If natality is represented by -B
If mortality is represented by -D
if immigration is represented -I
If emigration is represented by -E
If population density at time t+1 is represented by

Options

A. `N_(t+1)=N_t-[(B+1)]-[(D+E)]`
B. `N_(t+1)=N_t+[(B+1)]-[(D+E)]`
C. `N_(t+1)=N_t+[(B+1)]+[(D+E)]`
D. `N_(t+1)=N_t-[(B+1)]+[(D+E)]`

Answer

To find the population density at time \( t + 1 \), we need to consider the effects of natality, mortality, immigration, and emigration on the initial population density. Let's break this down step by step:

### Step 1: Understand the terms
- **Natality (B)**: This represents the number of births in the population during a specific time period. It contributes positively to the population density.
- **Mortality (D)**: This represents the number of deaths in the population during the same time period. It contributes negatively to the population density.
- **Immigration (I)**: This refers to individuals of the same species that move into the population from elsewhere. It also contributes positively to the population density.
- **Emigration (E)**: This refers to individuals of the population that leave to go elsewhere. It contributes negatively to the population density.

### Step 2: Define the initial population density
Let \( n \) be the population density at time \( t \).

### Step 3: Write the equation for population density at time \( t + 1 \)
The population density at time \( t + 1 \) can be calculated by starting with the initial population density and adjusting for the changes due to natality, mortality, immigration, and emigration.

The formula can be expressed as:
\[ n_{t+1} = n + B - D + I - E \]

### Step 4: Substitute the variables
From the question, we know:
- Natality is represented as \( B \)
- Mortality is represented as \( D \)
- Immigration is represented as \( I \)
- Emigration is represented as \( E \)

Thus, we can rewrite the equation as:
\[ n_{t+1} = n + B + I - D - E \]

### Step 5: Finalize the expression
The final expression for the population density at time \( t + 1 \) is:
\[ n_{t+1} = n + B + I - (D + E) \]

### Conclusion
This equation shows how the population density at time \( t + 1 \) is affected by the initial population density, the number of births, the number of individuals immigrating, and subtracts the number of deaths and individuals emigrating.