Active Inference: Courtship vs Survival

Courting to survive, and to learn: an active-inference reading of the courtship–survival trade-off

A classic life-history problem asks how an organism with a finite life should divide effort between surviving and reproducing. My earlier mathematical model of courtship versus survival [1] solved a two-year version by maximizing lifetime fitness over mating effort m, giving the optimal effort. So the key idea is invest hard now when survival is poor or mates are abundant now; conserve when the future is bright. 

Natural selection shapes organisms whose internal models encode adaptive prior preferences. Expected free energy minimization therefore provides a mechanistic process theory for achieving fitness rather than replacing evolutionary theory. Hence, I recast the same problem as active inference i.e. action selection by minimization of expected free energy (EFE) and show two things. First, the classic optimum is recovered almost exactly as the pragmatic (preference-satisfying) limit of EFE minimization, so nothing is lost. Second, active inference adds a term the optimizer [1] did not express: when mate availability is uncertain (rather than a known constant f), courtship, and more specifically, mate assessment, acquires epistemic value, and the agent engages in mate sampling i.e. prospecting to learn how good the mating market is before committing costly, risky courtship. 

In other words, the original optimization [1] assumes mate availability is known. Active inference instead treats it as a hidden state whose uncertainty naturally generates information-seeking behaviour without adding an extra objective.

All results are produced with SPM’s variational message passing (spm_MDP_VB_X).

1. The trade-off and its optimal solution

Consider a two-year life. In year 1 the organism allocates a fraction m ∈ [0,1] of its time to courtship and the rest to foraging. Courtship yields m·f₁ matings now but reduces survival to year 2, modelled as s = 1 − m²; a survivor then obtains f₂ matings. With a maximum survival probability Smax, expected lifetime reproductive success is

W(m) = m·f₁ + Smax·(1 − m²)·f₂

Because d²W/dm² = −2·Smax·f₂ < 0, W is concave and its unique interior stationary point maximizes it:

m* = min( f₁ / (2·Smax·f₂), 1 )

The optimum rises as Smax falls (a doomed animal should breed now i.e. terminal investment) or as f₁ grows, and falls as f₂ grows (bank on the future).

2. The same problem as active inference

An active-inference agent does not maximize an external fitness function; it holds a generative model of its world and selects the policy π that minimizes expected free energy,

G(π) = − E_Q[ ln P(o | C) ]         (pragmatic: expected prior preference)
       + E_Q[ H[P(o | s)] ] terms   (epistemic: expected information gain).

I build a partially-observable Markov decision process (POMDP) whose pragmatic term reproduces W, then relax an assumption to expose the epistemic term.

2.1 Generative model (core)

• Hidden states. Viability {alive, dead} (dead absorbing) and a courtship factor whose controllable transitions set the enacted effort level.

• Effort as a policy. The agent enacts one of K discrete effort levels e_k ∈ [0,1]; it infers which level minimizes G rather than solving calculus.

• Survival in the transitions. From alive, P(stay alive | e) = Smax·(1−e²) i.e. the survival cost s = 1−m² and Smax live in the transition matrix B.

• Fitness weights as preferences. A mating outcome carries log-preference cMate; a future / survival outcome carries cFuture. With P(mated | e) = e, the expected preference of effort e is

  V(e) = e·cMate + Smax·(1 − e²)·cFuture ,     e* = cMate / (2·Smax·cFuture),

  algebraically identical to m* under cMate ↔︎ f₁, cFuture ↔︎ f₂. The 2014 optimum [1] is the pragmatic limit of expected-free-energy minimization. 
  
  In active inference, agents possess prior preferences over outcomes rather than an explicit fitness function. Choosing logarithmic preferences proportional to expected reproductive success causes expected free energy minimization to recover the same optimal strategy.

2.2 Recovering the classic predictions

Solving the POMDP with spm_MDP_VB_X:

• Safe vs dangerous world (Fig. 1). With Smax = 1 the policy posterior peaks at e ≈ 0.5 (m* = 0.5); with Smax = 0.4 it collapses onto e → 1 i.e. terminal investment emerges as an inference, not an assumption.

Figure 1: effort posterior: safe vs dangerous world (terminal investment).

• Survival sweep (Fig. 2). The posterior-mean effort tracks m*(Smax) = min(f₁/(2·Smax·f₂),1) across Smax ∈ [0.3, 1].

Figure 2: active inference tracks m*(Smax). 

• Future-mates sweep (Fig. 3). Effort falls monotonically as f₂ rises, tracking m* i.e. the “bright future ⇒ conserve” prediction.

Figure 3: effort falls as future mate availability f₂ rises.

The active-inference curve lies slightly below the analytic one near the e = 1 boundary, reflecting (i) the bounded effort grid and (ii) the risk term in G, which makes the agent mildly risk-sensitive, a first thing the reframing adds over pure expected-value maximization. Unlike expected-value optimization, expected free energy penalizes uncertain outcomes, producing mildly conservative behaviour near decision boundaries.

3. What active inference adds: courting to learn

The 2014 model [1] assumes f₁, f₂ are known. Real animals rarely know how many receptive mates are around; assessing this is the ethological phenomenon of mate sampling. Active inference captures it for free through epistemic value.

I make the mating market a persistent hidden state {rich, poor} (rich markets rarer) and give the agent, alongside foraging and (risky) courtship, a cheap prospect action that returns a signal about the market but does not itself mate. Solving the two-decision (T = 3) model (Fig. 4):

Figure 4: uncertainty induces mate sampling; the drive is epistemic.

• When the market is known to be rich, the agent courts; when known poor, it forages. Neither needs to sample.
• When the market is unknown, the agent prospects first i.e. it courts (or forages) in year 2 only after learning the market in year 1.
• Crucially, prospecting is chosen only when it is informative (i.e. only when it is expected to reduce uncertainty about the mating market): with an identical prior but an uninformative prospect (signal precision zeta = 0), P(prospect) collapses from 1.00 to 0.17. The +0.83 difference is pure information gain i.e. the epistemic term the 2014 optimizer [1] does not represent.

Thus early courtship / assessment can be partly epistemic: organisms display and prospect not only to mate now but to estimate the reproductive market and allocate later effort accordingly. This is a qualitatively new, testable prediction (e.g. more sampling under greater market uncertainty), unavailable to a fitness optimizer [1] that takes f as given.

4. Discussion

Framing the courtship–survival trade-off as active inference is not merely a notational change. The active-inference formulation subsumes the classical optimizer as a limiting case while naturally extending it to partially observable environments. Rather than introducing separate objectives for fitness maximization and information gathering, both emerge from minimizing expected free energy. Classical life-history optimisation therefore appears as a special case of a more general inferential framework.

Active inference provides a generative-model interpretation of the original fitness function: Smax becomes a transition probability, f₁, f₂ become prior preferences, and the optimum becomes a belief about which policy minimizes expected surprise. It generalizes the account to uncertainty: the same machinery that recovers the optimum also predicts mate sampling, risk-sensitive hedging, and (with learnable A/B) experience-dependent tuning of effort, none of which the static optimizer [1] addresses.

The model is deliberately minimal and its parameters are illustrative levers, not data fits; the contribution is conceptual i.e. a demonstration that a canonical behavioural-ecology optimum is the pragmatic special case of a broader inferential principle, whose epistemic component turns “courtship versus survival” into “courtship to survive, and courtship to learn”.

Reference

[1] Pradeep D, (2014). "A mathematical model of courtship versus survival." 

https://blog.pradeepd.com/2014/11/mathematical-model-of-courtship-versus.html