Caring for parents: an evolutionary rationale

Background The evolutionary roots of human moral behavior are a key precondition to understanding human nature. Investigations usually start with a social dilemma and end up with a norm that can provide some insight into the origin of morality. We take the opposite direction by investigating whether the cultural norm that promotes helping parents and which is respected in different variants across cultures and is codified in several religions can spread through Darwinian competition. Results We show with a novel demographic model that the biological rule “During your reproductive period, give some of your resources to your post-fertile parents” will spread even if the cost of support given to post-fertile grandmothers considerably decreases the demographic parameters of fertile parents but radically increases the survival rate of grandchildren. The teaching of vital cultural content is likely to have been critical in making grandparental service valuable. We name this the Fifth Rule, after the Fifth Commandment that codifies such behaviors in Christianity. Conclusions Selection for such behavior may have produced an innate moral tendency to honor parents even in situations, such as those experienced today, when the quantitative conditions would not necessarily favor the maintenance of this trait. Electronic supplementary material The online version of this article (10.1186/s12915-018-0519-2) contains supplementary material, which is available to authorized users.


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Cultural analogues of the Fifth Commandment 23 Cultural norms that promote the help of the parents are widespread in both western and eastern 24 culture. The Fifth Commandment (of the Hebrew and protestant Bible, the Fourth one, 25 according to the catholic numbering) states: "Honor your father and your mother, that your 26 days may be long in the land that the LORD your God is giving you." (Exodus 20:12) 27 From the interpretations of this commandment by the western churches we recall the following: 28 Sefer Ha-chinukh (mitzva 33) elaborates: "A person should realize that his father and mother 29 are the cause of his existence in this world; therefore it is appropriate that he render them all 30 the honor and do them all the service he can". St. Thomas Aquinas wrote: "Since we receive 31 nourishment from our parents in our childhood, we must support them in their old age." Martin 32 Luther said: "For he who knows how to regard them in his heart will not allow them to suffer 33 want or hunger, but will place them above him and at his side, and will share with them 34 whatever he has and possesses" (Luther,M. p. 29). 35 We also note that in China, to take care of elderly parents is also a moral rule: e.g. Confucius 36 declared: "In serving his parents, a filial son reveres them in daily life; he makes them happy 37 while he nourishes them; he takes anxious care of them in sickness …" (26) 38 Based on the above, we introduce the so-called Fifth Rule, which is a translation of the Fifth 39 Commandment into biological terms and is inherent in the above interpretations: "During your 40 reproductive period, give away from your resources to your post-fertile parents." Here we propose a strictly Darwinian reasoning to see that the long-term growth rate is 48 maximized by natural selection: the number of offspring, in general, is much higher than the 49 carrying capacity, so only a part of the offspring and adults will survive. Let us consider random 50 survival, assuming that the survival probabilities of individuals do not depend on phenotypes 51 (in our case intergenerational help) and on the age of individuals. (Observe that this assumption 52 gives some advantage to the families in which the intergenerational help is less.) 53 Now let us consider two phenotypes A and B with respective long-term growth rates ( . Then the relative frequency of phenotype B tends to zero, as 66 it is shown below: 67 Indeed, let us suppose that the subpopulations start from initial states ) 0 ( x and ) 0 ( z , 68 respectively, and the time unit is chosen in such a way that in unit time the total density of the 69 system always exceeds the carrying capacity K, in particular 70 Now, by the selection the total density of the system is reduced to K proportionally: 72 We emphasize that in this model we consider the "intrinsic" survival (described by the Leslie 76 matrices) and the survival under selection independently. However, this model can be formally 77 considered as a particular Leslie-type model depending on the total density of the system, where 78 each demographic parameter in the Leslie matrices A L and B L is multiplied by 79 Similarly, for all t= 1, 2, 3,… we get our kin demographic selection model for two different 81 phenotypes: 82 Now, for the proportion of phenotype B we obtain 85 Here 87 Since we can suppose that in both phenotypes the last two fecundities are positive, so the 89 Perron-Frobenius theorem (see e.g. 28) implies that both . In fact, the Leslie matrices can be cut at the last fertile age class, apply 91 the Perron-Frobenius theorem to these matrices, and then the convergence can be extended to 92 the post fertile age groups by simple survival Therefore, Thus if B A    , then the relative frequency of phenotype B tends to zero as t tends to infinity.

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Observe that in our model, the fecundity of a phenotype is determined by a phenotype-96 dependent Leslie matrix, and the survival rates corresponding to the carrying capacity of 97 different phenotypes are the same, so the long-term growth rate of a phenotype determines the 98 fitness. 99 100 2. The general results 101 Consider the general K K  Leslie matrix, where the entries depend on the cost y spent to 102 grandparent support. Under the grandmother hypothesis, the grandmother support decreases the 103 fecundity and survival rate of fertile parents, but increases the survival rate of the grandmother, 104 who therefore increases the survival rate of pre-fertile grandchildren. Then the characteristic 105 equation is 106 (SI 9) 107 and its unique positive root is obtained as the root of equation 108 (SI 10) 109 It is easy to see, that if any of the numerators (i.e. the average numbers of offspring produced 110 by an individual of the corresponding age classes) in these fractions is changed to a greater one, 111 then the curve of the 'hyperbolic' function q shifts upwards, implying that the positive solution 112 *  of this equation also will be greater. Therefore, if in a population where within the families 113 grandparents are not supported, a new type emerges which supports grandparents, and all 114 mentioned numerators increase, then Fifth Rule as behaviour type will propagate. If all these 115 numerators decrease then this type will die out. Those mathematical cases when some of the 116 numerators increase, others decrease, would need further mathematical discussions. 117 can be written as 119 (SI 11) 120 Here factor   k i i y 1 ) (  measures how much child care by grandmothers increases the survival 121 of the children. Roughly speaking, factor 122 Under assumption 1 there is a threshold for the support to grandparents, above which 140 the survival of grandparents does not increase, and therefore the survival of grandchildren 141 either, but the fecundity and/or the survival of fertile parents still decrease. Over this threshold, 142 the support to grandparents has no evolutionary advantage. 143 144 Finally, we remark that the above reasoning can be applied not only to the grandmother 145 hypothesis, since either the mother hypothesis or the embodied capital model alone can ensure 146 the support to grandparents. For example, if any of the above two hypotheses implies the 147 increase of at least one of the numerators in (3) Finally, we note that the "altriciality" hypothesis can also be handled in terms of a 155 linear model with a matrix structured differently from the Leslie matrices (since the survivals 156 of children also depend on the age of their mothers). Thus, only a generalization our model 157 could deal with the development of menopause based on altriciality. In our opinion, our Fifth 158 Rule may be derived on the bases of "altriciality" hypothesis, but in such a future model the 159 formation of multi-generation families should also be included, since "altriciality" hypothesis 160 is the cost spent on survival to 181 post-fertile age (Fig. 3 depicts the situation). The fitness of the population is the long-term 182 growth rate which can be calculated from the characteristic equation of the Leslie matrix: 183 , and the optimal strategy is not to spend on own survival to post-fertile 184 age. (ii) Suppose that grandmothers help in child care ( Figure S 2 . This condition is satisfied e.g., if the efficiency of the support to post-211 fertile parents is sufficiently large compared to the basic post-fertile survival rate.
. We note that these technical conditions imply that 234 1  and 0  are the demographic parameters before the appearance of the considered 235 Observe that conditions c) and d) are mathematical descriptions of trade-offs. 239 ).
(SI 18) 247 The first order necessary condition for the maximum attained at an interior point is 248 Since p, q,   , are all positive in the interval (0,1), the above necessary condition is 251 equivalent to 252 Now, for a second order sufficient condition for the maximum of function z , we calculate its 260

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In this section, by numerical study, we illustrate the effect of different (linear, convex and 279 concave) trade-offs on the level of the optimal backward help (y*). We calculated the 280 maximal long-term growth rate (fitness) of various populations as a function of y from the 281 characteristic equation of the corresponding Leslie matrix. The value of y that gives the 282 highest long-term growth rate termed as the optimal backward help (y*). We also calculated 283 the number of offspring and the offspring survival given the optimal y*. We investigated the 284 effects of different cost-benefit parameters on the evolvability of backward help (y). Life-285 history parameters are based on the figures from Mace [1] . It is possible to generate all the 286 possible combinations of cost-benefit trade-offs by setting the appropriate cost, benefit 287 parameters to zero (c, d, h). Also, convex or concave cost-benefit functions can be achieved 288 by setting the appropriate parameters (c, d, h) to smaller or to greater than one (see Table S1  289 for a summary of parameters). We used the following general Leslie matrix (see Fig. 5 Table S1. Parameters of the model. give benefit only for the number of offspring; in the third case they only give benefit for the 303 survival of the offspring and finally, in the last case, they do not provide any benefit. This last 304 case is not interesting for us, thus it will not be investigated any further. 305 In the same way, four possible combinations exist in terms of the cost functions: (i) c, 306 d > 0; (ii) c > 0, d = 0, (iii) c = 0, d > 0; and (iv) c, d = 0. In the first case helping 307 grandmothers imposes a cost on both the parents' reproductive output and on the parents' 308 survival, in the second case only on the number of offspring, in the third only on the survival 309 of the parent, and finally, in the last case it imposes no cost at all. Just as before, this last case 310 is not interesting for us, thus it will not be investigated any further. See Table S2