Demography: Fecundity and Survival Probabilities

Questions and Answers

What is the formula to calculate fertility (Fi) for each age class, and what does it represent?

Fi = b(i) Pi, and it represents the number of offspring produced per female, discounting the survival probability for that age class.

What is the purpose of a Leslie Matrix, and how is it used in population demographics?

A Leslie Matrix is used to represent the growth of an age-structured population in matrix form, describing changes in population size due to mortality and reproduction.

In the context of a Leslie Matrix, what do the columns and rows represent?

Each column represents the age class at time t, and each row represents the age class at time t+1.

Why is it necessary to discount survival probability when calculating fertility (Fi) for each age class?

It is necessary to discount survival probability because the parent must survive through the age class to reproduce and have offspring counted. Signup and view all the answers

What is the difference between a fertility schedule and a survivorship schedule?

A fertility schedule shows the number of offspring per female for each age class, while a survivorship schedule shows the probability of survival for each age class. Signup and view all the answers

How does the Leslie Matrix incorporate both mortality and reproduction in population demographics?

The Leslie Matrix incorporates both mortality and reproduction by describing changes in population size due to mortality (survival probabilities) and reproduction (fertility rates). Signup and view all the answers

What is the significance of 'k' in the Leslie Matrix, and what does it represent?

k represents the number of age classes, and it is used to construct a k x k square matrix. Signup and view all the answers

What is the main advantage of using a Leslie Matrix to study population demographics?

The main advantage is that it provides a convenient matrix representation of life tables, allowing for projecting population size in the future. Signup and view all the answers

What is the per capita fecundity rate of females represented by the function b(x) in the context of population demographics?

The per capita fecundity rate of females. Signup and view all the answers

What does the value b(6) = 3 represent in the context of fecundity schedules?

A female of age 6 will give birth to an average of 3 female offspring. Signup and view all the answers

What is the purpose of tracking a cohort of individuals from birth to death in the context of survivorship schedules?

To measure the number of surviving individuals at the start of each year. Signup and view all the answers

What does the quantity l(x) represent in the context of survivorship schedules?

The proportion of the original cohort that survives to age x. Signup and view all the answers

How is the survivorship schedule l(x) calculated from the raw S(x) data?

By dividing the number of survivors to age x [Sx] by the original cohort [S(0)]. Signup and view all the answers

What does the survival probability g(x) represent in the context of life tables?

The probability of survival from birth to age x. Signup and view all the answers

What is the significance of the original cohort [S(0)] in the context of survivorship schedules?

It represents the total number of individuals at the start of the cohort. Signup and view all the answers

What is the purpose of using a life table in the context of population demographics?

To analyze the survival and mortality rates of a population. Signup and view all the answers

What is the term for the per capita fecundity rate of females in a population, as shown in the table?

b(x) Signup and view all the answers

What is the probability of survival from one age class to the next, represented by Pi in the life table?

l(i) / l(i-1) Signup and view all the answers

What is the term for the proportion of individuals surviving from birth to a given age, as represented by l(x) in the life table?

Survival probability Signup and view all the answers

How do age-based life tables, like the one shown, differ from age-class-based life tables?

Age-based life tables track individuals of specific ages, while age-class-based life tables group individuals into broader age categories. Signup and view all the answers

What is the purpose of a Leslie matrix, as depicted in the table?

To model the growth and decay of a population over time Signup and view all the answers

What is the term for the schedule of age-specific fecundity rates, as shown in the table?

Fecundity schedule Signup and view all the answers

What is the term for the schedule of age-specific survival probabilities, as shown in the table?

Survivorship schedule Signup and view all the answers

How do the elements of the Leslie matrix (F1, F2, ..., An) relate to the fecundity schedule and survivorship schedule?

They represent the per capita fecundity rates and survival probabilities for each age class. Signup and view all the answers

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Study Notes

Population Dynamics

Fecundity schedule refers to the number of offspring per female at each age class.

Survival Probabilities (Pi)

Pi is the probability of survival from one age class to the next, calculated as l(i) / l(i-1).
It represents the probability of an individual surviving from one age class to the next.

Fertility (Fi)

Fi is the fertility of a particular age class, calculated as b(i) Pi, which represents the number of offspring produced per female, discounting the survival probability for that age class.

The Leslie Matrix

The Leslie matrix is a convenient matrix representation of life tables, developed by P.H. Leslie in 1945.
It projects population size in the future, describing changes in population size due to mortality and reproduction.

Leslie Matrix Representation

A Leslie matrix is a k x k square matrix, where k is the number of age classes.
Each column represents the age class at time t, and each row represents the age class at time t+1.
Each entry in the matrix represents a transition or change in the number of individuals due to births or mortality.

Survivorship Schedule [l(x)]

The survivorship schedule, l(x), represents the proportion of the original cohort that survives to age x.
It is calculated as Sx / S(0), where Sx is the number of survivors to age x, and S(0) is the original cohort size.

Survival Probability [g(x)]

Survival probability, g(x), gives the probability of survival from birth to age x.
It is used to compare the survival of different growth patterns.