Evolution & Superorganism Genetics

Sisters (single-mated queen)

A haploid father contributes his entire genome to every daughter. Therefore all sisters share 100% of their paternal genes. From the mother (diploid), each daughter inherits a random half. The overall relatedness between full sisters:

\[ r_{\text{sisters}} = \frac{1}{2}\underbrace{(1)}_{\text{paternal}} + \frac{1}{2}\underbrace{\left(\frac{1}{2}\right)}_{\text{maternal}} = \frac{3}{4} \]

This \(r = 3/4\) exceeds the mother-daughter relatedness of \(r = 1/2\), creating a genetic incentive for workers to raise sisters rather than produce their own daughters.

Hamilton's Rule

\[ r \cdot B > C \]

where \(r\) is the coefficient of relatedness between actor and recipient,\(B\) is the fitness benefit to the recipient, and \(C\) is the fitness cost to the actor.

Inclusive Fitness Derivation

Consider a worker ant that can either (a) reproduce directly, producing offspring with relatedness \(r_{\text{off}} = 1/2\), or (b) help the queen produce sisters with relatedness \(r_{\text{sis}} = 3/4\). The inclusive fitness of helping:

\[ W_{\text{help}} = r_{\text{sis}} \cdot n_{\text{extra sisters}} = \frac{3}{4} \cdot n_s \]

The inclusive fitness of reproducing:

\[ W_{\text{repro}} = r_{\text{off}} \cdot n_{\text{offspring}} = \frac{1}{2} \cdot n_o \]

Helping is favored when \(W_{\text{help}} > W_{\text{repro}}\), i.e., when:

\[ \frac{n_s}{n_o} > \frac{r_{\text{off}}}{r_{\text{sis}}} = \frac{1/2}{3/4} = \frac{2}{3} \]

So helping is favored even when a worker can raise only 2/3 as many siblings as she could produce offspring. This threshold is lower than the diploid value of 1, making eusociality easier to evolve under haplodiploidy.

Optimal Fission Ratio

Let the mother colony have \(N\) workers. After fission, one daughter colony retains the old queen with \(fN\) workers, while the other gets a new queen with \((1-f)N\) workers, where \(f\) is the fission ratio. Colony growth follows a logistic model:

\[ \frac{dN}{dt} = r N \left(1 - \frac{N}{K}\right) \]

The fitness of the mother colony (measured as total reproductive output over time) depends on how quickly each daughter colony reaches the fission threshold \(N^*\). The time to reach \(N^*\) from initial size \(N_0\):

\[ T(N_0) = \frac{1}{r} \ln\!\left(\frac{N^*(K - N_0)}{N_0(K - N^*)}\right) \]

The optimal fission ratio maximizes the rate of colony production:

\[ \frac{d}{df}\left[\frac{2}{T(fN^*) + T((1-f)N^*)}\right] = 0 \]

Symmetry arguments show that \(f^* = 1/2\) is optimal for equal split, but empirical observations show asymmetric fission (\(f \approx 0.6{-}0.7\)) because the old queen has higher survival probability and can restart reproduction immediately without a mating delay.

Invasion Dynamics: Population Genetics

The founder effect during colonization reduces genetic diversity at recognition loci. Let \(n_a\) be the number of CHC recognition alleles in the native population and \(n_f\) the number in the founding population. The probability that two randomly chosen individuals share the same recognition profile:

\[ P_{\text{match}} = \sum_{i=1}^{n} p_i^2 \]

In the native range with \(n_a \gg 1\) equally frequent alleles:\(P_{\text{match}} \approx 1/n_a\). After a bottleneck reducing to\(n_f\) alleles:

\[ P_{\text{match}}^{\text{invaded}} \approx \frac{1}{n_f} \gg \frac{1}{n_a} = P_{\text{match}}^{\text{native}} \]

When \(P_{\text{match}}\) exceeds a critical threshold \(P_c\), nestmate discrimination fails and colonies merge into supercolonies. Tsutsui et al. (2000) showed that introduced populations have ~50% fewer microsatellite alleles than native populations.

The spread of a supercolony can be modeled as a Fisher-KPP reaction-diffusion wave:

\[ \frac{\partial u}{\partial t} = D \frac{\partial^2 u}{\partial x^2} + r u (1 - u) \]

where \(u(x,t)\) is the Argentine ant density (normalized),\(D\) is the diffusion coefficient (~0.1 km\(^2\)/year from budding dispersal), and \(r\) is the intrinsic growth rate (~2/year). The wave speed:

\[ c^* = 2\sqrt{Dr} \approx 2\sqrt{0.1 \times 2} \approx 0.9 \text{ km/year} \]

However, long-distance jump dispersal (via human transport) greatly accelerates spread. The effective wave speed is better modeled by an integrodifference equation with a fat-tailed dispersal kernel, giving rates of 10–100 km/year in practice.

Ants possess the largest known odorant receptor (OR) gene family in insects: over 400 OR genes in some species (vs. ~60 in Drosophila, ~170 in honeybees). This expansion reflects the central role of chemical communication in ant societies:

• 9-exon OR subfamily: Massively expanded in ants (~350 genes). These receptors detect cuticular hydrocarbons used for nestmate recognition, caste identification, and task allocation.
• Functional implications: McKenzie et al. (2016) showed that disrupting the OR co-receptor orco in Harpegnathos saltatorabolishes social behavior: mutant ants cannot follow trails, recognize nestmates, or respond to alarm pheromones.

DNA Methylation

Ant genomes have functional DNA methyltransferases (DNMT1, DNMT3). Differentially methylated regions (DMRs) between queens and workers affect:

• Alternative splicing of caste-biased genes
• Expression of insulin/TOR signaling pathway genes
• Juvenile hormone (JH) biosynthesis genes
• Vitellogenin (yolk protein) expression

\[ \text{JH titer} \xrightarrow{\text{high}} \text{Queen development} \qquad \text{JH titer} \xrightarrow{\text{low}} \text{Worker development} \]

Molecular Basis of Queen Longevity

• Telomere maintenance: Queens maintain telomere length throughout life (no shortening), while worker telomeres shorten normally. Queens upregulate telomerase reverse transcriptase (TERT) expression.
• Insulin signaling modification: In most organisms, reduced insulin signaling extends lifespan but reduces fecundity (the canonical aging tradeoff). Ant queens decouple this: they have high fecundity with modified insulin signaling that maintains somatic repair.
• Oxidative stress response: Queens upregulate superoxide dismutase (SOD) and catalase, providing enhanced protection against reactive oxygen species (ROS). The rate of aging can be modeled as:\[ \frac{d(\text{damage})}{dt} = k_{\text{ROS}} \cdot [\text{ROS}] - k_{\text{repair}} \cdot [\text{SOD}] \]Queens have higher \(k_{\text{repair}}\) and lower effective\(k_{\text{ROS}}\) due to protected nest environments.