Module 6: Phylloxera & Mildews

The late 19th century nearly destroyed European viticulture: the phylloxera catastrophe (root aphid Daktulosphaira vitifoliae, imported on American cuttings in the 1860s) killed >6 million hectares of vines across France, Italy, Spain, Germany, and the rest of Europe over three decades. Simultaneously, downy and powdery mildews—Plasmopara viticola and Erysiphe (Uncinula) necator—crossed the Atlantic in the opposite direction, attacking the newly-exposed V. vinifera monocultures of Europe. The solution—grafting onto American rootstocks and the Bordeaux mixture fungicide—permanently re-engineered European viticulture. This module traces the biology of phylloxera, the two mildews, Botrytis cinerea, Pierce’s disease, and the grapevine leafroll viruses, and formalises the population-dynamics and forecasting models that underpin modern vineyard protection.

1. Phylloxera: The 19th-Century Catastrophe

Daktulosphaira vitifoliae (originally Phylloxera vastatrix, Planchon 1868) is a tiny (~1 mm) sap-sucking aphid native to eastern North America, where it coevolved with American Vitis species (V. riparia, V. rupestris, V. berlandieri, V. labrusca) which evolved hypersensitive necrotic resistance. European V. vinifera, domesticated from the Caucasus-Anatolian wild grape (Module 0), has no such coevolutionary history and is almost completely defenceless.

Phylloxera was first recorded on V. vinifera in the southern Rhone in 1863; by 1870 it had destroyed vineyards across Languedoc; by 1880 it had spread to Bordeaux, Burgundy, Germany, Italy, and Spain. Total vineyard area in France collapsed from 2.4 million ha in 1875 to 1.5 million ha by 1889. Estimates of cumulative economic damage exceed 10 billion gold-franc equivalents (roughly 20% of French GDP at the time).

\[\text{Root-gall population:}\;\frac{dN}{dt} = r\,N\left(1 - \frac{N}{K\cdot S(\text{rootstock})}\right)\]

Logistic-carrying-capacity model with rootstock susceptibility factor $S$; $S = 1$ for V. vinifera, $S \approx 0.05$ for pure V. riparia.

Biology and Life Cycle

Phylloxera has a complex life cycle with up to five morphs in its native American range: (i) fundatrix (leaf-gall female), (ii) gallicola (leaf-gall feeder), (iii) radicicola (root-gall feeder), (iv) sexupara (winged dispersal form), and (v) sexuales (oviparous overwintering). On V. vinifera in Europe the cycle is reduced essentially to the root-gall parthenogenetic cycle, which makes European phylloxera populations genetically homogenous and easier to manage by uniform rootstock strategy.

Damage Mechanism

Root-feeding phylloxera injects saliva that induces nodosity (swelling) on young roots and tuberosity (gall) on older roots. The galls disrupt vascular continuity, and secondary infection by soil fungi (Fusarium, Pythium) accelerates tissue breakdown. Susceptible vines decline over 3–5 years from first infestation to total collapse.

2. The Rootstock Solution

The solution, proposed independently by Jules-Emile Planchon and Charles Valentine Riley in the 1870s, was to graft V. vinifera scion wood onto American Vitis rootstock. The American roots carry coevolved resistance; the vinifera fruiting canopy produces the wine we drink. After initial resistance from traditionalists, grafting became universal in Europe by 1900 and is today mandatory in every major wine region except a few phylloxera-free sanctuaries (pure-sand soils in parts of the Medoc, Colares in Portugal, Kanaan vineyards in Chile).

Commercial Rootstocks

Over 30 commercial rootstocks are available, each with different combinations of parent species:

Rootstock	Parentage	Phylloxera resistance	Niche
Riparia Gloire	V. riparia	Very high	Cool humid, low vigour
Rupestris du Lot	V. rupestris	Very high	Deep dry soils
3309 Couderc	riparia x rupestris	Very high	Temperate, Burgundy
101-14 Mgt	riparia x rupestris	Very high	Humid, cool
SO4	berlandieri x riparia	Very high	Moderate lime, Germany
5BB Kober	berlandieri x riparia	Very high	High lime, Germany/Italy
110 Richter	berlandieri x rupestris	Very high	Hot dry, Mediterranean
140 Ruggeri	berlandieri x rupestris	Very high	Very hot dry, Sicily
1103 Paulsen	berlandieri x rupestris	Very high	Warm dry, Tuscany
AxR1	vinifera x rupestris	Moderate (failed)	California 1960s-80s

The AxR1 Disaster

The most notorious rootstock failure is AxR1 (Aramon × Rupestris Ganzin 1), which carries partial V. vinifera parentage. It was widely planted in California from the 1960s with moderate phylloxera resistance but proved vulnerable to a new phylloxera biotype (“biotype B”) in the late 1980s. The resulting replanting wave, completed 1990–2005, cost California growers an estimated $1 billion+ and affected ~75% of North Coast acreage. The lesson: any residual V. vinifera genetic contribution to a rootstock is a ticking time bomb.

3. Downy Mildew (Plasmopara viticola)

Downy mildew, caused by the oomycete Plasmopara viticola (sister to the plant-pathogenic genus Phytophthora), was introduced from North America to Bordeaux around 1878. Like phylloxera, it struck the post-phylloxera replanted vineyards of Europe in the 1880s and caused multiple catastrophic vintages (notably 1878, 1882, 1885).

Biology

P. viticola overwinters as oospores in fallen leaf litter. In spring, a warm wet period (>10 °C, >10 mm rain) triggers oospore germination and release of zoospores. Zoospores splashed onto leaves encyst, germinate, and penetrate through stomata. Infection produces a white- grey sporulation on the abaxial leaf surface, along with yellow “oil spots” on the adaxial surface. Secondary cycles every 5–7 days amplify the epidemic during a wet summer.

\[\text{Infection risk:}\;\;R(T, \text{RH}) = f_T(T)\cdot f_{RH}(\text{RH})\]

Mills 1949 Scott-Mills model: infection favourable window at T 18-24 °C and RH > 90%.

Bordeaux Mixture (Millardet 1880s)

The Bordeaux mixture (bouillie bordelaise), a suspension of copper sulfate and hydrated lime, was discovered by Pierre-Marie-Alexis Millardet in 1885. He observed that vines near roadsides, which growers had sprayed with a copper-lime mixture to discourage theft (the blue residue being visibly unappetising), were free of downy mildew. Systematic trials confirmed the fungicidal effect, and Bordeaux mixture became the universal control through the 20th century.

\[\text{CuSO}_4 + \text{Ca(OH)}_2 \rightarrow \text{Cu(OH)}_2 + \text{CaSO}_4\]

The colloidal copper hydroxide adheres to leaf surface and releases Cu²⁺ ions toxic to zoospores.

Modern Fungicides

Contemporary downy-mildew control combines copper formulations (still the mainstay of organic viticulture; EU limit 4 kg Cu/ha/yr averaged over 7 years), phosphonates (Fosetyl-Al, systemic), CAA fungicides (mandipropamid, translaminar), QoI strobilurins (resistance risk high, so used sparingly), and the newer QiI class (ametoctradin, amisulbrom). Forecasting models (Mills-Scott, Broome, UC Davis UC-IPM, EPI, INRA Milvit) reduce spray count by timing applications to predicted infection-favourable periods rather than calendar intervals.

4. Powdery Mildew (Erysiphe necator)

Powdery mildew (Erysiphe necator, formerly Uncinula necator, Oidium tuckeri) is caused by an obligate biotrophic ascomycete fungus. Introduced to Europe from North America via Belgium in 1845, it preceded phylloxera and downy mildew and caused the 1850s European vintage crisis. Unlike downy mildew, powdery mildew does NOT require free water for infection; conidia germinate at 85% RH and temperatures of 15–28 °C. This makes it a bigger problem in dry Mediterranean climates than downy mildew.

Biology

Powdery mildew colonises the surface of leaves, shoots, and berries without penetrating beyond the epidermis (it is a surface parasite that extends haustoria into epidermal cells for nutrient uptake). White powdery mycelium on green tissue gives the characteristic appearance. Overwintering is by cleistothecia (sexual fruiting bodies) in bark crevices or by dormant mycelium in infected buds (“flag shoots”).

\[\text{Powdery (surface):}\;\;\text{biotroph} + \text{haustorium}\quad\text{vs.}\quad\text{Downy (internal):}\;\;\text{biotroph} + \text{endophytic}\]

Key contrast: powdery is sulfur-susceptible (surface contact); downy requires systemic or translaminar fungicides.

Sulfur Dusting

Elemental sulfur has been used against powdery mildew since the 1850s. Applications of 3–8 kg S/ha as a fine dust or wettable powder release H₂S vapour that inhibits fungal respiration. Sulfur remains effective and is the backbone of organic powdery-mildew control. Modern synthetic alternatives include DMI (demethylation-inhibitor, e.g. tebuconazole, myclobutanil), SDHI (boscalid, fluopyram), and QoI (kresoxim-methyl). Resistance has emerged against QoI and DMI in most growing regions, motivating rotation among modes of action.

Cultivar Susceptibility

Among V. vinifera, Chardonnay and Cabernet Sauvignon are highly susceptible; Carmenère and Syrah are moderately resistant. American Vitis species (V. labrusca, V. rotundifolia) and their hybrids (Concord, Muscadine, Seyval Blanc, many PIWI varieties) carry genetic resistance and are grown in eastern North America partly for this reason.

5. Botrytis cinerea: Noble Rot and Gray Rot

Botrytis cinerea (teleomorph Botryotinia fuckeliana) is a necrotrophic ascomycete fungus with a Jekyll-and-Hyde relationship with viticulture. In the right autumn conditions (humid misty mornings + dry warm afternoons), Botrytis infection of ripe white-grape berries produces “noble rot” (pourriture noble), concentrating sugar and developing glycerol and the aroma precursors of Sauternes, Tokaj, and Trockenbeeren- auslese. In the wrong conditions (sustained cool humidity), it produces “gray rot” (pourriture grise), a destructive disease that ruins harvests.

\[\text{Noble rot}:\;\;\text{humid AM} + \text{dry warm PM}\;\Rightarrow\;\text{slow dehydration} + \text{Botrytis metabolism}\]

Ideal Sauternes microclimate: Ciron-Garonne confluence generates autumn fog, followed by sunny afternoons.

Biochemistry of Noble Rot

Noble-rotted berries show (i) 30–50% water loss, concentrating sugar to 35–40 °Brix; (ii) partial metabolism of sugar by the fungus, producing 5–15 g/L glycerol; (iii) secretion of laccase enzyme, oxidising anthocyanins (hence noble rot is used for white wines only); (iv) development of botryticin and other extracellular polysaccharides; and (v) formation of C13-norisoprenoids and aromatic terpenes giving the honeyed, apricot, beeswax character of Sauternes.

Gray Rot and Control

Gray rot develops under sustained moisture and attacks berries with broken skin (hail damage, powdery mildew, bird peck). It propagates rapidly through clusters, producing off-flavors (oxidation, mouldy note), elevated volatile acidity, and laccase that destabilises finished red wine color. Control: canopy openness to promote air circulation, vineyard sanitation, anti-Botrytis fungicides (fenhexamid, boscalid, fludioxonil) at veraison and pre-harvest.

6. Xylella fastidiosa and Pierce’s Disease

Pierce’s disease, caused by the xylem-limited bacterium Xylella fastidiosa (subsp. fastidiosa), is endemic to the southern United States, Mexico, and Central America. The bacterium is transmitted by xylem-sap-feeding leafhoppers (sharpshooters), most notoriously the glassy- winged sharpshooter (Homalodisca vitripennis), which invaded southern California from the southeastern US in the 1990s.

Infected vines show scorched leaves, delayed ripening, and progressive dieback; V. vinifera vines typically die within 1–5 years. There is no cure. Control is entirely by vector management (systemic neonicotinoid insecticides, removal of riparian Xylella reservoirs) plus breeding of resistant cultivars (UC Davis PD-R hybrids carry resistance genes from V. arizonica).

European Spread

X. fastidiosa was detected on olive trees in Puglia (Italy) in 2013 (subsp. pauca), causing the catastrophic olive quick-decline syndrome. Related strains have since been detected on almond and ornamentals in France, Spain, and Portugal. The geographic expansion of Xylella is one of the top current threats to European Mediterranean viticulture.

7. Grapevine Leafroll and Other Viruses

Grapevine leafroll disease is a complex of at least nine serologically distinct viruses (GLRaV-1 through GLRaV-9), belonging to the genera Ampelovirusand Closterovirus. GLRaV-3 is the most economically damaging, causing yield losses of 20–40%, delayed ripening (7–14 days), reduced anthocyanin accumulation, and the characteristic red-pigmented inter-veinal downward-rolling leaves in late season on red cultivars.

Transmission

Leafroll viruses are primarily transmitted by mealybugs (Pseudococcus longispinus, Planococcus ficus) and soft scales (Neopulvinaria innumerabilis). They are also transmitted efficiently through grafting, which is why certified virus-tested planting material (indexed in tissue culture or by ELISA) is critical for new plantings. Once established in a vineyard, leafroll is effectively incurable; eradication requires vine removal and mealybug control.

Other Viruses

Grapevine red blotch virus (GRBV): relatively recently characterised (2012); causes similar symptoms to leafroll but is transmitted by treehoppers rather than mealybugs.
Grapevine fanleaf virus (GFLV): nepovirus transmitted by dagger nematodes (Xiphinema index); causes fanleaf degeneration and short-node symptoms.
Grapevine fleck virus (GFkV): endemic, largely latent on vinifera; diagnostic concern mostly in certification programs.
Rugose wood complex: GVA, GVB, GVD vitiviruses cause corky bark and stem pitting, disrupt graft unions.

8. Disease-Forecasting Models

Modern integrated pest management (IPM) replaces calendar-based spraying with forecasting-triggered applications. The approach is mathematically mature and uses weather-station data (often in-vineyard) plus phenological stage to estimate daily infection risk.

\[\text{Spray decision:}\;\;\int_{t_0}^{t} R(\tau)\,d\tau > \theta \Rightarrow \text{apply}\]

Cumulative risk above a threshold triggers a spray; reset after application with residual protection period.

Prominent Forecast Systems

Mills-Scott (1946, 1949): downy mildew T + leaf-wetness duration; foundational model.
UC Davis UC-IPM: powdery mildew risk based on three consecutive days > 21 °C at 6 h duration.
EPI (État Potentiel d’Infection, France): INRA forecast integrating oospore maturity, temperature, and rainfall.
Broome (Italy): downy-mildew model based on sporulation-infection-incubation cycle.
Milvit (INRA): next-generation Plasmopara model with spatial mesh coverage.
VineLogic / DMCast (Australia): integrated downy/powdery/Botrytis risk platform.

Biotrophic vs. Necrotrophic

A useful taxonomic distinction: biotrophs (powdery mildew, downy mildew, leafroll virus) require living host tissue and cause progressive disease without killing the host outright; necrotrophs (Botrytis gray rot, Fusarium) kill host tissue and feed on the dead substrate. Control strategies differ: biotrophs are vulnerable to systemic fungicides that move through the host; necrotrophs need surface-acting fungicides applied prophylactically.

Phylloxera life cycle and rootstock strategy

9. Resistance Breeding (PIWI Varieties)

The long-term alternative to chemical control is breeding grape cultivars with durable resistance genes introgressed from American and Asian Vitisspecies. The German acronym PIWI (Pilzwiderstandsfähig, “fungus-resistant”) denotes cultivars with stacked resistance loci for downy and powdery mildew, bred at institutions like JKI Geilweilerhof, Freiburg, and Udine.

Examples include Regent (downy/powdery resistance, Germany 1967 release), Solaris, Johanniter, Cabernet Cortis, Souvignier Gris, and Sauvignac. Resistance is typically conferred by the Rpv3, Rpv10, Rpv12 (downy) and Run1, Ren1, Ren3 (powdery) loci. These cultivars permit 70–90% reduction in fungicide spray count and are especially attractive for organic and biodynamic viticulture; EU member states are increasingly permitting them in appellations (notably Bordeaux approved a trial list in 2021 including Touriga Nacional and the resistant Arinarnoa, Castets, Marselan).

10. Synthesis

The 19th-century transatlantic disease exchange permanently rewired European viticulture: phylloxera forced grafting onto American rootstocks; downy mildew created the market for copper-based fungicides; powdery mildew drove sulfur dusting. The 20th century added synthetic fungicides, systemic insecticides, and forecasting models. The 21st century is returning toward biological and genetic control: PIWI cultivars, biocontrol agents (Ampelomyces quisqualis on powdery, Trichoderma on Botrytis), and precision spraying guided by canopy-level sensors and UAV imagery. Climate change is shifting disease pressure poleward and intensifying epidemics in newly humid regions (southern England, parts of Sweden now see downy mildew), while extending growing seasons in warm regions increases secondary-cycle risk. Module 7 now turns from vineyard pathology to the biochemistry of fermentation and wine-making.

Simulation 1: Phylloxera Root-Gall Population Dynamics

Integrate a logistic population-dynamics model for Daktulosphaira vitifoliae on own-rooted V. vinifera and on five commercial rootstocks (Riparia Gloire, 3309C, 110R, AxR1, and a fully-resistant hybrid). Reproduce the classic 3–5 year collapse on susceptible scion and the ~10 year failure curve of AxR1 under biotype-B pressure.

Python

script.py142 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from scipy.integrate import odeint

# Root-gall population dynamics of Daktulosphaira vitifoliae (phylloxera) on
# susceptible V. vinifera vs resistant American-hybrid rootstock.
#
# The population dynamics follow a logistic-carrying-capacity form modified
# by a rootstock-dependent suitability factor S(rootstock). On susceptible
# V. vinifera roots (S = 1.0) the carrying capacity is high and galls develop
# unconstrained; on resistant rootstocks (S << 1), the carrying capacity is
# sharply reduced because the root tissue forms a hypersensitive necrotic
# response (Granett 2001) that isolates the aphid's feeding site.
#
# Coupled vine-damage model:
#   dN/dt = r * N * (1 - N / (K * S))            phylloxera on roots
#   dH/dt = -d * N / (K * S)                     vine health (normalized)
#
# where r = intrinsic growth rate (~0.15 per week), K = max sustainable
# population on susceptible root (~50k per vine), S = rootstock susceptibility
# factor, d = damage rate coefficient.

weeks = np.linspace(0, 260, 1200)   # 5 years

# Rootstock susceptibility table (relative to ungrafted V. vinifera)
rootstocks = {
    'Own-rooted V. vinifera':    {'S': 1.00, 'color': '#f43f5e'},
    'Riparia Gloire (pure riparia)': {'S': 0.05, 'color': '#22d3ee'},
    '3309 Couderc (riparia x rupestris)': {'S': 0.08, 'color': '#fcd34d'},
    '110 Richter (berlandieri x rupestris)': {'S': 0.06, 'color': '#a855f7'},
    'AxR1 (vinifera x rupestris)': {'S': 0.35, 'color': '#fb923c'},
}

r = 0.06   # per week intrinsic growth
K = 5.0e4  # per vine max on susceptible
d = 0.0015 # damage rate per 1000 phylloxera

def model(y, t, S):
    N, H = y
    dN = r * N * (1 - N / (K * S + 1.0))
    dH = -d * N * H / (K * S + 1.0)
    return [dN, dH]

fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(15, 11))
fig.patch.set_facecolor('#0a0a1a')
for ax in [ax1, ax2, ax3, ax4]:
    ax.set_facecolor('#0a0a1a')
    ax.tick_params(colors='#e9d5ff')
    for spine in ax.spines.values():
        spine.set_color('#581c87')
    ax.grid(True, color='#3b0764', alpha=0.35)

N0 = 50.0    # initial inoculum
H0 = 1.0     # normalized vine health
populations = {}
healths = {}
for name, p in rootstocks.items():
    sol = odeint(model, [N0, H0], weeks, args=(p['S'],))
    populations[name] = sol[:,0]
    healths[name] = sol[:,1]

# Panel 1: phylloxera population trajectories (log scale)
for name, p in rootstocks.items():
    ax1.semilogy(weeks / 52.0, np.maximum(populations[name], 1),
                 color=p['color'], linewidth=2.3, label=name + f' (S={p["S"]:.2f})')
ax1.axhline(1000, color='#fde68a', linestyle='--', alpha=0.5, label='1000-insect economic threshold')
ax1.set_xlabel('Years after infestation', color='#e9d5ff', fontsize=11)
ax1.set_ylabel('Phylloxera per vine (log)', color='#e9d5ff', fontsize=11)
ax1.set_title('Root-gall population by rootstock',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax1.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=8)

# Panel 2: vine health trajectories
for name, p in rootstocks.items():
    ax2.plot(weeks / 52.0, healths[name], color=p['color'], linewidth=2.3, label=name)
ax2.axhline(0.3, color='#f43f5e', linestyle='--', label='vine dead (H<0.3)')
ax2.set_xlabel('Years after infestation', color='#e9d5ff', fontsize=11)
ax2.set_ylabel('Vine health index (0-1)', color='#e9d5ff', fontsize=11)
ax2.set_title('Vine decline vs. rootstock',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax2.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=8)

# Panel 3: time-to-vine-death on susceptible vs hybrid
death_times = {}
for name, p in rootstocks.items():
    idx = np.where(healths[name] < 0.3)[0]
    if len(idx) > 0:
        death_times[name] = weeks[idx[0]] / 52.0
    else:
        death_times[name] = np.nan
names_s = list(death_times.keys())
y_vals = [death_times[n] if not np.isnan(death_times[n]) else 10.0 for n in names_s]
colors_s = [rootstocks[n]['color'] for n in names_s]
ax3.barh(range(len(names_s)), y_vals, color=colors_s,
         edgecolor='#f3e8ff', linewidth=1.5)
ax3.set_yticks(range(len(names_s)))
ax3.set_yticklabels([n.split(' ')[0] for n in names_s], color='#e9d5ff', fontsize=9)
for i, v in enumerate(y_vals):
    lbl = f'{v:.1f} y' if not np.isnan(death_times[names_s[i]]) else 'no death'
    ax3.text(v + 0.15, i, lbl, color='#f3e8ff', fontsize=9, va='center')
ax3.set_xlabel('Years to vine death', color='#e9d5ff', fontsize=11)
ax3.set_title('Time to collapse: susceptible vs. resistant',
              color='#f3e8ff', fontsize=12, fontweight='bold')

# Panel 4: cumulative yield-loss integral over 10 years (trapezoid)
yrs_10 = 10 * 52
for name, p in rootstocks.items():
    sol = odeint(model, [N0, H0], np.linspace(0, yrs_10, 600), args=(p['S'],))
    yield_rel = np.maximum(sol[:,1], 0.0)
    total_yield = np.trapezoid(yield_rel, np.linspace(0, yrs_10, 600) / 52.0)
    ax4.bar(name.split(' ')[0], total_yield,
            color=p['color'], edgecolor='#f3e8ff', linewidth=1.5)
ax4.set_ylabel('Cumulative relative yield (vine-years)', color='#e9d5ff', fontsize=11)
ax4.set_title('10-year cumulative yield by rootstock (trapezoid)',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax4.tick_params(axis='x', rotation=25, labelsize=9)

print("Phylloxera (Daktulosphaira vitifoliae) population dynamics:")
print("Rootstock susceptibility factor S (ungrafted V. vinifera = 1.0):")
for name, p in rootstocks.items():
    print(f"  {name}: S={p['S']:.2f}")

print("\nTime to vine death (H<0.3) by rootstock:")
for name, t_death in death_times.items():
    if not np.isnan(t_death):
        print(f"  {name}: {t_death:.1f} years")
    else:
        print(f"  {name}: vine survives (resistance intact)")

# Summary: why AxR1 failed in California
print("\nHistorical note: AxR1 (vinifera x rupestris) was widely planted in")
print("California in 1970s-80s. Its vinifera parentage left a residual")
print("susceptibility (S~0.35) that a new biotype 'B' overcame in late 1980s,")
print("causing massive replant wave 1990-2000 at ~\$1B+ cost.")

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')
print("\nGranett 2001: hypersensitive necrotic response of American Vitis")
print("roots isolates phylloxera feeding sites; pure riparia/rupestris")
print("rootstocks remain the gold standard 150 years after Millardet 1880s.")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Simulation 2: Mills Downy-Mildew Forecast

Implement the Mills-Scott disease-severity index for Plasmopara viticola under a stochastic summer weather time series. Generate the 2-D temperature × humidity risk map, overlay primary and secondary infection cycles, and compare calendar-based vs. Mills-triggered spray strategies on cumulative disease severity over the season.

Python

script.py152 lines

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

# Mills disease-severity index for downy mildew (Plasmopara viticola).
# The Mills (1949) model predicts infection-favourable periods as a function
# of temperature and leaf-wetness duration. Downy mildew requires >90%
# relative humidity (free water) for sporangial germination; the rate is
# maximal near 22 C and falls off above 28 C and below 10 C.
#
# Primary infection (Mills-Scott):
#   Infection = 1 if (T, LW) falls within temperature-duration curve
#
# Risk integrates temperature and humidity:
#   R(T, RH) = f_T(T) * f_RH(RH)
# where f_T is a skew-normal peaking at 22 C and f_RH is a sigmoid rising
# steeply above 85% RH.

np.random.seed(1)
days = np.arange(1, 121)   # June 1 -> end September

# Synthetic weather time series (temperate Bordeaux-like)
T = 18.0 + 6.0 * np.sin(2*np.pi*days/120.0 + 0.6) + np.random.normal(0, 2.0, size=days.size)
RH = 70.0 + 15.0 * np.sin(2*np.pi*days/30.0) + np.random.normal(0, 6.0, size=days.size)
RH = np.clip(RH, 40.0, 100.0)
rain = np.random.exponential(3.0, size=days.size) * (np.random.rand(days.size) < 0.2)

# Mills-Scott temperature response
def f_T(T):
    # Asymmetric: sharp rise from 8 to 22, plateau 18-24, decline above 26
    return np.exp(-((T - 22.0)**2) / (2 * 6.0**2)) * (T > 8) * (T < 32)

def f_RH(RH):
    # Sigmoid risk above 85%
    return 1.0 / (1.0 + np.exp(-(RH - 88)/3.5))

def f_rain(rain):
    # Rain-splash amplifies sporangial release
    return 1 - np.exp(-rain / 3.0)

# Primary risk
risk = f_T(T) * f_RH(RH) * (1 + 0.5 * f_rain(rain))
risk = risk / risk.max()

# Secondary cycle: after initial infection, latent period 5-7 days, then
# renewed sporulation. This is what produces the "mildew explosion"
# pattern during wet summers.
latent = 6   # days from infection to new sporangia
secondary = np.zeros_like(risk)
for t in range(latent, len(days)):
    secondary[t] = 0.4 * risk[t-latent] * (risk[t] > 0.3)

# Cumulative disease severity
threshold = 0.4
infection_days = risk > threshold
cum_severity = np.cumsum(risk * infection_days + secondary)

# Panel 1: weather time series
ax1.plot(days, T, color='#fcd34d', linewidth=1.8, label='Temperature (C)')
ax1.plot(days, RH/5.0, color='#22d3ee', linewidth=1.8, label='RH/5 (%)')
ax1.bar(days, rain, color='#60a5fa', alpha=0.55, label='Rain (mm)')
ax1.set_xlabel('Day of summer', color='#e9d5ff', fontsize=11)
ax1.set_ylabel('T / RH / rain', color='#e9d5ff', fontsize=11)
ax1.set_title('Synthetic Bordeaux-like summer weather',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax1.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=8)

# Panel 2: Mills risk index
ax2.plot(days, risk, color='#f43f5e', linewidth=2.3, label='Primary risk')
ax2.plot(days, secondary, color='#a855f7', linewidth=2.0, linestyle='--', label='Secondary cycles')
ax2.axhline(threshold, color='#fde68a', linestyle=':', label='Spray threshold')
ax2.fill_between(days, 0, risk, where=(risk > threshold),
                 color='#f43f5e', alpha=0.25, label='Infection-favourable')
ax2.set_xlabel('Day of summer', color='#e9d5ff', fontsize=11)
ax2.set_ylabel('Mills risk index', color='#e9d5ff', fontsize=11)
ax2.set_title('Mills 1949 downy mildew risk',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax2.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=8)

# Panel 3: 2-D temperature x humidity risk map
T_grid = np.linspace(6, 34, 60)
RH_grid = np.linspace(40, 100, 60)
TT, RR = np.meshgrid(T_grid, RH_grid)
R2 = f_T(TT) * f_RH(RR)
R2 = R2 / R2.max()
cs = ax3.contourf(TT, RR, R2, levels=14, cmap='magma')
ax3.contour(TT, RR, R2, levels=[0.3, 0.6, 0.85], colors='#f3e8ff',
            linewidths=1.2)
ax3.set_xlabel('Temperature (C)', color='#e9d5ff', fontsize=11)
ax3.set_ylabel('Relative humidity (%)', color='#e9d5ff', fontsize=11)
ax3.set_title('Plasmopara viticola T x RH risk map',
              color='#f3e8ff', fontsize=12, fontweight='bold')
cb = fig.colorbar(cs, ax=ax3)
cb.set_label('Infection risk', color='#e9d5ff')

# Panel 4: cumulative severity + Bordeaux-mixture protection scenarios
# Scenario A: no spray, B: calendar every 14 d, C: Mills-forecast triggered
baseline = cum_severity
calendar_spray = np.copy(risk)
for t in range(0, len(days), 14):
    calendar_spray[t:t+10] *= 0.3   # 70% suppression for ~10 d after spray
cum_calendar = np.cumsum(calendar_spray * (calendar_spray > threshold))

triggered = np.copy(risk)
for t in range(2, len(days)):
    if risk[t-1] > threshold * 0.8 and RH[t] > 85:
        triggered[t:t+10] *= 0.25
cum_trig = np.cumsum(triggered * (triggered > threshold))

ax4.plot(days, baseline, color='#f43f5e', linewidth=2.3, label='No spray')
ax4.plot(days, cum_calendar, color='#fcd34d', linewidth=2.3, label='Calendar 14-d spray')
ax4.plot(days, cum_trig, color='#22d3ee', linewidth=2.3, label='Mills-triggered spray')
ax4.set_xlabel('Day of summer', color='#e9d5ff', fontsize=11)
ax4.set_ylabel('Cumulative severity', color='#e9d5ff', fontsize=11)
ax4.set_title('Management strategies: cumulative disease',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax4.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=9)

# Integrate seasonal infection-favourable days
favourable_days = np.sum(risk > threshold)
cum_infect_total = np.trapezoid(risk, days)
print(f"Seasonal infection-favourable days: {favourable_days}")
print(f"Cumulative Mills index integral (trapezoid): {cum_infect_total:.2f}")

# Summary
print("\nDowny mildew (Plasmopara viticola) Mills-Scott model:")
print("  - oomycete (sister to Phytophthora)")
print("  - requires free water >90% RH for germination")
print("  - temperature optimum 22 C, failure >28 C")
print("  - secondary cycle every 5-7 days during wet summers")
print("")
print("Control:")
print("  - Bordeaux mixture (CuSO4 + lime, Millardet 1880s)")
print("  - Copper fungicides: still 6-10 kg/ha/yr standard for organics")
print("  - Phosphonate fungicides (Fosetyl-Al) systemic")
print("  - CAA fungicides (mandipropamid) translaminar")
print("  - Forecasting: Mills-Scott, Broome, EPI, INRA Milvit")

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')
print("\nMills-triggered spray reduces severity with ~half the interventions")
print("of calendar spray -- the foundation of modern IPM in viticulture.")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Key References

• Planchon, J.-E. (1874). Les vignes américaines: leur culture, leur résistance au phylloxera, et leur avenir en Europe. Montpellier.

• Granett, J., Walker, M. A., Kocsis, L. & Omer, A. D. (2001). “Biology and management of grape phylloxera.” Annual Review of Entomology, 46, 387–412.

• Millardet, P.-M.-A. (1885). “Traitement du mildiou par le mélange de sulfate de cuivre et de chaux.” Journal d’Agriculture Pratique.

• Mills, W. D. (1944, 1949). “Efficient use of sulfur dusts and sprays during rain to control apple scab; extended to grape mildew.” Cornell Agricultural Extension Bulletin.

• Blanc, S., Wiedemann-Merdinoglu, S., Merdinoglu, D. & Mestre, P. (2012). “A reference genetic map of Muscadinia rotundifolia and identification of Ren5, a new major locus for resistance to grapevine powdery mildew.” TAG, 125, 1663–1675.

• Dell, K., Cobb, A. & Gubler, W. (2004). “Disease management in grape.” UC ANR Publication 3343.

• Gessler, C., Pertot, I. & Perazzolli, M. (2011). “Plasmopara viticola: a review of knowledge on downy mildew of grapevine and effective disease management.” Phytopathologia Mediterranea, 50, 3–44.

• Gubler, W. D., Rademacher, M. R. & Vasquez, S. J. (1999). “Control of powdery mildew using the UC Davis powdery mildew risk index.” APSnet.

• Ribera, A., Bai, Y., Wolters, A.-M. A., van Treuren, R. & Trindade, L. M. (2020). “A review on the genetic resources, domestication and breeding history of grapevine (Vitis vinifera L.).” Genetic Resources and Crop Evolution, 67, 1331–1350.

• Daane, K. M., Almeida, R. P. P., Bell, V. A. et al. (2012). “Biology and management of mealybugs in vineyards.” In: Arthropod Management in Vineyards, Springer.

• Almeida, R. P. P. & Purcell, A. H. (2003). “Biological traits of Xylella fastidiosa strains from grapes and almonds.” Applied and Environmental Microbiology, 69, 7447–7452.

• Maree, H. J., Almeida, R. P. P., Bester, R. et al. (2013). “Grapevine leafroll-associated virus 3.” Frontiers in Microbiology, 4, 82.

• Pouget, R. (1990). Histoire de la lutte contre le phylloxera de la vigne en France. INRA Editions.

← Module 5: Sugar, Acid & pH Balance Module 7: Fermentation & Wine Biochemistry →