The supervolcano eruption would disrupt the valley's ecosystem through a cascading chain of effects, impacting each trophic level with time lags. Here’s a structured analysis:

### **Immediate Effects (Weeks to Months):**
- **Plants**: 
  - Reduced sunlight (50%) severely limits photosynthesis, decreasing plant growth and biomass production. 
  - Ash deposition on leaves may further block light absorption, while soil acidification or nutrient imbalance from ash could stress root systems. 
  - Sensitive plant species may die off, while others adapt by conserving energy (e.g., shedding leaves, entering dormancy). 
  - **Result**: Rapid decline in plant productivity and population.

### **Medium-Term Effects (6 Months to 2 Years):**
- **Rabbits**: 
  - Depleted plant biomass leads to food scarcity. Herbivores face malnutrition, starvation, and reduced reproductive success (e.g., fewer offspring, lower survival rates). 
  - Increased competition for limited food accelerates population decline. 
  - **Result**: Rabbit population crashes due to elevated mortality and collapsed birth rates.
  
- **Plants (Secondary Effects)**: 
  - Reduced grazing pressure from declining rabbit populations might allow some plant recovery, but persistent ash and low light limit this. 
  - Resilient plant species (e.g., shade-tolerant shrubs) may gradually dominate, altering community structure.

### **Long-Term Effects (3+ Years):**
- **Foxes**: 
  - Depleted rabbit populations lead to food shortaship. Foxes experience starvation, reduced fertility, and increased juvenile mortality. 
  - Foxes may switch to alternative prey (e.g., rodents, insects), but if specialized, they struggle to adapt. 
  - **Result**: Sharp decline in fox population; possible local extinction if rabbits remain scarce.
  
- **Ecosystem-Wide Adjustments**: 
  - Trophic cascade stabilizes at lower biomass levels if ash persists. Energy flow remains reduced, sustaining smaller populations. 
  - Soil recovery (e.g., nutrient cycling from decomposing matter) could slowly benefit plants, but full recovery depends on sunlight restoration.

### **Additional Considerations:**
- **Climate Effects**: Prolonged dimming may lower temperatures, delaying plant growth cycles and stressing ectothermic species.
- **Disease & Stress**: Weakened plants and animals become more susceptible to pathogens, exacerbating declines.
- **Recovery Post-Eruption**: If ash clears after several years, plant regrowth could revive the ecosystem, but lag times in rabbit and fox reproduction may delay recovery.

### **Causal Chain Summary:**
**Sunlight reduction → Plant decline (immediate) → Rabbit starvation (medium-term) → Fox collapse (long-term)**, with secondary stressors (ash, temperature, disease) intensifying each step. The ecosystem may stabilize at reduced productivity or face irreversible changes if keystone species are lost.