Module 7

Symbiosis & Chemical Ecology

Fungus farming, aphid husbandry, ant-plant mutualisms, and zombie ant parasitism

Ants are the world's most prolific mutualists and farmers. Leaf-cutter ants invented agriculture approximately 60 million years ago — some 30 million years before humans. Ant-aphid farming, ant-plant defensive mutualisms, and the terrifying parasitic manipulation by Ophiocordyceps fungi all represent extremes of coevolution, driven by chemical signaling and precisely tuned cost-benefit calculations. In this module we derive the biophysics underlying these extraordinary relationships.

7.1 Fungus Farming (Leaf-Cutters)

The attine ants (tribe Attini), particularly the genera Atta and Acromyrmex, cultivate obligate fungal mutualists of the family Agaricaceae (primarily Leucoagaricus gongylophorus). This agricultural system evolved approximately 60 million years ago in South America and represents one of the most complex symbioses in nature, involving at least four organisms: the ant, the cultivated fungus, a parasitic fungus (Escovopsis), and antibiotic-producing bacteria (Pseudonocardia).

The Farming Pipeline

Leaf Cutting: Large workers (majors, head width ~4 mm) cut leaf fragments using mandibles that vibrate at ~1 kHz, creating a stridulatory signal that may stiffen the leaf via acoustic effects. Cutting force: ~50 mN.
Transport: Medias carry leaf fragments (often 10–50x their body mass) back to the nest along cleared trails spanning up to 250 m. Minim workers hitchhike on leaves to defend against parasitoid phorid flies.
Processing: Inside the nest, smaller workers chew leaves into a moist pulp, add fecal droplets containing enzymes, and incorporate the material into the fungus garden matrix.
Cultivation: The fungus grows on the leaf substrate, producing gongylidia — nutrient-rich hyphal swellings (50–100 \(\mu\)m diameter) that serve as the primary food source for the colony.
Harvesting: Workers selectively harvest gongylidia and feed them to larvae and the queen. Gongylidia contain lipids (40%), carbohydrates (30%), and proteins (20%) by dry weight.

Energetic Efficiency of Fungus Farming

The energetic efficiency of the leaf-cutter farming system can be derived by tracking energy flow through the pipeline. Let \(E_{\text{leaf}}\) be the energy content of harvested leaf material:

Energy Budget

\[ E_{\text{leaf}} \approx 18 \text{ kJ/g (dry weight, typical leaf)} \]

The fungal conversion efficiency (substrate to gongylidia biomass):

\[ \eta_{\text{fungus}} = \frac{m_{\text{gongylidia}} \cdot E_{\text{gong}}}{m_{\text{substrate}} \cdot E_{\text{leaf}}} \approx 0.10{-}0.15 \]

Including metabolic costs of the ants (cutting, transport, processing):

\[ \eta_{\text{total}} = \frac{E_{\text{gongylidia harvested}}}{E_{\text{leaf}} + E_{\text{ant metabolism}}} \]

\[ E_{\text{ant metabolism}} = N_{\text{workers}} \cdot \dot{E}_{\text{worker}} \cdot T_{\text{cycle}} \]

With a worker metabolic rate of \(\dot{E}_{\text{worker}} \approx 10\) mW and a processing cycle of ~24 hours, a mature Atta colony (5 million workers, with ~20% engaged in farming) processes ~200 kg of leaf material per year with an overall efficiency of \(\eta_{\text{total}} \approx 6{-}8\%\). This is comparable to modern human agriculture (5–10% for livestock).

Antibiotic Defense System

The fungus garden is vulnerable to the specialized parasite Escovopsis, a mycoparasitic fungus that can destroy gardens within days. The ants maintain a three-layer defense:

Weeding

Workers constantly patrol the garden, detecting and removing Escovopsishyphae mechanically. Detection is chemical: Escovopsis volatiles trigger grooming behavior at concentrations as low as 1 ppb.

Metapleural Gland

The metapleural gland (unique to ants) secretes phenylacetic acid and other antimicrobial compounds. Workers spread these over the garden substrate. Production rate: ~0.1 \(\mu\)L/day per worker.

Pseudonocardia Bacteria

Actinomycete bacteria (Pseudonocardia) grow on the ant cuticle in specialized crypts. They produce dentigerumycin and other antifungals that specifically target Escovopsis while sparing the cultivar.

7.2 Aphid Farming

Many ant species maintain mutualistic relationships with phloem-feeding hemipterans, particularly aphids. The ants protect aphids from predators (ladybird beetles, lacewing larvae, parasitoid wasps) and in return harvest honeydew — a sugar-rich excretion that constitutes a major energy source for the colony. This relationship has evolved independently in dozens of ant lineages, indicating strong selective advantages on both sides.

Honeydew Composition and Energetics

Aphid honeydew contains primarily sugars (sucrose, glucose, fructose, trehalose) at concentrations of 10–50% by weight, plus amino acids and lipids in trace amounts. A single aphid produces approximately 0.5–1.0 \(\mu\)L of honeydew per hour. The energy content per droplet:

\[ E_{\text{droplet}} = V \cdot \rho \cdot c_{\text{sugar}} \cdot \epsilon_{\text{sugar}} \]

\[ \approx 0.75 \,\mu\text{L} \times 1.1 \,\text{g/mL} \times 0.30 \times 16.7 \,\text{kJ/g} \approx 4.1 \,\text{mJ/droplet} \]

Chemical Manipulation

The mutualism is not entirely benign. Several ant species chemically manipulate their aphid “livestock” through compounds in their trail pheromone:

Wing suppression: The ant trail pheromone (containing \(\beta\)-farnesene, which mimics the aphid alarm pheromone) suppresses wing development in aphids, keeping them sessile and accessible. Wingless aphids produce 20–30% more honeydew than winged morphs.
Movement restriction: Some species (Lasius niger) clip aphid wings or apply chemical “tranquilizers” from the mandibular gland that reduce aphid walking speed by up to 50%.
Culling: Ants selectively consume aphids that are poor honeydew producers or that carry parasitoid eggs, effectively practicing artificial selection.

Cost-Benefit from Kin Selection Perspective

From the ant colony perspective, the investment in aphid tending must satisfy a cost-benefit condition. Let \(N_t\) be the number of tending workers,\(N_a\) the number of aphids, and \(\dot{E}_h\) the honeydew energy rate per aphid:

Mutualism Fitness Condition

\[ \underbrace{N_a \cdot \dot{E}_h \cdot \eta_{\text{harvest}}}_{\text{Benefit: energy from honeydew}} > \underbrace{N_t \cdot \dot{E}_{\text{forage}}}_{\text{Opportunity cost: lost foraging}} + \underbrace{N_t \cdot \dot{E}_{\text{defense}}}_{\text{Cost: predator defense}} \]

Dividing by \(N_t\) and defining the aphid-to-tender ratio\(R = N_a / N_t\):

\[ R > \frac{\dot{E}_{\text{forage}} + \dot{E}_{\text{defense}}}{\dot{E}_h \cdot \eta_{\text{harvest}}} \]

Empirical measurements show that profitable tending requires \(R > 5{-}10\)aphids per tender ant, consistent with observed ratios of 8–15 in Lasius niger colonies (Stadler & Dixon, 2005).

7.3 Myrmecophytes (Ant-Plant Mutualism)

Myrmecophytes are plants that have evolved specialized structures to house and feed ant colonies, receiving protection from herbivores in return. The best-studied system involves Cecropia trees and Azteca ants in the Neotropics, but similar mutualisms have evolved independently in over 100 plant genera across tropical ecosystems worldwide (e.g., Acacia-Pseudomyrmex in Central America, Macaranga-Crematogaster in Southeast Asia).

Plant Investment

Structural: Domatia

Hollow stems or swollen thorns providing nesting space. Cecropia internodes are hollow with thin internal septa that ants can penetrate. Construction cost: ~5% of stem biomass invested in cavity volume rather than structural wood.

Nutritional: Food Bodies

Müllerian bodies (Cecropia): glycogen-rich trichomes produced at the petiole base. Beltian bodies (Acacia): protein and lipid-rich leaflet tips. Pearl bodies: surface exudates on various myrmecophytes. Cost: 1–3% of total photosynthate.

Game-Theoretic Analysis: Nash Equilibrium

The ant-plant mutualism can be modeled as a two-player cooperative game. Let\(x\) be the plant's investment in ant rewards (food bodies + domatia volume) and \(y\) be the ant colony's investment in plant defense (worker allocation to patrolling). The fitness functions are:

Plant Fitness

\[ W_{\text{plant}}(x, y) = G(1 - x) \cdot \left[1 - H \cdot e^{-\lambda y}\right] \]

where \(G(1-x)\) is the growth rate with fraction \((1-x)\) of photosynthate retained, \(H\) is the herbivory damage rate without protection, and \(e^{-\lambda y}\) is the protection factor (exponentially decreasing herbivory with ant patrol effort).

Ant Colony Fitness

\[ W_{\text{ant}}(x, y) = F(x) \cdot (1 - y) + D(x) \]

where \(F(x)\) is the food reward (increasing in \(x\)),\((1 - y)\) is the fraction of workers available for colony growth, and\(D(x)\) is the domatia benefit.

Nash Equilibrium

At the Nash equilibrium, neither partner benefits from unilaterally changing its investment:

\[ \frac{\partial W_{\text{plant}}}{\partial x}\bigg|_{(x^*, y^*)} = 0 \quad \text{and} \quad \frac{\partial W_{\text{ant}}}{\partial y}\bigg|_{(x^*, y^*)} = 0 \]

For the plant: the marginal cost of providing rewards must equal the marginal benefit of additional defense:

\[ G'(1 - x^*) \cdot [1 - H e^{-\lambda y^*}] = G(1 - x^*) \cdot H \lambda \frac{\partial y^*}{\partial x} \cdot e^{-\lambda y^*} \]

Empirical data from Cecropia-Azteca systems show equilibrium values of \(x^* \approx 3{-}5\%\) (plant investment) and \(y^* \approx 20{-}30\%\)(ant defense allocation), consistent with model predictions (Fonseca 1994).

7.4 Ophiocordyceps: The Zombie Ant Fungus

Ophiocordyceps unilateralis sensu lato is a parasitic fungus that manipulates the behavior of its carpenter ant host (Camponotus spp.) in one of nature's most dramatic examples of extended phenotype manipulation. The fungal infection unfolds over 2–3 weeks and culminates in a precisely orchestrated “death grip” that positions the ant for optimal spore dispersal.

Infection Timeline

Day 0: Spore attachment — ascospore lands on ant cuticle, germinates, and penetrates via enzymatic degradation of chitin.
Days 1–14: Internal growth — fungal cells proliferate within the hemocoel, consuming ~40% of host soft tissue while carefully avoiding the brain and muscles. The ant continues normal colony behavior.
Day ~14: Behavioral manipulation — the fungus secretes compounds (including guanobutyric acid and sphingosine) that alter ant behavior. The infected ant leaves the canopy trail and descends to a specific height (25 ± 3 cm) above the forest floor — optimal for spore dispersal.
Day ~15: Death grip — at solar noon, the ant bites into a leaf vein on the north side of the leaf (in the Northern Hemisphere). The mandibular muscles are infiltrated by fungal cells that cause lockjaw. The ant dies within hours.
Days 15–25: Fruiting — the fungal stroma (stalk) erupts from the back of the ant's head, grows to 2–3 cm, and releases ascospores from a capsule at the tip.

Optimal Transmission Height: Spore Dispersal Physics

The fungus must position the ant at a height that maximizes spore dispersal to the forest floor where foraging ants walk. A spore released from height \(h\) with stalk length \(\ell\) experiences gravity and air drag:

Spore Trajectory

For a spherical spore of radius \(r_s \approx 5\) \(\mu\)m and density \(\rho_s \approx 1100\) kg/m\(^3\) in air, the terminal settling velocity is:

\[ v_t = \frac{2 r_s^2 (\rho_s - \rho_a) g}{9 \mu_a} \approx 3 \text{ mm/s} \]

With a horizontal wind velocity \(u(z)\) that follows a logarithmic boundary layer profile near the forest floor:

\[ u(z) = \frac{u_*}{\kappa} \ln\!\left(\frac{z}{z_0}\right) \]

where \(u_* \approx 0.05\) m/s is the friction velocity,\(\kappa = 0.41\) is the von Kármán constant, and\(z_0 \approx 0.01\) m is the roughness length. The horizontal dispersal distance for a spore released at height \(h + \ell\) is:

\[ x_{\text{disp}} = \int_0^{(h+\ell)/v_t} u(z(t))\, dt = \frac{u_*}{\kappa v_t} \int_0^{h+\ell} \ln\!\left(\frac{z}{z_0}\right) dz \]

Optimal Height for Infection

The probability of infecting an ant depends on: (1) the spore landing area\(\propto x_{\text{disp}}^2\) and (2) the spore concentration at ground level\(\propto 1/x_{\text{disp}}^2\). The infection probability per unit area is:

\[ P_{\text{inf}}(h) \propto \frac{N_{\text{spores}} \cdot A_{\text{ant}}}{\pi x_{\text{disp}}(h)^2} \cdot \rho_{\text{ant}}(0) \cdot \pi x_{\text{disp}}(h)^2 \]

This simplifies to \(P_{\text{inf}} \propto N_{\text{spores}} \cdot A_{\text{ant}} \cdot \rho_{\text{ant}}(0)\), which is independent of height! The height optimum arises from additional factors: humidity requirements (the fungus needs\(> 95\%\) RH for fruiting, which decreases with height) and temperature stability (less fluctuation near the ground). The observed 25 cm height represents the tradeoff between sufficient wind for dispersal and sufficient humidity for fruiting:

\[ h^* = \arg\max_h \left[ x_{\text{disp}}(h) \cdot P_{\text{fruit}}(h) \right] \]

\[ P_{\text{fruit}}(h) = e^{-h/h_{\text{humid}}} \quad \text{where } h_{\text{humid}} \approx 30 \text{ cm} \]

7.5 Leaf-Cutter Fungus Garden System

The diagram below illustrates the complete leaf-cutter ant farming system, from leaf cutting through fungal cultivation to waste management, including the antibiotic defense system.

7.6 Simulation: Fungus Garden Productivity & Spore Dispersal

This simulation models three aspects of ant symbiosis: (1) nutrient cycling in a leaf-cutter fungus garden, (2) spore dispersal physics for Ophiocordyceps, and (3) cost-benefit analysis of aphid farming.

Fungus Garden, Spore Dispersal & Aphid Farming

Python

script.py254 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

fig, axes = plt.subplots(2, 2, figsize=(16, 12))
fig.suptitle('Ant Symbiosis: Biophysics of Mutualism & Parasitism',
             fontsize=16, color='#fca5a5', fontweight='bold')

# ========== Panel 1: Fungus Garden Nutrient Cycling ==========
ax1 = axes[0, 0]

# Simulate fungus garden dynamics over 365 days
days = np.arange(0, 365)
leaf_input_rate = 0.5 + 0.3 * np.sin(2 * np.pi * days / 365)  # kg/day, seasonal

# Garden biomass dynamics
substrate = np.zeros(365)
fungus = np.zeros(365)
gongylidia = np.zeros(365)
waste = np.zeros(365)

substrate[0] = 5.0   # kg
fungus[0] = 2.0      # kg
gongylidia[0] = 0.5   # kg
waste[0] = 1.0       # kg

k_conversion = 0.12  # substrate to fungus
k_gong = 0.08        # fungus to gongylidia
k_harvest = 0.15     # gongylidia harvest rate
k_decay = 0.02       # fungus to waste
k_waste_removal = 0.05

for i in range(1, 365):
    ds = leaf_input_rate[i] - k_conversion * substrate[i-1]
    df = k_conversion * substrate[i-1] - k_gong * fungus[i-1] - k_decay * fungus[i-1]
    dg = k_gong * fungus[i-1] - k_harvest * gongylidia[i-1]
    dw = k_decay * fungus[i-1] + k_harvest * gongylidia[i-1] * 0.1 - k_waste_removal * waste[i-1]

substrate[i] = max(0, substrate[i-1] + ds)
    fungus[i] = max(0, fungus[i-1] + df)
    gongylidia[i] = max(0, gongylidia[i-1] + dg)
    waste[i] = max(0, waste[i-1] + dw)

ax1.plot(days, substrate, color='#22c55e', linewidth=2, label='Leaf substrate')
ax1.plot(days, fungus, color='#a855f7', linewidth=2, label='Fungal biomass')
ax1.plot(days, gongylidia, color='#fbbf24', linewidth=2, label='Gongylidia')
ax1.plot(days, waste, color='#6b7280', linewidth=1.5, linestyle='--', label='Waste')
ax1.fill_between(days, 0, leaf_input_rate * 10, alpha=0.1, color='#22c55e', label='Leaf input (scaled)')

ax1.set_xlabel('Day of Year', fontsize=11, color='white')
ax1.set_ylabel('Biomass (kg)', fontsize=11, color='white')
ax1.set_title('Fungus Garden Nutrient Cycling', fontsize=13, color='#fca5a5', fontweight='bold')
ax1.legend(fontsize=9, facecolor='#1a1a1a', edgecolor='#ef4444', labelcolor='white', loc='upper right')
ax1.set_facecolor('#0a0a0a')
ax1.tick_params(colors='white')
ax1.grid(True, alpha=0.15, color='white')

# ========== Panel 2: Ophiocordyceps Spore Dispersal ==========
ax2 = axes[0, 1]

heights = np.linspace(0.05, 1.5, 200)  # meters above ground
r_s = 5e-6       # spore radius (m)
rho_s = 1100     # spore density (kg/m3)
rho_a = 1.2      # air density
mu_a = 1.8e-5    # air viscosity (Pa*s)
g = 9.81

# Terminal velocity (Stokes)
v_t = 2 * r_s**2 * (rho_s - rho_a) * g / (9 * mu_a)

# Wind profile (log boundary layer)
u_star = 0.05    # friction velocity (m/s)
kappa = 0.41
z0 = 0.01        # roughness length (m)

# Dispersal distance vs height
def dispersal_distance(h):
    # Integrate u(z) * dz / v_t from z=0 to h
    # Integral of ln(z/z0) dz from z0 to h = h*ln(h/z0) - h + z0
    integral = h * np.log(h / z0) - h + z0
    return u_star / (kappa * v_t) * integral

x_disp = np.array([dispersal_distance(h) for h in heights])

# Humidity decay with height
h_humid = 0.30  # humidity scale height (m)
P_fruit = np.exp(-heights / h_humid)

# Infection probability (dispersal area * ant density * fruiting probability)
ant_density = 50  # ants per m2
P_inf = x_disp * P_fruit * ant_density

# Normalize
P_inf_norm = P_inf / P_inf.max()

ax2.plot(heights * 100, x_disp, color='#60a5fa', linewidth=2, label='Dispersal distance (m)')
ax2_twin = ax2.twinx()
ax2_twin.plot(heights * 100, P_fruit, color='#22c55e', linewidth=1.5, linestyle='--', label='Fruiting prob.')
ax2_twin.plot(heights * 100, P_inf_norm, color='#ef4444', linewidth=2.5, label='Infection score')
ax2_twin.set_ylabel('Probability / Score', fontsize=10, color='white')
ax2_twin.tick_params(colors='white')

# Mark optimal height
h_opt_idx = np.argmax(P_inf)
h_opt = heights[h_opt_idx]
ax2.axvline(h_opt * 100, color='#ef4444', linestyle=':', alpha=0.7)
ax2.text(h_opt * 100 + 3, x_disp.max() * 0.9,
         f'Optimal: {h_opt*100:.0f} cm', fontsize=10, color='#fca5a5')

# Observed range
ax2.axvspan(22, 28, alpha=0.2, color='#ef4444')
ax2.text(25, x_disp.max() * 0.1, 'Observed\nrange', ha='center', fontsize=9, color='#fca5a5')

ax2.set_xlabel('Height above ground (cm)', fontsize=11, color='white')
ax2.set_ylabel('Dispersal distance (m)', fontsize=11, color='#60a5fa')
ax2.set_title('Ophiocordyceps Spore Dispersal', fontsize=13, color='#fca5a5', fontweight='bold')
ax2.set_facecolor('#0a0a0a')
ax2.tick_params(colors='white')
ax2.grid(True, alpha=0.15, color='white')

lines1, labels1 = ax2.get_legend_handles_labels()
lines2, labels2 = ax2_twin.get_legend_handles_labels()
ax2.legend(lines1 + lines2, labels1 + labels2, fontsize=8, facecolor='#1a1a1a',
           edgecolor='#ef4444', labelcolor='white', loc='upper left')

# ========== Panel 3: Aphid Farming Cost-Benefit ==========
ax3 = axes[1, 0]

# Aphid-to-tender ratio
R = np.linspace(1, 30, 200)

# Energy rates
E_honeydew = 4.1e-3  # J per droplet
droplets_per_hour = 1.0
E_h = E_honeydew * droplets_per_hour  # J/hour per aphid
eta_harvest = 0.85

E_forage = 3.0e-3    # J/hour opportunity cost
E_defense = 1.0e-3   # J/hour defense cost

# Net benefit per tender ant
net_benefit = R * E_h * eta_harvest - (E_forage + E_defense)

# Breakeven ratio
R_breakeven = (E_forage + E_defense) / (E_h * eta_harvest)

ax3.plot(R, net_benefit * 1000, color='#ef4444', linewidth=2.5)
ax3.axhline(0, color='#6b7280', linewidth=1, linestyle='--')
ax3.axvline(R_breakeven, color='#fbbf24', linewidth=1.5, linestyle=':', alpha=0.8)
ax3.fill_between(R, net_benefit * 1000, 0, where=net_benefit > 0, alpha=0.15, color='#22c55e')
ax3.fill_between(R, net_benefit * 1000, 0, where=net_benefit < 0, alpha=0.15, color='#ef4444')

ax3.text(R_breakeven + 0.5, net_benefit.max() * 1000 * 0.8,
         f'Breakeven\nR = {R_breakeven:.1f}', fontsize=10, color='#fbbf24')
ax3.text(20, net_benefit.max() * 1000 * 0.5, 'Profitable\nregion', fontsize=11, color='#86efac', ha='center')
ax3.text(3, -0.5, 'Loss\nregion', fontsize=11, color='#fca5a5', ha='center')

# Observed range
ax3.axvspan(8, 15, alpha=0.15, color='#fbbf24')
ax3.text(11.5, net_benefit.max() * 1000 * 0.3, 'Observed\n(8-15)', fontsize=9, color='#fbbf24', ha='center')

ax3.set_xlabel('Aphids per Tender Ant (R)', fontsize=11, color='white')
ax3.set_ylabel('Net Benefit (mJ/hour per tender)', fontsize=11, color='white')
ax3.set_title('Aphid Farming Cost-Benefit', fontsize=13, color='#fca5a5', fontweight='bold')
ax3.set_facecolor('#0a0a0a')
ax3.tick_params(colors='white')
ax3.grid(True, alpha=0.15, color='white')

# ========== Panel 4: Ant-Plant Mutualism Game Theory ==========
ax4 = axes[1, 1]

# Plant investment (x) vs ant defense (y) Nash equilibrium
x_vals = np.linspace(0.001, 0.15, 100)
y_vals = np.linspace(0.001, 0.60, 100)
X, Y = np.meshgrid(x_vals, y_vals)

# Plant fitness: G(1-x) * (1 - H * exp(-lambda*y))
G0 = 1.0
H = 0.8
lam = 5.0

W_plant = G0 * (1 - X) * (1 - H * np.exp(-lam * Y))

# Ant fitness: F(x) * (1-y) + D(x)
F0 = 2.0
D0 = 0.5
W_ant = F0 * X * (1 - Y) + D0 * X

# Combined fitness (product, for visualization)
W_combined = W_plant * W_ant

# Plot as contour
contour = ax4.contourf(X * 100, Y * 100, W_combined, levels=20, cmap='inferno')
plt.colorbar(contour, ax=ax4, label='Combined fitness', shrink=0.8)

# Find Nash equilibrium (approximate)
# dW_plant/dx = 0: -G0*(1 - H*exp(-lam*y)) = 0 -> never zero, so boundary
# For ant: dW_ant/dy = -F0*x = 0 -> boundary at y=0
# Real Nash: mutual best response
# Plant BR: x that max W_plant given y -> x=0 (always, plant wants min x)
# Ant BR: y that max W_ant given x -> y=0 (always, ant wants min y)
# Cooperation maintained by conditionality (sanctions model)

# Mark cooperative equilibrium
x_star = 0.04
y_star = 0.25
ax4.plot(x_star * 100, y_star * 100, 'o', color='#ef4444', markersize=12, markeredgecolor='white', markeredgewidth=2)
ax4.annotate(f'Cooperative eq.\n(x*={x_star*100:.0f}%, y*={y_star*100:.0f}%)',
             xy=(x_star * 100, y_star * 100), xytext=(8, 45),
             fontsize=10, color='white', fontweight='bold',
             arrowprops=dict(arrowstyle='->', color='white', lw=1.5))

# Defection point
ax4.plot(0.5, 5, 's', color='#fbbf24', markersize=10, markeredgecolor='white', markeredgewidth=1.5)
ax4.annotate('Mutual\ndefection', xy=(0.5, 5), xytext=(5, 15),
             fontsize=9, color='#fbbf24',
             arrowprops=dict(arrowstyle='->', color='#fbbf24', lw=1))

ax4.set_xlabel('Plant Investment in Rewards (%)', fontsize=11, color='white')
ax4.set_ylabel('Ant Defense Allocation (%)', fontsize=11, color='white')
ax4.set_title('Ant-Plant Mutualism (Game Theory)', fontsize=13, color='#fca5a5', fontweight='bold')
ax4.set_facecolor('#0a0a0a')
ax4.tick_params(colors='white')

fig.patch.set_facecolor('#0a0a0a')
plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a0a')
plt.close()

print("=== Ant Symbiosis Biophysics Results ===")
print(f"\n--- Fungus Garden ---")
print(f"Steady-state substrate: {substrate[-1]:.2f} kg")
print(f"Steady-state fungal biomass: {fungus[-1]:.2f} kg")
print(f"Steady-state gongylidia: {gongylidia[-1]:.2f} kg")
print(f"Total leaf input (year): {np.trapezoid(leaf_input_rate, days):.1f} kg")
print(f"Overall conversion efficiency: {gongylidia[-1] * 25 / (substrate[-1] * 18) * 100:.1f}%")

print(f"\n--- Ophiocordyceps Spore Dispersal ---")
print(f"Spore terminal velocity: {v_t*1000:.2f} mm/s")
print(f"Optimal height for infection: {h_opt*100:.1f} cm")
print(f"Observed range: 22-28 cm")
print(f"Dispersal distance at optimal height: {x_disp[h_opt_idx]:.2f} m")

print(f"\n--- Aphid Farming ---")
print(f"Honeydew energy per droplet: {E_honeydew*1000:.1f} mJ")
print(f"Breakeven aphid/tender ratio: {R_breakeven:.1f}")
print(f"Observed ratio: 8-15 aphids per tender")
print(f"Net benefit at R=10: {(10 * E_h * eta_harvest - E_forage - E_defense)*1000:.2f} mJ/hr")

print(f"\n--- Ant-Plant Game Theory ---")
print(f"Cooperative equilibrium: x*={x_star*100:.0f}% plant, y*={y_star*100:.0f}% ant")
print(f"Combined fitness at equilibrium: {W_combined[25, 3]:.3f}")
print(f"Herbivory reduction at y*=25%: {(1 - H * np.exp(-lam * y_star))*100:.1f}%")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

5. Ant Pheromones & Flowers: An Evolutionary Arms Race

The interaction between ant pheromones and flowering plants reveals one of the most subtle evolutionary conflicts in nature. While ants exploit floral nectar as a food source, they are almost universally poor pollinators — lacking the body hair that carries pollen, and secreting metapleural gland antimicrobials that can inhibit pollen viability. The result is an arms race played out in chemistry.

5.1 Deterrence of Pollinators by Ant Pheromones

When ants walk on flowers, they deposit trail pheromones (pyrazines, fatty acid derivatives) and alarm pheromones on petal surfaces. Bees and other pollinators detect these residues and actively avoid ant-contaminated flowers. This has been quantified in controlled experiments:

Pollinator avoidance model

The probability that a bee visits a flower with ant pheromone concentration \(c\) follows an inhibitory Hill function:

\[ P_{visit}(c) = P_0 \cdot \frac{K_{i}^n}{K_{i}^n + c^n} \]

where \(P_0\) = baseline visitation probability (~0.85 per foraging trip),\(K_i\) = inhibition constant (concentration at 50% deterrence),\(n\) = Hill coefficient (steepness of avoidance response, typically \(n \approx 2\text{--}3\)).

Derivation: The bee olfactory system integrates ant-pheromone receptor activation over the flower surface. Each odorant receptor binding event follows:

\[ \text{OR} + \text{L} \underset{k_{off}}{\overset{k_{on}}{\rightleftharpoons}} \text{OR·L} \quad \implies \quad \theta = \frac{[L]}{K_d + [L]} \]

For cooperative binding across \(n\) receptor subunits (or \(n\) independent detection events required for behavioural threshold), the fractional occupancy becomes\(\theta = c^n/(K_d^n + c^n)\). The avoidance probability is \(1 - \theta\)times the baseline, giving the Hill inhibition model above.

Experimental data (Willmer & Stone, 2004): flowers visited by Formica ants showed a 50–75% reduction in bee visits within 30 minutes of ant contact. The effect persisted for 2–4 hours (matching pheromone half-life). See also our Bee Olfaction module for how bees detect these chemical traces via their 170 odorant receptors.

5.2 Floral Defense: Cheater Exclusion

Some plants have co-evolved to actively repel ants from their flowers. They secrete ant-repellent compounds from petals or stems near the flower — a phenomenon called cheater exclusion, because ants steal nectar without providing pollination.

Floral Repellent Chemistry

Lotus corniculatus: cyanogenic glycosides on stem below flower
Cytisus scoparius: alkaloid-rich trichomes on calyx
Acacia hindsii: extra-floral nectaries lure ants AWAY from flowers
Many Lamiaceae: terpenoids in glandular trichomes repel crawling insects

Evolutionary Cost-Benefit

The plant faces a trade-off: repellent compounds are metabolically costly to produce, but ant exclusion preserves nectar for legitimate pollinators.

\[ W_{plant} = B_{poll} \cdot P_{bee}(c_{ant}) - C_{repellent} - L_{nectar \, theft} \]

Optimal repellent investment maximises \(W_{plant}\) where\(B_{poll}\) = pollination benefit and \(L_{theft}\) = nectar loss to ants.

5.3 Metapleural Gland Secretions & Pollen Viability

A key reason ants are poor pollinators: their metapleural gland secretes antimicrobial compounds (phenylacetic acid, myrmicacin = \(\beta\)-hydroxydecanoic acid) that inhibit fungal and bacterial growth on the cuticle. These same compounds reduce pollen germination by 40–90%.

\[ G_{pollen}(c_m) = G_0 \cdot e^{-\alpha c_m} \]

where \(G_0\) = germination rate without ant contact (~85%),\(c_m\) = concentration of metapleural secretion on pollen surface,\(\alpha\) = inhibition coefficient (\(\approx 0.15\,\mu\text{g}^{-1}\)). The mechanism: myrmicacin disrupts the pollen tube cell membrane, preventing the Ca\(^{2+}\)gradient required for tip growth.

This is fundamentally why evolution has driven most angiosperms to chemically exclude ants from flowers: even if an ant transfers pollen physically, the pollen it carries is largely non-viable. Beaman et al. (2012) showed that pollen exposed to Lasius ant cuticle for >10 minutes had germination rates below 15% (vs 80% for control).

5.4 Myrmecochory: Ant-Dispersed Seeds

Despite the flower conflict, ants play a crucial positive role in seed dispersal (myrmecochory). Over 11,000 plant species (~5% of all angiosperms) produce seeds with elaiosomes — lipid-rich appendages that mimic insect prey and attract ants. The ant carries the seed to its nest, eats the elaiosome, and discards the seed in nutrient-rich nest refuse — an ideal germination site.

Elaiosome Chemistry

Elaiosomes contain 1,2-diacylglycerols and oleic acid (\(\text{C}_{18:1}\)) — the same lipids found in insect hemolymph. This chemical mimicry triggers the ant's prey-retrieval behaviour (Hughes et al., 1994). The deception is so effective that ants preferentially collect elaiosome-bearing seeds over plain seeds by a factor of 5–10x.

5.5 When Ants Do Pollinate: Rare Mutualisms

In a minority of cases — typically arid or tropical environments where flying pollinators are scarce — ants serve as effective pollinators:

Polygonum cascadense: small prostrate flowers in alpine habitat; ants are the primary pollinator
Microtis parviflora (orchid): wingless wasps and ants pollinate ground-level flowers
Euphorbia cyparissias: extrafloral nectaries attract ants that incidentally transfer pollen

These ant-pollinated flowers share common adaptations: small size, ground-level position, reduced petal area, reduced or absent nectar production (using pollen as the reward), and crucially — pollen that is resistant to metapleural gland secretions. Cross-reference with our Bee Vision & Navigation module for how bees use UV nectar guides and polarization compass to find flowers that ants cannot easily access.

Simulation: Ant–Flower–Pollinator Dynamics

Modelling pollinator deterrence by ant pheromones, pollen viability loss from metapleural secretions, plant fitness under different ant densities, and the optimal floral repellent investment.

Python

script.py147 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

fig, axes = plt.subplots(2, 2, figsize=(16, 14))
fig.patch.set_facecolor('#030712')
fig.suptitle("Ant-Flower-Pollinator Chemical Ecology", fontsize=16, color='white', fontweight='bold', y=0.98)

# ============================================================
# Panel 1: Pollinator deterrence by ant pheromone concentration
# ============================================================
ax1 = axes[0, 0]
ax1.set_facecolor('#1a0505')

c = np.linspace(0, 10, 200)  # pheromone concentration (arbitrary units)
P0 = 0.85  # baseline visitation probability
Ki_vals = [1.0, 2.0, 4.0, 8.0]
n_hill = 2.5
colors1 = ['#ef4444', '#fbbf24', '#34d399', '#60a5fa']

for Ki, col in zip(Ki_vals, colors1):
    P_visit = P0 * Ki**n_hill / (Ki**n_hill + c**n_hill)
    ax1.plot(c, P_visit * 100, color=col, linewidth=2.5, label=f'Ki = {Ki}')

ax1.axhline(P0 * 50, color='white', linewidth=1, linestyle=':', alpha=0.4)
ax1.text(9, P0 * 50 + 1, '50% deterrence', color='white', fontsize=9)
ax1.set_xlabel('Ant Pheromone Concentration (a.u.)', color='white', fontsize=12)
ax1.set_ylabel('Bee Visitation Probability (%)', color='white', fontsize=12)
ax1.set_title('Pollinator Deterrence by Ant Pheromones\n(Hill inhibition model)', color='#fca5a5', fontsize=13, fontweight='bold')
ax1.legend(fontsize=10, facecolor='#1a0505', edgecolor='#ef4444', labelcolor='white', title='Inhibition constant', title_fontsize=9)
ax1.tick_params(colors='white')
ax1.grid(True, alpha=0.15, color='#ef4444')
for sp in ax1.spines.values(): sp.set_color('#ef4444')
ax1.set_ylim(0, 95)

# ============================================================
# Panel 2: Pollen viability vs metapleural gland exposure
# ============================================================
ax2 = axes[0, 1]
ax2.set_facecolor('#1a0505')

exposure_time = np.linspace(0, 60, 200)  # minutes
G0 = 85  # baseline germination rate (%)
alpha_vals = [0.02, 0.05, 0.10, 0.15]
colors2 = ['#60a5fa', '#34d399', '#fbbf24', '#ef4444']

for alpha, col in zip(alpha_vals, colors2):
    G = G0 * np.exp(-alpha * exposure_time)
    ax2.plot(exposure_time, G, color=col, linewidth=2.5, label=f'alpha = {alpha}')

# Experimental data points (Beaman et al. 2012 approximate)
exp_time = [0, 5, 10, 20, 30, 60]
exp_germ = [85, 62, 38, 18, 12, 8]
ax2.scatter(exp_time, exp_germ, color='white', s=80, zorder=5, edgecolors='#ef4444', linewidth=1.5, label='Lasius (exp.)')

ax2.axhline(50, color='white', linewidth=1, linestyle=':', alpha=0.4)
ax2.text(55, 52, '50%', color='white', fontsize=9)
ax2.set_xlabel('Exposure Time to Ant Cuticle (min)', color='white', fontsize=12)
ax2.set_ylabel('Pollen Germination Rate (%)', color='white', fontsize=12)
ax2.set_title('Pollen Viability Loss from Metapleural Secretions\n(exponential inhibition model)', color='#fca5a5', fontsize=13, fontweight='bold')
ax2.legend(fontsize=9, facecolor='#1a0505', edgecolor='#ef4444', labelcolor='white')
ax2.tick_params(colors='white')
ax2.grid(True, alpha=0.15, color='#ef4444')
for sp in ax2.spines.values(): sp.set_color('#ef4444')

# ============================================================
# Panel 3: Plant fitness vs ant density
# ============================================================
ax3 = axes[1, 0]
ax3.set_facecolor('#1a0505')

ant_density = np.linspace(0, 50, 200)  # ants per flower per hour
# Bee visitation drops with ant density
P_bee = P0 * 4**n_hill / (4**n_hill + (ant_density * 0.2)**n_hill)
# Pollen viability drops
pollen_viab = G0 * np.exp(-0.05 * ant_density * 10 / 60) / 100
# Seed set = f(bee visits) * f(pollen viability)
seed_set = P_bee * pollen_viab * 100
# Nectar theft cost
nectar_loss = 1 - np.exp(-0.1 * ant_density)
# Net plant fitness
fitness_no_defense = seed_set * (1 - 0.3 * nectar_loss)
# With ant repellent
repellent_cost = 5  # % fitness cost
effective_ant = ant_density * 0.3  # repellent reduces effective ant density by 70%
P_bee_def = P0 * 4**n_hill / (4**n_hill + (effective_ant * 0.2)**n_hill)
pollen_viab_def = G0 * np.exp(-0.05 * effective_ant * 10 / 60) / 100
seed_set_def = P_bee_def * pollen_viab_def * 100
fitness_with_defense = seed_set_def * (1 - 0.3 * nectar_loss * 0.3) - repellent_cost

ax3.plot(ant_density, fitness_no_defense, color='#ef4444', linewidth=2.5, label='No floral defense')
ax3.plot(ant_density, fitness_with_defense, color='#34d399', linewidth=2.5, label='With ant repellent')
ax3.fill_between(ant_density, fitness_no_defense, fitness_with_defense,
                  where=fitness_with_defense > fitness_no_defense,
                  alpha=0.15, color='#34d399', label='Defense advantage')
ax3.set_xlabel('Ant Density (ants/flower/hour)', color='white', fontsize=12)
ax3.set_ylabel('Relative Plant Fitness (%)', color='white', fontsize=12)
ax3.set_title('Plant Fitness: Cheater Exclusion Pays Off\nat High Ant Density', color='#fca5a5', fontsize=13, fontweight='bold')
ax3.legend(fontsize=10, facecolor='#1a0505', edgecolor='#ef4444', labelcolor='white')
ax3.tick_params(colors='white')
ax3.grid(True, alpha=0.15, color='#ef4444')
for sp in ax3.spines.values(): sp.set_color('#ef4444')

# ============================================================
# Panel 4: Pheromone persistence on flowers over time
# ============================================================
ax4 = axes[1, 1]
ax4.set_facecolor('#1a0505')

t = np.linspace(0, 300, 200)  # minutes
pheromones = [
    ('Formic acid', 0.03, '#34d399'),       # fast decay
    ('4-Me-3-heptanone', 0.015, '#60a5fa'), # medium
    ('Trail pyrazine', 0.008, '#fbbf24'),    # slow
    ('Cuticular HC (C27)', 0.001, '#ef4444'),# very slow
]

for name, lam, col in pheromones:
    c_t = np.exp(-lam * t)
    ax4.plot(t, c_t * 100, color=col, linewidth=2.5, label=name)
    # Mark half-life
    t_half = np.log(2) / lam
    if t_half < 300:
        ax4.plot(t_half, 50, 'o', color=col, markersize=8, markeredgecolor='white', linewidth=0.8)

ax4.axhline(50, color='white', linewidth=1, linestyle=':', alpha=0.3)
ax4.axhline(10, color='white', linewidth=1, linestyle=':', alpha=0.3)
ax4.text(280, 52, '50%', color='white', fontsize=9)
ax4.text(280, 12, '10% (bee threshold)', color='white', fontsize=9)
ax4.set_xlabel('Time After Ant Visit (minutes)', color='white', fontsize=12)
ax4.set_ylabel('Pheromone Remaining (%)', color='white', fontsize=12)
ax4.set_title('Pheromone Persistence on Flower Surface\n(first-order decay)', color='#fca5a5', fontsize=13, fontweight='bold')
ax4.legend(fontsize=10, facecolor='#1a0505', edgecolor='#ef4444', labelcolor='white')
ax4.tick_params(colors='white')
ax4.grid(True, alpha=0.15, color='#ef4444')
for sp in ax4.spines.values(): sp.set_color('#ef4444')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#030712')
print("=== Ant-Flower-Pollinator Simulation ===")
print(f"Bee visitation at ant density 10/hr: {P0 * 4**n_hill / (4**n_hill + (10 * 0.2)**n_hill) * 100:.1f}%")
print(f"Pollen viability after 10 min ant contact: {G0 * np.exp(-0.10 * 10):.1f}%")
print(f"Formic acid half-life on petals: {np.log(2)/0.03:.1f} min")
print(f"Trail pyrazine half-life: {np.log(2)/0.008:.1f} min")
print(f"CHC (C27) half-life: {np.log(2)/0.001:.1f} min")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

6. Ecosystem Simulation: The Ant–Bee–Flower–Tree Arms Race

The chemical arms race between ants, bees, flowers, and trees is a complex multi-species coevolutionary dynamic. Below we simulate how ant pheromone deposition, bee avoidance, plant defense investment, and tree-ant mutualism interact over ecological and evolutionary time. The model tracks population dynamics, pollination efficiency, seed production, and fitness across all four players simultaneously.

Python

script.py270 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from matplotlib.gridspec import GridSpec

fig = plt.figure(figsize=(18, 20))
gs = GridSpec(3, 2, figure=fig, hspace=0.4, wspace=0.35)
fig.patch.set_facecolor('#030712')
fig.suptitle("Multi-Species Arms Race: Ants, Bees, Flowers & Trees", fontsize=18, color='white', fontweight='bold', y=0.98)

# ============================================================
# Panel 1: Coevolutionary dynamics over 200 generations
# ============================================================
ax1 = fig.add_subplot(gs[0, 0])
ax1.set_facecolor('#0a0505')

generations = 200
dt_gen = 1

# State variables (trait values, 0-1 scale)
ant_exploit = np.zeros(generations)      # ant nectar exploitation intensity
plant_defense = np.zeros(generations)    # plant chemical defense investment
bee_sensitivity = np.zeros(generations)  # bee sensitivity to ant pheromones
tree_mutualism = np.zeros(generations)   # tree-ant mutualism strength

# Initial conditions
ant_exploit[0] = 0.3
plant_defense[0] = 0.1
bee_sensitivity[0] = 0.5
tree_mutualism[0] = 0.2

np.random.seed(42)
for t in range(1, generations):
    # Ant exploitation increases when plant defense is low
    d_ant = 0.02 * (1 - plant_defense[t-1]) - 0.01 * ant_exploit[t-1] + 0.003 * np.random.randn()
    # Plant defense increases when ant exploitation is high
    d_plant = 0.015 * ant_exploit[t-1] - 0.008 * plant_defense[t-1] + 0.003 * np.random.randn()
    # Bee sensitivity increases with ant pheromone exposure (learning)
    d_bee = 0.01 * ant_exploit[t-1] - 0.005 * bee_sensitivity[t-1] + 0.002 * np.random.randn()
    # Tree mutualism strengthens when ant defense benefits exceed costs
    d_tree = 0.008 * (1 - plant_defense[t-1]) * ant_exploit[t-1] - 0.004 * tree_mutualism[t-1] + 0.002 * np.random.randn()

ant_exploit[t] = np.clip(ant_exploit[t-1] + d_ant, 0, 1)
    plant_defense[t] = np.clip(plant_defense[t-1] + d_plant, 0, 1)
    bee_sensitivity[t] = np.clip(bee_sensitivity[t-1] + d_bee, 0, 1)
    tree_mutualism[t] = np.clip(tree_mutualism[t-1] + d_tree, 0, 1)

gen = np.arange(generations)
ax1.plot(gen, ant_exploit * 100, color='#ef4444', linewidth=2.5, label='Ant exploitation')
ax1.plot(gen, plant_defense * 100, color='#4ade80', linewidth=2.5, label='Plant defense')
ax1.plot(gen, bee_sensitivity * 100, color='#fbbf24', linewidth=2.5, label='Bee sensitivity')
ax1.plot(gen, tree_mutualism * 100, color='#a78bfa', linewidth=2.5, label='Tree mutualism')
ax1.set_xlabel('Generations', color='white', fontsize=12)
ax1.set_ylabel('Trait Value (%)', color='white', fontsize=12)
ax1.set_title('Coevolutionary Arms Race Dynamics\n(Red Queen dynamics)', color='#fca5a5', fontsize=13, fontweight='bold')
ax1.legend(fontsize=10, facecolor='#1a0505', edgecolor='#ef4444', labelcolor='white')
ax1.tick_params(colors='white')
ax1.grid(True, alpha=0.15, color='#ef4444')
for sp in ax1.spines.values(): sp.set_color('#ef4444')

# ============================================================
# Panel 2: Pollination network efficiency
# ============================================================
ax2 = fig.add_subplot(gs[0, 1])
ax2.set_facecolor('#0a0505')

# Pollination efficiency depends on bee visits and pollen viability
poll_efficiency = (1 - bee_sensitivity * ant_exploit) * (1 - 0.5 * ant_exploit) * 100
# Seed production
seed_prod = poll_efficiency * (1 + 0.3 * plant_defense) * (1 - 0.1 * plant_defense)

ax2.plot(gen, poll_efficiency, color='#fbbf24', linewidth=2.5, label='Pollination efficiency')
ax2.plot(gen, seed_prod, color='#4ade80', linewidth=2.5, label='Seed production')
ax2.axhline(np.mean(poll_efficiency), color='#fbbf24', linestyle=':', alpha=0.5)
ax2.axhline(np.mean(seed_prod), color='#4ade80', linestyle=':', alpha=0.5)
ax2.fill_between(gen, poll_efficiency, seed_prod, alpha=0.1, color='#86efac',
                  where=seed_prod > poll_efficiency)
ax2.set_xlabel('Generations', color='white', fontsize=12)
ax2.set_ylabel('Efficiency / Production (%)', color='white', fontsize=12)
ax2.set_title('Pollination Efficiency & Seed Production\n(ecosystem-level outcomes)', color='#fca5a5', fontsize=13, fontweight='bold')
ax2.legend(fontsize=10, facecolor='#1a0505', edgecolor='#ef4444', labelcolor='white')
ax2.tick_params(colors='white')
ax2.grid(True, alpha=0.15, color='#ef4444')
for sp in ax2.spines.values(): sp.set_color('#ef4444')

# ============================================================
# Panel 3: Spatial foraging — ant vs bee territory
# ============================================================
ax3 = fig.add_subplot(gs[1, 0])
ax3.set_facecolor('#0a0505')

# Simulate spatial distribution of flowers, ants, and bees
np.random.seed(123)
n_flowers = 80
flower_x = np.random.uniform(0, 100, n_flowers)
flower_y = np.random.uniform(0, 100, n_flowers)

# Ant nest at (20, 50) — trail pheromone decays with distance
ant_nest = np.array([20, 50])
ant_dist = np.sqrt((flower_x - ant_nest[0])**2 + (flower_y - ant_nest[1])**2)
ant_pheromone = np.exp(-ant_dist / 25)  # pheromone concentration on each flower

# Bee hive at (80, 50)
bee_hive = np.array([80, 50])
bee_dist = np.sqrt((flower_x - bee_hive[0])**2 + (flower_y - bee_hive[1])**2)

# Bee visit probability: inversely proportional to ant pheromone
P_bee_visit = 0.85 * (1 - ant_pheromone**2) * np.exp(-bee_dist / 60)

# Color flowers by pollination success
pollinated = P_bee_visit > 0.3

# Plot
ax3.scatter(flower_x[pollinated], flower_y[pollinated], c='#4ade80', s=60, alpha=0.8,
            edgecolors='white', linewidth=0.5, label=f'Pollinated ({np.sum(pollinated)})', zorder=3)
ax3.scatter(flower_x[~pollinated], flower_y[~pollinated], c='#ef4444', s=60, alpha=0.6,
            edgecolors='white', linewidth=0.5, label=f'Ant-deterred ({np.sum(~pollinated)})', zorder=3)

# Ant territory (pheromone contour)
xx, yy = np.meshgrid(np.linspace(0, 100, 100), np.linspace(0, 100, 100))
ant_field = np.exp(-np.sqrt((xx - ant_nest[0])**2 + (yy - ant_nest[1])**2) / 25)
ax3.contour(xx, yy, ant_field, levels=[0.2, 0.4, 0.6, 0.8], colors='#ef4444', alpha=0.3, linewidths=1)
ax3.contourf(xx, yy, ant_field, levels=[0.4, 1.0], colors=['#ef444415'], alpha=0.15)

# Nests
ax3.plot(*ant_nest, 's', color='#ef4444', markersize=15, markeredgecolor='white', zorder=5)
ax3.text(ant_nest[0], ant_nest[1] - 5, 'Ant Nest', color='#ef4444', fontsize=11, ha='center', fontweight='bold')
ax3.plot(*bee_hive, 'h', color='#fbbf24', markersize=15, markeredgecolor='white', zorder=5)
ax3.text(bee_hive[0], bee_hive[1] - 5, 'Bee Hive', color='#fbbf24', fontsize=11, ha='center', fontweight='bold')

ax3.set_xlabel('x (m)', color='white', fontsize=12)
ax3.set_ylabel('y (m)', color='white', fontsize=12)
ax3.set_title('Spatial Foraging: Ant Pheromone Territory\nvs Bee Pollination Zone', color='#fca5a5', fontsize=13, fontweight='bold')
ax3.legend(fontsize=10, facecolor='#1a0505', edgecolor='#ef4444', labelcolor='white', loc='upper left')
ax3.tick_params(colors='white')
ax3.set_xlim(0, 100); ax3.set_ylim(0, 100)
ax3.set_aspect('equal')
for sp in ax3.spines.values(): sp.set_color('#ef4444')

# ============================================================
# Panel 4: Phase portrait — ant exploitation vs plant defense
# ============================================================
ax4 = fig.add_subplot(gs[1, 1])
ax4.set_facecolor('#0a0505')

# Phase portrait with vector field
a_grid = np.linspace(0.05, 0.95, 15)
p_grid = np.linspace(0.05, 0.95, 15)
A, P = np.meshgrid(a_grid, p_grid)
dA = 0.02 * (1 - P) - 0.01 * A
dP = 0.015 * A - 0.008 * P
speed = np.sqrt(dA**2 + dP**2)
ax4.quiver(A * 100, P * 100, dA, dP, speed, cmap='RdYlGn_r', alpha=0.7, scale=0.15)

# Plot trajectory
ax4.plot(ant_exploit * 100, plant_defense * 100, color='white', linewidth=2, alpha=0.8)
ax4.plot(ant_exploit[0] * 100, plant_defense[0] * 100, 'o', color='#4ade80', markersize=12,
         markeredgecolor='white', label='Start', zorder=5)
ax4.plot(ant_exploit[-1] * 100, plant_defense[-1] * 100, '*', color='#fbbf24', markersize=15,
         markeredgecolor='white', label='End (equilibrium)', zorder=5)

# Nullclines
a_null = np.linspace(0.01, 0.99, 100)
p_null_a = 1 - 0.5 * a_null  # dA/dt = 0
p_null_p = 1.875 * a_null     # dP/dt = 0
ax4.plot(a_null * 100, p_null_a * 100, '--', color='#ef4444', linewidth=1.5, label='dA/dt = 0 (ant nullcline)')
ax4.plot(a_null * 100, np.clip(p_null_p, 0, 1) * 100, '--', color='#4ade80', linewidth=1.5, label='dP/dt = 0 (plant nullcline)')

ax4.set_xlabel('Ant Exploitation Intensity (%)', color='white', fontsize=12)
ax4.set_ylabel('Plant Defense Investment (%)', color='white', fontsize=12)
ax4.set_title('Phase Portrait: Ant vs Plant Coevolution\n(nullclines and trajectory)', color='#fca5a5', fontsize=13, fontweight='bold')
ax4.legend(fontsize=9, facecolor='#1a0505', edgecolor='#ef4444', labelcolor='white', loc='upper right')
ax4.tick_params(colors='white')
ax4.set_xlim(0, 100); ax4.set_ylim(0, 100)
for sp in ax4.spines.values(): sp.set_color('#ef4444')

# ============================================================
# Panel 5: Multi-species fitness landscape
# ============================================================
ax5 = fig.add_subplot(gs[2, 0])
ax5.set_facecolor('#0a0505')

# Bar chart: fitness of each species at equilibrium vs no-interaction baseline
species = ['Ants', 'Bees', 'Flowers\n(no defense)', 'Flowers\n(with defense)', 'Trees\n(ant mutualism)']
fitness_baseline = [1.0, 1.0, 1.0, 0.95, 0.9]
fitness_with_interaction = [
    0.7 + 0.3 * np.mean(ant_exploit[-20:]),  # ants benefit from exploitation
    1.0 - 0.4 * np.mean(bee_sensitivity[-20:]) * np.mean(ant_exploit[-20:]),  # bees lose from avoidance
    1.0 - 0.6 * np.mean(ant_exploit[-20:]),  # undefended flowers lose most
    1.0 - 0.2 * np.mean(ant_exploit[-20:]) * (1 - np.mean(plant_defense[-20:])),  # defended flowers
    0.9 + 0.2 * np.mean(tree_mutualism[-20:]),  # trees with ant guards
]

x_bar = np.arange(len(species))
w = 0.35
bars1 = ax5.bar(x_bar - w/2, fitness_baseline, w, color='#60a5fa', edgecolor='white', linewidth=0.8, label='Baseline (no interaction)')
bars2 = ax5.bar(x_bar + w/2, fitness_with_interaction, w, color='#ef4444', edgecolor='white', linewidth=0.8, label='With arms race')

for i, (b, f) in enumerate(zip(fitness_baseline, fitness_with_interaction)):
    change = (f - b) / b * 100
    color = '#4ade80' if change >= 0 else '#ef4444'
    ax5.text(i + w/2, f + 0.02, f'{change:+.0f}%', ha='center', color=color, fontsize=10, fontweight='bold')

ax5.set_xticks(x_bar)
ax5.set_xticklabels(species, color='white', fontsize=10)
ax5.set_ylabel('Relative Fitness', color='white', fontsize=12)
ax5.set_title('Species Fitness: Winners & Losers\nin the Chemical Arms Race', color='#fca5a5', fontsize=13, fontweight='bold')
ax5.legend(fontsize=10, facecolor='#1a0505', edgecolor='#ef4444', labelcolor='white')
ax5.tick_params(colors='white')
ax5.grid(True, alpha=0.15, color='#ef4444', axis='y')
for sp in ax5.spines.values(): sp.set_color('#ef4444')
ax5.set_ylim(0, 1.3)

# ============================================================
# Panel 6: Temporal flower visitation — 24-hour cycle
# ============================================================
ax6 = fig.add_subplot(gs[2, 1])
ax6.set_facecolor('#0a0505')

hours = np.linspace(0, 24, 200)
# Ant activity peaks at warm midday
ant_activity = 0.3 + 0.7 * np.exp(-((hours - 13)**2) / (2 * 3**2))
# Bee activity peaks in morning and late afternoon (avoiding midday heat)
bee_activity = 0.6 * np.exp(-((hours - 9)**2) / (2 * 2**2)) + 0.4 * np.exp(-((hours - 16)**2) / (2 * 2**2))
# Flower nectar production (peaks in morning)
nectar = 0.8 * np.exp(-((hours - 7)**2) / (2 * 3**2)) + 0.2
# Pheromone accumulation on flowers (integral of ant activity with decay)
pheromone_on_flower = np.zeros_like(hours)
for i in range(1, len(hours)):
    dt_h = hours[1] - hours[0]
    pheromone_on_flower[i] = pheromone_on_flower[i-1] * np.exp(-0.5 * dt_h) + ant_activity[i] * 0.3 * dt_h

# Effective bee visitation (product of bee activity and avoidance of pheromone)
effective_visits = bee_activity * (1 - 0.8 * pheromone_on_flower / max(pheromone_on_flower))

ax6.fill_between(hours, ant_activity * 100, alpha=0.15, color='#ef4444')
ax6.plot(hours, ant_activity * 100, color='#ef4444', linewidth=2.5, label='Ant foraging activity')
ax6.fill_between(hours, bee_activity * 100, alpha=0.15, color='#fbbf24')
ax6.plot(hours, bee_activity * 100, color='#fbbf24', linewidth=2.5, label='Bee foraging activity')
ax6.plot(hours, nectar * 100, color='#4ade80', linewidth=2, linestyle='--', label='Nectar availability')
ax6.plot(hours, effective_visits * 100, color='#22d3ee', linewidth=2.5, label='Effective bee visits')
ax6.plot(hours, pheromone_on_flower / max(pheromone_on_flower) * 80, color='#a78bfa', linewidth=1.5,
         linestyle=':', label='Pheromone on petals')

# Dawn/dusk shading
ax6.axvspan(0, 6, alpha=0.1, color='#1e293b')
ax6.axvspan(20, 24, alpha=0.1, color='#1e293b')
ax6.text(3, 95, 'Night', color='#94a3b8', fontsize=10, ha='center')
ax6.text(22, 95, 'Night', color='#94a3b8', fontsize=10, ha='center')

ax6.set_xlabel('Hour of Day', color='white', fontsize=12)
ax6.set_ylabel('Activity / Availability (%)', color='white', fontsize=12)
ax6.set_title('Daily Rhythm: Temporal Partitioning\nBees forage when ant pheromones are lowest', color='#fca5a5', fontsize=13, fontweight='bold')
ax6.legend(fontsize=9, facecolor='#1a0505', edgecolor='#ef4444', labelcolor='white', loc='upper right')
ax6.tick_params(colors='white')
ax6.grid(True, alpha=0.15, color='#ef4444')
ax6.set_xlim(0, 24)
ax6.set_xticks([0, 4, 8, 12, 16, 20, 24])
for sp in ax6.spines.values(): sp.set_color('#ef4444')

plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#030712')
print("=== Multi-Species Arms Race Simulation ===")
print(f"Equilibrium ant exploitation: {np.mean(ant_exploit[-20:])*100:.1f}%")
print(f"Equilibrium plant defense: {np.mean(plant_defense[-20:])*100:.1f}%")
print(f"Equilibrium bee sensitivity: {np.mean(bee_sensitivity[-20:])*100:.1f}%")
print(f"Flowers pollinated (spatial model): {np.sum(pollinated)}/{n_flowers} ({np.sum(pollinated)/n_flowers*100:.0f}%)")
print(f"Peak ant-bee overlap hour: ~13:00 (midday)")
print(f"Optimal bee foraging window: 7-10 AM (low pheromone, high nectar)")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

References

Schultz, T.R. & Brady, S.G. (2008). Major evolutionary transitions in ant agriculture. Proceedings of the National Academy of Sciences, 105(14), 5435–5440.
Currie, C.R., Scott, J.A., Summerbell, R.C. & Malloch, D. (1999). Fungus-growing ants use antibiotic-producing bacteria to control garden parasites. Nature, 398(6729), 701–704.
Stadler, B. & Dixon, A.F.G. (2005). Ecology and evolution of aphid-ant interactions. Annual Review of Ecology, Evolution, and Systematics, 36, 345–372.
Oliver, T.H., Mashanova, A., Leather, S.R., Cook, J.M. & Jansen, V.A.A. (2007). Ant semiochemicals limit apterous aphid dispersal. Proceedings of the Royal Society B, 274(1629), 3127–3131.
Fonseca, C.R. (1994). Herbivory and the long-lived leaves of an Amazonian ant-tree. Journal of Ecology, 82(4), 833–842.
Heil, M. & McKey, D. (2003). Protective ant-plant interactions as model systems in ecological and evolutionary research. Annual Review of Ecology, Evolution, and Systematics, 34, 425–453.
Hughes, D.P., Andersen, S.B., Hywel-Jones, N.L., Himaman, W., Billen, J. & Boomsma, J.J. (2011). Behavioral mechanisms and morphological symptoms of zombie ants dying from fungal infection. BMC Ecology, 11, 13.
de Bekker, C., Ohm, R.A., Loreto, R.G., Sebastian, A., Albert, I., Merber, M., Brachmann, A., Calabrese, S. & Hughes, D.P. (2015). Gene expression during zombie ant biting behavior reflects the complexity underlying fungal parasitic behavioral manipulation. BMC Genomics, 16, 620.
Weber, N.A. (1972). Gardening Ants: The Attines. American Philosophical Society.
Mehdiabadi, N.J. & Schultz, T.R. (2010). Natural history and phylogeny of the fungus-farming ants (Hymenoptera: Formicidae: Myrmicinae: Attini). Myrmecological News, 13, 37–55.

M6. Collective Intelligence M8. Evolution & Superorganism