Here is some data for a cohort of 400 individuals of a species whose abundance was tracked for 6 years (its maximum lifespan).For one-year age intervals from birth to 6 years, the number of survivors 400,200,100,40,20,10 & 0. The corresponding per capita birth rate are 0.1,2.0,3.0, 4.0,4.0,3.0 and 0.0 .What is the basic reproductive rate $$R_0$$.​

Correct option is A

• The basic reproductive rate (R0R_0$$R_0$$)is defined as the average number of offspring that an individual is expected to produce over its lifetime.
• It is a measure of reproductive success under specific environmental conditions and serves as an indicator of population trends (increasing, stable, or decreasing).

Interpretation of  $$R_0$$ Values:

• If R0>1R_0 > 1R0​>1 → The population is expected to grow, as each individual, on average, produces more than one offspring.
• If R0=1R_0 = 1R0​=1 → The population remains stable, as each individual replaces itself on average.
• If R0<1R_0 < 1R0​<1 → The population is expected to decline, as each individual produces, on average, fewer than one offspring.

Survivorship (lxl_xlx​)

• lxl_xlx​ represents the proportion of the original cohort that survives to age $x$.
• It is calculated by dividing the number of individuals surviving to age $x$ by the initial number of individuals in the cohort.

Age-Specific Fertility (mxm_xmx​)

• mxm_xmx​ represents the per capita birth rate or the number of offspring produced by an individual of age $x$.

Basic Reproductive Rate (R0R_0R0​) Formula

Where:

• lxl_xlx​ = Survivorship at age $x$
• mxm_xmx​ = Age-specific fertility rate at age $x$
• $\omega$ = Maximum lifespan of the cohort

Given data:

The number of survivor at age (x) : 400,200,100,40,20,10,0

Per capita birth rates (mx): 0.1,2.0,3.0,4.0,4.0,3.0,0.0

we need to calculate the proportion of survivors (lx) for each age class by dividing the number of survivors of each age by the initial number of 400.

​$$l_0$$= $$\frac{400}{400}$$  = 1.0

​$$l_1$$= $$\frac{200}{400}$$  = 0.5

$$l_2$$​= $$\frac{100}{400}$$  =0.25

​$$l_3$$ = $$\frac{40}{400}$$  = 0.1​

$$l_4$$ =$$\frac{20}{400}$$  =0.05

​$$l_5$$ = $$\frac{10}{400}$$ = 0.025

​$$l_6$$ = $$\frac{0}{400}$$ = 0.0

Now Calculate $$R_0$$ = 

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