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Module 4: Pollination Ecology

A flower without a vector is an evolutionary dead end. Over 85 percent of angiosperms depend on animal pollinators, and the resulting coevolution has produced some of the most striking syndromes in biology: ornithophilous red tubes, chiropterophilous bat pollination, bee orchids that mimic mating partners. This module derives pollination syndromes from first principles, calculates optimal nectar concentration from viscosity and caloric density, dissects deceptive pollination via game theory, and closes on fidelity, constancy and majoring-minoring foraging strategies. Cross-reference Bee M2 for the vision and waggle-dance navigation that feed back into this ecology.

1. Pollination Syndromes

Correlated suites of floral traits that predict a pollinator guild are called pollination syndromes. They arose by convergent evolution: unrelated plants exploiting the same pollinator class converge on similar trait combinations:

Melittophily (bees)

Yellow, blue, UV-patterned; no red
Sweet floral scent (terpenoids)
Landing platform, often zygomorphic
Sucrose-rich nectar 30-50% w/w
Examples: Lamiaceae, Fabaceae

Ornithophily (birds)

Red, orange, sometimes green (not UV)
Odourless (birds have weak olfaction)
Long tubular corolla; no landing platform
Dilute hexose-rich nectar 15-25%
Examples: Heliconia, Fuchsia, Passiflora

Sphingophily (hawk moths)

White / pale; reflects moonlight
Strong sweet scent at dusk
Very long, narrow tube; nectar at base
Moderate concentration 20-40%
Examples: Petunia, Datura, Angraecum

Chiropterophily (bats)

Drab white/green, nocturnal anthesis
Fermented / sulfurous scent
Robust flowers on trunk (cauliflory)
Very dilute 10-20%, huge volumes
Examples: Agave, Ceiba, baobab

Sapromyophily (carrion flies)

Dark red/purple, often spotted
Rotten-meat odour (DMDS, indole)
Thermogenic heat cue
No reward - brood-site deceit
Examples: Rafflesia, Amorphophallus

Anemophily (wind)

Reduced perianth, inconspicuous
No nectar, no scent
Feathery stigmas, exposed anthers
Enormous pollen production
Examples: grasses, oaks, pines

1.1 Deriving Tube Length from Pollinator Tongue Length

Nilsson (1988) observed that across 19 co-occurring orchids in Madagascar, flower tube length is, on average, 1.2 times longer than the corresponding moth's tongue. The reasoning:

If \(L_{\text{tube}} < L_{\text{tongue}}\), the moth can reach nectar without pressing against the anthers -> no pollen transfer -> plant has low fitness.
If \(L_{\text{tube}} > L_{\text{tongue}}\), the moth cannot reach nectar -> switches to other flowers -> plant has no pollination.
The optimum is \(L_{\text{tube}} \approx L_{\text{tongue}} + \epsilon\) where \(\epsilon\)forces contact with anthers/stigma.

The canonical example is Darwin's prediction: Angraecum sesquipedale has a 28-cm spur; in 1862 Darwin predicted "there must be moths with tongues of nine or ten inches." In 1903 Xanthopan morganii praedicta was described, with a 22-cm tongue. The simulation below runs a co-evolutionary arms race.

Python

script.py116 lines

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

# ======================================================================
# Tube length vs pollinator tongue length: fitness landscape
# ----------------------------------------------------------------------
# Pollinator feeding efficiency is maximal when tongue length slightly
# exceeds tube length. The classic case: Angraecum sesquipedale (Darwin's
# orchid) with 30 cm spur, pollinated by Xanthopan morganii praedicta
# (hawk moth with 22 cm tongue).
#
# We model:
#   - Nectar mass extractable by a moth with tongue L_m visiting a tube L_t
#   - Visitation probability sigmoidal in energy gain
#   - Plant fitness ~ visits per flower
#
# The model exhibits sharp frequency-dependent coevolution: if mean
# L_m > L_t, plants with longer tubes have higher outcrossing fitness
# and the tube evolves longer; eventually moths lose access to shorter
# flowers, favouring longer tongues.
# ======================================================================

Lt = np.linspace(5, 35, 200)              # tube length (cm)
moth_tongues = [5, 10, 15, 22, 28]         # various moth species
colors = plt.cm.spring(np.linspace(0.1, 0.9, len(moth_tongues)))

# Extractable nectar = flower has 1 mL; moth reaches depth min(Lt, L_m)
# handling time grows with both; efficiency = reward / time
def efficiency(Lt, Lm):
    reach = np.minimum(Lm, Lt)
    # proportion reachable
    frac = reach / Lt
    # handling time grows with tube depth squared (laminar)
    t_hand = 1.0 + 0.02*Lt**1.2
    # flight cost proportional to time
    return frac / t_hand

fig, axes = plt.subplots(1, 3, figsize=(16, 5))
fig.patch.set_facecolor('#0a0308')

ax = axes[0]; ax.set_facecolor('#1a0612')
for Lm, col in zip(moth_tongues, colors):
    E = efficiency(Lt, Lm)
    ax.plot(Lt, E, color=col, linewidth=2.2, label=f"Tongue {Lm} cm")
    peak_idx = np.argmax(E)
    ax.scatter([Lt[peak_idx]], [E[peak_idx]], color=col, edgecolors='white', s=60, zorder=5)
ax.set_xlabel('Flower tube depth (cm)', color='white')
ax.set_ylabel('Feeding efficiency (reward/time)', color='white')
ax.set_title('Optimal flower tube for each moth tongue length',
             color='#fbcfe8', fontsize=11)
ax.legend(facecolor='#1a0612', edgecolor='#f472b6', labelcolor='white', fontsize=9)
ax.grid(True, alpha=0.2, color='#f472b6'); ax.tick_params(colors='white')

# Plant fitness = sum over moths of (visits * pollen transfer)
# assume moths visit whatever they can feed on sufficiently
Lm_population = np.array([5, 8, 12, 15, 18, 20, 22, 25, 28])
Lm_freq       = np.array([0.05,0.08,0.15,0.20,0.18,0.15,0.10,0.06,0.03])
Lm_freq /= Lm_freq.sum()

def plant_fitness(Lt_val):
    F = 0
    for Lm, freq in zip(Lm_population, Lm_freq):
        eff = efficiency(Lt_val, Lm)
        # Visits only if positive efficiency above threshold
        if eff > 0.05:
            F += freq * eff * min(Lt_val/10.0, 1.0)  # outcrossing bonus with tube length
    return F

F = np.array([plant_fitness(l) for l in Lt])

ax = axes[1]; ax.set_facecolor('#1a0612')
ax.fill_between(Lt, 0, F, color='#f472b6', alpha=0.3)
ax.plot(Lt, F, color='#f472b6', linewidth=2.5)
opt_idx = np.argmax(F)
ax.axvline(Lt[opt_idx], color='#fde68a', linestyle='--', linewidth=1.5,
           label=f"optimum {Lt[opt_idx]:.1f} cm")
ax.set_xlabel('Flower tube depth (cm)', color='white')
ax.set_ylabel('Plant fitness', color='white')
ax.set_title('Plant fitness vs tube depth\n(integrated over moth population)',
             color='#fbcfe8', fontsize=11)
ax.legend(facecolor='#1a0612', edgecolor='#f472b6', labelcolor='white')
ax.grid(True, alpha=0.2, color='#f472b6'); ax.tick_params(colors='white')

# Coevolution time-series
ax = axes[2]; ax.set_facecolor('#1a0612')
n_gen = 200
tube = np.zeros(n_gen); tongue = np.zeros(n_gen)
tube[0] = 8.0; tongue[0] = 6.0
for t in range(1, n_gen):
    # tube evolves to maximise plant fitness given current tongue distribution
    # tongue slightly longer than tube is advantageous
    grad_tube   = min(0.3, (tongue[t-1] - tube[t-1]) * 0.1 + 0.05)
    grad_tongue = 0.05 * max(0.0, tube[t-1] - tongue[t-1] + 1)
    tube[t]   = tube[t-1]   + grad_tube   + 0.1*np.random.randn()
    tongue[t] = tongue[t-1] + grad_tongue + 0.1*np.random.randn()
ax.plot(tube,   color='#f472b6', linewidth=2.2, label='Flower tube (cm)')
ax.plot(tongue, color='#fbbf24', linewidth=2.2, label='Moth tongue (cm)')
ax.fill_between(np.arange(n_gen), tube, tongue, where=(tube<tongue), alpha=0.2, color='#fbbf24')
ax.fill_between(np.arange(n_gen), tube, tongue, where=(tube>=tongue), alpha=0.2, color='#f472b6')
ax.set_xlabel('Generation', color='white')
ax.set_ylabel('Length (cm)', color='white')
ax.set_title('Coevolutionary arms race\n(Darwin\'s orchid scenario)',
             color='#fbcfe8', fontsize=11)
ax.legend(facecolor='#1a0612', edgecolor='#f472b6', labelcolor='white')
ax.grid(True, alpha=0.2, color='#f472b6'); ax.tick_params(colors='white')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0308')

print(f"Initial tube/tongue: {tube[0]:.1f} / {tongue[0]:.1f} cm")
print(f"Final   tube/tongue: {tube[-1]:.1f} / {tongue[-1]:.1f} cm")
print(f"Tube grew by {tube[-1]-tube[0]:.1f} cm in {n_gen} generations")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

2. Nectar Economics

Nectar is a solution of sucrose, glucose and fructose with minor amino acids. There is a fundamental trade-off between energy per unit volume (rises linearly with sugar concentration) and drinking rate (falls exponentially with viscosity). The viscosity of a sucrose solution is approximately:

\[ \mu(c) = \mu_0 \exp(\alpha c), \qquad \alpha \approx 7 \text{ for w/w } c<0.6 \]

Three pollinator feeding mechanisms have different scaling of drinking rate with viscosity:

Suction feeding (hawk moths): Poiseuille-driven flow through the proboscis; rate \(\propto 1/\mu\). Optimum at ~35-40% sucrose.
Licking (hummingbirds, sunbirds): tongue uses capillary and elastic-recovery action; rate \(\propto 1/\sqrt\mu\). Optimum at ~20-25%.
Viscous dipping (bumblebees): tongue extension with hairy surface creates boundary-layer adhesion; rate \(\propto 1/\mu^{1/3}\). Optimum near 50%.

\[ \eta(c) = \frac{c \rho(c) \Delta H_{\text{sucrose}}}{\tau_{\text{drink}}(c)} \]

energy intake rate as function of concentration

Empirical measurements (Nicolson 2002; Pyke & Waser 1981) match these predictions remarkably well: bird-pollinated flowers average 22% sucrose, bee-pollinated 35%, bat- pollinated 17%.

2.1 Nectar Reward vs Production Cost

Nectar is not free. A single sunflower inflorescence produces about 2 mg of sugar per day - roughly 2% of the plant's daily photosynthate in peak bloom. Too little nectar reduces pollinator visitation; too much invites robbers and reduces outcrossing. The optimum is set by marginal fitness return:

\[ \frac{\partial W}{\partial N} = \frac{\partial W_{\text{visit}}}{\partial N} - \frac{\partial C_{\text{prod}}}{\partial N} = 0 \]

Python

script.py99 lines

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

# ======================================================================
# Optimal nectar concentration vs pollinator
# ----------------------------------------------------------------------
# Kim et al. (2011) derived the optimum:
#    eta(c) = E_dense(c) / T_drink(c)
# where
#    E_dense(c) = c * rho_s                         (energy per volume)
#    T_drink(c) = L^2 / (viscosity * pipe_action)
# viscosity of sucrose solution grows exponentially with c:
#    mu(c) = mu_water * exp(alpha*c)
#
# Suction feeders (bees, hawk moths):  peak at ~35% sugar
# Licking feeders (hummingbirds):       peak at ~23%
# Capillary feeders (butterflies):      peak at ~30%
# ======================================================================

c = np.linspace(0.01, 0.70, 300)             # mass fraction sucrose

mu_water = 1.0e-3
alpha    = 7.0                                 # mu(50%) ~ 30 mPa.s
mu       = mu_water * np.exp(alpha*c)

rho_sol  = 1000 + 385*c                        # kg/m^3
E_per_m3 = c * rho_sol * 16.7e6                # 16.7 MJ/kg sucrose

# Generic suction feeder (pressure-driven, Poiseuille):
#   Q ~ Delta_P * r^4 / (8 mu L)   ->   rate prop to 1/mu
rate_suct = 1.0 / mu
# Licking/capillary feeder:
#   Q prop to capillary rise v ~ sqrt(sigma/(mu)) ... but also tongue
#   refill time with viscosity
rate_lick = 1.0 / np.sqrt(mu)
# Viscous dipping (bumblebee): Q ~ 1/mu^(1/3) due to tongue retraction
rate_dip  = 1.0 / mu**(1./3.)

eta_suct = E_per_m3 * rate_suct
eta_lick = E_per_m3 * rate_lick
eta_dip  = E_per_m3 * rate_dip

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))
fig.patch.set_facecolor('#0a0308')

ax1.set_facecolor('#1a0612')
ax1.plot(c*100, eta_suct/eta_suct.max(), color='#f472b6', linewidth=2.2, label='Suction (hawk moth)')
ax1.plot(c*100, eta_lick/eta_lick.max(), color='#fde68a', linewidth=2.2, label='Licking (hummingbird)')
ax1.plot(c*100, eta_dip /eta_dip.max(),  color='#c084fc', linewidth=2.2, label='Viscous dipping (bumblebee)')

for rate, col, lbl in [(eta_suct,'#f472b6','Hawk moth'),
                       (eta_lick,'#fde68a','Hummingbird'),
                       (eta_dip ,'#c084fc','Bumblebee')]:
    idx = np.argmax(rate)
    ax1.scatter([c[idx]*100], [rate[idx]/rate.max()], color=col, edgecolors='white', s=80, zorder=5)
    ax1.annotate(f"{c[idx]*100:.0f}%", (c[idx]*100, rate[idx]/rate.max()),
                 xytext=(5,5), textcoords='offset points',
                 fontsize=10, color=col)
ax1.set_xlabel('Sucrose concentration (% w/w)', color='white')
ax1.set_ylabel('Normalised feeding rate (E/time)', color='white')
ax1.set_title('Optimal nectar concentration per pollinator',
              color='#fbcfe8', fontsize=11)
ax1.legend(facecolor='#1a0612', edgecolor='#f472b6', labelcolor='white')
ax1.grid(True, alpha=0.2, color='#f472b6'); ax1.tick_params(colors='white')

# Measured nectar concentration per pollinator type
ax2.set_facecolor('#1a0612')
data = [
    ('Hawk moth',   40, '#f472b6'),
    ('Butterfly',   35, '#fde68a'),
    ('Honeybee',    40, '#fbbf24'),
    ('Bumblebee',   35, '#c084fc'),
    ('Hummingbird', 22, '#60a5fa'),
    ('Sunbird',     22, '#86efac'),
    ('Bat',         17, '#f97316'),
]
names = [d[0] for d in data]
concs = [d[1] for d in data]
cols  = [d[2] for d in data]
ax2.barh(names, concs, color=cols, edgecolor='#fbcfe8', linewidth=1)
for i, v in enumerate(concs):
    ax2.text(v+0.8, i, f"{v}%", color='white', va='center', fontsize=10)
ax2.set_xlabel('Nectar sucrose concentration (%)', color='white')
ax2.set_title('Empirical nectar concentration vs pollinator\n(Nicolson et al. 2007)',
              color='#fbcfe8', fontsize=11)
ax2.tick_params(colors='white')
for sp in ax2.spines.values(): sp.set_color('#f472b6')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0308')

print("Optimum sucrose concentrations:")
print(f"  Suction (hawk moth)     : {c[np.argmax(eta_suct)]*100:4.1f}%")
print(f"  Licking (hummingbird)   : {c[np.argmax(eta_lick)]*100:4.1f}%")
print(f"  Viscous-dipping (bee)   : {c[np.argmax(eta_dip)]*100:4.1f}%")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

3. Deceptive Pollination

About one third of orchids (and many other families) offer no reward to pollinators, relying on deception. Three categories:

Food-source mimicry

Plant resembles a rewarding co-flowering species (Ophrys apifera mimicking bee orchids; Dactylorhiza sambucina with both yellow and purple morphs).

Sexual mimicry

Flower resembles and smells like a female insect of the pollinator species; males attempt copulation ("pseudocopulation"). Ophrys orchids use species-specific cuticular hydrocarbons identical to the female bee's sex pheromone.

Brood-site mimicry

Flower resembles a rotting animal or dung where flies lay eggs (Rafflesia, Amorphophallus, Stapelia).

3.1 The Ophrys Pheromone Trick

Ophrys sphegodes (early spider orchid) is pollinated by males of Andrena nigroaenea. The flower synthesises a pheromone mixture identical to that of the female bee's cuticular hydrocarbons: (Z)-7-pentacosene, (Z)-7-heptacosene, (Z)-9-heptacosene, (Z)-12-nonacosene. Males attempt to copulate with the labellum, hitting the pollinium and transferring it to the next flower. The orchid's pheromone is indistinguishable from the bee's by electroantennogram - a triumph of chemical mimicry.

3.2 Game-Theoretic Stability

Why don't pollinators evolve complete avoidance of deceivers? The answer is negative frequency dependence: when deceivers are rare, pollinators don't learn to avoid them fast enough. Formally, replicator dynamics on a simplex of strategies (honest / deceptive / signal-rich deceiver) admits interior equilibria as long as deception rate \(x_D\) stays below a learning-threshold. The simulation below integrates replicator dynamics with a pollinator-avoidance term.

Python

script.py94 lines

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

# ======================================================================
# Game theory of deceptive pollination
# ----------------------------------------------------------------------
# Honest plants produce costly nectar but earn pollinator fidelity;
# deceptive plants save on nectar but pollinators learn to avoid them.
# Solve a replicator dynamics on three strategies:
#   H (honest) : pays cost c, always delivers reward
#   D (deceptive) : no reward, pays nothing
#   S (signal-rich deceiver) : no reward, extra signal cost c_s
#
# Pollinator fraction that visits a plant type decays with fraction of
# deceptive flowers nearby (learned avoidance).
# ======================================================================

from scipy.integrate import odeint

c_h   = 0.3       # nectar cost of honest plant
c_s   = 0.1       # scent cost of deceptive plant
b     = 1.0       # pollination benefit per visit
# Plant frequencies x_H, x_D, x_S, x_H+x_D+x_S = 1

def visits(frac_deceptive, alpha=4.0):
    # learned avoidance: pollinators avoid all flowers if D fraction high
    return np.exp(-alpha * frac_deceptive)

def replicator(y, t):
    xH, xD, xS = y
    tot = xH + xD + xS
    xH /= tot; xD /= tot; xS /= tot
    frac_dec = xD + xS
    V   = visits(frac_dec)
    fH  = b * V - c_h
    fD  = b * V * 0.3                              # much lower than H
    fS  = b * V * 0.7 - c_s                        # signals help attract
    fbar = xH*fH + xD*fD + xS*fS
    return [xH*(fH-fbar), xD*(fD-fbar), xS*(fS-fbar)]

t = np.linspace(0, 100, 500)
inits = [[0.9, 0.05, 0.05],
         [0.5, 0.25, 0.25],
         [0.1, 0.45, 0.45],
         [0.33, 0.33, 0.34]]
colors = ['#f472b6','#fbbf24','#c084fc','#93c5fd']

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))
fig.patch.set_facecolor('#0a0308')

ax1.set_facecolor('#1a0612')
for y0, col in zip(inits, colors):
    sol = odeint(replicator, y0, t)
    ax1.plot(t, sol[:,0], color=col, linewidth=1.8, linestyle='-')
    ax1.plot(t, sol[:,1], color=col, linewidth=1.8, linestyle='--', alpha=0.8)
    ax1.plot(t, sol[:,2], color=col, linewidth=1.8, linestyle=':', alpha=0.8)

ax1.set_xlabel('Generation', color='white')
ax1.set_ylabel('Strategy frequency', color='white')
ax1.set_title('Replicator dynamics: honest vs deceptive\n(solid=H, dashed=D, dotted=S)',
              color='#fbcfe8', fontsize=11)
ax1.grid(True, alpha=0.2, color='#f472b6'); ax1.tick_params(colors='white')

# Phase portrait on simplex (project to xH vs xD, xS = 1 - xH - xD)
ax2.set_facecolor('#1a0612')
for y0 in inits:
    sol = odeint(replicator, y0, t)
    ax2.plot(sol[:,0], sol[:,1], linewidth=1.5)
    ax2.scatter([sol[0,0]], [sol[0,1]], color='white', s=60, zorder=5)
    ax2.scatter([sol[-1,0]], [sol[-1,1]], color='#fde68a', marker='*', s=150, zorder=5)

# Simplex edges
ax2.plot([0,1],[0,0],'#f472b6', linewidth=1)
ax2.plot([0,0],[0,1],'#f472b6', linewidth=1)
ax2.plot([0,1],[1,0],'#f472b6', linewidth=1)
ax2.set_xlim(0, 1); ax2.set_ylim(0, 1)
ax2.set_xlabel('x_Honest', color='white')
ax2.set_ylabel('x_Deceptive', color='white')
ax2.set_title('Phase portrait on strategy simplex', color='#fbcfe8', fontsize=11)
ax2.grid(True, alpha=0.2, color='#f472b6'); ax2.tick_params(colors='white')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0308')

# Analyse equilibrium
sol = odeint(replicator, [0.5,0.25,0.25], t)
print(f"Final honest      fraction: {sol[-1,0]:.3f}")
print(f"Final deceptive   fraction: {sol[-1,1]:.3f}")
print(f"Final signal-rich fraction: {sol[-1,2]:.3f}")
print("Interior equilibrium persists if deceivers keep some visitors.")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

4. Pollinator Fidelity & Constancy

From the plant's perspective, a pollinator is useful only if it consistently moves pollen between conspecifics. Pollinator constancyis the tendency of an individual to visit successive flowers of the same species even when alternatives are present (Darwin 1876). Three behavioural regimes:

Majoring: bees specialise on one abundant species for long bouts (hours or days). Driven by perceptual priming and spatial memory.
Minoring: brief opportunistic switches to a minor resource, often a novel or rewarding species. Exploration-vs-exploitation (see Bee M7).
Switching: frequency-dependent pollination; above a threshold abundance, switching rate declines rapidly.

Chittka et al. (1999) demonstrated that constancy depends on flower handling time: complex zygomorphic flowers require long learning so bees are reluctant to switch. Simple actinomorphic flowers favour generalist foraging.

From the plant perspective, attracting a specialist (one that visits only conspecifics) maximises pollen transfer efficiency but demands high signalling investment; attracting generalists is cheap but wastes pollen on heterospecifics. This trade-off shapes the diversity of flowers within a community: specialists bloom in narrow windows, generalists throughout the season.

4.1 Pollen-transfer Efficiency

If a pollinator visits species A a fraction \(p\) of the time and species B the remaining \(1-p\), then the fraction of A->A conspecific transfers is\(p^2\) (assuming independence). At \(p = 0.9\) this is 0.81; at\(p = 0.5\) only 0.25. Constancy is an enormous fitness advantage.

\[ W_{\text{plant}} \propto p^2, \quad \text{where } p = \text{pollinator fidelity} \]

5. Summary Table

Syndromes

Correlated trait suites: melittophily (bees, yellow/blue/UV, 35% nectar), ornithophily (birds, red, 20%), sphingophily (hawk moths, white, long tube), chiropterophily (bats, fermented, 17%), sapromyophily (carrion flies, dark, sulfide odour), anemophily (wind)

Tube-tongue matching

L_tube = L_tongue + epsilon; Darwin's 1862 prediction for Angraecum fulfilled by Xanthopan morganii 1903

Nectar optimum

Suction feeders (moths) ~35%; licking (birds) ~22%; viscous dipping (bumblebees) ~50%

Deception

Food mimicry (Ophrys-flowers), sexual mimicry (Ophrys apifera -> male Andrena), brood mimicry (Rafflesia, Stapelia)

Game theory

Replicator dynamics: interior equilibrium of honest + deceptive strategies persists with negative frequency dependence

Fidelity

Constancy maximises pollen transfer; W_plant proportional to p^2; complex flowers favour majoring behaviour

Majoring vs minoring

Bouts of specialised foraging with brief exploratory switches; complexity-dependent

Cross-reference

See /bee-biophysics/module2-vision-navigation for waggle dance coupling

References

Faegri, K. & van der Pijl, L. (1979). The Principles of Pollination Ecology, 3rd ed. Pergamon.
Proctor, M., Yeo, P. & Lack, A. (1996). The Natural History of Pollination. Harper Collins.
Darwin, C. (1862). On the Various Contrivances by Which British and Foreign Orchids are Fertilised by Insects. John Murray.
Nilsson, L. A. (1988). The evolution of flowers with deep corolla tubes. Nature, 334, 147-149.
Pauw, A., Stofberg, J. & Waterman, R. J. (2009). Flies and flowers in Darwin's race. Evolution, 63, 268-279.
Kim, W., Gilet, T. & Bush, J. W. M. (2011). Optimal concentrations in nectar feeding. PNAS, 108, 16618-16621.
Nicolson, S. W. (2002). Pollination by passerine birds: why are the nectars so dilute? Comparative Biochemistry and Physiology B, 131, 645-652.
Nicolson, S. W., Nepi, M. & Pacini, E. (eds) (2007). Nectaries and Nectar. Springer.
Schiestl, F. P. et al. (1999). Orchid pollination by sexual swindle. Nature, 399, 421-422.
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