**Immediate Effects:**

1. **Plants:** With sunlight reduced by 50%, the rate of photosynthesis in plants will significantly decrease. This will lead to slower growth and reduced reproduction, resulting in a lower biomass and a scarcity of food resources for rabbits. Some plant species may be unable to survive the reduced sunlight, leading to decreased plant diversity.

2. **Rabbits:** As plant growth slows and food becomes scarce, the rabbit population will experience immediate stress due to the reduced availability of their primary food source. This will likely result in decreased reproductive rates, increased competition for food, and higher mortality rates.

3. **Foxes:** Initially, foxes may experience minimal impacts since the rabbit population won't decline instantly. However, as rabbits become scarce, foxes will face increased competition for food, and their population may start to decrease due to starvation and lowered reproductive rates.

**Medium-term Effects:**

1. **Plants:** Over time, the reduced sunlight continues to suppress plant growth and reproduction. Plant populations may not recover to previous levels, leading to long-term changes in the ecosystem structure. More resilient vegetation that can survive with less sunlight may dominate, altering the plant community composition.

2. **Rabbits:** With persistently limited food supply, the rabbit population will significantly decrease. This decline will lead to a dramatic reduction in rabbit density, and potentially result in local extirpations if food scarcity is extreme. The reduced rabbit population also means a potential decrease in genetic diversity.

3. **Foxes:** As rabbits become scarce, foxes will face a critical food shortage. The fox population will undergo a more marked decline as individuals struggle to find sufficient food, leading to increased mortality, lowered reproductive success, and possibly migration to other areas in search of food.

**Long-term Effects:**

1. **Plants:** If the ash-induced solar dimming persists for several years, the plant ecosystem may stabilize at a new equilibrium. Species adapted to lower light conditions might dominate, potentially transforming the valley’s ecological landscape, with lasting reductions in biomass and biodiversity.

2. **Rabbits:** The rabbit population, having undergone significant reductions, may reach a new equilibrium at a much lower density. This population might consist of individuals better adapted to the changed environment, but the population size and genetic diversity may take years, if ever, to recover to pre-eruption levels.

3. **Foxes:** In the long term, if food resources remain diminished, the fox population may stabilize at a lower density, or be forced to migrate permanently to areas with more resources. The fox population may not recover to its original size unless the rabbit population rebounds significantly and the overall ecosystem recuperates.

In summary, the eruption of the supervolcano sets off a chain of events where diminished sunlight leads to reduced plant growth, impacting the rabbit population, and subsequently causing stress on the fox population. Each step of this chain reflects the interdependent nature of ecological networks, demonstrating how changes in one component can cascade through the entire system.