Ant Foraging Dynamics Explorer

Trail noise & recruitment linearity — two mechanisms for collective decision-making flexibility

Real ant colonies must balance commitment with adaptability. Both tabs explore the same question from different angles: how do colonies tune between decisive winner-take-all allocation and flexible proportional tracking of a changing environment? In Tab ①, individual noise in trail-following acts like a stochastic temperature — too little and the colony locks in; just right and it can escape a bad attractor; too much and it wanders randomly (Dussutour et al., 2009). In Tab ②, the shape of the recruitment function (linear vs. nonlinear) determines whether strong attractors exist at all (Shaffer et al., 2013) — analogous to adjusting the temperature divider in softmax. Both mechanisms can be understood as collective Boltzmann thermostats.

Species Preset

Both Pheidole megacephala and Lasius niger establish coherent trails to food sources, but they differ in persistence and the ability to track changes in food availability. Use these presets to explore differences in trailing mechanisms and performance.

Y-Maze — ant colony PAUSED

Branch B — short (superior)

Branch A — long (inferior)

Blocked

…

Allocation history t = 0 min

B (short) — actual

target (ideal)

Pheromone concentrations (τ) τ_A & τ_B — raw SDE state

τ_A (long)

τ_B (short)

Individual Ant Decision Rule

① Sense

At the fork, the ant contacts pheromone on each branch via chemoreception.

P_B = (k+τ_B)^α Σ_i(k+τ_i)^α

② Choose

She samples stochastically: stronger trails are more attractive, amplified nonlinearly by α.

③ Deposit

Returning with food (orange), she lays q pheromone per step, reinforcing the trail for nestmates.

Pheromone Dynamics — SDE Model (Dussutour et al. 2009, Eq. 3.4)

dc_i = [ p_i · q_i · f(t) − ρ · c_i ] dt + σ dW_i

p_i ≜ (k + c_i)^α / Σ_j(k + c_j)^α

c_ipheromone trail strength on branch i — built up by returning ants, eroded by evaporation

p_ichoice probability — Hill function; nonlinearity α amplifies small pheromone differences

q_ideposit rate per return trip (q_B > q_A encodes feeder quality)

f(t)effective colony flow — f_blk when B is blocked; low (Pheidole) keeps A weak, high (Lasius) lets A build

kspontaneous baseline — inverse-temperature-like; higher k → more uniform exploration

σ dWItô white noise — drives stochastic resonance; optimal σ enables escape from the A-attractor

Species Preset

Parameters

σ 1.5

Trail-following noise (Itô SDE amplitude). σ≈0: deterministic, gets locked in (Lasius). σ≈3: Pheidole — optimal noise for tracking. σ≫3: random walk, trails dissolve. Tracking MI peaks at the resonance.

α 2.0

Pheromone nonlinearity exponent. Higher α → more decisive winner-take-all. α=2 fits L. niger.

ρ 0.015

Pheromone evaporation rate (min⁻¹). Higher ρ → faster forgetting, more flexible but less stable. Default tuned for convergence in ~60 sim-min.

Feeder Quality & Trail Persistence

q_B/q_A 1.44×

Quality ratio: deposit rate of B (short) vs A (long). Paper default ≈ 1.44.

f_blk 0.50

Recruiter flow when B is blocked (fraction of normal F). Low → Pheidole-like: colony quickly stops recruiting to a lost feeder, so A barely builds. High → Lasius-like: ants persist on established trail, A pheromone builds strongly → locked in.

Simulation

speed 1.5×

Phase duration (min) 60

Continuous cycling

When on, phases repeat indefinitely — useful for observing stochastic resonance over many switching events.

3-Phase: B open → B blocked → B restored. Replicates Dussutour et al. 2009.

Statistics

% on B (short)

—

% on A (long)

—

τ Branch B

—

τ Branch A

—

Consensus |p_B − p_A|

split (0)committed (1)

Tracking MI — I(feeder ; majority on B)

random (0)perfect tracking (1)

Forager Allocation — 5 Feeders proportional

Allocation share — solid = actual · dashed outline = proportional reference (α=1)

The Formula

p_i = (k+q_i)^α / Σ_j(k+q_j)^α

q_ifeeder quality — the input driving allocation

αnonlinearity exponent — identical role to inverse temperature β in softmax

kspontaneous baseline — compresses quality differences; k=0 gives a pure power law

Recruitment Nonlinearity

α 1.0

LTAequalproportionalWTA

Feeder Qualities

Drag to set quality q_i of each feeder. The proportional reference (dashed bar) always shows where α=1 would put each feeder.

Current Regime

—

Spontaneous Baseline

k 1.0

Added to each quality before raising to α. At k=0 the formula is a pure power law q_i^α. Higher k compresses quality differences toward equal allocation.

The Graph — p_i vs q_i

Two-option experiment: p_i = (k+q_i)^α / [(k+q_i)^α + (k+q_B)^α], q_B=2.5 fixed. Solid = current α. Dashed = α ∈ {−2, 0, 1, 2, 5, 10}. All curves cross P=0.5 at q_i=q_B (vertical dashed line). Changing k shifts the whole family; changing α moves only the solid curve.

Recruitment Mechanisms & Linearity

Waggle Dance

Proportional

A scout performs a figure-8 dance; the waggle run encodes food direction and distance. Each dance bout recruits roughly the same number of followers — no feedback between the number already foraging and the recruitment rate (linear recruitment).

Tandem Running

Proportional

An informed ant leads a single naive follower who maintains antennal contact from behind. Strictly 1-to-1: one leader can only guide one follower per run. Recruitment scales directly with the number of leaders — no amplification (linear recruitment).

Trail Laying

Nonlinear

Returning foragers deposit pheromone; more foragers → stronger trail → yet more followers. This positive feedback between trail strength and follower count is what the Hill function with α>1 models — recruitment is amplified, not just proportional.