Changes in Population Sizes SBI4U Miss Richardson

Measuring Population Change Populations can be open (have migration) or closed (have no migration, ie: island) Populations are affected by births, deaths, immigration and emigration Change =  [(births + immigration)] – (death + emigration)]    x 100% per capita                           Initial population size (n)

Population Growth Models Population growth depends on the interaction between the population and the environment. There are three common models: Geometric Growth Exponential Growth Logistic Growth

Geometric Growth, λ The population grows at a fixed rate over a fixed time interval Expressed as a decimal or percent Seen in individuals who reproduce at fixed time intervals N(t) = N(0) λt λ = N(t+1)/N(t)

Example Deer exhibit geometric growth.  With an initial population of 1000 deer there are 250 births, 100 deaths in a year.  Calculate the geometric growth rate The population in 3 years The population in 10 years

Example

Exponential Growth Describes a population growing continuously at a constant rate The rate constant for exponential growth is r and r = birth rates (b) – death rates (d) The instantaneous growth rate is derived through calculus and represented by this equation. dN/dt = rN0 The doubling time of this type of growth can be approximated by this simplified formula td = 0.69            r

Example Bacteria exhibit exponential growth with sufficient food and space. If you start with 100 bacteria and they have an exponential growth rate of 0.4 per hour, calculate the instantaneous rate the doubling time how many bacteria will there be in 3 doubling times?

Example

Logistic Growth This type of growth describes a population growing continuously at a constant rate but is limited by the carrying capacity of the environment, K. The instantaneous growth is represented by this equation. r = the intrinsic growth rate N = population at a given time K is the carrying capacity of the environment

Example Population of Moose r (K-N)/K Growth Rate dN/dt 10 0.4 990/1000 3.96 20 980/1000 7.84 100 900/1000 36

r-strategists Species that live close to their biotic potential (r) are referred to as r-strategists These individuals: Have short life span Become sexually mature at young age Produce large broods of offspring Provide little/no parental care

K-strategists Species that live close to their carrying capacity (K) These individuals: Have long life spans Become sexually mature later in life Produce few offspring per reproductive cycle Provide a high level of parental care