The eruption of a supervolcano that dims sunlight by 50% in the valley for several years would trigger a cascading ecological response across plants, rabbits, and foxes. Below is the breakdown of effects across timeframes:

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### **Immediate Effects (First Months)**  
1. **Plants**:  
   - **Reduced photosynthesis**: With 50% less sunlight, plants experience a rapid drop in energy production. Growth stalls, flowering/seed production declines, and some species (especially light-demanding ones) begin to die off.  
   - **Stress responses**: Plants may shed leaves or allocate resources to survival over reproduction, reducing overall biomass.  

2. **Rabbits**:  
   - **Food scarcity**: Herbivores face reduced plant availability. Competition intensifies, and rabbits may shift to less nutritious or novel food sources (e.g., bark, roots) to survive.  
   - **Physiological stress**: Poor nutrition weakens individuals, lowering reproduction rates and increasing vulnerability to disease.  

3. **Foxes**:  
   - **Minimal immediate impact**: Rabbit populations remain high initially, so foxes continue hunting without noticeable disruption. However, increased hunting effort may emerge as rabbits disperse more widely to forage.  

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### **Medium-Term Effects (1–3 Years)**  
1. **Plants**:  
   - **Population decline**: Many plant species collapse due to prolonged low energy input. Shade-tolerant or perennial species may dominate, but overall diversity and biomass drop sharply.  
   - **Soil degradation**: Reduced root systems lead to erosion, further impairing plant recovery.  

2. **Rabbits**:  
   - **Population crash**: Starvation and low reproduction reduce rabbit numbers significantly. Weakened individuals are more susceptible to predation, disease, or harsh environmental conditions.  
   - **Behavioral shifts**: Survivors may expand their diets or migrate (if possible), but valley isolation limits options.  

3. **Foxes**:  
   - **Food shortages escalate**: Declining rabbit populations force foxes to hunt alternative prey (if available) or scavenge. Specialized foxes face starvation, leading to reduced survival and reproduction.  
   - **Social disruption**: Intraspecific competition increases as territories break down.  

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### **Long-Term Effects (Beyond 3 Years, Continued Ash Cover)**  
1. **Plants**:  
   - **New equilibrium**: Only highly resilient species (e.g., mosses, lichens, or shade-adapted perennials) persist. Ecosystem productivity stabilizes at a much lower level, with simplified plant communities.  
   - **Feedback loops**: Reduced herbivory (from fewer rabbits) may allow limited plant recovery, but low sunlight caps biomass.  

2. **Rabbits**:  
   - **Stabilized at low densities**: Populations persist only if plants stabilize and rabbits adapt to scarce, low-quality food. Genetic diversity may plummet, increasing extinction risk.  
   - **Evolutionary pressure**: Survivors might develop traits like slower metabolisms or broader diets.  

3. **Foxes**:  
   - **Local extinction likely**: With rabbits critically reduced, foxes face trophic collapse. Generalist predators might survive by switching prey (e.g., insects, rodents), but specialists likely vanish.  
   - **Ecosystem reorganization**: If foxes disappear, mesopredators or omnivores may rise, altering food-web dynamics.  

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### **Causal Chain Summary**  
1. **Energy reduction**: Dimmed sunlight slashes primary productivity, shrinking the energy base for the entire ecosystem.  
2. **Trophic cascade**: Lower plant biomass → fewer rabbits → fewer foxes, with time-lagged effects propagating up the food chain.  
3. **Resilience thresholds**: Species with broad niches or rapid reproduction (plants/rabbits) have marginal survival advantages, while specialists (foxes) face extinction.  

**Conclusion**: The valley’s ecosystem transitions to a depauperate state, with simplified communities and disrupted interactions. Recovery hinges on the ash clearing and the persistence of remnant populations to repopulate or recolonize.