Step 1: Understanding the Concept:
Gross Primary Productivity (GPP) is the total rate at which solar energy is captured by autotrophs to produce organic matter.
Community Respiration (R) is the total energy consumed by all organisms (producers, consumers, and decomposers) in the ecosystem for metabolic processes.
Stability in an ecosystem refers to a state of equilibrium, often achieved in a climax community.
Step 2: Detailed Explanation:
In a stable ecosystem, there is a balance between energy gain (production) and energy loss (respiration).
During the early stages of succession, GPP is typically greater than R, leading to an accumulation of biomass.
As the community reaches its stable climax stage, the rate of organic matter production (GPP) becomes almost equal to the rate of consumption (R).
This means the Net Ecosystem Productivity (NEP = GPP $-$ R) approaches zero.
If GPP were less than R, the ecosystem would lose its biomass and eventually collapse.
Thus, for long-term stability, GPP must be equal to R.
Step 3: Final Answer:
In a stable or climax ecosystem, the total production is balanced by total community respiration, resulting in the relationship GPP = R.