Comparing the ultrasociality of humans and ants, Gowdy & Krall (G&K) argue that ants and humans “face similar problems,” and “similar patterns of economic organization emerge through similar selection pressures” (sect. 1, para. 1). As the results of the “convergent selection” (sect. 1, para. 1), both ultrasocieties capture an advantage of the division of labor and increasing returns to larger scale and larger group size. Complementary to G&K's qualitative arguments, here I give a few quantitative considerations and discuss the similarity and difference between ant and human ultrasocieties from the viewpoint of scaling laws.
It has been found recently that the metabolic rate (energy usage rate) of an ant colony is significantly lower than the sum of individual energy usages, and scales sublinearly with colony size (Cao & Dornhaus Reference Cao and Dornhaus2013; Hou et al. Reference Hou, Kaspari, Vander Zanden and Gillooly2010; Shik et al. Reference Shik, Hou, Kay, Kasari and Gillooly2012; Waters et al. Reference Waters, Holbrook, Fewell and Harrison2010), indicating that per capita, a worker requires less energy to function in a larger colony. Similarly, properties of a human society that account for infrastructure, such as total road surface and the length of electrical cables, also scale sublinearly with population size (Bettencourt & West Reference Bettencourt and West2010; Bettencourt et al. Reference Bettencourt, Lobo, Helbing, Kuhnert and West2007). The similar economies of scaling in both ant and human societies reflect, as G&K point out for ants, that a larger group size is more energetically efficient.
The origin of the sublinear scaling is unclear. Here I hypothesize that individual variation gives rise to the nonlinearity of group energetics. Social inequality is believed to be closely associated with the transition to agriculture (Price Reference Price, Price and Feinman1995). Let us consider a group with p classes, each class with n
i
members, where subscript i denotes the class. The total population of the group is: N=∑
i=1
p
n
i
. Assuming that each member in class i acquires (or consumes) an amount of energy, E
i
, then the total energy usage of the group is: E=∑
i=1
p
n
i
× E
i
. It is straightforward to see that if energy is evenly distributed across the classes, that is, E
i
is a constant for all of the classes, then the group energy usage will be linearly proportional to the group size, that is, E=E
i
×∑
i=1
p
n
i
=E
i
× N. The sublinear scale will emerge only if the fraction of the class that acquires more energy decreases when the whole group size increases. In other words, when the group size increases, relatively fewer individuals consume a lot, and more consume a little.
I need to clarify that the division of labor may not be the only cause of inequality. In fact, as mentioned by G&K and observed by Waters et al. (Reference Waters, Holbrook, Fewell and Harrison2010), the number of ant caste members may stay as a constant fraction, when colony size gets larger. However, ultrasocial living, such as managing crop production, requires a network of social interaction, and the inequality may originate from the heterogeneity in the activity level of individuals in the network; for example, few members are highly active and have more interactions with others, and most are inactive, as seen in ants (Pinter-Wollman et al. Reference Pinter-Wollman, Wollman, Guetz, Holmes and Gordon2011). Needless to say, the active individuals consume more energy. I hypothesize that this activity heterogeneity is the consequence of the trade-off between two evolutionary optimization rules. First, the speed of information flow is maximized in the network, which would require most individuals to be highly interactive, but this would also result in high group energy expenditure. Second, the group energy expenditure is minimized, which would require most individuals to be inactive, but this would also result in a slow information speed. If only one of these rules were applied, linearity between energy expenditure and group size would be observed, because the variation among individuals would be the minimal (individuals are either all active or all inactive). It remains to be revealed how exactly the transition to agriculture plays a role in these optimization rules.
In the last two sections of the target article, G&K discuss the expansionary nature of the ultrasocial society and compare the sustainability of ant and human societies as the consequence of the expansion. They argue that as it expands, human ultrasociality faces collapse due to the exhaustion of resources (among other negative factors), whereas ant ultrasocialities have achieved sustainability. G&K believe that the reason for the difference is that social insects have gone through a much longer “evolutionary trial and error to hone sustainable cultures” than humans. They ask: “Can human[s] learn something about sustainability from insect farmers?” (sect. 5.1, para. 3).
Here, in the light of the work by Bettencourt, West, and their colleagues (Bettencourt & West Reference Bettencourt and West2010; Bettencourt et al. Reference Bettencourt, Lobo, Helbing, Kuhnert and West2007), I discuss the difference in the economies scaling laws between humans and ants, which may be the fundamental reason for the different sustainable cultures in these species, in addition to what G&K suggest. Bettencourt et al. (Reference Bettencourt, Lobo, Helbing, Kuhnert and West2007) show that, besides the infrastructure properties that scale with the population size in the same way as in ant colonies, human society also has a suite of unique properties “reflecting wealth creation and innovation” (p. 7301), which have no counterpart in ant society. These properties, such as wages, rate of new patents, and bank deposits, scale superlinearly with the population size; that is, in contrast to the infrastructure properties, the unique human properties are associated with higher per capita values in larger populations (increasing return).
The growth (expansion) of an ant colony is driven by the colonial energy usage rate (efficiency driven) with sublinear scaling, whereas the expansion of a human society is probably, as suggested by Bettencourt et al., driven by innovation and wealth creation, which scale superlinearly. Theoretical models predict that driving forces with different scaling powers will generate sharply different growth patterns. Supporting the theory, the data of ant colonies show sigmoidal growth curves; that is, the growth eventually levels off (Hou et al. Reference Hou, Kaspari, Vander Zanden and Gillooly2010). In contrast, the superlinear scaling in a human society inevitably results in unbounded growth (Bettencourt et al. Reference Bettencourt, Lobo, Helbing, Kuhnert and West2007), which is obviously unsustainable.
How to solve the dilemma imposed by a desirable increasing of wealth and the unsustainable consequences of unbounded growth? Perhaps G&K are right: “Solving the daunting problems we face requires structural changes in the human economy, not merely changing individual values” (sect. 6, para. 7).
Comparing the ultrasociality of humans and ants, Gowdy & Krall (G&K) argue that ants and humans “face similar problems,” and “similar patterns of economic organization emerge through similar selection pressures” (sect. 1, para. 1). As the results of the “convergent selection” (sect. 1, para. 1), both ultrasocieties capture an advantage of the division of labor and increasing returns to larger scale and larger group size. Complementary to G&K's qualitative arguments, here I give a few quantitative considerations and discuss the similarity and difference between ant and human ultrasocieties from the viewpoint of scaling laws.
It has been found recently that the metabolic rate (energy usage rate) of an ant colony is significantly lower than the sum of individual energy usages, and scales sublinearly with colony size (Cao & Dornhaus Reference Cao and Dornhaus2013; Hou et al. Reference Hou, Kaspari, Vander Zanden and Gillooly2010; Shik et al. Reference Shik, Hou, Kay, Kasari and Gillooly2012; Waters et al. Reference Waters, Holbrook, Fewell and Harrison2010), indicating that per capita, a worker requires less energy to function in a larger colony. Similarly, properties of a human society that account for infrastructure, such as total road surface and the length of electrical cables, also scale sublinearly with population size (Bettencourt & West Reference Bettencourt and West2010; Bettencourt et al. Reference Bettencourt, Lobo, Helbing, Kuhnert and West2007). The similar economies of scaling in both ant and human societies reflect, as G&K point out for ants, that a larger group size is more energetically efficient.
The origin of the sublinear scaling is unclear. Here I hypothesize that individual variation gives rise to the nonlinearity of group energetics. Social inequality is believed to be closely associated with the transition to agriculture (Price Reference Price, Price and Feinman1995). Let us consider a group with p classes, each class with n i members, where subscript i denotes the class. The total population of the group is: N=∑ i=1 p n i . Assuming that each member in class i acquires (or consumes) an amount of energy, E i , then the total energy usage of the group is: E=∑ i=1 p n i × E i . It is straightforward to see that if energy is evenly distributed across the classes, that is, E i is a constant for all of the classes, then the group energy usage will be linearly proportional to the group size, that is, E=E i ×∑ i=1 p n i =E i × N. The sublinear scale will emerge only if the fraction of the class that acquires more energy decreases when the whole group size increases. In other words, when the group size increases, relatively fewer individuals consume a lot, and more consume a little.
I need to clarify that the division of labor may not be the only cause of inequality. In fact, as mentioned by G&K and observed by Waters et al. (Reference Waters, Holbrook, Fewell and Harrison2010), the number of ant caste members may stay as a constant fraction, when colony size gets larger. However, ultrasocial living, such as managing crop production, requires a network of social interaction, and the inequality may originate from the heterogeneity in the activity level of individuals in the network; for example, few members are highly active and have more interactions with others, and most are inactive, as seen in ants (Pinter-Wollman et al. Reference Pinter-Wollman, Wollman, Guetz, Holmes and Gordon2011). Needless to say, the active individuals consume more energy. I hypothesize that this activity heterogeneity is the consequence of the trade-off between two evolutionary optimization rules. First, the speed of information flow is maximized in the network, which would require most individuals to be highly interactive, but this would also result in high group energy expenditure. Second, the group energy expenditure is minimized, which would require most individuals to be inactive, but this would also result in a slow information speed. If only one of these rules were applied, linearity between energy expenditure and group size would be observed, because the variation among individuals would be the minimal (individuals are either all active or all inactive). It remains to be revealed how exactly the transition to agriculture plays a role in these optimization rules.
In the last two sections of the target article, G&K discuss the expansionary nature of the ultrasocial society and compare the sustainability of ant and human societies as the consequence of the expansion. They argue that as it expands, human ultrasociality faces collapse due to the exhaustion of resources (among other negative factors), whereas ant ultrasocialities have achieved sustainability. G&K believe that the reason for the difference is that social insects have gone through a much longer “evolutionary trial and error to hone sustainable cultures” than humans. They ask: “Can human[s] learn something about sustainability from insect farmers?” (sect. 5.1, para. 3).
Here, in the light of the work by Bettencourt, West, and their colleagues (Bettencourt & West Reference Bettencourt and West2010; Bettencourt et al. Reference Bettencourt, Lobo, Helbing, Kuhnert and West2007), I discuss the difference in the economies scaling laws between humans and ants, which may be the fundamental reason for the different sustainable cultures in these species, in addition to what G&K suggest. Bettencourt et al. (Reference Bettencourt, Lobo, Helbing, Kuhnert and West2007) show that, besides the infrastructure properties that scale with the population size in the same way as in ant colonies, human society also has a suite of unique properties “reflecting wealth creation and innovation” (p. 7301), which have no counterpart in ant society. These properties, such as wages, rate of new patents, and bank deposits, scale superlinearly with the population size; that is, in contrast to the infrastructure properties, the unique human properties are associated with higher per capita values in larger populations (increasing return).
The growth (expansion) of an ant colony is driven by the colonial energy usage rate (efficiency driven) with sublinear scaling, whereas the expansion of a human society is probably, as suggested by Bettencourt et al., driven by innovation and wealth creation, which scale superlinearly. Theoretical models predict that driving forces with different scaling powers will generate sharply different growth patterns. Supporting the theory, the data of ant colonies show sigmoidal growth curves; that is, the growth eventually levels off (Hou et al. Reference Hou, Kaspari, Vander Zanden and Gillooly2010). In contrast, the superlinear scaling in a human society inevitably results in unbounded growth (Bettencourt et al. Reference Bettencourt, Lobo, Helbing, Kuhnert and West2007), which is obviously unsustainable.
How to solve the dilemma imposed by a desirable increasing of wealth and the unsustainable consequences of unbounded growth? Perhaps G&K are right: “Solving the daunting problems we face requires structural changes in the human economy, not merely changing individual values” (sect. 6, para. 7).