# ISU 14.2presentation ```14.2 MEASURING AND MODELLING
POPULATION CHANGES
Lucshman Raveendran
Dhruv Jasani
Factors that
Affect
Population
Population
Dynamics
Natality
Mortality
Immigration
Emigration
Population
Immigration
Emigration
Closed
Population
Natality
Mortality
Open
Population
Natality
Mortality
Fecundity
• The potential for a species to produce offspring in one
• Species that live older can have more reproductive
cycles but usually produce less offspring.
Age
Number of Survivors
Low
Fecundity
High
Morality At
Young Age
Uniform
Mortality
Number of Survivors
Number of Survivors
High
Mortality At
Older Age
Age
High
Fecundity
Age
Formula:
[ 𝒃𝒊𝒓𝒕𝒉𝒔 + 𝒊𝒎𝒎𝒊𝒈𝒓𝒂𝒕𝒊𝒐𝒏 − 𝒅𝒆𝒂𝒕𝒉𝒔 + 𝒆𝒎𝒊𝒈𝒓𝒂𝒕𝒊𝒐𝒏 ]
&times; 𝟏𝟎𝟎%
𝒊𝒏𝒊𝒕𝒊𝒂𝒍 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒔𝒊𝒛𝒆
Omg math!
Geometric
Population
Growth
Models
Logarithmic
Exponential
Geometric Growth
 A pattern of population growth where organisms
reproduce at fixed intervals at a constant rate.
 𝑁 𝑡 + 1 = 𝑁(𝑡)λ
 λ-Geometric Growth Rate
 𝑁(𝑡)-Reference Population
 𝑁 𝑡 + 1 -Population one cycle ahead of reference
population
𝑡
 Basically same thing as 𝑁 𝑡 = 𝑁&deg; (λ )
 SO EZ!
Omg more math!
Exponential Growth
 A pattern of population growth where organisms reproduce
continuously at a constant rate

𝑑𝑁
𝑑𝑡
= 𝑟𝑁
𝑡𝑑 =
0.69
𝑟
𝑑𝑁
 -instantaneous growth rate at a specific time or population
𝑑𝑡
 r-biotic potential; maximum rate a population can increase under
ideal conditions
N=2500
Population
r=o.03 per hour
𝑑𝑁
=750/hour
𝑑𝑡
math y u do dis
Time
N=500
r=o.03 per hour
𝑑𝑁
= 1.5/hour
𝑑𝑡
Logarithmic Growth
 A model of population growth that levels off as the size of the
population approaches its carrying capacity
 Carrying Capacity-The maximum number of organisms that can be
sustained by available resources over a given period of time

𝑑𝑁
𝑑𝑡
= 𝑟𝑚𝑎𝑥 𝑁
𝑑𝑁

𝑑𝑡
𝐾−𝑁
𝐾
Produces
Sigmoid Curve
‘S’ Shaped
- population growth rate at a given time
 𝑟𝑚𝑎𝑥 - maximum growth rate
 N-population size at a given time
 K- carrying capacity of the environment
Slow Growth
lim
𝑁→𝐾
𝐾−𝑁
𝐾
lim
𝑁≪𝐾
i cry evertim math
→0
𝐾−𝑁
𝐾
→1
Dynamic
Equilibrium
Birth rate=Death rate
No net change in
population
The initialsize
stage
in which
population
growth rates are
slow as a result
of a small
population size
Lag Phase
Stationary
Phase
The phase in which
population growth rates
decrease as the population
size reaches the carrying
Log Phase
capacity; the defining
The stage in whichcharacteristic of logistic
population growthpopulation growth
rates are very rapid
```