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Biol Lett. 2023 May; 19(5): 20230061.
Published online May 10, 2023. doi:10.1098/rsbl.2023.0061
PMCID: PMC10170189
PMID: 37161292
Antti O. Tanskanen, Funding acquisition, Investigation, Project administration, Resources, Writing – original draft, Writing – review & editing,
1,2 Samuli Helle, Formal analysis, Methodology, Writing – original draft, Writing – review & editing,2 and Mirkka Danielsbacka, Funding acquisition, Resources, Writing – original draft, Writing – review & editing1,2
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Abstract
Grandparents can increase their inclusive fitness by investing time and resources in their grandchildren. However, not all grandparents make such investments equally, and between-grandparent differences in this regard can be predicted based on paternity uncertainty, lineage and grandparents' sex. Using population-based data for English and Welsh adolescents (n = 1430), we examined whether the death of the most important grandparent (in terms of investment), the maternal grandmother (MGM), changes relative support for existing hypotheses predicting differential grandparental-investment patterns. To contrast the predictions of the grandparental investment hypotheses, we used generalized order-restricted information criterion approximation. We consequently found that, when MGMs are alive, the most-supported hypothesis is ‘discriminative grandparental solicitude’, which ranks grandparental investment as MGMs > maternal grandfathers (MGFs) > paternal grandmothers (PGMs) > paternal grandfathers (PGFs). However, when MGMs are deceased, the paternity uncertainty hypothesis (MGFs = PGMs > PGFs) receives the most support; this is due to increased investment by PGMs. Thus, when the heaviest investors (i.e. MGMs) are deceased, PGM investments are closer to—but do not exceed—MGF investments.
Keywords: grandparental investment, informative hypotheses, lineage, sex
1. Introduction
Grandparents share, on average, 25% of their genes with their grandchildren and, by investing time and resources in their descendants, can improve their inclusive fitness [1]. However, the four grandparent types may not invest equally in this regard. It is well known that maternal grandmothers (MGMs) invest the most in grandchildren, while paternal grandfathers (PGFs) invest the least [2–6]. Evolutionary studies examine whether the investment differences are based on paternity uncertainty, lineage or grandparents' sex, and thus the key question often is whether maternal grandfathers’ (MGFs) investments are greater than, equal to or less than paternal grandmothers (PGMs). It has been suggested that the presence or absence of MGMs alters other grandparents' levels of investment and, thus, influences the biased grandparental investment pattern. First, when MGMs invest in grandchildren, their spouses (i.e. MGFs) may be ‘incidentally exposed’ to their grandchildren without making much actual investment in them [5]; this means that the absence of MGMs (e.g. through their death) can consequently lead to a decrease in the MGFs' contact with their grandchildren and, thus, their apparent investment. Second, the absence of MGMs may increase PGMs’ levels of investment, because such absence can both increase the need and make more room, for PGMs' investment [7]. In the present paper, we consider the key hypotheses concerning the differential grandparental investment; namely, sex effect, sex-specific reproductive strategies, matrilateral bias, paternity uncertainty and ‘discriminative grandparental solicitude’ (table 1).
Table 1.
Key hypotheses for differential grandparental investment. MGF: maternal grandfather; MGM: maternal grandmother; PGF: paternal grandfather; PGM: paternal grandmother.
| hypothesis | abbreviation | prediction when | prediction when |
|---|---|---|---|
| MGM is alive | MGM is deceased | ||
| sex effect | Hse | MGM = PGM > MGF = PGF | PGM > MGF = PGF |
| sex-specific reproductive strategies | Hrs | ½(MGM + PGM) > ½(MGF + PGF) | MGF > ½(MGF + PGF) |
| matrilateral bias | Hmb | ½(MGM + PGM) > ½(MGF + PGF) | MGF > ½(MGF + PGF) |
| paternity uncertainty | Hpu | MGM > MGF = PGM > PGF | MGF = PGM > PGF |
| discriminative grandparental solicitude | Hds | MGM > MGF > PGM > PGF | MGF > PGM > PGF |
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The sex effect hypothesis, which concentrates on differences between grandmothers and grandfathers [8], claims that, because of internal gestation, lactation and paternity uncertainty, female mammals (including human women) are typically more caring towards their relatives than their male counterparts [9]. Second, according to the sex-specific reproductive strategies hypothesis, women tend to care more for young children while men tend to desire additional children with additional partners; consequently, maternal grandparents (MGPs) are expected to promote their daughters' agendas (i.e. parental investment), while paternal grandparents (PGPs) are expected to promote their sons’ agendas (i.e. opportunities to have several descendants) [4,10]. Next, the model of matrilateral bias posits that, as mothers tend to bear the main responsibility for childcare, grandparental investment increases the mothers' ‘nepotistic value' (i.e. mothers’ ability to invest in natal kin) [11]. In this model, a crucial difference exists between MGPs (who gain inclusive-fitness benefits from all investments their daughters make in natal kin) and PGPs (who receive inclusive-fitness benefits only from daughters-in-law's investment in their own children) [11]. Notably, sex-specific reproductive strategies and matrilateral bias make the same prediction regarding the ranking of grandparental investment, although the underlying theoretical reasoning differs. Fourth, the paternity uncertainty hypothesis is the most commonly used evolutionary explanation for differential grandparental investment [12,13]. According to this hypothesis, MGMs are the only ones who can be certain that they are related to their grandchild; by contrast, MGFs (between themselves and their daughter) and PGMs (between their son and their son's child) have one uncertain link of paternity, while PGFs (between themselves and their son, and between their son and their son's child) have two uncertain links [12,13]. Finally, Euler & Weitzel [4] have formulated the model of discriminative grandparental solicitude. This model combines paternity uncertainty and sex-specific reproductive strategies to explain both sex and lineage differences in grandparental investment. Since the publishing of Euler & Weitzel's [4] seminal paper, the discriminative grandparental solicitude has been used as a ‘general term’ to explain differential investment by grandparent types; however, in the present paper, we apply it using its original meaning (as described in the previous sentence). While the five hypotheses partially overlap in theoretical reasoning and predictions, each also has unique features (table 1).
In the present study, using population-based data for English and Welsh adolescents (n = 1430), we examine whether the death of MGMs changes the relative support for evolutionary hypotheses explaining differential grandparental investment. The novelty of the present analyses is that no prior study has examined whether the death of MGMs (who are the heaviest investors) influences the relative investments of other grandparent types in their grandchildren. Moreover, a previously unrecognized problem regarding evaluating direct statistical evidence for any of the hypotheses for the differential grandparental investment pattern is that the statistical tests contrasting investment among grandparent types have not been informative, as they have only contained equality constraints; they have not contained inequality constraints (e.g. MGMs invest more than MGFs who invest more than PGMs) [14]. This mismatch between theoretical predictions and statistical tests could lead to a higher risk of type II errors and, thus, reduce the statistical power to detect underlying patterns in grandparental investment. Herein, we apply recently developed information criteria to directly contrast those informative hypotheses.
2. Methods and materials
(a) Data
We used data from the Involved Grandparenting and Child Well-Being 2007 survey, which was conducted on a nationally representative sample of English and Welsh adolescents aged 11–16 years (mean = 13.4, s.d. = 1.4) who were in secondary school (n = 1566) [15–18]. To ensure that schools with more students had a greater chance of inclusion in the sample, we used probability proportionate-to-size sampling. Next, classes within every selected school were randomly chosen. Seventy schools participated in the study, and children completed the questionnaires in their school classrooms. The response rate was 68%. The sample included 51% boys and 49% girls; 89% reported ‘White’ ethnicity. Grandparental investment questions referred only to living grandparents. Hence, only data for respondents who had at least one living grandparent (n = 1488) were recorded. We excluded children who were co-residing with their grandparents (n = 58); this was because we could not separate cases where grandparents were the sole caretakers of grandchildren (in which case, their investment would be much more obligatory) from those involving three-generation households. The total number of children included in our analyses was 1430: 1197 with living MGMs and 233 whose MGMs were deceased.
To measure grandparental investment, we examined responses to four items, which were sourced from a scale developed by [19]. These items were ‘how often do you see them’ (Q15), ‘their grandparents had looked after them’ (Q26), ‘they could depend on their grandparents’ (Q27) and ‘provided financial assistance or help’ (Q38). Question 26 was reverse-scored to match the meaning and order of the other items. Questions 26, 27 and 38 were measured using a four-point Likert-type scale ranging from 1 (not at all/never) to 4 (a lot/every day), while question 15 was measured using a three-point Likert-type scale ranging from 1 (never) to 3 (usually). Missing data for these questions were imputed using predictive mean matching [20]: randomly selecting a value from a pool of five potential donors with complete cases that most closely resembled the cases with missing entries [21]. Predictive mean matching is a robust method providing realistic imputations, and the use of five donors is generally shown to provide good results for our sample size [21]. However, we were limited to a single imputation because the hypothesis evaluation method did not accommodate multiple imputations.
(b) Statistical analysis
We used structural equation modelling (SEM) with multiple-indicator latent variables [22] to model and compare grandparental investment (see electronic supplementary material); the lavaan package in R was used to perform this modelling [23]. To contrast the hypotheses regarding differential grandparental investment, we used generalized order-restricted information criterion approximation (GORICA) to evaluate the relative evidence for each of the hypotheses [24,25]. GORICA is an Akaike-type information criterion that uses structural parameters and their covariance matrix (determined through SEM) to select (in)equality-constrained (i.e. informative) hypotheses from a set of candidate hypotheses [26]. It should be noted that the Akaike information criterion (AIC) only evaluates hypotheses with equality constraints or no constraints at all and, hence, was unsuited for use in this analysis. By contrast, GORICA weights, which present the relative likelihood of each hypothesis given the data, can be used to select the most-supported hypothesis [26]. When multiple hypotheses show comparable GORICA weights and overlap in their predictions, log-likelihood and penalty term values can be used to rank the hypotheses (larger log-likelihood and smaller penalty terms are preferred). In such cases, the preferred hypothesis can also be further contrasted with its complement (i.e. all hypotheses except the hypothesis in question) [26].
The predictions of the hypotheses contrasted in this analysis are shown in table 1. As a safeguard hypothesis to avoid simply choosing the best hypothesis among weak hypotheses (as we have not included all possible hypotheses, i.e. the whole parameter space), we included an unconstrained hypothesis (Hu) with no parameter restrictions (i.e. where any ordering is equally likely; Huc: MGM, MGF, PGM, PGF) [24]. We compared hypothesis using package ‘GORICA’ in R [27].
3. Results
Table 2a shows that, when MGMs were alive, the most-supported hypothesis for these data was discriminative grandparental solicitude (Hds): this had the lowest GORICA value and the highest GORICA weight (for full model results, please see electronic supplementary material). The discriminative grandparental solicitude hypothesis showed approximately three times greater support than the next best hypotheses: sex-specific reproductive strategies (Hrs) and matrilateral bias (Hmb), respectively. This was also reflected in the means for grandparental investment: compared to MGFs, PGMs and PGFs had −0.099 (standard error (s.e.) = 0.026, z = −3.88, p < 0.0001) and −0.222 (s.e. = 0.027, z = −8.18, p < 0.0001) lower investment, respectively, whereas MGMs had 0.157 (s.e. = 0.016, z = 9.99, p < 0.0001) higher investment (electronic supplementary material, table S1). Moreover, the discriminative grandparental solicitude hypothesis was not a weak hypothesis because its GORICA weight clearly exceeded that of the unconstrained hypothesis (Huc; this was also true for the sex-specific reproductive strategies and matrilateral bias hypotheses).
Table 2.
Results of comparisons of the hypotheses explaining between-grandparent investment in grandchildren when an MGM is living (a) or deceased (b). MGM: maternal grandmother.
| hypothesis | log-likelihood | penalty | GORICA | GORICA weight |
|---|---|---|---|---|
| (a)MGM living | ||||
| Hse | −39.472 | 0.498 | 79.939 | 0.000 |
| Hmb / Hrs | 9.364 | 2.500 | −13.726 | 0.216 |
| Hpu | −32.562 | 1.498 | 68.121 | 0.000 |
| Hds | 9.364 | 1.396 | −15.936 | 0.653 |
| Huc | 9.364 | 3.000 | −12.727 | 0.131 |
| (b)MGM deceased | ||||
| Hse | 1.157 | 0.500 | −1.314 | 0.019 |
| Hmb / Hrs | 4.375 | 1.499 | −5.751 | 0.171 |
| Hpu | 4.228 | 0.499 | −7.458 | 0.401 |
| Hds | 4.375 | 0.915 | −6.920 | 0.306 |
| Huc | 4.375 | 2.000 | −4.750 | 0.104 |
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Table 2(b) describes the MGM-deceased results. For this scenario, the most-supported hypothesis was paternity uncertainty (Hpu). However, the data also gave almost as much support for the discriminative grandparental solicitude (Hds) hypothesis and some weak support for the sex-specific reproductive strategies (Hrs) and matrilateral bias (Hmb) hypotheses. When the paternity uncertainty hypothesis was compared to its complement, paternity uncertainty was 2.36 times more supported (GORICA weights: Hpu = 0.702; Hco = 0.298). In this scenario, the difference between the respective investment of MGFs and PGMs was no longer statistically significant (s.e. = 0.065, z = −0.54, p = 0.59); however, PGFs still invested significantly less than MGFs (electronic supplementary material, table S3).
4. Discussion
Our data showed that, when MGMs are alive, discriminative grandparental solicitude (i.e. MGM > MGF > PGM > PGF) is the most-supported hypothesis and that MGFs invest more than PGMs. Several prior studies support this pattern of discriminative solicitude [2–6], and Euler & Weitzel [4] argued that it can be explained by a combination of the sex-specific reproductive strategies hypothesis and the paternity uncertainty hypothesis. Thus, when MGMs are alive, the investment of MGFs exceeds that of PGMs. As MGMs are, by far, the most important grandparents in terms of investment and, thus, their investment (which drops to zero when deceased) may influence the investment of other grandparent types (particularly MGFs and PGMs) [7,10], we tested whether the grandparental investment pattern changes when MGMs are deceased.
Indeed, we found that when MGMs are deceased, the paternity uncertainty hypothesis becomes the most supported (i.e. MGF = PGM > PGF). The greatly increased support for paternity uncertainty when MGMs are deceased is associated with PGMs' increased (but not MGFs’ reduced) investment [7], which statistically now equals that of MGFs (electronic supplementary material, table S3). This association may reflect the need (and room) for more PGM investment when MGMs are deceased and show that PGMs may at least partly compensate for the lack of the investment of MGMs. Our findings also support Helle et al. [7] by showing that the increased PGM investment when MGMs are deceased does not result in greater total PGM investment compared to MGFs. When the other grandparent-type investments are independent of the investment of MGMs, the biased investment pattern starts to follow the prediction derived from paternity uncertainty. Furthermore, when MGMs are deceased, the discriminative grandparental solicitude hypothesis (MGF > PGM > PGF) also receives some support. This is not surprising, as the predictions of these hypotheses are very similar and partly overlap (i.e. both hypotheses predict PGM > PGF) and, thus, the discriminative grandparental solicitude hypothesis also entails support for paternity uncertainty.
Some studies have attempted to explain differences in the respective investments of MGFs and PGMs by advancing the preferential investment hypothesis, which predicts that PGMs invest more in grandchildren if they do not have more preferable investment options (i.e. grandchildren via daughters); however, these studies have provided mixed results [2,3,5]. Due to data limitations (i.e. we have no information on grandparental investment towards the participants' cousins), we were unable to test the preferential investment hypothesis here; thus, further studies are needed to assess whether the biased grandparental-investment pattern is influenced by the PGM's alternative investment options after the death of the MGM. Additionally, further studies are needed to examine whether PGMs invest more in grandchildren than MGFs when MGMs are deceased before the grandchild is born.
To conclude, using, for the first time, a recently developed AIC-based tool to contrast informative hypotheses on differential grandparental investment, we found that, when MGMs are alive, the discriminative grandparental solicitude hypothesis is clearly the most-supported hypothesis for explaining the pattern of differential grandparental investment. However, when the MGMs are deceased, the pattern of investment by surviving grandparents accords with the paternity uncertainty hypothesis, mainly due to increased investment by PGMs [7]. Hence, PGMs seem to respond to MGMs' deaths by increasing their investment in their grandchildren.
Acknowledgements
We are grateful to Ann Buchanan for making the data available, and to Caspar van Lissa and Rebecca Kuiper for help. We thank Martin Daly and Gretchen Perry for helpful comments and discussion.
Data accessibility
The data we used in this study are freely available from: http://doi.org/10.5255/UKDA-SN-6075-1 [28], but interested readers should be aware that, as the data are ‘safeguarded’ (https://www.ukdataservice.ac.uk/get-data/data-access-policy), a user will be required to register with the UK Data Service to access the data. The authors did not have any special access privileges to these data that future researchers would not have.
The data are provided in the electronic supplementary material [29].
Authors' contributions
A.O.T.: funding acquisition, investigation, project administration, resources, writing—original draft and writing—review and editing; S.H.: formal analysis, methodology, writing—original draft and writing—review and editing; M.D.: funding acquisition, resources, writing—original draft and writing—review and editing.
All authors gave final approval for publication and agreed to be held accountable for the work performed therein.
Conflict of interest declaration
The authors have no conflicts of interest to declare.
Funding
Financial support was received from the Strategic Research Council (grant no. 345183) and the Academy of Finland (grant nos. 320162, 325857 and 331400).
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