Exponential growth and age structure

The number of individuals born (B) =

bN

• b = per capita birth rate

• N = population already

The number of deaths in a population (D) =

dN

• d = per capita death rate

• N = population already

N_t+1 =

N_t + bN_t - dN_t or (N_t) (lambda)

r =

b - d

what is r equal to ?

The intrinsic rate of population increase per capita

lambda =

1 + r

What is lambda equal to?

Geometric rate of population increase

N_t =

(N₀) (lambda)^t

The equation N_t = (N₀) (lambda)^t is the equation for ___

exponential growth

dN/dt =

rN

What is dN/dt

the rate at which the population is increasing or decreasing

The calculus notation of exponential growth happens applies when

births and deaths happen continuously as opposed to during a specific breeding season

The calculus notation for N_t =

N₀ e^rt

What is a cohort?

All of the individuals born in a given year

Age structure is good to study what

Following a cohort through their life

What type of scale is a survivorship curve plotted on?

A logarithmic scale

Why are survivorship curves plotted on a logarithmic scale?

It makes a constant rate of mortality appear as a straight line

Type 1 survivorship

Juvenile survivorship is high and most mortality is among older individuals

Type 2 survivorship

Mortality rate is constant regardless of age

Type 3 survivorship

Older individual survivorship is high and most mortality is among juvenile individuals

Survivorship curves can take any shape except

They can’t go back up again as individuals cannot rise from the dead

How do you determine the survivorship curve of a species that is hard to monitor?

Measure the age at which skulls are found

What is Ro of a life table?

The net reproductive rate per individual

How do you determine Ro from a life table?

The sum of the column that multiplies proportion of surviving to day x and average number of seeds per individual during time interval

The net reproductive rate (LxMx) is calculated for overlapping generations. What is the underlying math principle?

A weighted average

How to determine the generation time from a life table?

The sum of the column: x lx mx. Then this sum is divided by Ro (=the sum of lxmx)

How to get from Ro to r in a generational population?

lambda = Ro so