplay between cooperation and competition, context-based trade-offs, and socioecological complexity. We explored multiple hypotheses simultaneously, rather than focusing on the grandmother hypothesis or cooperative breeding theory alone. This approach led to the interesting and nonintuitive finding that even in patrilineal societies, maternal Hum Nat (2011) 22:201–222 217 grandparents are more positively associated with grandoffspring survival than paternal grandparents. We called this “covert matriliny,” but it also resembles “complementary filiation,” which Meyer Fortes and Jack Goody (among other theorists) recognized as the close association that people have with kin who are outside their own descent group. Although political and public forms of status and wealth are conferred through paternal relations in a patrilineage, maternal relations are still important on the domestic level (Fortes 1953, 1969; Goody 1962). Thus, our meta-analysis provides quantitative evidence in support of an anthropological theory developed half a century ago.

Methodological Limitations

A caveat is needed in regard to methodology. It is tempting to assume that increased survival of grandoffspring in the presence of a surviving grandparent is due to investment by that grandparent. However, there may be no firm basis for concluding that correlations of this kind are causal. An assumption of causation implies that the studies adequately captured the heterogeneity in grandoffspring survival that is due to factors other than grandparental investment. An important concern is that results may be driven by a variable such as wealth that simultaneously improves grandoffspring and grandparental survival (Nöel-Miller 2005). In the entire data set, only 6 of 17 studies controlled for wealth, and this was true even after omitting the studies that Sear and Mace (2008) excluded on account of having insufficient controls. The forest plots (Fig. 1) show that across the nine studies included in the effect-size meta-analysis, the mean RR for all four grandparents was less than 1, which signifies a lower risk of grandoffspring mortality when the grandparent survived. It is difficult to tease apart confounding by unmeasured variables that would tend to produce RR estimates below 1 from the actual effect of grandparental investment. In view of this concern, it would be inadvisable to take the effect size of 9% lower RR of grandchild mortality given a surviving MM and 8% lower RR given a surviving MF at face value. Among the 17 studies included in our meta-analysis, nine were observational and eight were family reconstitution analyses that used historical records. Among the nine observational studies, only two had a prospective as opposed to retrospective research design (Table 2). It is extremely difficult to measure the heterogeneity in family structure and wealth that is relevant to the survival of a given grandchild when using a retrospective design, especially if one is considering the mortality of offspring other than the most recently born child. The retrospective study of the Chewa of Malawi (which we omitted because the Chewa are matrilineal) included a single-round survey of women’s reproductive histories and covered children born during the preceding 10 years, resulting in unequal durations of follow-up (a form of censoring bias) (Sear 2008). In the retrospective studies that we did include, the quality of research designs was quite variable. In the prospective study of the Dogon, time-varying covariates on multiple aspects of family structure and wealth were measured annually, and these covariates were used to predict child survival from the year in which the predictor variables were measured to the following year. The Gambian study (Sear et al. 2002)wasalso 218 Hum Nat (2011) 22:201–222 prospective, but it lacked controls for wealth. We attempted to see if the results of the meta-analysis were driven by presence or absence of controls for wealth or by study design, but unfortunately our sample size was too small to conduct a meaningful analysis of moderator effects. Despite these caveats, it is noteworthy that we obtained significant results only for the maternal and not the paternal grandparents. We can think of no reason why confounding should have been greater on the maternal than the paternal side, which suggests that the results are valid. Speculatively, the observed pattern might be artifactual if the negative effects for the paternal side in studies such as that of Strassmann (2011) cancelled out the positive associations that otherwise would have emerged in the grand mean RR on the paternal side. In other words, might the impression of opposite results for the paternal and maternal side be due to the pooling of studies? The sensitivity analyses cast doubt on this suggestion, as they showed that no single study had undue influence, and that if any given study were omitted, the overall mean RR for each grandparent type would still lie within the overall confidence intervals shown in the forest plots (Fig. 1). Moreover, although many of the studies included in our meta-analysis found positive associations across all four grandparent types (an outcome that raises concerns about confounding), there were also individual studies that found opposite results for maternal and paternal grandparents in a given study population (e.g., Voland and Beise 2002). In human evolutionary ecology there is an urgent need for both prospective, longitudinal field studies and high-quality historical studies (with large samples sizes and numerous control variables—such as Derosas 2002). In the meantime, hypotheses about grandparental investment can be usefully, albeit tentatively, evaluated using the studies presently available. We hope that the field will move away from retrospective studies because they cannot capture the dynamic nature of family interactions over time.

Why Meta-Analysis?

One last concern has to do with the challenge of conducting a meta-analysis of studies that focus on populations that differ in regard to socioecology. We attempted to eliminate some of the variability by focusing on patrilineal populations and excluding matrilineal ones. Nonetheless, we do not expect that grandparents should exhibit precisely the same behavior in all patrilineal populations, which raises the question: Why conduct a meta-analysis in the first place? One answer to this question is that if we take the view that each society is unique and must be understood on its own terms, then comparative generalizations are impossible. This view is akin to postmodernist thought in cultural anthropology, which, in our opinion, has not been very productive. Instead, we were motivated to conduct a meta-analysis on account of the review by Sear and Mace (2008), which based theoretical conclusions about the role of grandmothers and cooperative breeding in humans on a synthesis of the literature. Our goal was to see if the conclusions of Sear and Mace held up when a more systematic approach was taken. These authors found a positive effect for maternal and paternal grandmothers in 64% and 60% of studies, respectively, and a positive effect for grandfathers in 20% of studies on both Hum Nat (2011) 22:201–222 219 the maternal and paternal side. By contrast we found significant positive associations for both the maternal grandparents, but not for the paternal grandparents. The results of the two syntheses have divergent theoretical implications. Literature reviews will inevitably compare populations that differ in regard to many features; we hope that the present analysis has made a convincing case for using meta-analytic procedures over more subjective approaches. We also hope to have made a coherent argument that the recent emphasis on kin cooperation (cooperative breeding theory) needs to be balanced by deeper scrutiny of kin competition.

Acknowledgements We thank Mary K. Shenk and Siobhan M. Mattison for inviting us to contribute to the special issue on quantitative kinship. We gratefully acknowledge the suggestions of three anonymous reviewers and the statistical advice of Kathy Welch. We thank Nikhil Kurapati, Hawah Freeman, and Erin E. Gager for help in identifying source studies and in preparing the figures and tables. We are grateful to Conrad Kottak for bringing the theory of complementary filiation to our attention. Several authors graciously sent us statistical data through email (Monique Borgerhoff Mulder, Jan Beise, Renzo Derosas, and Rebecca Sear). BIS thanks the Dogon of Mali for their generous participation in her research and for the insights into grandparental investment gained from their friendship. The Dogon research has been supported by the LSB Leakey Foundation, the National Science Foundation (BNS-8612291, SBR- 9727229, BCS-0509019, BCS-1029056), the National Institutes of Health (NIH HD 07480–02, NIH 09- PAF00653), and the American Philosophical Society.

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Beverly I. Strassmann directs a 25-year longitudinal study of human evolutionary ecology among the Dogon of Mali, West Africa. This project has emphasized menstrual cycling, paternity certainty, polygyny, child mortality, fertility, and the role of biology within culture. Her current research interests include anthropological genetics, religion, and evolutionary medicine. She is affiliated with the department of anthropology and the Research Center for Group Dynamics (Institute for Social Research) at the University of Michigan.

Wendy M. Garrard is a research investigator within the Center for Group Dynamics at the Institute for Social Research (ISR), University of Michigan in Ann Arbor. She received her Ph.D. in psychology from Vanderbilt University in Nashville and her M.A. in applied social psychology from Loyola University Chicago. Areas of specialization include quasi-experimental research and evaluation methods, and meta- analysis. Her primary research interests involve the prevention of aggressive and antisocial behavior, with a focus on conflict resolution and collaborative interpersonal competencies.