Rate of biomass production is expressed as :
(a) `(kcalm^(-2))yr^(-1)`
(b) `kcalg m^2yr^(-1)`
(c) `gm^3yr`
(d) `gm^(-2)yr`

Options

A. `(kcalm^(-2))yr^(-1)`
B. `kcalg m^2yr^(-1)`
C. `gm^3yr`
D. `gm^(-2)yr`

Answer

To determine the correct expression for the rate of biomass production, we need to analyze the options provided and understand the concept of productivity in ecological terms.

### Step-by-Step Solution:

1. **Understanding Biomass Production**: Biomass production refers to the generation of organic matter by living organisms, primarily through photosynthesis in plants. This process is measured in terms of productivity, which can be expressed in weight or energy.

2. **Units of Measurement**: Productivity can be measured in two main ways:
- **Weight**: This is often expressed in grams per square meter per year (g/m²/yr).
- **Energy**: This is typically expressed in kilocalories per square meter per year (kcal/m²/yr).

3. **Analyzing the Options**:
- **Option (a)**: `(kcal m^(-2)) yr^(-1)` - This represents energy per unit area per unit time, which is a valid unit for measuring productivity.
- **Option (b)**: `kcal g m^2 yr^(-1)` - This is incorrect as it mixes units of energy with weight and area inappropriately.
- **Option (c)**: `gm^3 yr` - This is incorrect as it represents volume per time, which is not applicable for biomass production.
- **Option (d)**: `gm^(-2) yr` - This is incorrect as it does not represent the correct units for biomass production.

4. **Conclusion**: The only correct option that accurately represents the rate of biomass production is option (a) `(kcal m^(-2)) yr^(-1)`.

### Final Answer:
The rate of biomass production is expressed as: **(a) `(kcal m^(-2)) yr^(-1)`**.