Exponential and Logistics Growth Curve - Environmental Science

Exponential and Logistics Growth Curve - Environmental Science

1. 91600103027 91600103039 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

6. LET’S EXPLORE

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 ​​= r ​ max N Where, r ​ max is 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. 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​ = r ​ max ​​( 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.

9. 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

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