Which of the following is the unit of productivity of an Ecosystem?

The correct answer is (KCal m^–2)yr^–1.

Productivity of an ecosystem refers to the rate at which organic matter or biomass is accumulated per unit area over a specified time period. It is essentially a measure of the rate of energy flow or biomass production.

Let's break down the components of the units:
1. Energy/Biomass: Measured in kilocalories (KCal) for energy content, or grams (g) for mass.
2. Area: Measured in square meters (m^–2).
3. Time: Measured per year (yr^–1) to represent the rate of production over time.

Therefore, the rate of productivity is expressed as energy accumulated per unit area per unit time, which gives the unit:
$(\mathrm{KCal}{m}^{–2}){\mathrm{yr}}^{–1}$
Alternatively, in terms of biomass, it can also be expressed as $g{m}^{–2}{\mathrm{yr}}^{–1}$.

Comparing the options:
- gm^–2 and KCal m^–2 represent standing crop or biomass/energy at a given time (not a rate).
- KCal m^–3 represents energy per unit volume, which is not standard for ecosystem productivity (since ecosystems are typically mapped by surface area).
- (KCal m^–2)yr^–1 correctly represents the rate of energy accumulation per unit area per year.