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Lecture 10

BIOL 230 Lecture 10: BIOL 230- Week 5 Learning Outcomes

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BIOL 230
Christopher Kopp

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 immigrationpopulation sizenumber of individuals leave populations: deaths and emigration  Closed population dynamics o Number of individuals enter population: birth population sizenumber 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  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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