# BISC 102 Chapter Notes - Chapter 52: Exponential Growth

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10 Aug 2016

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Read Chapter 52: pages 1147-1152

Population Growth

Quantifying the growth rate

a population’s growth rate is the change in the

number of individuals in the population per

unit time

if no immigration or emigration is occurring,

the an population’s growth rate is equal to the

number of individuals (N) in the population

times the diﬀerent between the birth rate per

individual (b) and the death rate per individual

(d). The diﬀerence between the birth rate and

the death read per individual is called the per

capita rate of increase, and is symbolized

if the per capita birth rate is higher than the

per capita death rate then r is positive and the

population is growing

the opposite is also true

when conditions are optimal for a particular

species - meaning birth rates per individual are

as high as possible and death rates aper

individual are as low as possible - then r

reachers a maximal value called the intrinsic

rate of increase rmax

each species has a characteristic r-max, that

does not change. But any speciﬁc time, a

population has an instantaneous growth rate,

or per capita rate of increase

Exponential Growth

exponential population growth occurs when r

does not change with population size or

density

the key point about exponential growth is that

the growth rate does not depend on the

number of individuals in the population

this type of population growth is called

density dependant

in nature exponential growths observed in two

circumstances

1. a few individuals found a new

population in a new habitat

2. a population has been devastated by a

storm or some other type of catastrophe

and then begins to recover, starting with

a few starting individuals

many populations in unstable or unfavourable

environments have periods of exponential

growth, but it is not possible for exponential

growth to continue indeﬁnitely

population density refers to the number of

individual per unit area - gets very high, the

population’s per capita death rate will

increase, causing r to decline

Logistic Growth

to analyze when growth is density dependant,

biologists use a parameter called carrying

capacity

carrying capacity (k) is deﬁned as the

maximum number of individuals in a

population that can be supported in a

particular habitat over a sustained period of

time

the carrying capacity of a habitat depends on

a large number of factors; food, space, water,

soil quality, and resting or nesting sites.

carrying capacity can change from year to

year, depending on conditions

The Logistic Growth Equation

if a population of size N is below the carrying

capacity K, then the population should

continue to grow

a populations growth rate is proportional to (K-

N)/K:

when N is small, then (K-N)/K is closer to 1

and the growth rate should be high

as N gets larger (K-N)/K gets smaller

when N is at carrying capacity - meaning that

K-N then (K-N)/K is equal to 0 and growth

stops

Graphing Logistic Growth

1. initially, growth is exponential - meaning that r

is constant

2. with time, N increases to the point where

competition for resources of other density-

dependant factors begins to occur. As a result,

the growth rate begins to decline

3. when the population is at the habitat’s carrying

capacity, the growth rate is 0 - the graph of

population size versus time is ﬂat

What Limits Growth Rates and Population Sizes?

population sizes change as a result of two

general types of factors

density indépendant factors alter birth

rates and death rates irrespective of the

number of individuals in the population

and usually involve changes in the

abiotic environment

density dependant factors change in

intensity as a function of population size

and are usually biotic in nature. When

trees crowd each other, they have less

water, nutrients, and sunlight at their

disposal and make fewer seeds

A Closer Look at Density Dependance

density-dependant changes in survivorship

and fecundity cause logistic population growth

in this way, density-dependant factors deﬁne a

particular habitat’s carrying capacity

Carrying Capacity is NOT Fixed

its important to recognize that K varies

between species and populations.

k varies in space, it also varies with time, as

conditions in some years are better than in

others

these observations help to explain the

variation in total population size that exists

among species and among populations of the

same species