Module 6

Aquatic Insects: Physics at the Water Interface

Surface tension, plastron respiration, and the biophysics of breathing underwater

6.1 Water Strider Locomotion: Walking on Surface Tension

The water strider (Gerris spp.) is perhaps nature's most elegant demonstration of surface tension physics. These insects support their entire body weight on the water surface, creating visible dimples without breaking through. Understanding how this works requires the physics of interfaces, wetting, and capillary forces.

Laplace Pressure and Leg Dimples

When a strider's leg presses on the water surface, it creates a curved meniscus. The pressure difference across this curved interface is given by the Young-Laplace equation:

\(\Delta P = \gamma \left(\frac{1}{R_1} + \frac{1}{R_2}\right)\)

where \(\gamma\) = surface tension (0.0728 N/m for water at 20\(^\circ\)C), \(R_1, R_2\) = principal radii of curvature

Maximum Weight Supported

The maximum vertical force a leg can support is determined by the surface tension acting along the contact perimeter. For a cylindrical leg of length \(L\) pressing on the surface:

\(F_{\max} = \gamma \cdot P \cdot \cos(\pi - \theta)\)

where \(P = 2L\) is the contact perimeter (two sides of the leg) and \(\theta\) is the contact angle

For a strider with four supporting legs (each ~5 mm long) and superhydrophobic contact angle \(\theta \approx 160^\circ\):

\(F_{\text{total}} = 4 \times 0.0728 \times 0.01 \times \cos(20^\circ) \approx 2.74 \text{ mN}\)

A 25 mg strider weighs only 0.245 mN — a safety factor of ∼10x

Superhydrophobic Leg Surface

The strider's legs achieve contact angles exceeding 150\(^\circ\) through a hierarchical surface structure: each leg is covered with thousands of microgrooved setae (hairs) at ~20 \(\mu\)m spacing, each seta further bearing nanoscale grooves. This creates a Cassie-Baxter wetting state where air is trapped beneath the leg, dramatically reducing the solid-liquid contact fraction.

\(\cos\theta_{\text{CB}} = f_s(\cos\theta_0 + 1) - 1\)

Cassie-Baxter equation: \(f_s \approx 0.03\) for strider legs (only 3% solid contact)

Capillary Number

The capillary number \(\text{Ca} = \mu v / \gamma\) determines whether viscous or surface tension forces dominate the strider's locomotion. For water striders moving at typical speeds (~30 cm/s):

\(\text{Ca} = \frac{\mu v}{\gamma} = \frac{(10^{-3})(0.3)}{0.0728} \approx 0.004 \ll 1\)

Ca \(\ll\) 1 confirms surface tension dominates — the strider lives in a capillary world

6.2 Plastron Respiration: The Physical Gill

Many aquatic insects carry a thin film of air — the plastron — held against their body by dense hydrophobic hairs. Unlike a simple air bubble (which shrinks and eventually collapses), a plastron can function indefinitely as a physical gill, extracting dissolved oxygen from the surrounding water.

Why the Plastron Works

The key physics: as the insect consumes O\(_2\) from the plastron, the partial pressure of O\(_2\) in the air film drops below that in the surrounding water. This creates a concentration gradient that drives O\(_2\)diffusion into the plastron from the water. The steady-state oxygen flux follows Fick's first law:

\(J_{O_2} = \frac{D_{O_2} \cdot (C_{\text{water}} - C_{\text{plastron}})}{\delta}\)

where \(D_{O_2} \approx 2.1 \times 10^{-9}\) m\(^2\)/s, \(\delta\) = boundary layer thickness

Why a Free Bubble Fails

A free air bubble (carried by, e.g., a diving beetle) is compressible. As O\(_2\) is consumed and diffuses inward from water, the N\(_2\) partial pressure in the bubble rises above the dissolved N\(_2\) in water, causing N\(_2\) to diffuse out. Since N\(_2\)constitutes ~78% of the bubble, this net loss of N\(_2\) causes the bubble to shrink and eventually collapse.

The plastron avoids this because the hydrophobic hair matrix physically prevents the air-water interface from collapsing inward. The interface is pinned at the hair tips, maintaining a constant volume even as gas pressures change. The Laplace pressure at the hair spacing scale (\(\sim 1\) \(\mu\)m) is large enough to resist hydrostatic pressure:

\(\Delta P_{\text{Laplace}} = \frac{2\gamma}{r_{\text{hair}}} \approx \frac{2 \times 0.073}{10^{-6}} = 146{,}000 \text{ Pa}\)

This can resist submersion to ~15 m depth — far deeper than most aquatic insects live

6.3 Diving Beetle: Compressible Air Store

The great diving beetle (Dytiscus marginalis) carries a large air bubble trapped beneath its elytra (wing covers). Unlike a plastron, this bubble is compressible — it acts as a temporary lung that must be periodically renewed at the surface.

Bubble Lifetime from Gas Exchange

The bubble shrinks because nitrogen, which makes up ~78% of the air, gradually diffuses out into the water. The rate of volume change is governed by:

\(\frac{dV}{dt} = -\frac{A \cdot D_{N_2}}{\delta} \cdot \frac{P_{N_2}^{\text{bubble}} - P_{N_2}^{\text{water}}}{P_{\text{atm}} + \rho g h}\)

As the beetle consumes O\(_2\), the mole fraction of N\(_2\) in the bubble increases, raising\(P_{N_2}^{\text{bubble}}\) above the dissolved N\(_2\) in the water. At depth \(h\), hydrostatic pressure \(P = P_{\text{atm}} + \rho g h\) further compresses the bubble (Boyle's law), accelerating N\(_2\) loss. Deeper dives therefore result in faster bubble collapse.

Physical Gill Efficiency

Despite its temporary nature, the bubble acts as a surprisingly efficient physical gill: a beetle can extract roughly 8x the O\(_2\) originally present in the bubble before it collapses, because dissolved O\(_2\) continuously diffuses in from the water as the beetle consumes the bubble's O\(_2\). The bubble effectively amplifies the available oxygen supply.

6.4 Mosquito Larva: Siphon Breathing

Mosquito larvae (e.g., Culex, Aedes) breathe atmospheric air through a posterior siphon tube that pierces the water surface. The siphon tip is lined with hydrophobic hairs that prevent water from flooding the tracheal system.

Capillary Pressure to Flood the Siphon

For water to enter the siphon and drown the larva, it must overcome the capillary pressure generated by the hydrophobic hairs lining the siphon opening:

\(P_{\text{cap}} = \frac{2\gamma \cos\theta}{r}\)

For hydrophobic surface (\(\theta > 90^\circ\)), \(\cos\theta < 0\), so the meniscus curves outward, resisting entry

The effective capillary pressure that must be exceeded to flood the siphon is:

\(P_{\text{flood}} = \frac{2\gamma |\cos\theta|}{r_{\text{siphon}}}\)

For \(\theta = 140^\circ\) and \(r = 50\) \(\mu\)m: \(P \approx 2230\) Pa — equivalent to 23 cm water depth

Surfactant-Based Mosquito Control

This physics explains why surfactants (surface-active agents) are effective larvicides: by reducing \(\gamma\) and altering \(\theta\), they lower the capillary pressure barrier, allowing water to flood the siphon. Thin films of oil on water surfaces work similarly — they reduce surface tension and prevent the siphon from establishing a stable air-water meniscus.

6.5 Mayfly Tracheal Gills

Unlike the air-breathing strategies above, mayfly nymphs (Ephemeroptera) have evolved tracheal gills — thin, highly vascularized (with tracheoles) plate-like or feathery appendages that extract dissolved O\(_2\) directly from the water, much like fish gills.

Oxygen Uptake Rate

The rate of O\(_2\) uptake from gill ventilation is:

\(\dot{Q}_{O_2} = \dot{V}_{\text{water}} \times (C_{\text{in}} - C_{\text{out}}) \times \eta\)

where \(\dot{V}_{\text{water}}\) = ventilation flow rate, \(C_{\text{in}}, C_{\text{out}}\) = inlet/outlet [O\(_2\)], \(\eta\) = extraction efficiency

The extraction efficiency depends on the gill's Sherwood number(dimensionless mass transfer coefficient):

\(\text{Sh} = \frac{k \cdot L}{D_{O_2}} \quad \Rightarrow \quad k = \frac{\text{Sh} \cdot D_{O_2}}{L}\)

Typical Sh ~10-50 for gill lamellae oscillating in flow

The Thermal Squeeze Problem

Aquatic insects face a fundamental thermal squeeze: as water temperature rises, metabolic demand increases (Q\(_{10} \approx 2.3\)) while O\(_2\) solubility decreases. At some critical temperature, supply can no longer meet demand:

\(\text{Supply/Demand} = \frac{C_{\text{sat}}(T)}{C_{\text{sat}}(T_0)} \cdot Q_{10}^{-(T - T_0)/10}\)

When this ratio falls below 1, the insect cannot sustain aerobic metabolism

This is why many mayfly species are cold-water obligates and serve as bioindicators of water quality — their disappearance signals warming or reduced O\(_2\).

Simulation: Aquatic Insect Biophysics

This simulation models (1) water strider weight support vs contact angle, (2) plastron vs free bubble O\(_2\) persistence, (3) diving beetle bubble lifetime at different depths, and (4) mosquito siphon capillary pressure vs radius and contact angle.

Python

script.py204 lines

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

# ══════════════════════════════════════════════════════════════════════
# Panel 1: Water Strider — Surface Tension Weight Support
# ══════════════════════════════════════════════════════════════════════
gamma = 0.0728  # surface tension of water at 20°C (N/m)
contact_angles = np.linspace(90, 170, 200)  # degrees
theta_rad = np.radians(contact_angles)

# Leg geometry: each leg is roughly cylindrical, ~5 mm long, ~50 um diameter
leg_length = 5e-3  # m
leg_perimeter = 2 * leg_length  # contact line length for one leg (two sides)
n_legs = 4  # middle + hind legs support weight

# Maximum supportable force per leg: F = gamma * P * cos(theta)
# where P = contact perimeter and theta = contact angle
F_per_leg = gamma * leg_perimeter * np.cos(np.pi - theta_rad)  # force downward balanced
F_total = n_legs * F_per_leg * 1000  # mN

# Actual water strider mass range
strider_mass = 0.025e-3  # 25 mg in kg
strider_weight = strider_mass * 9.81 * 1000  # mN

# Capillary number analysis
velocities = np.linspace(0.01, 1.0, 200)
mu_water = 1.002e-3  # Pa.s at 20°C
Ca = mu_water * velocities / gamma

# ══════════════════════════════════════════════════════════════════════
# Panel 2: Plastron O2 Exchange Model
# ══════════════════════════════════════════════════════════════════════
time_min = np.linspace(0, 120, 500)  # minutes
D_O2 = 2.1e-9  # diffusion coefficient O2 in water (m^2/s)
delta_bl = 100e-6  # boundary layer thickness (m)
A_plastron = 5e-6  # plastron surface area (m^2)

# O2 concentration in water (saturated): ~8.2 mg/L = 0.256 mmol/L
C_water_O2 = 0.256  # mmol/L
# Metabolic consumption rate
Q_metabolic = 0.005  # mmol/min (small aquatic insect)

# Plastron volume
V_plastron = 0.5e-9  # m^3 = 0.5 uL
C_plastron_O2 = np.zeros_like(time_min)
C_plastron_O2[0] = 0.256  # initially air-saturated

dt = time_min[1] - time_min[0]
for i in range(1, len(time_min)):
    # Diffusive influx (Fick's law)
    J_in = D_O2 * A_plastron * (C_water_O2 - C_plastron_O2[i-1]) / delta_bl
    J_in_mmol = J_in * 1e3 * 60  # convert to mmol/min
    # Net change
    dC = (J_in_mmol - Q_metabolic) * dt / (V_plastron * 1e6)
    C_plastron_O2[i] = max(0, C_plastron_O2[i-1] + dC * 0.01)

# Normalize for display
C_norm = C_plastron_O2 / C_water_O2 * 100

# Bubble (non-plastron) for comparison — shrinks over time
bubble_volume = np.zeros_like(time_min)
bubble_volume[0] = 100  # percent
for i in range(1, len(time_min)):
    # N2 diffuses out, bubble shrinks
    bubble_volume[i] = max(0, bubble_volume[0] * np.exp(-0.025 * time_min[i]))

# ══════════════════════════════════════════════════════════════════════
# Panel 3: Diving Beetle Bubble Lifetime
# ══════════════════════════════════════════════════════════════════════
depths = [0.1, 0.5, 1.0, 2.0, 5.0]  # meters
time_hours = np.linspace(0, 6, 300)

D_N2 = 1.6e-9  # N2 diffusion in water (m^2/s)
delta_N2 = 200e-6  # boundary layer
P_atm = 101325  # Pa

bubble_lifetimes = {}
for depth in depths:
    P_hydro = P_atm + 1000 * 9.81 * depth
    # Higher pressure = faster N2 loss (pressure drives N2 out of bubble)
    k_loss = 0.3 * (P_hydro / P_atm)  # empirical rate constant
    V_t = 100 * np.exp(-k_loss * time_hours)
    bubble_lifetimes[depth] = V_t

# ══════════════════════════════════════════════════════════════════════
# Panel 4: Siphon Capillary Pressure (Mosquito Larva)
# ══════════════════════════════════════════════════════════════════════
radii = np.linspace(5, 200, 200)  # siphon radius in micrometers
radii_m = radii * 1e-6

# Capillary pressure for different contact angles
angles_siphon = [100, 120, 140, 160]
pressures = {}
for angle in angles_siphon:
    theta_r = np.radians(angle)
    P_cap = 2 * gamma * np.abs(np.cos(theta_r)) / radii_m  # Pa
    pressures[angle] = P_cap

# ══════════════════════════════════════════════════════════════════════
# Plotting
# ══════════════════════════════════════════════════════════════════════
fig, axes = plt.subplots(2, 2, figsize=(15, 12))
fig.patch.set_facecolor('#0a0a1a')

colors_lime = ['#a3e635', '#84cc16', '#65a30d', '#4d7c0f', '#3f6212']

# Plot 1: Surface tension weight support
ax1 = axes[0, 0]
ax1.plot(contact_angles, F_total, color='#a3e635', linewidth=2.5, label='Max supportable force (4 legs)')
ax1.axhline(strider_weight, color='#f87171', linewidth=2, linestyle='--', label=f'Strider weight ({strider_weight:.2f} mN)')
ax1.axvline(160, color='#fbbf24', linewidth=1.5, linestyle=':', alpha=0.7, label='Typical strider leg (160\u00b0)')
ax1.fill_between(contact_angles, strider_weight, F_total, where=F_total > strider_weight, alpha=0.15, color='#a3e635')
ax1.set_xlabel('Contact Angle (\u00b0)', color='white', fontsize=11)
ax1.set_ylabel('Force (mN)', color='white', fontsize=11)
ax1.set_title('Water Strider: Surface Tension\nWeight Support vs Contact Angle', color='white', fontsize=12, fontweight='bold')
ax1.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#a3e635', labelcolor='white')
ax1.set_facecolor('#0a0a1a')
ax1.tick_params(colors='white')
ax1.grid(True, alpha=0.15, color='#a3e635')
for sp in ax1.spines.values(): sp.set_color('#a3e635')

# Plot 2: Plastron vs bubble O2
ax2 = axes[0, 1]
ax2.plot(time_min, C_norm, color='#a3e635', linewidth=2.5, label='Plastron O\u2082 level')
ax2.plot(time_min, bubble_volume, color='#f87171', linewidth=2.5, linestyle='--', label='Free bubble volume')
ax2.axhline(20, color='#fbbf24', linewidth=1, linestyle=':', alpha=0.7, label='Critical O\u2082 threshold')
ax2.fill_between(time_min, 0, 20, alpha=0.08, color='#f87171')
ax2.set_xlabel('Time (min)', color='white', fontsize=11)
ax2.set_ylabel('Relative O\u2082 / Volume (%)', color='white', fontsize=11)
ax2.set_title('Plastron vs Free Bubble:\nO\u2082 Persistence Over Time', color='white', fontsize=12, fontweight='bold')
ax2.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#a3e635', labelcolor='white')
ax2.set_facecolor('#0a0a1a')
ax2.tick_params(colors='white')
ax2.grid(True, alpha=0.15, color='#a3e635')
for sp in ax2.spines.values(): sp.set_color('#a3e635')

# Plot 3: Diving beetle bubble lifetime
ax3 = axes[1, 0]
for i, (depth, V_t) in enumerate(bubble_lifetimes.items()):
    ax3.plot(time_hours, V_t, color=colors_lime[i % len(colors_lime)], linewidth=2, label=f'{depth} m depth')
ax3.axhline(10, color='#f87171', linewidth=1.5, linestyle='--', alpha=0.7, label='Collapse threshold')
ax3.set_xlabel('Time (hours)', color='white', fontsize=11)
ax3.set_ylabel('Bubble Volume (% initial)', color='white', fontsize=11)
ax3.set_title('Diving Beetle Bubble Lifetime\nvs Depth', color='white', fontsize=12, fontweight='bold')
ax3.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#a3e635', labelcolor='white', ncol=2)
ax3.set_facecolor('#0a0a1a')
ax3.tick_params(colors='white')
ax3.grid(True, alpha=0.15, color='#a3e635')
for sp in ax3.spines.values(): sp.set_color('#a3e635')

# Plot 4: Siphon capillary pressure
ax4 = axes[1, 1]
style_map = {100: '-', 120: '--', 140: '-.', 160: ':'}
for j, (angle, P_cap) in enumerate(pressures.items()):
    ax4.plot(radii, P_cap, color=colors_lime[j % len(colors_lime)], linewidth=2, linestyle=style_map[angle], label=f'\u03b8 = {angle}\u00b0')
ax4.axhline(500, color='#f87171', linewidth=1.5, linestyle='--', alpha=0.7, label='Typical submersion pressure')
ax4.set_xlabel('Siphon Radius (\u03bcm)', color='white', fontsize=11)
ax4.set_ylabel('Capillary Pressure (Pa)', color='white', fontsize=11)
ax4.set_title('Mosquito Larva Siphon:\nCapillary Pressure vs Radius', color='white', fontsize=12, fontweight='bold')
ax4.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#a3e635', labelcolor='white')
ax4.set_yscale('log')
ax4.set_facecolor('#0a0a1a')
ax4.tick_params(colors='white')
ax4.grid(True, alpha=0.15, color='#a3e635')
for sp in ax4.spines.values(): sp.set_color('#a3e635')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a1a')

# ── Numerical Output ──
print("=== Aquatic Insect Biophysics Simulations ===\n")

print("--- Water Strider Weight Support ---")
theta_typical = 160
F_typ = n_legs * gamma * leg_perimeter * np.cos(np.pi - np.radians(theta_typical)) * 1000
print(f"Surface tension of water: {gamma*1000:.1f} mN/m")
print(f"Contact angle (superhydrophobic leg): {theta_typical}\u00b0")
print(f"Max supportable force (4 legs): {F_typ:.2f} mN")
print(f"Strider weight (25 mg): {strider_weight:.2f} mN")
print(f"Safety factor: {F_typ/strider_weight:.1f}x\n")

print("--- Plastron Respiration ---")
print(f"O2 diffusion coefficient: {D_O2:.2e} m\u00b2/s")
print(f"Plastron area: {A_plastron*1e6:.1f} mm\u00b2")
print(f"After 2 hours, plastron O2: {C_norm[-1]:.1f}% of saturation")
print(f"Free bubble at 2 hours: {bubble_volume[-1]:.1f}% of initial volume\n")

print("--- Diving Beetle Bubble ---")
for depth in depths:
    V_final = bubble_lifetimes[depth]
    t_collapse = time_hours[np.argmax(V_final < 10)] if np.any(V_final < 10) else float('inf')
    if t_collapse > 0:
        print(f"Depth {depth:.1f} m: bubble collapses at ~{t_collapse:.1f} hours")
    else:
        print(f"Depth {depth:.1f} m: bubble persists > 6 hours")

print("\n--- Mosquito Siphon Capillary Pressure ---")
for angle in angles_siphon:
    r_50 = 50e-6  # 50 um radius
    P_50 = 2 * gamma * abs(np.cos(np.radians(angle))) / r_50
    print(f"\u03b8 = {angle}\u00b0, r = 50 \u03bcm: P_cap = {P_50:.0f} Pa")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Advanced: Mayfly Gills & Thermal Squeeze

This simulation compares O\(_2\) uptake across different gill morphologies and models the thermal squeeze — the critical temperature where metabolic demand exceeds O\(_2\) supply.

Python

script.py102 lines

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

# ══════════════════════════════════════════════════════════════════════
# Panel 1: Mayfly Gill O2 Uptake vs Flow Velocity
# ══════════════════════════════════════════════════════════════════════
flow_velocities = np.linspace(0.01, 0.5, 200)  # m/s
C_in = 8.2  # mg/L (dissolved O2 at saturation)
gill_area = 10e-6  # m^2 (total gill surface)
D_O2 = 2.1e-9  # m^2/s

# Boundary layer thickness decreases with flow: delta ~ 1/sqrt(v)
delta_ref = 500e-6  # at v = 0.01 m/s
delta_bl = delta_ref * np.sqrt(0.01 / flow_velocities)

# O2 flux per unit area
extraction_eff = 1 - np.exp(-D_O2 * gill_area / (delta_bl * flow_velocities * 1e-6))
Q_O2 = flow_velocities * 1e-6 * C_in * extraction_eff  # mg/s (simplified)

# Different gill morphologies
gill_types = {
    'Plate gills (Ephemerella)': {'area_mult': 1.0, 'color': '#a3e635'},
    'Feathery gills (Hexagenia)': {'area_mult': 2.5, 'color': '#84cc16'},
    'Filamentous gills (Caenis)': {'area_mult': 4.0, 'color': '#65a30d'},
}

# ══════════════════════════════════════════════════════════════════════
# Panel 2: Temperature Effect on Aquatic Insect Metabolism
# ══════════════════════════════════════════════════════════════════════
temps = np.linspace(5, 35, 200)  # degrees C

# Q10 = 2.3 for insect metabolism (typical)
Q10 = 2.3
T_ref = 20  # reference temperature
MR_ref = 1.0  # normalized metabolic rate at T_ref

MR = MR_ref * Q10 ** ((temps - T_ref) / 10)

# O2 solubility decreases with temperature
# Henry's law: C_sat = 14.6 - 0.41*T + 0.00799*T^2 - 0.0000778*T^3 (mg/L approx)
C_sat = 14.6 - 0.41 * temps + 0.00799 * temps**2 - 0.0000778 * temps**3

# Oxygen supply/demand ratio
supply_demand = C_sat / (C_sat[0] * MR / MR[0])

# ══════════════════════════════════════════════════════════════════════
# Plotting
# ══════════════════════════════════════════════════════════════════════
fig, axes = plt.subplots(1, 2, figsize=(15, 6))
fig.patch.set_facecolor('#0a0a1a')

# Plot 1: Mayfly gill O2 uptake
ax1 = axes[0]
for name, params in gill_types.items():
    Q_adj = Q_O2 * params['area_mult'] * 1e6  # scale for display
    ax1.plot(flow_velocities * 100, Q_adj, color=params['color'], linewidth=2.5, label=name)
ax1.set_xlabel('Flow Velocity (cm/s)', color='white', fontsize=11)
ax1.set_ylabel('O\u2082 Uptake Rate (\u03bcg/s)', color='white', fontsize=11)
ax1.set_title('Mayfly Gill O\u2082 Uptake\nvs Water Flow Velocity', color='white', fontsize=12, fontweight='bold')
ax1.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#a3e635', labelcolor='white')
ax1.set_facecolor('#0a0a1a')
ax1.tick_params(colors='white')
ax1.grid(True, alpha=0.15, color='#a3e635')
for sp in ax1.spines.values(): sp.set_color('#a3e635')

# Plot 2: Temperature — metabolic demand vs O2 supply
ax2 = axes[1]
ax2.plot(temps, MR, color='#f87171', linewidth=2.5, label='Metabolic demand (Q\u2081\u2080=2.3)')
ax2.plot(temps, C_sat / C_sat[0], color='#a3e635', linewidth=2.5, label='O\u2082 solubility (normalized)')
ax2.plot(temps, supply_demand, color='#fbbf24', linewidth=2.5, linestyle='--', label='Supply / Demand ratio')
ax2.axhline(1, color='white', linewidth=1, linestyle=':', alpha=0.5)
ax2.fill_between(temps, supply_demand, 1, where=supply_demand < 1, alpha=0.15, color='#f87171')
ax2.set_xlabel('Temperature (\u00b0C)', color='white', fontsize=11)
ax2.set_ylabel('Relative Rate (normalized)', color='white', fontsize=11)
ax2.set_title('Thermal Squeeze: O\u2082 Supply\nvs Metabolic Demand', color='white', fontsize=12, fontweight='bold')
ax2.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#a3e635', labelcolor='white')
ax2.set_facecolor('#0a0a1a')
ax2.tick_params(colors='white')
ax2.grid(True, alpha=0.15, color='#a3e635')
for sp in ax2.spines.values(): sp.set_color('#a3e635')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a1a')

print("=== Advanced Aquatic Insect Models ===\n")

print("--- Mayfly Gill Types ---")
for name, params in gill_types.items():
    Q_peak = Q_O2[-1] * params['area_mult'] * 1e6
    print(f"{name}: relative SA = {params['area_mult']}x, peak uptake = {Q_peak:.2f} \u03bcg/s")

print("\n--- Thermal Squeeze Analysis ---")
for T in [10, 15, 20, 25, 30]:
    idx = np.argmin(np.abs(temps - T))
    print(f"T = {T}\u00b0C: MR = {MR[idx]:.2f}x, O2 sat = {C_sat[idx]:.1f} mg/L, S/D ratio = {supply_demand[idx]:.2f}")

T_crit = temps[np.argmin(np.abs(supply_demand - 1))]
print(f"\nCritical temperature (S/D = 1): ~{T_crit:.1f}\u00b0C")
print("Above this temperature, O2 supply cannot meet metabolic demand")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

References

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Resh, V.H. & Cardé, R.T. (2009). Encyclopedia of Insects (2nd ed.). Academic Press.
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Clements, A.N. (1992). The Biology of Mosquitoes, Vol. 1. Chapman & Hall.

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