Productivity is the rate of production of biomass expressed in terms of
i) `("kcal" m^3)yr^(-1)` ii) `g^(-2) yr^(-1)`
iii) `g^(-1) yr^(-1)` iv) `("kcal " m^(-2))yr^(-1)`

Options

A. ii
B. iii
C. ii and iv
D. i and iii

Answer

To determine the correct expression for productivity in terms of biomass, we need to analyze the given options step by step.

### Step 1: Understanding Productivity
Productivity refers to the rate at which biomass is produced in an ecosystem. It can be expressed in terms of energy or weight.

### Step 2: Analyzing the Options
We have four options to evaluate:

1. **`("kcal" m^3) yr^(-1)`**: This unit represents energy per volume per year. While productivity can be expressed in terms of energy, it is typically not in cubic meters (m³) but rather in square meters (m²) for area-based productivity.

2. **`g^(-2) yr^(-1)`**: This unit is not correctly formatted. It suggests grams per square meter per year, but the negative exponent indicates an incorrect representation of units.

3. **`g^(-1) yr^(-1)`**: This unit also suggests grams per individual per year, which is not a standard way to express productivity in an ecosystem context.

4. **`("kcal" m^(-2)) yr^(-1)`**: This unit represents energy per area per year, which is a standard way to express productivity in terms of energy.

### Step 3: Identifying Correct Options
From the analysis:
- The second option is incorrect due to the negative exponent.
- The third option is also incorrect due to its representation.
- The first option is incorrect as it uses volume instead of area.
- The fourth option is correct as it expresses productivity in terms of energy per area.

### Conclusion
The correct expressions for productivity in terms of biomass are:
- **`g m^(-2) yr^(-1)`** (weight-based productivity)
- **`("kcal" m^(-2)) yr^(-1)`** (energy-based productivity)

Thus, the correct answer is option **(iv)** and option **(ii)**.

### Final Answer
The correct options for expressing productivity are:
- ii) `g m^(-2) yr^(-1)`
- iv) `("kcal" m^(-2)) yr^(-1)`