The complex mathematical theory proposed by Hamilton (1964) explains altruistic behaviors in inclusive fitness model. The theory explains why individuals help one another at his or her own cost. In a simplified format explained by West-Eberhard (1975), the equation could be written as rb> c, r = coefficient of relatedness, b= benefits and c = cost. How much of the fitness benefits (passing on the genes) an individual gain is dependent on the degree of relatedness the other to the helper, and whether the cost exceeds the benefits by helping the other individual in the end. (One thing to note is that we do not consciously think or calculate about the factors or equations when we are helping our family members.)
So between parent and offspring, the relatedness (r) is 0.5. Between half-siblings, r is 0.25, between identical twin r is 1.0. Between grandparent and grandchild, r-value is 0.25. To better understand how r would be calculated between full siblings, see equations below.
Mom- X & Y alleles x Dad – Z & B alleles
4 possible different combinations that can arise in offspring
X and Z- 0.5 (relatedness to actual offspring alleles)
X and B- 0
Y and Z- 1.0
Y and B- 0.5
The alleles in the offspring say is Y and Z then average r would be
r = (0.5+ 0+1.0+ 0.5) / 4 = 0.5
Evolutionarily speaking, it will pay siblings to help each other if the gene for helping spread the alleles frequency in the gene pool.
What does it have to do with grandmother love? The point is that the grandmother will love/ help you because you share the value of r = 0.25. Generally speaking, all the grandparents all share an average r of 0.25 with you. However, the real issue is paternal uncertainty in humans and many animals.
Males face paternal uncertainty because the offspring is given birth by the mother, not by the father. A female can cuckolds her husband with other man. Therefore, a paternal investment of perhaps life-long resources in an offspring that is not his is a huge loss for the father. He both fails in passing his genes (r = 0) and loses his resources, which he could have invested in his actual offspring, which he share r =0.5
If we apply this logic to grandparents, maternal grandmother are most surest about their grandchild in terms of genetic relatedness while paternal grandfather are least certain about whether the grand child is his. Study the figure below. Several studies seem to support that maternal grandmother invested in grandchild the most.
r means Degree of relatedness
r = ? means Are We Really Related?
In the study with a sample of 120 undergraduates, Dekay (1995) found that, maternal grandmother invested more than maternal grandfather, maternal grandfather, more than paternal grandmother, and paternal grandmother, more than paternal grandfather in grandchildren. The investment was measured by the measure of closeness, time spent together and gifts that the grandchildren received.
Maternal grandmother care was also rated higher than paternal grandmother on all measures although the certainty of r is the same with one male link. DeKay (1995) suggested that infidelity or cuckoldry (sexual infidelity) rate were lower in grandparent’s generations than the parent’s generations.
Another study in Germany with 603 participants by Euler and Weitzel (1996) also had similar results. The effect of where grandparents live was controlled in the study. The maternal grandmother cares the most, followed by maternal grandfather, followed by paternal grandmother and followed by paternal grandfather.
However another study in Greek by Pashos (2000) showed a different pattern because the care bias in grandchildren between Grandmother and grandfather was not found. The study found that the paternal grandparent solicitude towards their children were higher than maternal grandparent. One important thing to consider is the widespread practice of patrilocal culture in rural Greece i.e. paternal grandparents live with their grandchildren more than maternal grandparents. Perhaps, the uncertainty of r values go up to 0.25 rather than 0 (if the grandfather is not related to the grandchild at all), because males might be guarding their partners more closely. Females might have lower opportunities to cuckoldry her husband.
So does your grandmother, especially your maternal grandmother, love you more than your grandfather? There might be an evolutionary explanation for this.
I was formally introduced and asked to read original papers on evolutionary analysis grandmother solicitude, mentioned in this article, by Dr. Hughes in Evolutionary Psychology class at Albright College. I also read about evolutionary explanations of Grandmother care in Cartwright (2008). Thank you to all the parties involved in sharing the insight.
Cartwright, J. (2008). Evolution and Human Behavior (2nd ed). Cambridge, Massachusetts, The MIT press.
DeKay, W. T. (1995). Grandpaternal investment and the uncertainty of kinship. Seventh annual meeting of the Human Behavior and Evolution Society, Santa Barbara, CA.
Euler, H. A. and Weitzel, B. (1996). Discriminating grandparental solicitude as reproductive strategy. Human Nature, 7: 39-59.
Hamilton, W. D. (1964). The genetical evolution of social behavior, 1. Journal of Theoretical Biology, 7: 1-16.
Pashos, A. (2000). Does paternal uncertainty explain discriminative grandpartenal solicitude? Evolution and Human Behavior, 21: 97-111.
West-Eberhard, M. J. (1975). The evolution of social behavior by kin selection. Quarterly Review of Biology, 50: 1-33.