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Lecture 10

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Biology

BIOL 230

Christopher Kopp

Fall

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BIOL 230- Week 5 Learning Outcomes
Population Growth & Regulation
Work through geometric and exponential population growths
Reindeer on Pribilof Islands, Alaska
o 1910: 4 males and 22 female reindeer introduced to St. Paul Island
Increased to 2000 in 30 years (1940)
o 1944: 5 males and 24 female reindeer, introduced to St. Matthew Island
Increased to 6000 in 19 years
o After reach peaks, quickly crashed
St. Matthew went from 6000 to 42 in a short period of time
The deer ran out of food
Lichens (significant component of the winter diet) had been eliminated
Why don’t populations expand infinitely?
o Why care about this question?
o For thousands of years our population grew relatively slowly, reaching 1 billion for the first time
in 1825.
o Now we are adding 1 billion people every 13 years
Explosive growth of the Human Population
o Why do we (humans) believe that factors and natural laws governing all other specie survival,
not apply to us?
Exponential growth
o Population can grow exponentially when conditions are favorable, but exponential growth cannot
continue indefinitely.
What would be some of the potential consequences if the world human population
continued to increase at the current rate?
Clean water will become scare and water bourn diseases and contamination more
common
Many animal species that we rely on for food such as fish will go extinct
Etc
Understand that population growth is the difference between growth and deaths
Understand that changes in population size are the product of perc capita growth rate and population
size
Explain the difference between geometric and exponential growth using examples from natural
populations
Explain when the geometric and exponential growth curves XX
Population dynamics
o Number of individuals enter population: birth and immigrationpopulation sizenumber of
individuals leave populations: deaths and emigration
Closed population dynamics
o Number of individuals enter population: birth population sizenumber of individuals leave
populations: deaths
Group activity- in slides Jan 31- how to calculate per capita birth rate, etc…
Geometric Population Growth
o If the population doubles every year, then: N1 = N0 * 2^t
N0 is a short hand way to say Nxx
o N2=N1*2, N3=N0*2^3
o More generally, for any geometric growth rate lamda: Nt=N0*lamda^t
Lambda o Nt=N0*lambda^t
o If lambda =1, to population doesn’t grow
o XXXXX
Geometric growth is a discrete model
o If a population reproduces in synchrony at regular time intervals XXX
o Snow geese are counted in August. We don’t know exactly what the population is rest of year
o If we don’t know exactly what the population is rest of year, it doesn’t make sense to ask about
how fast the population is growing at any instant.
Exponential Growth
o In many species, individuals do not reproduce in synchrony at discrete time periods, they
reproduce continuously and generations can overlap (ex. Humans)
o When these populations increase smoothly XXXbu
o What if we could assume that births and deaths occurred continuously over time?
Rate of growth at a point in time= dN/dt
=(births-deaths)/dt
=(per capita birth rate*N*dt-per capita death rate*N*dt)/dt
=(per capita birth rate-per capita death rate)*N
=(per capita rate of change in number of individuals*N
=r*N
o R is constant, it doesn’t change, but N does and that leads to the exponential increase
What if we integrate dN/dt= Rn?
o Nt=N0*e^rt
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