# 19.2 Population growth and regulation

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By the end of this section, you will be able to:
• Explain the characteristics of and differences between exponential and logistic growth patterns
• Give examples of exponential and logistic growth in natural populations
• Give examples of how the carrying capacity of a habitat may change
• Compare and contrast density-dependent growth regulation and density-independent growth regulation giving examples

Population ecologists make use of a variety of methods to model population dynamics. An accurate model should be able to describe the changes occurring in a population and predict future changes.

## Population growth

The two simplest models of population growth use deterministic equations (equations that do not account for random events) to describe the rate of change in the size of a population over time. The first of these models, exponential growth, describes theoretical populations that increase in numbers without any limits to their growth. The second model, logistic growth, introduces limits to reproductive growth that become more intense as the population size increases. Neither model adequately describes natural populations, but they provide points of comparison.

## Exponential growth

Charles Darwin, in developing his theory of natural selection, was influenced by the English clergyman Thomas Malthus. Malthus published his book in 1798 stating that populations with abundant natural resources grow very rapidly; however, they limit further growth by depleting their resources. The early pattern of accelerating population size is called exponential growth    .

The best example of exponential growth in organisms is seen in bacteria. Bacteria are prokaryotes that reproduce largely by binary fission. This division takes about an hour for many bacterial species. If 1000 bacteria are placed in a large flask with an abundant supply of nutrients (so the nutrients will not become quickly depleted), the number of bacteria will have doubled from 1000 to 2000 after just an hour. In another hour, each of the 2000 bacteria will divide, producing 4000 bacteria. After the third hour, there should be 8000 bacteria in the flask. The important concept of exponential growth is that the growth rate—the number of organisms added in each reproductive generation—is itself increasing; that is, the population size is increasing at a greater and greater rate. After 24 of these cycles, the population would have increased from 1000 to more than 16 billion bacteria. When the population size, N , is plotted over time, a J-shaped growth curve    is produced ( [link] a ).

The bacteria-in-a-flask example is not truly representative of the real world where resources are usually limited. However, when a species is introduced into a new habitat that it finds suitable, it may show exponential growth for a while. In the case of the bacteria in the flask, some bacteria will die during the experiment and thus not reproduce; therefore, the growth rate is lowered from a maximal rate in which there is no mortality. The growth rate of a population is largely determined by subtracting the death rate    , D , (number organisms that die during an interval) from the birth rate    , B , (number organisms that are born during an interval). The growth rate can be expressed in a simple equation that combines the birth and death rates into a single factor: r . This is shown in the following formula:

#### Questions & Answers

what are the properties of lipids?
They are: Fatty acids, fats, oils, waxes, phospholipid, glycolipids, steroids and some vitamins
Rachel
explain why a fresh water fish excrete ammonia
plz answer my question
Leonard
sorry i meant it has a nucleous unlike plant cells lol
Lailah
Ammonia is the end product of protein catabolism and is stored in the body of the fish in high concentrations relative to basal excretion rates. Ammonia, if allowed to accumulate, is toxic and is converted to less toxic compounds or excreted
Rachel
What are eukaryotic cells?
cell with no nucleous so not a plant cell
Lailah
eukaryotic cells are membrane bound organelles that have a membrane bound nucleus
ojeen
where does the cell get energy for active transport processes?
IDK maybe glucose
Lailah
what is synapsis
how many turns are required to make a molecule of sucrose in Calvin cycle
why Calvin cycle occurs in stroma
Amina
why do humans enhale oxygen and exhale carbondioxide?
why do humans enhale oxygen and exhale carbondioxide? For the purpose of breaking down the food
dil
what is allele
process of protein synthesis
what is cell
a cell is a smallest basic, structural and functional unit of life that is capable of self replication
Lucas
why does a fresh water fish excrete ammonia
Leonard
plz answer my question
Leonard
Ammonia is a toxic colorless gas and when its inside the fish biological system is converted to a less toxic compound then excreted in the form of urea. However too much ammonia will kill the fish " Ammonia Poisoning " which is a very common disease among fish.
This
what is cytoplasm
cytoplasm is fluid of cell.
Deepak
how many major types of Cloning
two
amir
two
Zulf
comparative anatomy of gymnosperms?
anatomy of gymnosperms
Meenakshi
how genes are regulated
what is storage of glycogen
glycogen is a protein content
Najeem