# ZOL 355 Lecture Notes - Lecture 15: Doubling Time, Exponential GrowthPremium

6 pages98 viewsSpring 2018

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**preview**shows pages 1-2. to view the full**6 pages of the document.**Lecture 15: Population Structure & Growth

• Introduction

o Why study populations

▪ Key to saving endangered species

▪ Helps us control pests

▪ Managing fish and game

populations

▪ Study Diseases/Parasites

▪ Population response to humans

o Characteristics of populations

▪ Size or abundance (number of

individuals)

▪ Growth

▪ Reproductive rate

▪ Age distribution

▪ Immigration/emigration

▪ Spacing

• Population Growth

o Factors that influence population growth:

▪ factors leading to Increases in pop size

• number of births in the entire population (B)

• number of immigrants in the entire population (I)

▪ factors leading to decrease in pop size

• number of deaths in the entire population (D)

• number of emigrants in the entire population (E)

▪ Population size is N = B + I - D - E

o Equation to estimate population size (N) at time t+1

▪ Nt+1 = Nt + B + I - D - E

o If the population size in 2012 = 1000 what will the population size be in 2013 if there

are 20 births, 5 deaths and there is no immigration or emigration.

▪ Nt = N2012 = 1000

▪ B = 20

▪ D= 5

▪ Nt+1 = 1000 + 20 – 5 =1015

▪ From this point forward we assume I = 0 and E = 0, a closed population

▪ (WILL HAVE A PROBLEM LIKE THIS ON THE EXAM - AND MANY OTHERS)

o Equation to estimate change in population size (population growth) over a specific time

period

▪ Nt+1-Nt = B - D

▪ ΔN = B – D

o Now we want to understand how N changes over time and to estimate N at any point

in time.

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• Models of population growth

o Exponential growth - continuous addition of new

individuals

o Exponential growth equation

▪ Nt = Noert

▪ Nt = number individuals at time t (size at time t)

▪ No = initial number of individuals

▪ r = per capita growth rate

▪ e = base of natural log (2.72)

o Understanding r

▪ r = per capita (per individual) growth rate

▪ r = b – d

▪ b = per capita birth rate (average births per individual) number of births per

individual per unit time units are births/(individual * time)

▪ d = per capita death rate number of deaths per individual per unit time units are

deaths/(individual * time)

▪ r = births/(individual *time) – deaths/(individual *time)

o Average number of births (b) = 2 births per person per year,

o Average number of deaths (d) = 0.5 deaths per person per year

o r = 2 births/(person* year) – 0.5 deaths/(person*year) = 1.5 individuals added per

person per year

o Can r be less than 0?

▪ Yes, the case would be; population growth rate is declining.

o Now that we understand r we can find Nt, the population size at any point in time

▪ Nt = Noert (KNOW EQUATIONS)

▪ Nt = number individuals at time t (size at time t)

▪ No = initial number of individuals

▪ r = per capita growth rate

▪ e = base of natural log (2.72)

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