The eruption of a supervolcano and the subsequent reduction in sunlight by 50% would have a profound impact on the ecosystem of the valley, affecting the populations of plants, rabbits, and foxes in a cascading manner. Here's the likely chain of events:

**Immediate Effects (0-6 months):**

1. **Plants:** With a 50% reduction in sunlight, photosynthesis rates would decrease significantly. This would lead to a reduction in plant growth and productivity, as they struggle to generate enough energy to sustain themselves. This effect would be immediate, as the plants would quickly respond to the reduced light availability.
2. **Rabbits:** Initially, the rabbit population might not be directly affected, as they would still have existing plant material to consume. However, the reduced plant growth would mean less new vegetation for them to eat, and their food supply would begin to dwindle.
3. **Foxes:** The fox population would not immediately feel the effects of the eruption, as they would still have a stable prey population (the rabbits) to hunt.

**Medium-Term Effects (6-24 months):**

1. **Plants:** As the reduced sunlight persists, plant populations would continue to decline due to reduced growth and reproduction. This would lead to a decrease in the overall biomass of the plant community, making it even harder for the ecosystem to recover.
2. **Rabbits:** With the plant population in decline, the rabbit population would begin to feel the effects of reduced food availability. They would start to compete more intensely for the limited resources, leading to malnutrition, reduced reproduction, and increased mortality.
3. **Foxes:** As the rabbit population begins to decline, the foxes would start to feel the effects of reduced prey availability. They would need to work harder to find food, leading to increased energy expenditure and potentially reduced reproduction rates.

**Long-Term Effects (2-5 years and beyond):**

1. **Plants:** If the reduced sunlight persists, the plant community may undergo a compositional shift, with more shade-tolerant species becoming dominant. However, the overall plant biomass and diversity would likely remain reduced, as the ecosystem adapts to the new, lower-energy environment.
2. **Rabbits:** The rabbit population would likely decline significantly, potentially by 50% or more, as they struggle to survive on the reduced plant resources. This decline would be driven by malnutrition, reduced reproduction, and increased mortality.
3. **Foxes:** The fox population would decline even more severely, potentially by 70% or more, as they face a severe shortage of prey. Without sufficient rabbits to hunt, the foxes would need to adapt to alternative food sources, which might not be readily available. This could lead to a trophic cascade, where the loss of a key predator (the foxes) has further effects on the ecosystem.

The reasoning behind this chain of events is based on the following principles:

1. **Energy limitation:** The reduction in sunlight reduces the energy available to the ecosystem, which cascades through the food chain.
2. **Trophic cascades:** Changes in one population (e.g., plants) affect the populations that depend on them (e.g., rabbits), which in turn affect the populations that depend on them (e.g., foxes).
3. **Competition and adaptation:** Populations will compete for limited resources, leading to reduced growth, reproduction, and survival. Over time, populations may adapt to the new environment, but this can take years or even decades.
4. **Ecosystem resilience:** The ecosystem's ability to recover from the disturbance will depend on factors like the duration of the reduced sunlight, the diversity of the plant and animal populations, and the presence of alternative food sources.

Keep in mind that this is a hypothetical scenario, and the actual effects of a supervolcano eruption on an ecosystem would depend on various factors, including the severity of the eruption, the duration of the reduced sunlight, and the specific characteristics of the affected ecosystem.