When to exhibit Social Behavior [Cooperation, Altruism]? Clara B. Jones [Graph, Legend]

Fig. 1. When should an Actor or a Recipient exhibit Social* Behavior [Cooperation, Altruism]? Clara B. Jones, 3/13/2019

1. This [idealized] graph**** depicts & predicts when an [idealized] organism--an Actor or a Recipient--should give/exhibit Cooperation or Altruism, defined, formally, as those interactions during which the Recipient benefits [in relative reproductive units].
2. X-axis: Time [T], Energy [E] investment in Social Behavior [reflects organism's T/E budget for a given interaction].
3. Y-axis: Costs [C, in reproductive units to Actor or Recipient] or Benefits [B, in reproductive units to Actor or Recipient] to Inclusive Fitness** [IF= selfish reproductive units (usually, & clasically,  offspring, though, offspring might be delayed, such as when transaction in wealth or other goods--see "Altruism" below) + reproductive units of kin]. r, coefficient of relatedness, is incorporated in measure/estimate of IF [how to measure?].
4. C rise or reach asymptote over T. Costs, for Actor or Recipient, or both, may prevent Cooperation or Altruism between kin when, for example, Cooperation or Altruism increases Competition [for limiting resources such as food, mates, burrows], increasing [for ego or ego's offspring] likelihoods of  dispersal, "competitive exclusion" [demand for ~identical limiting resources], death, etc. Cooperation and Altruism are expected, by definition, to be responses for the avoidance or neutralization of Competition.
5. B rise, then decrease over T.
6. "x" represents the optimal point at which an Actor or a Recipient should exhibit Cooperation [both Actor and Recipient gain reproductive units] or Altruism. [Actor loses, Recipient gains reproductive units]. "x" is the extension to the X-axis of the vertical, black line connecting the points with the greatest separation between the C and B curves--where B > C. "x" is the idealized point maximizing inclusive fitness benefits.
7. The shaded area represents the zone around "x" for which Actor's benefits from Social Behavior are highest. Ideally, the broken vertical lines extend vertically & downward from those points on either side of "x" on the B curve at which the B curve first begins to descend. The shaded area represents the zone of maximal benefit to Inclusive Fitness of A or B, in this case, maximum benefit from an act of Cooperation or Altruism ["IF maximizing"].
8. Actor & Recipient curves and values will usually be asymmetric, by definition [possibly, even, for clones (e.g., identical twins)]. In other words, zones of maximal benefit from social behavior should differ for Actor and Recipient. Overlaying Actor's & Recipient's curves will determine whether there is overlap between Actor & Recipient zones of greatest benefit to ego from Cooperation or Altruism. If there is overlap, the zone of mutual benefit is defined, so that Actor & Recipient should exhibit Cooperation [+, +] within these parameters [of T, E]. If there is no overlap, then conflict arises [between Actor and Recipient &, possibly, kin of one or both].
9. Similarly, an Actor should exhibit Altruism [-, +] to a Recipient when the long-term B of such action[s] outweigh the short-term C [determined by hard-wired Hamiltonian algorithm?].
10. If B from Social Behavior are minimal or non-existent [e.g., low T/E "budget;" little or no overlap between Actor-Recipient zones of greatest benefit], then interactants should adopt an alternate behavior [Alternative Reproductive Behavior--tactic or strategy], such as fight***, avoidance, flight, force, coercion, persuasion, manipulation, exploitation, coexistence--or some combination of these.
11. Group-living organisms experience relatively ongoing "decisions" about how to behave relative to conspecifics; however, it is important to keep in mind that "fitness budgets" change over T and that behavior is condition- [context-] dependent.
12. Ceteris paribus, and on average, curves, B & C, as well as, shapes of zones of maximum benefits for Males [time-minimizers] and Females [energy-maximizers] should differ. Curves, also, are expected to be Age-, Class-, & Role-dependent.

*After Hamilton (1964), "Social Behavior" is defined as Cooperation [both Actor and Recipient gain reproductive units] or Altruism [Actor forfeits reproductive units; Recipient gains reproductive units]
**The term "inclusive fitness" can be confusing since, technically, "fitness" is the frequency of an allele in a population averaged across the reproductive success of all individuals in the population bearing the allele, leading one to inquire how important it is to measure individual variation of traits [since individual variation will be subsumed in the measure of an allele's "fitness"].
***As pointed out by Geoff Parker [1974], aggression should not usually be a first resort because the C of damaging behavior generally outweigh the B.
****The same graphical/conceptual framework could be used for Coexistence if axes modified so that X-axis= savings in T, E to Mean fitness of allele 1 [or 2]; Y-axis= B, C from T, E savings to fitness [Mean frequency] of allele 1 [or 2] in a population. In the case of Coexistence, a Community Ecology process, the population would be escaping Competitive Exclusion. [See, also, my 2014 Springer Brief, Ch 2, for discussion of Coexistence in relation to Hamilton's Rule.]

Acknowledgments: Thanks to my son, Luke [M. Luke Jones] for stimulating discussion and for drawing the figure. Further, via e-mail, I asked Andrew Bourke [Univ. of E. Anglia] to comment on this blogpost. On 4/11/2019, I received the following reply [n.b.: my original blogpost above, including, the graph, have NOT been revised subsequent to Bourke's comments]:

1.     Perhaps the X axis needs clarifying a little – after all, time and energy seem to have most relevance in this context insofar as they are proxies for fitness, so then there would be some relationship between the metrics on the X axis and on the Y axis, and how these interact might then require consideration.

2.     It would be good to have concrete, empirical examples of when the scheme in the figure needs invoking, i.e. showing how considering the time/energy investment dimension in the manner advocated in the figure enlarges our understanding of the occurrence of social behaviours.  Personally I find it hard to think of things in the abstract all the time, so even some hypothetical biological examples/applications might be useful.

3.     I think your footnote 8 makes a good point, i.e. that actor and recipient interests need not overlap even for altruistic and cooperative interactions.  This point was explored theoretically in a fairly old paper by Yamamura and Higashi (1992)*****.  Their work does not seem to have been followed up empirically to any great extent, perhaps because the usual assumption that one of the parties has most control over the interaction (in which case conflict is minimised – e.g. an insect larva may often have little choice but to accept the level of care it’s given) holds.

References
Hamilton WD (1964) The genetical evolution of social behaviour. J Theor Biol 7: 1-52.
Parker, G (1974) Assessment strategy and the evolution of fighting behavior. J Theor Biol 47: 223-243.
*****Yamamura N, Higashi M (1992) An evolutionary theory of conflict-resolution between relatives: altruism, manipulation, compromise. Evolution 46: 1236-1239.

http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/0827-14.pdf

Fragment: Inferences from West-Eberhard (1975) pertinent to Mammals (Clara B. Jones)

2.4 Inferences Pertinent To Mammalian Sociality Can Be Drawn From West-Eberhard (1975)

West-Eberhard’s (1975) summary of general models of social evolution reducible to mechanisms dependent upon inclusive-fitness maximizing is useful as a reminder that Hamilton’s rule is manifested in several ways, dependent upon local condition, sex, role (e.g., reproductive or helper), and lineage. It is noteworthy that each of the six strategies (1a – 3b) is, in one manner or another, applicable to social mammals and to mammalian females living mutualistically or cooperatively in groups. In insects and most mammals, olfaction is the primary mechanism of communication. Thus, coordination and control of conspecifics is expected to be constrained by the spatiotemporal dynamics of chemical properties (rapid delivery, relatively rapid decay, pheromonal repression of selfishness). Despite interspecific similarities, it is possible to derive inferences from West-Eberhard’s (2005) outline that may pertain, especially, to social mammals.

Inference 1: Because the variance on reproductive success is lower among females than among males, ceteris paribus (Trivers 1972), mammalian females will be more closely related, on average, to other females in their group or population than will males be, on average, to each other, to group or population females, and to each other’s offspring. For the same reasons, a mammalian population is likely to include more females than males, and females are more likely to exhibit sociality.

Inference 2: Trivers’ (1972) model, fundamentally, concerns differential energetic investments by males and females and the life-history trajectories deriving from polymorphic allocation patterns. Thus, because female “fitness budgets” are more constrained energetically that those of males, the reproductive female component of a group or population is expected to be more stable, spatiotemporally, than the dispersion of males in the same population. For the same reason, on average, female turnover is likely to be lower, female survivorship higher, female emigration rates lower than for males.

Verbal Model I was advanced by Trivers (1972) and was not, originally, presented as a general model of social evolution. However, this author predicts that social evolution will be biased by initial reproductive allocations or energetic investments (Schoener, 1971). This verbal model is not limited to evolution by sex, encompasses all conditions in which organisms make (“Hebbian”) “decisions”, including, decisions to join (group-formation), or, remain in (group-maintenance), groups, and has the potential to be developed, qualitatively, and, expressed, quantitatively, as a synthetic formulation.

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Inference 3: On average, since females are “energy-maximizers”, “inclusive-fitness maximizing” is expected to mitigate energy losses, and, on average, females should benefit from transferring some component “fitness budget” to others. Thus, females and their female offspring are likely to be the major donors and beneficiaries of the benefits of cooperation and altruism, and, relative to males in her population, an adult female has more to gain in her reproductive lifetime from facilitation.

Inference 4: Since males, “time-minimizers”, are expected to favor direct over indirect reproduction, “inclusive-fitness maximizing”, a relatively time-intense strategy, is unlikely to characterize reproductive males, on average.

Inference 4: Ceteris paribus, and, depending upon threshold reproductive effects relative to ecological conditions, where males cannot discriminate their own young, they should be indiscriminately selfish, concentrating on mating allocation strategies rather than facilitation of conspecifics.

Inference 5: It follows from “parental manipulation” and “maternal control” models that females can discriminate their mothers and, there own offspring, where females are not “promiscuous” and do not express “favoritism” of a single male during an estrus cycle. On the other hand, cortical circuitry may be favored, permitting females to make “decisions” based on likelihoods of paternity. In order for this neurophysiological strategy to be favored by selection, losses from error must not, on average, compromise relative reproductive success (of the pertinent genotype). It is important to note that “decisions” based on kinship may yield lower group sizes than those based on selfish strategies (Hamilton 1964); thus, the Malthusian optimum for a reproductive female may not concord with idealized mean fitness of her population.

Inference 6: Following from previous inferences, a reproductive female, on average, is expected to lose less from probabilistic tactics and strategies than will a reproductive male of the same population. Related to the previous inference, “inclusive-fitness maximizing” is expected to mitigate the maternal investment : ageing tradeoff for tactical and strategic females, on average, possibly explaining the reproductive advantage of extended post-reproductive lifespan in humans and killer whales: ////.

The previous discussion of West-Eberhard’s (1975) classification (1a-3b) suggests that “inclusive-fitness maximizing” should be more characteristic of reproductive females, on average, than of reproductive males in the same conditions. It is hypothesized that this condition obtains since, theoretically, females are expected to be “energy-maximizers”. The latter life-history strategy should privilege time-intense (“non-damaging”) rather than energy-intense (“damaging”) strategies, theoretically, characteristic of males. Should the aforementioned allocation (thermal) trajectories withstand quantitative, including, experimental, testing, each of them will yield information pertinent to the evolution of mammalian sociality. In particular, on average, each reproductive morph in the same population will respond differentially to density effects that are expected to impact “energy-maximizers” to a greater degree than “time-minimizers” since an increase in population density should correlate positively, ceteris paribus, with increased intensities of competition. Under these regimes, reproductive females should “switch” to or increase dependence upon, time-intense, energy-saving, helper tactics and strategies, including, in some regimes, self- (suicide, “give-up” points) or offspring-elimination (foetal resorbtion, abortion).