Lec 20 and 21 - BIS2B Lectures 20 & 21 Fall 2009...

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1 BIS2B Lectures 20 & 21 Fall 2009 Population 1798-1830 1859
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2 A population is a group of interbreeding individuals, which means that populations are single species. Population growth is the change (or not) in numbers of individuals with time. Growth can be positive, numbers increase. It can be negative, numbers decrease. And, growth can be “zero,” which means numbers do not change.
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3 Change in population, In open populations: number of + Births - Deaths + Immigrants (immigration), - Emigrants (emigration) Closed, isolated populations: (new species, island populations) Births – Deaths (no immigration or emigration).
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4 Birth
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5 The simplest model population growth considers birth only, simple binary fission with no death, bacteria, yeast, or any other cell divide mitotically, split in two each time period. Let’s consider that all daughter cells live. This kind of growth occurs early in growth phase, culture is uncrowded, plenty of resources, Little accumulated waste.
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6 Binary Fission Model 1* 2 = 2, 2* 2 =4, 4* 2 =8, 8* 2 =16, etc. N t = number in population after t time periods. N 0 = number at beginning, zero time periods. Nt = 1*2*2*2*2, which is 1* 2 4 (or 1* 2 ^4) N 0 in this case equals 1. The reproductive rate in this case is 2 .
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7 The full name is, net, per capita, finite rate of growth usually termed λ or R. Finite implies whole units, not subdivided, countable on your fingers. Synonym “discrete.” The finite equation of population growth is what you worked at in lab.
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8 Rates as distinguished from numbers of birth and death events . B is the number of births. b is the birth rate, per capita , per unit time b = B/ N /t D is the number of deaths. d is the death rate, per capita, per unit time d= D/ N /t “net” means considering both births and deaths. λ is the net, per capita growth rate per unit time, λ = (b - d) λ =(b - 0) when there are no deaths, as per the simplest equation.
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Now to generalize this finite equation, Nt = 1*2*2*2*2, which is 1*2 4 (or 1*2^4) (dropping the * for multiplication) N 1 = λ N 0 (N 0 = 1) N 2 = λ N 1 = λλ N 0 N 3 = λλλ N 0 , which is N 3 = λ 3 N 0 , …. etc . N
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Lec 20 and 21 - BIS2B Lectures 20 & 21 Fall 2009...

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