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
6.
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.
8.
9.
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.
11.
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
Editor's Notes
r is the per capita rate of increase –that is, how quickly the population grows per individual already in the population.
Exponential growth may happen for a while, if there are few individuals and many resources. But when the number of individuals gets large enough, resources start to get used up, slowing the growth rate.
A term comes the carrying capacity. It is the amount of resources available in an environment which can sustain a limited amount of population is carrying capacity of that environment.