Investment Cascades and Fitness Capital

1. Introduction

Selfish genes sometimes prosper by promoting compassion. As Hamilton showed, a gene can spread by making its bearer act altruistically toward relatives, provided the cost to the actor is outweighed by the benefit to the recipient — if the benefit is appropriately discounted by relatedness. The simplest version of this logic, known as Hamilton’s rule, established the concept of inclusive fitness (Hamilton, 1963; 1964). This proved to be one of the most powerful extensions of Darwinian thinking in the modern era (Dawkins, 2004), giving rise to the genes-eye-view of evolution (Dawkins, 1996; Hamilton, 1996). Kin-Selection is a major mechanism for explaining why altruism can evolve in a competitive world otherwise red in tooth and claw and has illuminated phenomena ranging from patterns of social organization such as the evolution of eusociality (Bourke, 2011) to intragenomic conflict (Haig, 2001). However, its role is usually cast as stabilizing rather than as a factor in runaway evolutionary dynamics. Explanations for the rapid evolution of extreme traits more often invoke sexual selection (Fisher, 1930), arms races (Dawkins & Krebs, 1979), or a dramatic environmental event such as causing the splitting of populations by geographic isolation (Eldredge & Gould, 1972). The present article reinforces the argument that, under certain conditions that are likely satisfied in many contexts in nature where kin-selected traits have evolved, they can be expected to catalyse rapid phenotypic changes in a certain type of trait (Hawkes, 1983).

That type of trait is one that can be modified by altruistic forms of investment wherever such modification enhances the capacity of the individual to, in turn, invest and thereby improve the same trait in others. Evidence of such investment is widespread. Many varieties of birds, for instance, provide sustained care for their relatives in ways that enhance their future reproductive success, usually in the form of food provisioning (e.g., McKinnon et al., 2024). In many types of mammals, such as dolphins, impressive hunting tactics and techniques are transmitted from parent to offspring, with evidence of deliberate instructed practice (e.g., Krützen et al., 2005). In primates, maternal care, grooming, and coalitionary support create durable advantages for offspring in social hierarchies (Silk, 2007). In humans, parental choices about nutrition, education, and socialization may systematically shape children’s life chances, with effects potentially multiplying across generations (Sowell, 2016). Across these and many other species, altruism is often not an act with transient effect on the recipient’s wellbeing but may be seen as a strategic allocation problem with cumulative consequences.

Below we consider that, under special (but psychobiologically plausible) conditions, investments in kin have the potential to cascade across overlapping generations, accumulating like a form of “fitness capital” within lineages. To explore this, we develop a unified framework linking Hamilton’s Kin-Selection logic with Becker’s theory of parental investment from economics. Here, the present thesis draws heavily on analyses and concepts from Becker (1993; 1996), notes taken from courses he taught at the University of Chicago titled “Lectures on Human Capital” and “Chicago Price Theory”, and accompanying textbooks (Friedman, 1962; Jaffe et al., 2019). This integration suggests how parental allocation decisions can generate strong correlations between ability, altruism, and fitness capital, particularly under assortative mating. Moreover, these forces may produce runaway increases in investment, stratification of lineages, and even set the stage for evolutionary transitions often attributed solely to other mechanisms, such as sexual selection for “good genes” or ornamental traits. By reframing Hamiltonian altruism as a mediator of intergenerational investment, it is concluded that Kin-Selection is not merely a force favouring some calibrated level of beneficence towards relatives but also potentially a powerful accelerant of evolutionary change.

2. Investment and Fitness Capital

We begin with three premises. First, we assume a species in which Hamilton’s logic already applies. That is, one where individuals exist in a system where genes for altruistic behaviours can persist if the benefit they confer on relatives, weighted by relatedness, exceeds the cost to the actor. Second, we extend the notion of “benefit” to include not only direct gains to a recipient’s fitness but also indirect gains, such as improvements in traits that enhance the recipient’s later success, inclusive of the capacity to confer similar benefits on others. This is intended as the evolutionary analogue of the economic concept of human capital — characteristics like skills, knowledge, health, or attractiveness that increase an individual’s productivity (Becker, 2002). Human capital is a sort of “capital” because it can be built up through investment (e.g., training, nutrition, education) and because greater stocks of it tend to yield higher returns, whether in allowing higher wages to be earned or by enhancing wellbeing through richer consumption opportunities (e.g., being able to read allows more benefit to be derived from books). Finally, we assume that there is an appreciable, additive genetic variance directly determining every characteristic described (e.g., altruism) except fitness capital.

For present purposes, we generalize this idea beyond humans. For any species, we may define a stock of fitness capital as characteristics that improve an animal’s ability to secure resources, survive, and reproduce. Just as in economics, fitness capital can be increased by investment and affects the individual’s future wellbeing and fitness. Fitness capital can be manifested through both direct and indirect parental effects. Maternal effects and transgenerational plasticity provide direct pathways: nutrient provisioning, epigenetic modifications, or early-life experiences can enhance offspring survival, growth, and reproductive potential (Marshall & Uller, 2007; Mousseau & Fox, 1998). More broadly, niche construction illustrates how parents and lineages modify environments (physical, social, or cultural) in ways that increase the returns to offspring traits over time. Examples range from cooperative breeding networks in birds and mammals to the transmission of knowledge and tools in humans (Laland et al., 2016; Odling-Smee et al., 2003). Together, these mechanisms show that fitness capital is both genetically and environmentally mediated.

2.1. Fitness Capital and Effective Relatedness

Becker’s models of altruism provide a useful starting point for our present purposes. He assumed that an individual’s utility depends not only on their own consumption but also on the wellbeing of others they care about – especially their own offspring. Consider a simple scenario where each adult has only one child and an income $y$, which can be spent either on their own consumption, $c$, or on investment, $I$, in their child’s fitness capital. Then:

$U=u\left(c\right)+\theta B\left(I\right),$Where $u\left(c\right)$ is the parent’s utility from consumption, $B\left(I\right)$ is the benefit to the child from investment, and $\theta$ is an “altruism parameter” approximating the parent’s concern for the child’s wellbeing. Since $c=y-I$, the parent’s first-order condition for optimal investment is found by differentiating $U$ with respect to $I$:

${\displaystyle \frac{dU}{dI}}={\displaystyle \frac{d}{dI}}\left[u\left(y-I\right)\right]+{\displaystyle \frac{d}{dI}}\left[\theta B\left(I\right)\right]$Using the chain rule for the first term:

${\displaystyle \frac{d}{dI}}\left[u\left(y-i\right)\right]={\displaystyle \frac{du}{dc}}. {\displaystyle \frac{du}{dI}}=u^{\text{'}}\left(y-I\right).-1=-u^{\text{'}}(y-I)$The derivative of the second term is:

${\displaystyle \frac{d}{dI}}\left[B\left(I\right)\right]=\theta B^{\text{'}}\left(I\right)$Setting the first order condition to zero for a maximum

${\displaystyle \frac{dU}{dI}}=-u^{\text{'}}\left(y-I\right)+ \theta B^{\text{'}}\left(I\right)=0$Or more simply

$u^{\text{'}}\left(c\right)= \theta B^{\text{'}}\left(I\right)$ (1)

This means that parents invest until the marginal utility cost to themselves equals the weighted marginal benefit to their child. Hamilton’s rule provides a biological analogue in that it argues altruism may evolve if:

$r\Delta B>\Delta C$Or, put in marginal terms,

$r{B}^{\text{'}}\left(I\right)=C^{\text{'}}\left(I\right)$Where $r$ is relatedness, $B^{\text{'}}\left(I\right)$ is the marginal gain in offspring fitness, and $C^{\text{'}}\left(I\right)$ is the marginal cost to the parent’s fitness. These ideas can be unified if we treat Becker’s altruism weight $\theta$ as equivalent to relatedness $r$, if utility is measured in the same “currency” as fitness. To make map in this way, let us introduce $\kappa$ as a conversion factor which scales marginal utility into marginal fitness. This acknowledges that not all parental investments that feel rewarding (in utility terms) translate perfectly into genetic returns. Some activities may raise subjective wellbeing without affecting survival or reproduction, while others may have strong fitness consequences. Formally, let the marginal fitness cost of reducing parental consumption be:

$C^{\text{'}}\left(I\right)=\kappa u^{\text{'}}\left(c\right).$Substituting into (1) gives:

$C^{\text{'}}\left(I\right)=\left(\kappa \theta \right)B^{\text{'}}\left(I\right)$.

Thus, the effective relatedness governing altruistic investment is

$r_{eff}=\kappa \theta$This captures both the biological fact of genetic relatedness ($r$) and the psychological or economic fact of how strongly a given investment in the child’s wellbeing translates into fitness outcomes1.

In sum, the Becker and Hamilton perspectives are likely looking at related phenomena from different perspectives. The two can be bridged with the concept of fitness capital and a scaling factor for translating utility into fitness. This permits us to say that, if there are forms of fitness capital that can be enhanced through investment, then parental altruism need not operate as only a direct transfer of benefits to offspring (or other kin): for example, shifting consumption from the parent to consumption by the child. Instead, parents may weigh against their own consumption the opportunity to invest in ways that improve their children’s underlying traits or capacities. This means that investment decisions should scale with both genetic relatedness and the reliability of wellbeing cues as predictors of fitness outcomes. Put another way, this distinction is the difference between giving a fish to eat and teaching how to fish: parents may not be motivated merely helping offspring now — they could be responding to cues that help them to build the fitness capital in their offspring and yield higher fitness later2. Thus, more altruistic parents will tend to invest a higher fraction of their budget on their children, and this could be favoured if this investment is adjudicated appropriately given effective relatedness.

2.2. Overlapping Generations and the Legacy of Altruism

An important question in economics is “and then what happens?”. This is because the short- and long-run impact of decisions can be quite different, whether in magnitude, direction, or both. Answering this question brings us to the heart of the present thesis, and to do so we follow Becker (reference). Let the child’s fitness capital during the next time period be described by a production function:

$h_{t+1}=F\left(I_t, h_t\right), F_I>0, F_{II}<0$ (2)

Where $I$ is parental investment and $h$ is the child’s baseline level of fitness capital. This is to say that $F\left(I_t, h_t\right)$ describes how an individual’s eventual fitness potential emerges from the interaction between what it starts out with and with how much this is boosted by their parents’ investment. More investment always helps, but there are diminishing returns. Each additional bit of investment matters less than the last bit3. When adult, the child’s “income” then follows from its fitness capital, such as:

$y_{t+1}=w{h}_{t+1}$Where $w$ can be thought of as a “wage rate” that represents the strength with which capital determines income. Or, more generally, income may be thought of as any increasing function of $h$. Either way, we are assuming that differences in the total budget that individuals earn to then spend on their own consumption and investment are only explained by differences in capital. This means that parents with more income are generally going to invest more income in their offspring, even if altruism is equal. So, variation among individuals in income at any given time is here determined by their developed capabilities which in turn flows from differences in the capital of their parents (Figure 1).

We also assume inter-individual differences in how altruistic parents are and that they pass on their altruism to offspring:

${\theta }_{t+1}=T\left({\theta }_t\right)+\epsilon ,$Where $T\left({\theta }_t\right)$ represents genetic and potentially epigenetic and cultural transmission of altruism, such as $T\left(\theta \right)=\overline{\theta }+\rho \left(\theta -\overline{\theta }\right),$ with $\rho$ representing the heritability or persistence of altruism across generations, ranging from zero to perfect, $\rho \in \left[\mathrm{0,1}\right]$.

The parent’s optimization problem at time $t$ is to spend their budget across consumption and investment in a way that maximises their utility. So, selecting the amount to investment in offspring is and optimization problem of the form:

$\underset{I_t}{maxU\left(I_t\right)=}u\left(y_t-I_t\right)+ {\theta }_{t}B\left(I\right), y_t=w{h}_t$We differentiate with respect to $I$${\displaystyle \frac{dU}{d{I}_t}}={\displaystyle \frac{d}{d{I}_t}}\left[u\left(y_t-I_t\right)\right]+{\displaystyle \frac{d}{d{I}_t}}\left[{\theta }_{t}B\left(I\right)\right]$Using the chain rule for the first term the derivative of $u\left(y_t-I_t\right)$ is $u^{\text{'}}\left(y_t-I_t\right)$times the derivative of $\left(y_t-I_t\right)$, which is $-1$. For the second term (${\theta }_{t}B\left(I\right)$), we treat ${\theta }_t$ as a constant with respect to $I_t$. Thus, the first order condition is:

${\displaystyle \frac{dU}{d{I}_t}}=-u^{\text{'}}\left(y_t-I_t\right)+{\theta }_t{B}^{\text{'}}\left(I_t\right)$Which, if we set equal to zero (${\displaystyle \frac{dU}{d{I}_t}}=0$) to find the optimum gives:

$u^{\text{'}}\left(y_t-I_t\right)={\theta }_t{B}^{\text{'}}\left(I_t\right)$ (3)

Equation (3) states that the marginal utility lost from foregoing a unit of personal consumption, $u^{\text{'}}\left(c_t\right)$, equals the marginal altruism-weighted gain from investing that same unit in the offspring, ${\theta }_t{B}^{\text{'}}\left(I_t\right)$. At equilibrium, the parent allocates its resources sot that these terms are balance. The key implication is that, at any given period (e.g., $t+1$), a parent will invest more if they are more altruistic (${\theta }_{t+1}$), if they have higher capital themselves ($h_{t+1}$), and if their own parents invested more ($I_t$) in them (because that increased their $h$). Lineages of more altruistic parents therefore invest more, and the more that they invest, the more capital their children accumulate. The more capital their children have, the larger their future incomes and budgets will be for investment in their own offspring (higher $y_t$ leads to greater $I_t^{*}$). Hence, rising capital of subsequent generations is driven by increases in equilibrium investment and capital of the preceding generation. With equation 2, this dynamic produces a positive feedback loop:

$h_{t+1}=F(I_t^{*},h_t)$With lineages with higher altruism systematically choose higher investment, generating children with greater human or fitness capital, and transmit above-average altruism (Figure 2). This induces a positive correlation between altruism and capital, both in cross-sectional snapshots and over time. This is a Becker-based insight, but it can be reinterpreted in Hamiltonian terms by translating utility into fitness units and altruism anchored in effective relatedness.

If parental investments produce benefits that can compound across multiple generations (investment in a child increase their capital and so raises the fitness of the grandchildren they produce), then the discounted sum of benefits flowing from investment will be larger than that of any single period. Put in marginal terms, this is equivalent to multiplying the right side of equation 3 by some variable representing the present value of these future benefits. To express this as a symbol, suppose that parent values their child’s fitness with a discount factor or $\gamma$, which we will assume is positive. This discounts the effect on utility of a parent from the fitness of each generation separated from the parent in time when he or she makes their investment decision4. Then parental utility is

$U=u\left(y-I\right)+\theta \gamma B\left(I\right),$And maximised when

$u^{\text{'}}(y-I)= \theta \gamma B^{\text{'}}\left(I\right)$So, in “fitness units”, this can be written as

$C^{\text{'}}\left(I\right)= \kappa \theta \gamma B^{\text{'}}\left(I\right)$With the Hamilton weight being

$r_{eff}= \kappa \theta \gamma$Thus, a single-period Hamiltonian calculation may significantly under-predict investment when multi-generational returns are large. Greater overlap between generations (less discounting or higher $\gamma$) tightens the link from Becker’s economic framework where individuals are concerned about the impact of their current decisions on posterity to Hamilton’s biological one. The more that a parent’s actions today influence their child’s future reproduction and survival, the larger the effective Hamiltonian weight. We may think of this as a parent’s inclusive-fitness horizon: the further ahead they look (e.g., valuing not only their child’s fitness a little but a lot, as well as additionally being concerned with that of their grandchildren, and beyond), the greater the effective overlap and the stronger the incentive to invest becomes. In short, the same first-order conditions subsume Becker’s altruistic investment with Hamilton’s inclusive fitness logic: $C^{\text{'}}\left(I\right)= \kappa {\theta }_{\gamma }{B}^{\text{'}}\left(I\right)$,$r_{eff}= \kappa {\theta }_{\gamma }$. Overlapping generations, through the discount factor $\gamma$, extend the weight parent’s place on the benefits of current investment for future fitness. This predicts a positive coevolutionary correlation between altruism and fitness capital, given transmission of altruism may also be genetically based and diminishing returns in $F\left(I, h\right)$.

The alert reader may notice that, although this model tracks one cohort per period, it is effectively an overlapping generations system in the causal sense. This is because each parent’s investment in $h_{t+1}$ and ${\theta }_{t+1}$ influences the reproductive capacity of descendants. Terms like “overlapping generations” and “lineage-level feedback” refer to causal persistence across generations, not literal simultaneous co-occurrence of multiple cohorts. The geometric sum in $r_{eff}$ quantifies this cumulative inclusive fitness impact, reconciling simple recursion with biologically interpretable and meaningful multigenerational feedback. For readers preferring the overlapping-generation logic to be fully explicit, a minimal model is presented in Appendix A. This demonstrates the same first order conditions and that intergenerational feedbacks naturally arise through recursive inheritance of capital and altruism.

2.3. Ability, Altruism, and Investment

Becker (1991) extended his framework by considering the possibility that parents invest in their children according to the efficiency with which each child translates that investment into future capital. Even if parents are equally altruistic to each child, they are not blindly egalitarian but may rationally pattern their investments among children in ways calibrated according to how they differ in the rates of return they provide. The same idea can be applied in an evolutionary framework. Sexual reproduction and genetic variation mean that offspring can differ in their intrinsic capacities for translating parental investment into traits related to fitness. Some individuals may grow faster, achieve greater size, be more resistant to parasites, or demonstrate greater capacity to learn skills and use knowledge. If parents can detect and act on cues for these prospective differences, we should expect them to make the necessary adjustments. Although Becker did not originally consider its interaction with altruism, we can extend the production function described in 2.1 like so:

$h_{t+1}=F\left(I, h_t, a\right),$ when ${\displaystyle \frac{\partial F}{\partial I}}>0, {\displaystyle \frac{\partial F}{\partial h}}>0, {\displaystyle \frac{\partial F}{\partial I\partial a}}>0$Where $I$ remains parental investment, $h$ is the offsprings baseline endowment of fitness at birth (e.g., health, size, immunity), and $a$ represents the offspring’s ability to convert investment into fitness (essentially a multiplier of parental efforts). In words, ability acts like an “efficiency weight”. If two siblings, one with ability $a_1$ and the other $a_2$, each receive the same amount of, say, food ($I_1=I_2$), but $a_1>a_2$ , then the sibling with $a_1$will translate food into more reproductive potential. The utility function of the parent who must choose how they will invest in two children with differing ability, $a_1$ and $a_2$, is:

$U_{parent}=u\left(c\right)+\theta B_1\left(I_1\right)+\theta B_2\left(I_2\right)$Assuming that the altruistic coefficient is the same across all children, and given our assumptions, if parents invest until the rate of returns in each child are the same then that will imply that ${I^{*}}_1>{I^{*}}_2$ (unless progressively more investment produces sufficiently drastic diminished or negative returns5). Or, supposing parents have $n$ offspring, a fixed budget of investment resources, they must decide how to allocate their resources across children:

$\underset{\{I_1, \dots I_n\}}{max}\sum _{j=1}^n[u\left(c_j\right)+\theta B\left(I_j,a_j\right)]$ all subject to $\sum _{j=1}^n{I}_j\le I_T$Where $a_j$ is the ability of child $j$. Taking the first order condition with respect to $I_j$ (investment in child $j$):

${\displaystyle \frac{\partial B}{\partial I_j}}={\displaystyle \frac{\partial u}{\partial c}}.{\displaystyle \frac{\partial c}{\partial I_j}}+\theta {\displaystyle \frac{\partial B^{\text{'}}}{\partial I_j}}=0$Since ${\displaystyle \frac{\partial c}{\partial I_j}}=-1$ and ${\displaystyle \frac{\partial u}{\partial c}}=u^{\text{'}}\left(c\right)$, we get:

${-u}^{\text{'}}\left(c\right)+\theta {\displaystyle \frac{\partial B^{\text{'}}}{\partial I_j}}=0$Which implies that, for every child $j$:

$u^{\text{'}}\left(c\right)={\displaystyle \frac{\partial B^{\text{'}}}{\partial I_j}}({I_j}^{*},a_j)$For two children, $j$ and $k$, the optimal allocation requires that:

$\theta {\displaystyle \frac{\partial {U_j}^{\text{'}}}{\partial I_j}}({I_j}^{*},a_j)=\theta {\displaystyle \frac{\partial {U_k}^{\text{'}}}{\partial I_k}}({I_k}^{*},a_k)$Assuming altruism is constant:

${\displaystyle \frac{\partial {U_j}^{\text{'}}}{\partial I_j}}({I_j}^{*},a_j)={\displaystyle \frac{\partial {U_k}^{\text{'}}}{\partial I_k}}({I_k}^{*},a_k)$As ${\displaystyle \frac{\partial B}{\partial I\partial a}}>0$, if, say, $a_j>,a_k$, then to make marginal returns from each child equal implies $I_j>,I_k$ (unless returns to investment fall so fast that the equality is reversed). This means that the optimal allocation will generally favour children with higher ability because the marginal benefit of investing in them (in terms of future fitness capital) is greater even if parents are equally altruistic towards each of their children (see Figure 3). The important point here is that ability does more than simply arrange patterns of investment within families. It can accelerate the overall process of capital accumulation. It can be expected to do this through two channels. The first may be referred to as “Roy sorting amplification” (after Roy, 1951). Because the marginal return of investing in a higher ability child will remain higher than the cost for longer, parents can achieve higher levels of returns (and smarter children overall) if they invest accordingly. If parents preferentially invest in offspring who appear to have higher ability, then those children will accumulate disproportionately more capital over time. This feedback loop produces a self-reinforcing sorting process, where high-ability individuals become both the most invested-in and the most capital-rich (so have the most to invest).

The second is related to the complementarity between ability and investment. If ability not only raises returns to investment but also amplifies the effectiveness of already accumulated capital, then ability and capital interact multiplicatively. For example, perhaps a child who is cognitively gifted and learns faster than expected also gets taught more, and if they are taught more then they learn faster. This produces accelerating differences in outcomes across siblings within and between families.

Figure 4. Hypothetical relationship between parent and offspring characteristics highlighting the role of ability. Ability is integrated with the same relationships depicted in Figure 2. Offspring tend to inherit ability from parents, while the child’s ability both enhances the effect of the parental investment and induces more of that investment. Red arrows depict genetic transmission from parent to offspring, solid arrows with pluses represent positive causal effects of behaviour, and the dotted line represents where these effects, if recuring over generations, produce a correlation. Red arrows depict genetic transmission from parent to offspring, solid arrows with pluses represent positive causal effects of behaviour, and the dotted line represents where these effects, if recuring over generations, produce a correlation. .

Figure 4. Hypothetical relationship between parent and offspring characteristics highlighting the role of ability. Ability is integrated with the same relationships depicted in Figure 2. Offspring tend to inherit ability from parents, while the child’s ability both enhances the effect of the parental investment and induces more of that investment. Red arrows depict genetic transmission from parent to offspring, solid arrows with pluses represent positive causal effects of behaviour, and the dotted line represents where these effects, if recuring over generations, produce a correlation. Red arrows depict genetic transmission from parent to offspring, solid arrows with pluses represent positive causal effects of behaviour, and the dotted line represents where these effects, if recuring over generations, produce a correlation. .

Together, Roy sorting and complementarity mean that ability, altruism, and capital can be expected to become rapidly correlated within the population. In other words, signals of higher ability draw more investment, and the higher ability amplifies the effect of that investment. If ability and altruism are heritable, then parents who are more altruistic towards higher ability children will generate lineages where ability and capital accumulate together, and these lineages will in turn reinforce the apparent payoff to altruism.

In summary, adding ability to the model generates the following predictions: (1) parents should preferentially invest in children who signal higher ability, (2) because ability accelerates the accumulation of capital, even small initial differences may snowball into larger disparities over time, and (3), this creates a natural correlation between ability, capital, and the expression of altruism. The strength of the correlation between ability, investment, and fitness capital can weaken if abilities are poorly detectable by parents, if investment has very strong diminishing returns, or if environmental shocks randomly reduce the translation of investment into fitness. Nevertheless, it seems reasonable to conclude based on reasonable assumptions that families that hit upon this alignment will tend to flourish disproportionately.

2.4. Parenting Synergies and Mate Choice

We have so far examined how altruism and fitness capital can reinforce each other across generations through altruism’s directing of parental investment. A further channel may come from mate choice. The more impactful that decisions become about how to invest in offspring, the weightier the consideration of who to mate with becomes beyond just their genetic contribution. In any species where individuals invest in kin in ways receptive to the sorts of feedback we have described, such as where it is rewarding to see relatives do well, it is unlikely that mates are chosen at random with respect to traits such as altruism or the capacity to obtain and command resources (whether through “good genes”, markers of fitness capital, or both). In a variety of animals, investments in children are also not made solely by one parent in isolation but by both, and these investments plausibly interact to produce the fitness of the offspring that result.

Becker (1973, 1974) analysed how human capital shapes partner choice in marriage markets. We can build on this framework, linking it explicitly to altruism as considered so far. Following Becker’s treatment of marriage markets, consider a model in which each male and female adult has two key traits. Firstly, they vary in their altruism, denoted by ${\theta }_i$ for individual $i\in \{f, m\}$ (where$, m$ means male and $f$ means female). As before, this measures how much weight they put on their child’s wellbeing relative to their own consumption. Secondly, they have “fitness” capital $h$. A “household” (i.e., marriage or cooperative breeding pair) forms between two adults, (${\theta }_f,h_f$) and (${\theta }_m,h_m$), to produce a combined income:

$y=y_f+y_m=f(h_f,h_m)$Where $f$ is a non-decreasing function reflecting the productive complementarity between reproductive partners.

If we think of the household as the decision-making unit, the effective altruism of it will be:

$\overline{\theta }=\Phi ({\theta }_f,{\theta }_m)$, ${\displaystyle \frac{\partial \Phi }{\partial {\theta }_i}}>0$For instance, this might be a simple average, or a function that gives extra weight to couples who are both altruistic. The couple then must decide how much of their income to consume themselves and how much to invest in their offspring $I$:

$U=u\left(c_f\right)+u\left(c_m\right)+\overline{\theta }B\left(I\right)$Where $u\left(c\right)$ is the utility from consumption, which is constrained by the budget $c_f+c_m=y-I$, and $B\left(I\right)$ is the payoff to the offspring from parental investment, which can be measured in the same units as utility or fitness as discussed 2.1. Assuming parents both consume much the same under optimal conditions ($u^{\text{'}}\left(c_f\right)=u^{\text{'}}\left(c_m\right)=u^{\text{'}}\left(c\right)$) for simplicity, the first order conditions are:

$u^{\text{'}}\left(y-I\right)=\overline{\theta }B\left(I\right)$This means that the marginal cost of giving up consumption equals the marginal benefit of investing in the child, scaled by the altruism of the breeding pair. Meanwhile, the child’s human capital during the next period will be

$h_{t+1}=F\left(I,h_f,h_m\right), {\displaystyle \frac{\partial F}{\partial I}}>0, {\displaystyle \frac{\partial F}{\partial h_i}}>0$where $F$ is increased by investment to capture the idea that returns on investing in the child are higher when parents have more income and when they are more altruistic. This implies that, at equilibrium, higher household altruism or parental capital leads to greater investment and higher offspring capital.

We next assume “supermodularity” between male and female characteristics. In other words, their joint efforts of each parent are force multipliers of one another, particularly their fitness capital:

${\displaystyle \frac{{\partial }^{2}f\left(h_f,h_m\right)}{\partial h_f,h_m}}>0$If the household income produced by a breeding pair is greater than the sum of its parts, this makes it rational for males and females to seek each other out and mate based on matching features6. Such positive assortative mating (hereinafter PAM for brevity) on $h$ would then raise the correlation between $h_f$ and $h_m$, hence raising income variation and the average income of the most productive households7. At equilibrium, this generates correlations between partners’ traits and increases the variance and average of household income. Since equilibrium investment rises when income increases, higher-$h$ couples invest more, so $h^{\text{'}}$of the children rises too via this budget pathway.

It is important to note, however, that unless $\theta$ and $h$ are already correlated, positive assortative mating on $h$ would not directly raise $\overline{\theta }$. If how altruistic parents are is independent of their capital, the distribution of altruism throughout the population should remain unchanged. By contrast, suppose partners choose their mates on the basis of altruism (i.e., how much they expect their partners will care about investing in their jointly produced offspring). This is not a difficult assumption to motivate: an individual wanting to spend more on their children than consume themselves would likely want to find a like-minded partner to mate with so that there is less conflict about how the household budget is allocated. Meanwhile, relatively selfish couples would be happier together because that produces more income to spend on themselves. This would directly make ${\theta }_f$ and ${\theta }_m$ positively correlated, and so there will be a higher average $\overline{\theta }$ and higher variation in household altruism than random mating. Because the optimal investment in offspring rises with higher household altruism, high-$\overline{\theta }$ couples invest disproportionately more of their income, raising their children’s $h_{t+1}$even if their incomes remain the same. As we are assuming transmission of altruism (${\theta }^{\text{'}}$is an increasing function of $\overline{\theta }$ ), then high-$\overline{\theta }$ couples produce children with more altruism and more capital. In other words, if couples prefer to mate based on altruism in one generation, then this will create and/or increase the correlation between altruism and capital in the next generation. Alternatively expressed, let the covariance between household altruism and offspring fitness at generation $t+1$ be:

${Covariation}_{t+1}\left(\theta ,h_{t+1}\right)>{Covariation}_t\left(\theta ,h_t\right)$This can be expressed in an equation of the manner pioneered by Price (1970)8 as follows,

$\Delta Cov\left(\theta ,h\right)=Cov\left(\theta ,{\displaystyle \frac{\partial h_{t+1}}{\partial \overline{\theta }}}\right)+Cov\left(\theta ,{\displaystyle \frac{\partial h_{t+1}}{\partial y}}\right)$Where positive assortative mating based on altruism makes $Cov\left(\theta ,{\displaystyle \frac{\partial h_{t+1}}{\partial \overline{\theta }}}\right)>0$ and so increases the correlation (this feedback process is depicted in Figure 5), while positive assortative mating based on capital only affects $Cov\left(\theta ,{\displaystyle \frac{\partial h_{t+1}}{\partial y}}\right)$, whose sign already mirrors whatever correlation already exists between altruism and human capital. If mates select each other on both altruism and human capital (or ability), then this should produce the most rapid stratification of human capital within the population, leading to extreme combinations of all traits.

This feature opens the door to an important dynamic in evolutionary biology, originally described by Fisher (1930). Whereas the Becker model proposes people mate for reasons of supermodularity that make seeking out partners with similarly high levels of ability, capital, or (as we have considered, altruism) because it is optimal from the standpoint of utility, once there is a correlation between altruism and preferences for altruism, this sets the stage for potentially runaway sexual selection. To see how, consider Lande’s (1981) model of the joint evolution of a traits with preferences, e.g., trait $z$ and sexual preferences for that trait in partners $p$. From Lande’s analysis, if both have a genetic basis, and these are positively correlated, $G_{zp}$, positive feedback can ensue when:

$G_{zp}>S{\displaystyle \frac{G_{zz}}{\alpha }}$Where $G_{zz}$ represents is genetic variance for trait $z$, $\alpha$ is the strength with which preference ($p$) for trait $z$ confers a mating advantage to individuals higher in this trait, and $S$ refers to the strength of stabilizing selection pushing $z$ back towards some optimal level. So, the larger the genetic covariance is between trait and preference, the more that selection favouring an increase in the trait also increases strength of preference for that trait, and vice versa. Larger $\alpha$ makes sexual selection stronger for a given level of covariance between trait and preference ($G_{zp}$), a larger $G_{zz}$increases the required $\alpha$ needed for runaway to occur. When a trait variance is large relative to covariance with preference, stronger sexual selection pressures are needed to build the coupling. Strong natural selection also resists exaggerated $z$. This builds the covariance between preference and the trait, leading to exaggerated traits and stronger preferences. As with the model so far considered, Lande-like runaway selection does not in itself require new genetic variation to arise: the runaway process comes from restructuring the patterns of correlation (linkage disequilibrium) between preference and trait throughout the population, increasingly concentrating genes for extremes in these features in more extraordinary individuals (Dawkins, 1976).

In summary, if fitness capital, ability, or altruism have a strong genetic component, they may quickly become genetically correlated through the investment and mating decisions of parents. If these mating decisions are made based on supermodularity or utility-maximising considerations (e.g., choosing a wife or husband because they are altruistic), any innate sexual preference for any of these traits (e.g., finding a wife or husband sexually attractive because they are altruistic) could in turn drive runaway evolution of these correlated traits. In other words, mating initially based on supermodularity may be a pump-priming or ignition system that gets the engine of runaway sexual selection of these traits going (Figure 6), and this may extend the evolution of these traits to beyond what would otherwise be optimal. Likewise, a preference for partners based on “good genes” (if a marker for ability), could fan the flames of marriages motivated by supermodularity of altruism or human capital as these would become correlated through the rational investment decisions of preceding generations.

It is worth emphasizing that the present analysis follows the classic approach to runaway sexual selection, as pioneered by Fisher (1930) and formalized by Lande (1981). In this tradition, the focus is on identifying conditions under which traits and preferences can covary positively across generations, generating self-reinforcing feedbacks, rather than on explicitly iterating full generational dynamics. In our model, these feedbacks are captured by the covariance between parental altruism and offspring fitness capital ($\Delta Cov\left(\theta ,h\right)=Cov\left(\theta ,{\displaystyle \frac{\partial h_{t+1}}{\partial \overline{\theta }}}\right)+Cov\left(\theta ,{\displaystyle \frac{\partial h_{t+1}}{\partial y}}\right)$). PAM on altruism ensures $Cov\left(\theta ,{\displaystyle \frac{\partial h_{t+1}}{\partial \overline{\theta }}}\right)>0$, demonstrating a mechanism by which more altruistic households produce children with both greater altruism and higher fitness capital. Similarly, PAM on fitness capital influences $Cov\left(\theta ,{\displaystyle \frac{\partial h_{t+1}}{\partial y}}\right)$, amplifying variation in household investment potential. As in Fisher and Lande, these equilibrium-based covariances indicate the potential conditions for accelerating correlations between traits and preferences, without asserting that trait divergence is inevitable or unbounded. In this sense, our “runaway” description refers to self-reinforcing increases in correlations across generations, consistent with the logic of the locus classicus of this literature (to see an example of how these conditions could be explicitly formalized for mate choice and altruism complementarity generate covariation, see Appendix B).

To round off this discussion of mate choice, it is worth addressing a point related to the nature versus nurture determination of fitness capital. A perhaps intuitive objection to the above is that parents may often use investment to compensate in children lacking good genes. For example, if there is a sibling that requires more resources to grow to the same size than another, redirecting some of the food provided by the parents from the latter towards the former may be wisest – especially if there are diminishing returns to such investment as intensified by the effect of ability. There might be important implications for mate choice dynamics hinging on whether investment and ability generally function more as substitutes in this way $F_{Ia}<0$ or as complements $F_{Ia}>0$ (i.e., where more ability leads to higher returns on investment, as assumed so far). If $F_{Ia}>0$ and parents match based on altruism, high-θ households make larger investments, and target more of this investment to higher-$a$ children. Selection will then favour genotypes carrying both high $\theta$ and high $a$, leading to positive covariance building between altruism, ability, and fitness capital. If instead $F_{Ia}<0$ extra investment helps low-$a$ offspring catch up more than it propels high-$a$ individuals, potentially weakening or even reversing the correlation between altruism and ability. We may still expect higher levels of fitness capital to accumulate in high altruistic yet low ability lineages, so the correlation between $\theta$ and capital may remain positive, but the correlation between altruism and ability would be lessened or even become negative.

If instead parents match directly based on ability – as many models of mate choice assume they do if this is a stand in for “good genes” (Hamilton, 2001)– then we should find good genes concentrated in high-$a$ households. If $F_{Ia}>0$ , such that even large investments earn bigger returns in high-$a$ individuals, then it will be rational for even parents with moderate altruism to bias their investment in high-$a$ offspring. That selection on returns should pull altruism upward in high-a lineages because high ability offspring benefit most from more altruism. This should generate a positive linkage over time between ability and altruism despite the fact mates are choosing each other solely based on good genes. If instead $F_{Ia}<0$, high levels of investment are not needed as much in high-$a$ lineages to reach high levels of fitness capital. So, selection pressure on altruism is weakened within those lineages. This may still result in a strong correlation between ability and fitness capital, a weak altruism-fitness capital link, and perhaps a negligible or negative correlation between ability and altruism.

Finally, if partners choose based on manifest fitness capital, $h$, then this is effectively mating based indirectly on whatever trait mix produces high fitness capital. If $F_{Ia}>0$ , then, this means there is a straightforward route towards a positive three-way correlation between altruism, ability, and fitness capital. If instead either cues signalling capital function as a direct readout of ability or there are such strong diminishing returns to investment that $F_{Ia}<0$, then PAM on manifest $h$ could weaken or slow linkages between altruism and human capital because altruism is less important or negligible. More realistically, investment and ability are unlikely to be strong substitutes in a species where altruistic investment operates and only compensate for each other partially. Even if $F_{Ia}$ is only mildly positive, we would expect selection, then, to favour ability but drive the system towards a positive correlation between ability and altruism through greater returns on investment in higher-$a$ offspring.

2.5. Altruism-based mating and Green Beard Effects

While the processes considered so far increase correlations between altruism and investment they do not, by themselves, extend altruistic behaviour to levels beyond what would be considered adaptive based on a sufficiently inclusive definition of Hamilton’s rule. However, they do create conditions whereby specific genes may be favoured to push investment to levels beyond what would be advantageous to the rest of the genome based on relatedness between individuals. This is because PAM on altruism may be especially conducive to the evolution of “supergenes” (Hamilton, 1996) or “Green Beards” (Dawkins, 1976). This refers to how a hypothetical gene can be favoured by selection for directing altruistic behaviour of the organism carrying it towards another individual likely carrying the same gene (regardless of the chances the two individuals are likely to share other genes). To evolve and spread, Green Beards require the gene to (1) produce a recognizable effect (the green beard), (2) make its bearers recognize that trait in others, and (3) cause its bearer to preferentially direct benefit to those individuals (Dawkins, 1982).

We have assumed genetic variation influencing willingness to invest in offspring (altruism) and later supposed that this may become linked to genetic variation for preference to mate with individuals who also display cues of altruism towards offspring. If there is a genetic variant that combines (1) unusually high altruism with (2) desiring of unusually high altruism in a partner, then positive assortative mating on altruism could reinforces their connection and spread. In other words, instead of a literal green beard, such a gene could recognize itself in other bodies through the behavioural or cognitive cues related to altruism and preference for altruistic partners (which we have supposed might exist for reasons already explored). By choosing to mate with an especially altruistic partner and direct a large amount of own investment to the offspring of that, this gene is likely helping itself. Put another way, as far as the result of the genome is concerned, optimal investment in offspring (or the wider kin-network) is determined by $r$. But from the standpoint of the genetic variant for noticeably higher altruism, relatedness with offspring is now approaching one hundred per cent.

Assuming simplified genetics and breeding (haploid and one offspring per mating), we can proceed to illustrate the above point by presuming the qualitative conclusions hold in more complicated models. Consider an allele $A$, which codes for unusually high parental investment in offspring, with an allele $a$, which codes for the non or usual altruistic investment. When an $A$ -carrier provides parental help to a recipient offspring, the actor pays the cost (this reduces the actor’s direct reproductive fitness), and the recipient offspring obtains a benefit to their own survival or fecundity9. If we assume baseline random mating in the population gives a frequence of allele. Next, suppose that the offspring inherits the allele of one randomly chosen parent. So, if parents are $A$ and $a$, then it has a fifty per cent probability of carrying $A$ (and likewise for $a$); if both parents have $A$, then it certainly inherits $A$, and if both parents have $a$, its probability of inheriting it is zero. This means mating with another $A$-carrier increases the probability of offspring carrying $A$.

Next, imagine parents select mates via preference (the sexual green beard) such that carriers of a preference allele (which we will assume is tightly linked to $A$ or comes part of the same package by inheritance) prefer to mate with partners who they judge to also be good parents – that is, parents carrying allele $A$. Let’s say, then, that the probability that an $A$ -carrier mates with another $A$ -carrier partner is

$P\left(mate=A|actor=A\right)=p+a_m$Where $a_m$ is the how much more probable it is above some baseline frequency $p$ that an $A$ meets and matches with another $A$ (this may be thought of as an assortment coefficient). If mating were random, then $a_m=0$.

We may expect the number of $A$-copies in the next generation that are caused by an $A$-carrier’s actions. Spread occurs when the expected gain from altruistic investment exceeds the neutral expectation. We have supposed that the offspring has a baseline fifty per cent chance of inheriting the $A$ allele from an $A$-parent, and from this must be subtracted the cost of performing the altruistic act of investment $c$. So, there is a direct lost equal to ${\displaystyle \frac{1}{2}}c$. The benefit is an indirect increase caused to the offspring’s fitness, $b$. So, ordinarily, the question would be whether this is greater than ${\displaystyle \frac{1}{2}}c$. But here is the crucial twist: that benefit will more often be delivered to offspring that carry $A$ when the actor mates assortatively with another $A$. When both partners have probability of $p+a_m$, both parents might have $A$, so the offspring assuredly inherits $A$. When the actor mates with an $a$-partner ($1-p-a_m$), the offspring inherits $A$ with a probability of fifty percent. So, the probability that the recipient offspring carries A (conditional on the actor being an $A$ -carrier) is:

$P\left(offspring carries A|actor=A\right)=\left(p+a_m\right)+{\displaystyle \frac{1}{2}}(1-p-a_m)$$={\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}(p+a_m)$Therefore, the expected indirect genetic benefit to the actor from increasing his or her offspring’s success by $b$ is:

$Indirect gain=b\left({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}\left(p+a_m\right)\right)$The allele $A$ will increase in frequency when the indirect gain is greater than the direct loss, which is:

$b\left({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}\left(p+a_m\right)\right)-c\left({\displaystyle \frac{1}{2}}\right)>0$Which can be multiplied by two to simplify and rearranged to into the Hamilton form:$b\left(1+p\right)+{ba}_m>c$So, the term ${ba}_m$ is the extra inclusive fitness advantage to the allele because carriers preferentially mate with other carriers and invest in joint offspring. This may be thought of as the “sexual green beard bonus”, with the standard Hamilton rule for the rest of the genome applying with $a_m=0$. The larger $a_m$ becomes for gene $A$, the easier it becomes for the benefit to outweigh the costs. Even if the benefit of altruistically investing some amount in offspring is insufficient to justify it based on the standard Hamiton rule, may be strong enough to escalate from the standpoint of the altruistic genes if the effect of assortative mating is strong10.

3. Discussion

By connecting Hamilton’s insight with an adjusted Becker’s Human Capital framework, we can see how Kin-Selection may be a more potent driving force of evolutionary change than previously recognized. Central to this proposal are two constructs (1) fitness capital – that is, an adaptive characteristic of an individual that can be built up by investment from others, and which contributes to how much resources the individual can in turn acquire and invest in others – and (2) altruism defined here as the determining willingness to invest in kin. Such investment may constitute anything from simply sourcing and providing infants with more food rather than eating it themselves, to spending time and attention transmitting knowledge (e.g., teaching foraging skills) or even constructing tools or other extended phenotypes to pass on for the benefit their children when they mature. Whether manifest in brain or brawn, the critical feature is that the trait being invested in improves proportional to investment, and that there is potential for the trait to build cumulatively. In a species where parents are motivated to invest altruistically in their offspring, genetic variation promoting altruism will tend to become correlated with prowess in acquiring resources for investment. Lineages that are more altruistic invest more, which causes their descendants to inherit both higher altruism and greater fitness capital. These descendants, in turn, have more resources to invest and a higher propensity to invest in their own offspring, producing cascading investments in inclusive fitness.

Other factors may act as force multipliers of this general effect such as when there the feedback guiding the parental decisions is psychological. Given generations overlap, altruistic parents find it rewarding to observe signs that their children prosper, and so investing efforts can become reinforced accordingly. This extends the time horizons over which investment in a lineage can feedback to affect the motivation of parents, grandparents, and so forth. Another amplifier arises when mate choice is assortative on altruism. A male strongly motivated to invest in his children benefits by pairing with a female who is similarly motivated, and vice versa. Partnerships based on shared altruism increase the value placed on offspring investment and simultaneously command greater resources. As a result, descendants of these pairings inherit both higher altruism and higher fitness capital, further intensifying the cascade.

The decision to match and mate positively based on altruism or capital may initially be purely practical: matching based on either or both likely represent an unbeatable or stable strategy if they are complements in the total “utility” each couple jointly produces because, under such an arrangement, no partner can benefit from splitting and “remarrying” with another willing partner. If there is also genetic variation affecting preferences for partner characteristics indicating or correlated with altruism, then the process or assortative mating would build the correlation between genes for higher altruism and genes for preferring altruistic partners. This produces precisely the conditions that can make mate choice become a self-reinforcing amplifier of the process (i.e., Fisher’s runaway effect), potentially leading to sexual selection for signals of willingness to invest highly in offspring.

Another interesting complication we considered was genes in children affecting how receptive they are to their parents’ investments. We summarized this as “ability” and it also likely accelerates the process of altruism and fitness capital becoming linked. This is because parents should be generally motivated to invest more in abler children even if they value each child the same as this should yield higher overall returns than if all children were invested in evenly or randomly. Although under some assumptions ability and investment may act like substitutes, and ability may act like an eddy current in investment cascades, it seems the most straightforward implication is that ability, altruism, and fitness capital all become positively intercorrelated. This means an increase in selection for or mating advantage of one of these characteristics will induce increase in the other characteristics as well.

The recursiveness of these forces is one of two critical features for understanding the implications of cascading fitness capital. The other is their complementarity in building adaptive fitness. Rank-ordered pairings of the varieties described, such as pairing mates high in the same attributes (whether capital or altruism) or by pairing higher ability with higher investment in the same bodies of offspring, maximizes both the total and average level of the resulting traits, compared to what would be produced from random sorting or negative sorting. Such arranging also increases variation, since pairing large multipliers produces disproportionately large outputs, while pairing smaller multipliers together produces little change. The income is greater disparity between lowest and highest levels of fitness capital across lineages. Thus, although the processes we have described do not assume any genetic change at the loci affecting the traits involved, it can produce large levels of phenotypic change and variation exposed to selection resulting from decisions parents make given the circumstances we have assumed11.

Crucially, the processes described do not presuppose any genetic change at loci underlying the traits. Rather, they generate large amounts of phenotypic change and variation exposed to selection, arising purely from the investment and mating decisions parents make under the assumed conditions. This implies both a higher average level of altruistic effort toward kin and a more unequal distribution of fitness capital than would be predicted by simplistic interpretations of Hamilton’s rule. In nature, how we define “fitness capital” will be decisive for which lineages thrive, and which decline. Thus, although the model shows how phenotypic change can occur without shifts in allele frequencies, in practice genetic evolution will follow wherever greater fitness capital confers a Darwinian advantage. If the advantage is strong, our framework identifies mechanisms by which phenotypic change —whether in fitness capital or parental altruism — could rise explosively, with broad evolutionary consequences.

One such consequence arises from the Fisher-Lande-like dynamics of assortative mating on altruism because these create ideal conditions for a distinctive form of Green Beard effect. When a preference allele is linked to an altruism allele, assortative mating allows carriers to preferentially pair with altruists and invest in those carrying the same gene, with the children carrying the green beard enjoying extra investment from both parents. Mathematically, the impact of this mechanism can be expressed as an additional positive term, added to the usual $rb$ benefit in Hamilton’s rule. This “assortative mating bonus” allows elevated levels of altruism to spread in situations where conventional pedigree-based relatedness would not be sufficient. In nature, this mechanism may be vulnerable to cheaters, but, unlike other forms of Green Beards, we might expect it to be less vulnerable to recombination splitting the link between the green beard expression and preference or costs of detecting the green beard because, in this case, sexual selection would be continuously acting to mitigate these factors.

Previous research has shown that multi-generational effects, vertical cultural transmission, spatial population structure, and ecological interactions can shape the evolution of social traits and investment behaviours (e.g., Brown et al., 2009; Lehmann, 2008; Mullon & Lehmann, 2017; Van Cleve & Akçay, 2014). For instance, Mullon and Lehmann (2017) examine gene–culture co-evolution in family-structured populations, highlighting how vertically transmitted cultural information interacts with genetically determined learning behaviours. Their analysis demonstrates that vertical transmission can modestly increase adaptive information and constrain evolutionary branching, emphasizing kin structure in cultural evolution. While conceptually related, this framework focuses on cultural knowledge rather than direct fitness capital or altruistic traits, and it does not consider assortative mating or amplification of trait covariance across generations.

Lehmann (2008) investigated the evolution of niche-constructing traits whose phenotypic effects extend beyond the actor’s lifespan. By modelling spatially subdivided populations and the future fitness consequences of environmental modifications, he showed that selection can favour traits influencing subsequent generations. This resonates with our focus on multi-generational feedbacks, but our model emphasizes direct behavioural traits—altruism, parental investment, and mate choice—while avoiding the complexity of environmental or spatial dynamics. This simplification allows clearer predictions regarding trait covariance, amplification of altruism, and potential runaway selection.

Van Cleve and Akçay (2014) explore how behavioral responsiveness, genetic relatedness, and synergistic interactions jointly shape social evolution. Their results illustrate that these factors can produce feedbacks not easily captured by simple assortment indices. While our model shares the goal of understanding interaction-driven trait evolution, it abstracts from ecological or reciprocal dynamics to isolate heritable links among parental investment, mate choice, and offspring fitness capital, providing a tractable mechanism for generating positive correlations and potential runaway dynamics.

The main advantage of our framework is its combination of simplicity, interpretability, and predictive clarity. By linking parental investment, assortative mating, and heritable traits, it predicts: (i) the emergence of positive correlations between altruism and fitness capital, (ii) amplification of these correlations via assortative mating on altruism or ability, and (iii) conditions under which these mechanisms may generate runaway evolution, without requiring complex spatial or ecological modelling. Moreover, by bridging Becker’s economic models of parental investment with biological models of inclusive fitness and sexual selection (Hamilton, Fisher, Lande), it provides a unified perspective on multi-generational feedbacks. In sum, while prior work has explored gene–culture co-evolution, social synergy, and niche construction, our model identifies a parsimonious pathway by which behavioural traits, parental investment, and mate choice interact to generate accelerating evolutionary dynamics. By focusing on heritable variation, investment decisions, and mating preferences, it reproduces qualitative effects observed in previous studies while allowing transparent derivation of covariances, correlations, and potential for runaway evolution. This simplicity facilitates causal interpretation and generates broadly applicable, empirically testable predictions, including positive three-way correlations among altruism, ability, and offspring fitness.

3.1. Evidence and Implications

The dynamics we have considered do not disqualify the classic Hamilton calculus, but it does mean that the variables involved may not be as obvious from observation as a naïve application of Hamilton’s rule would suggest. For instance, the benefit caused by altruistic acts, when seen as investment in fitness capital, may require inclusion of multigenerational and indirect returns – not only on the recipient’s survival or fecundity. The cost to the altruist is not simply the risk or effort involved, but the opportunity costs that can be moderated by the wider effects of the decision on the parent’s economy. This could include complementarities between what the parent is doing and with what the partner, and how this combines to determines their offspring’s fitness. Finally, the relatedness should be understood as effective relatedness, which may be altered by assortative mating. This point is illustrated by the opportunity this system creates for otherwise rare “Green Beard” effects, which means genes that have an evolutionary incentive to invest more in the offspring produced by such a mating than the rest of the genome should prefer12.

In addition to humans, many species present the preconditions for altruistic investment in fitness capital. A useful starting point may be to distinguish between one-off benefits to offspring (e.g., gifts, feedings, discrete acts) and investments that enhance long-term potential (e.g., provisioning, protection, or training). If this distinction is valid, the models predict that parental effort devoted to investment should exceed what would be expected from simple relatedness-based heuristics. Measuring this directly is difficult, since the line between “gift” and “investment” is blurred. What is more tractable is to examine resources that parents are motivated to acquire: when parents are experimentally provided with additional resources, their energy and time for investment should increase even if the precise channels are harder to track. For example, it has been documented that meerkats will sometimes capture and disable (but not kill) prey items and release them close to their infants for them to apparently practice hunting (Thornton & McAuliffe, 2006). Providing meerkat mothers with plenty of dead food to eat might increase the chances she will reserve more of the live prey she encounters for her offspring to build their hunting capacities rather than eat them herself instead. Anecdotes and natural history documentaries have similarly interpreted some behaviours among other mammalian mothers, such as in big cats, where a mother will bring live but injured prey to her cubs to apparently facilitate their learning prey capture skills – although this is difficult to demonstrate experimentally (Thornton & Raihani, 2010).

From this follows the prediction that experimental boosts to parental resources should yield compounding effects over generations. This is because this increases the income of the parents, which should increase reserves available for investment. Children should acquire greater fitness capital, and grandchildren disproportionately so, as the lineage accumulates advantages. Crucially, if the cascade is sustained, these lineages should also evolve to become more altruistic, as we predict that lineages with more to invest and lineages with higher altruism tend to become intertwined13. Conversely, when historical links between resources and genes become abruptly decoupled, the distribution of fitness capital should shift. Historical episodes such as mass migration, famine, epidemic disease, or war may temporarily weaken the link between inherited capital, mate choice, and altruism. For one or more generations, assortative matching based on these traits may be disrupted, leading to less skewed distributions of capital and weaker correlations between altruism and resources.

A further prediction concerns variation among offspring. Higher-ability offspring should attract greater investment, even if parents show no explicit preference in terms of altruism per se. This aligns with widespread observations. For example, in many mammals, “runts” receive less postnatal care (Clutton-Brock, 1991), while in birds, weaker hatchlings are often fed less, with parents apparently being indifferent to them being effectively culled by their stronger siblings (Mock & Forbes, 2022). Experimental manipulations of cues associated with ability could directly test whether such signals alter parental investment decisions14. It should be noted that previous theories already make this prediction (Olson et al., 2008). What may be novel here is the added prediction that this should also be observed across couples: families with higher ability children should also tend to invest more in them than families with lower ability children. Experiments where couples with are effectively made to “adopt” low ability young should invest in them less than if given high ability young to raise.

The classic model of parental investment by Smith and Fretwell (1974) provides foundational insight into the trade-off between offspring size and number, assuming that each unit of investment yields the same marginal fitness return. While touching on similar issues to the present thesis, their framework applies most directly to species producing many small offspring with minimal postnatal care. More recent refinements, such as Johnson et al. (2024), have shown that incorporating indirect reproductive costs that scale nonlinearly with offspring traits can substantially modify predicted investment patterns. Building on these ideas, the present model explicitly considers heterogeneity in offspring ability as a multiplier of parental investment returns, allowing for differential allocation even when parents are equally altruistic toward all offspring. Unlike the previous frameworks, our approach captures intergenerational feedbacks, whereby investment, ability, and capital accumulation reinforce each other over time, and extends naturally into domains of mate choice and signalling. This produces testable predictions that are not addressed by earlier models: for example, parents should preferentially invest in offspring with higher ability, leading to lineages that accumulate disproportionately more capital, and small initial differences in ability or investment can snowball into larger disparities across generations. In this way, our model retains the simplicity of the foundational Smith–Fretwell logic while highlighting novel mechanisms by which parental investment can interact with offspring traits to shape evolutionary trajectories.

3.2. Limitations

Can the processes we have considered here be expected to push investment indefinitely high? In principle, escalation may be rapid, but there are realistic constraints to consider. Ever more extreme levels of parental investment may, for instance, be resisted if they require changes that sacrifice other fitness components. In the same way that the sheer size of egg produced by kiwi bird or the head size of human foetuses are likely near limits balanced against the capacity of mothers to produce such infants, limits imposed by constraints may be less elastic to selection than altruism. Thus, as with other potential drivers of runaway evolution (e.g., Dawkins & Krebs, 1979), there may be direct costs of rising investment in terms of viability, energy, time, or other factors that curtail the process. Another obvious limitation is environmental resources. For example, we can imagine a predator evolving to specialize in hunting ever larger prey because both hunting skills and meat are the sorts of resources that can be concentrated and invested in offspring. But it such a predator may find it increasingly less worthwhile as such prey become scarcer, or if this induces overwhelming counter-adaptations on the part of the prey species, or if it falls victim to its own success if it drives the over-exploited prey species extinct. For these and other reasons, we have assumed diminishing returns on investment in fitness capital.

A yet more interesting theoretical limitation was that we did not consider the role of altruism, ability, or capital in decisions about the quantity of children to have. On the one hand, there may be quantity–quality trade-offs, where higher-ability parents decide to invest more in fewer children (e.g., Becker, 1991), while lower-ability parents produce more children with less investment. This might result in a r–K distribution of traits, as has been suggested to exist in humans (e.g., Eysenck and Gudjonsson, 1989). On the other hand, if having higher-ability children, valuing their fitness more, and having more to invest in those children goes hand in hand, then this may be a pressure in the other direction, motivating high-altruism couples to produce more children15. Modelling variation in family size along these lines would also make it clearer why the parent’s own “consumption” cannot be treated as irrelevant in a Darwinian model: even when parents have only one child at a time, resources reserved for their own well-being may contribute indirectly to the survival of additional children in the future, or serve as a buffer against risk if current offspring die. Thus, modelling a division between “consumption” and “investment” remains defensible (cf. Trivers, 1974; Kaplan, 1996).

We have also not considered how the same predictions may play out within a wider kin-network, (cousins, nephews and nieces, etc.), much less when the genetic relatedness among such networks departs from the standard r=.5 assumed for parents and offspring. Finally, different types of mating structure may be important. For example, systems without monogamy, or where not all of one sex get paired (e.g., more adult males than females are available for mating), or truncated, soft versus hard selection regimes. Any of these aspects may reveal conditions under which altruism is less reliable connected with capital, potentially weakening the recursive dynamic and other conclusions.

3.3. Extensions

The discussion turns here to speculative extensions and future directions. We have so far assumed that parents act based on accurate knowledge about the characteristics of others, such as their partner’s altruism and offspring ability. While the present model did not address deception or signalling, the logic extends naturally into these domains, offering testable hypotheses. Introducing errors or deceptive signalling may mean selection favouring altruism can be expected to weaken or otherwise become more complicated as investment no longer reliably translates into transgenerational returns. In particular, a disconnect between altruism ability and actual relatedness raises opportunities for exploitation and parasitism. Haig’s (1997; 2001) Intergenomic Conflict theory, for example, may make the following prediction in situations where there is paternal uncertainty. Paternally-imprinted genes might be expected to program offspring to inflate their apparent ability — or play up issues of equity — to better extract resources from the mother and her partner, who may or may not be the actual father. Meanwhile, maternally imprinted genes should want optimal allocation in agreement with the mother’s genetic perspective. Exaggerated signals that investment in a particular child are especially effective may work because they hijack parental responsiveness to this as a reward signal. Further thought is required to clarify whether the resulting pressures on parents to be discerning is enough to nullify this exploitation, or if some other result is likely to emerge from an arms race between children obscuring their ability and parents striving to allocate their scarce resources efficiently.

The same logic may explain why parent birds parasitized by cuckoos have often been observed behaving as if strongly motivated to continue feeding cuckoo chicks even when they have grown enormous (Krüger, 2007a). A classic interpretation is that this is despite the cuckoo’s enormous rate of growth, and due to the parents responding slavishly to especially salient stimuli the cuckoo chic has evolved to convey (Rojas Ripari et al., 2021). Based on the present model, it may be partly because the cuckoo bird’s accelerated development mimics high ability that explains the parasitized bird’s behaviour: they may have been selected to respond with more investment to this as a sign that of underlying ability in their own offspring, inadvertently benefiting the cuckoo. Species where parents pattern their investment in this way may be especially vulnerable to parasitism by cuckooing. This may explain why most cuckoos parasitize species that are smaller than or similarly sized to themselves (Krüger, 2006b). In the exceptions where the cuckoo grows to a smaller adult size than the parasitized species, they nonetheless grow at faster rates when young (e.g., Kleven et al., 1999).

The present thesis may have applications to understanding so-called “handicap” signals as well (Zahavi, 1975). Conceivably, animals can be selected to pay high costs to transmit honest signals of their underlying qualities because they advertise their underlying qualities, such as having good genes. A classic example is gazelle stoting in response to predators like leopards, with the idea being that the healthiest can afford to jump the highest in this way, thereby displacing the predator’s efforts to target whichever individuals cannot afford to advertise their vigour in this way – even though all gazelle would be faster at putting distance between themselves and the leopard by simply running away instead (Dawkins, 1976). Crucially, Grafen (1990) showed that such a signalling system is stable only when the cost of signal strength is proportional to the underlying quality it is supposed to indicate. The kind of cascading investment process we have been considering may naturally set up such a set of conditions for costly signalling of either ability or altruism. This is because these characteristics can be expected to correlate over time with earnings on our model, thus making signals costing a given amount of earnings being disproportionately cheaper for more altruistic individuals to afford, and we have seen why there may be advantages to conveying such signals to prospective mates. Our model could be extended to predict, for example, that a highly altruistic predator may signal its quality as a parent by tackling more dangerous or elusive prey than they would otherwise choose (serving as a trophy to impress potential mates or rivals). Obviously, there may be reasons for preferring high ability and capital individuals, but this approach could explain why costly or handicapped signalling of these attributes might be expected to evolve.

Finally, something may be said about other types of altruism to close this survey of potential implications of the general model. Recall our assumption that returns in a child diminish incrementally as more is invested. On Becker’s analysis of human behaviour, this means there is a point at which parents might become motivated to allocate some of their investment in that of the capital of unrelated children. This is because, if combined with the assumption of efficient capital markets, lending investment in this way to non-relatives means that this may yield higher returns later when the non-relatives grow up and effectively repay the loan to the descendants who made the loan. Obviously, the assumption of perfect capital markets does not hold well in most biological systems including the ancestral environments of human beings. However, an extension of the foundational concepts of Trivers (1971; 2002) and Axelrod and Hamilton (1981) on altruism among non-relatives to include fitness capital may be workable provided that the unrelated children invested in are likely to interact cooperatively with the offspring of the parents investing. The age-old problem for altruism based mutual reciprocation is how to reinforce repayment (Ridley, 1997). In Becker’s case, this can be done through contracts, while in the biological case reciprocal altruism relies on effective deterrence of defection. In some cases, it may be plausible that parents who have had a proven history of cooperation with individuals in another lineage might expect their own children and the children of the unrelated lineage to also cooperate, in a way substituting for a contract and the need to directly enforce it16. Further modelling may be needed to develop this point, but it is intuitive that the present value of cooperating now might be enhanced if it is felt that the “shadow of the future” extends across overlapping generations. For example, in addition to having higher than average relatedness to other lionesses within a pride, each mother lioness has some level of certainty that their offspring will grow up to later rely on the skills and cooperation of the offspring of other mothers in the pride. This is one way that altruism for kin might influence the evolution of altruism in other forms.

Another potential implication is, more generally, the effect of practice on competence. If partners in cooperation improve in their capacity to provide benefits through the practice of reciprocal altruism, then this may have implications that have been underappreciated. Previous models have considered what happens with tit-for-tatters find each other and avoid defectors: in the same way that binding altruism with investment leads to higher variance and average fitness capital, non-random association and repeated mutually beneficial interactions by cooperators (another type of altruism) might magnify average levels of cooperation. Simply basing cross lineage investment on track record might be enough to justify an enlightened “Benselfishness”17.

4. Conclusions

If altruism can be understood as motivating investments in fitness capital, then its evolutionary significance may be more profound than previously appreciated. Investment cascades can bind the capacity to acquire resources with the motivation to invest them in kin, thereby increasing both average altruism and fitness capital. Such dynamics may interact with mating systems and other evolutionary forces to shape how individuals cooperate and compete. This preliminary synthesis of ideas from evolutionary biology and economics not only points to novel empirical predictions but is rich with implications that can be further explored to build a richer understanding of how perhaps some of the strongest and intimate social bonds have been, and are being, evolved.