Information-based fitness & criticality

Research summary

One paper, summarised for reference. Information-based fitness and the emergence of criticality in living systems — Jorge Hidalgo, Jacopo Grilli, Samir Suweis, Miguel A. Muñoz, Jayanth R. Banavar & Amos Maritan, PNAS (2014) 111(28), 10095. doi:10.1073/pnas.1319166111.

The question

Empirically, many living systems look near-critical, but why would evolution or adaptation drive them there? Unlike mechanistic self-organized criticality (which applies to inanimate systems), this paper gives an adaptive/evolutionary answer: criticality is the functional optimum for a system that must build compact internal representations of a complex, variable, heterogeneous environment — the best possible compromise between accuracy and flexibility.

The framework

A living system carries an internal distribution $P_{\text{int}}(s\mid\beta)$ that tries to represent an environmental source $P_{\text{src}}(s\mid\alpha)$; the quality of the representation is the Kullback–Leibler divergence $D(\alpha\mid\beta)=\sum_s P_{\text{src}}\log(P_{\text{src}}/P_{\text{int}})$, and fitness decreases with the mean KL divergence across the sources an agent must cope with. The key analytical result: for two agents with nearby parameters,

$$D(\beta_A+\delta\beta\mid\beta_A) - D(\beta_A\mid\beta_A+\delta\beta) \approx \tfrac{1}{6}\,\nabla\chi(\beta_A)\,\delta\beta^3,$$

where $\chi$ is the generalized susceptibility = Fisher information. The agent with the larger $\chi$ has the smaller KL divergence — it is fitter. Since $\chi$ peaks at the critical point, the fittest agent sits at criticality: the region of maximal variability, where a small parameter change can account for many different complex sources (echoing Mastromatteo–Marsili on the extra distinguishable outputs of near-critical models).

Two models

• Coevolutionary. Each agent’s environment is the rest of the community — pairs compete, the lower-KL agent reproduces, the other dies. From any start (ordered, disordered, or broad), the community converges robustly to a unique steady state peaked exactly at the Fisher-information peak, i.e. a shared “collective language” that is critical.
• Evolutionary. Agents face $S$ external sources drawn from a pool $\rho_{\text{src}}(\alpha)$. A homogeneous environment yields specialised, non-critical internal states; a sufficiently heterogeneous one drives the population near criticality (less precisely than the coevolutionary case). This is not an artifact of a critical environment — even non-Zipfian heterogeneous environments give the same result.

Why it’s collected here

This is the theoretical backbone for why a collective would evolve toward criticality, and it is cited throughout the rest of this list. Two things make it load-bearing for us: it is Fisher-information-centred (the same quantity Crosato and Chen–Prokopenko use, and a criticality probe we could adopt), and it is the claim Klamser & Romanczuk directly refute — their spatial predator–prey model shows individual-level selection driving the group away from criticality (a social dilemma), precisely where Hidalgo et al.’s non-spatial, mutual-representation setup drives it toward criticality. Holding the two side by side sharpens exactly what our own two-scale, spatial, non-mutual-representation setting is and isn’t.

References

Hidalgo et al. (2014), PNAS 111, 10095 · Mora & Bialek (2011), J. Stat. Phys. 144, 268 · Mastromatteo & Marsili (2011), J. Stat. Mech. P10012 · Kauffman (1993), The Origins of Order · Kinouchi & Copelli (2006), Nat. Phys. 2, 348 · Schwab, Nemenman & Mehta (2014), Phys. Rev. Lett. 113, 068102 · Goudarzi et al. (2012), Phys. Rev. Lett. 108, 128702 · Klamser & Romanczuk (2021), PLoS Comput. Biol. 17, e1008832.