Solution (source code)

= Solution

With response rates and elasticity effectively fixed, changing $\lambda_2$ changes $m_2$ and hence intrinsic noise but not the environmental term. Observation (i) therefore indicates \b[extrinsic noise dominates], making the mean-dependent intrinsic contribution negligible. For a general feedback law whose elasticity changes substantially with the mean, compensation between terms is another possibility; independence from $\lambda_2$ alone would then not logically identify the dominant term.

Observation (ii) measures the local relaxation rate $\beta_2H$, which is larger under negative feedback. Observation (iii) is not explained by faster adjustment alone. At fixed susceptibility, increasing the response rate increases $\beta_2H/(\beta_1+\beta_2H)$, reducing time averaging and increasing transmitted environmental noise. Feedback lowers <variance> primarily by reducing susceptibility and the intrinsic term. Thus \b[rapid adjustment and low noise share a feedback mechanism but are not a direct causal equivalence].