To solve this problem, we need to understand the relationship between Net Primary Productivity (NPP) and Gross Primary Productivity (GPP) in an ecosystem.$\newline$The relationship is given by the equation:$\newline$GPP = NPP + R, where R is the energy used in respiration.$\newline$In this question, we are given the NPP of the first trophic level as $100x \ \mathrm{(kcal \ m^{-2} \ yr^{-1})}. \newline$The energy transfer between trophic levels is typically around 10\% efficient.$\newline$This means that each trophic level receives about 10\% of the energy from the level below it.$\newline$Let's calculate the energy available at each trophic level:$\newline \bullet$First trophic level (producers): NPP = $100x \ \mathrm{(kcal \ m^{-2} \ yr^{-1})} \newline \bullet$Second trophic level (primary consumers): Energy received = $\frac{10}{100} \times 100x = 10x \ \mathrm{(kcal \ m^{-2} \ yr^{-1})} \newline \bullet$Third trophic level (secondary consumers): Energy received = $\frac{10}{100} \times 10x = x \ \mathrm{(kcal \ m^{-2} \ yr^{-1})} \newline$Since the energy received by the third trophic level is x, this is the NPP for that level.$\newline$To find the GPP of the third trophic level, we need to consider the energy used in respiration.$\newline$However, the question asks for the GPP of the third trophic level, which is essentially the energy available to it, as calculated.$\newline$Therefore, the GPP of the third trophic level is $x \ \mathrm{(kcal \ m^{-2} \ yr^{-1})}. \newline$This corresponds to Option 4.