Exponential and Logistics Growth Curve - Environmental Science

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Exponential and Logistic Growth Curve

2. Introduction
 In theory, any kind of organism could take over the Earth just by reproducing.
 In practical, all living organisms need specific resources, such as nutrients and
suitable environments, in order to survive and reproduce.
 These resources aren’t unlimited, and a population can only reach a size that
match the availability of resources in its local environment.
Continued………………………

3.  Population ecologists use a variety of mathematical methods to
model ”population dynamics”.
 Some of these models represent growth without environmental constraints, while
others include "ceilings" determined by limited resources.
 Mathematical models of populations can be used to accurately describe changes
occurring in a population and, importantly, to predict future changes.

4. Modeling population growth rates
 General Equation of the population growth rate:
dN/dT=rN
Where,
dN/dT is the growth rate of the population a given instant
N is population size
T is time
r is the per capita rate of increase
Continued………………………

5.  The Equation derived in previous slide was very general.
 We can make more specific forms of it to describe two different kinds of growth
models.
Growth
Models
Exponential Growth
Logistic Growth

7. Exponential growth
 Exponential growth takes place when a population's per capita growth rate stays
the same, regardless of population size, making the population grow faster and
faster as it gets larger. It's represented by the equation:
dN/dT = rmaxN
Where,
rmaxis the maximum per capita rate of increase for a particular species under ideal
conditions, and it varies from species to species.
 Exponential growth produces a J-shaped curve.

10. Logistic Growth
 Logistic growth takes place when a population's per capita growth rate decreases
as population size approaches a maximum imposed by limited resources, the
carrying capacity(K). It's represented by the equation:
dN/dT=rmax(K−N)*N/K
Where,
(K-N)/K is the fraction of population which can still live in the enviornment and
survive.
 Logistic growth produces an S-shaped curve.

12. Factors Determining the Carrying Capacity
 Any kind of resource important to a species’ survival can act as a limit.
 For plants, the water, sunlight, nutrients, and the space to grow are some key
resources.
 For animals, important resources include food, water, shelter, and nesting space.
 Limited quantities of these resources results in competition between members of
the same population, or intraspecific competition.
 However, as population size increases, the competition intensifies

13.  Don’t worry if u didn’t understand all of it above……Here’s a sneak peak