What is a population? Population: A population is a group of interbreeding organisms of the same species. Population size: The number of individuals in a population. Population growth rate: The rate with which the number of individuals change over time.

Time (days, months or years) Population size N Population Dynamics: The fluctuation of population size through time.

Different types of Population Dynamics: Time N Random fluctuation N Time unchanging Time N Periodic oscillation Time increasing decreasing N

Human population growth Billions of People "It has been estimated that the human population of 6000 B.C. was about five million people, taking perhaps one million years to get there from two and a half million. The population did not reach 500 million until almost 8,000 years later -about 1650 A.D. This means it doubled roughly once every thousand years or so. It reached a billion people around 1850, doubling in some 200 years. It took only 80 years or so for the next doubling, as the population reached two billion around We have not completed the next doubling to four billion yet, but we now have well over three billion people. The doubling time at present seems to be about 37 years. Quite a reduction in doubling times: 1,000,000 years, 1,000 years, 200 years, 80 years, 37 years." Paul Ehrlich, Ph.D.,1968,

Population Size: N(t) = 8 N(t+1) = 6 The population declined. 1 year later Members of the population

Population Size: N(t) = 8 N(t+1) = N(t) = 6 The population declined: One was born, four died, two moved in, one moved out. X X X X 1 year later

Population growth models describe birth, death, immigration and emigration. Population size at time t+1 Number of births Number of deaths Number of immigrations Number of emigrations Population size at time t

Thomas Robert Malthus ( ) Wrote “Essay on Population” (1798)

Malthusian growth is unchecked population growth: A lot more…. N = 2 N = 4 N = 8 N = 16 N = 32 N = 64, 128, 256…

The “closed population” assumption: Let’s assume that there is no immigration and emigration..

Deriving Malthusian growth in mathematical terms:

substitute:

The discrete-time Malthusian growth model: One  parameter:  1+ b’ - d’  the finite per-capita population growth rate. One variable: N: the population size.

Excel Worksheets: Malthusian and Exponential growth

Number of viable bacteria LAG PHASE EXPONENTIAL GROWTH PHASE STATIONARY PHASE DEATH PHASE Time During the first hours of bacterial growth in a fresh nutrient solution:

Diagnosed HIV/AIDS cases in the United States: data by avert.org When a disease (virus,bacterium) first infects a new host:

The introduction of ring-necked pheasants to Destruction Island, Washington

2 male and 4 female pheasant were introduced in 1937 and monitored until 1942.

The introduction of reindeer to St. Paul and St.George Islands, Alaska

The accidental introduction of Bromus tectorum to Northwestern America:

1901

1976

Before 1900 Mack, 1981

1930

Fraction of eventual range (1930) Year

When do we see Malthusian growth? 1.In general, when birth rates exceed death rates: any species has the potential to grow exponentially. 2.Exponential growth can occur : when resources are many and risks are few (new introductions), when a species expands its range. 3.Exponential growth always ends after a while.

Summary: 1.Malthusian growth is “unchecked” population growth = growth without limits. 2.The Malthusian growth model has one parameter:, the difference of per capita birth and death rates. N(t+1) = N(t) 3.  populations grow, 0<  populations decline. 4.Any species has the potential to grow by constant multiples. 5.However, Malthusian growth always ends after a while.