- First, we will look at the definition of population dynamics.
- After, we will talk about the characteristics of a population.
- Then, we will learn about models in population dynamics.
- After, we will discuss population dynamics in ecology.

## Definition of Population Dynamics

What exactly is meant when using the term population dynamics in biology? A ** population **is a convergence of individuals of the same species who live, interact, and reproduce in the same geographic region. The word

**dynamics****means forces that produce change. Combine the two and we get**

**population dynamics!**

The definition of population dynamics is as follows.

**Population dynamics** is the study of the fluctuations of a population’s size over time, as observed through rates of birth, death, immigration, and emigration.

Before we start our discussion on population dynamics, we should review some terminology to better visualize the interactions of a population with its surroundings (Fig. 1).

A **community** is all the diverse species populations that cohabitate a geographic region.

An **ecosystem** is defined by all the communities in a geographic region, and that region's abiotic factors.

**Abiotic factors** are non-living parts of the environment, such as water, air, rock, soil, or sunlight.

**Biotic factors** are living parts of the environment, within the community. They are interactions between organisms, such as predation, competition, social hierarchy, mating, or illness. They can occur within the population, or with a population of another species.

## Population Characteristics

Population *dynamics* observes the changes in the *static* physical properties of populations. Here are the main observable characteristics of populations:

Size

Density

Dispersion

Sex distribution

Age distribution

### Size

**Size** is the count of individuals within a population. This count represents a specific and unique point in time. When observing population dynamics, we thus need at least two data points at time A and time B. In population ecology, the common symbol for population size is the uppercase letter '**N**'.

### Density

**Density **is the number of individuals of a population per region.

For example, a very dense population of squirrels may have one individual per square meter, whereas a more scattered population may have one individual per square kilometer.

The denser the population, the higher the level of competition. The multiple squirrels in the square meter may all have to tussle for the same acorn. __Density is strongly correlated with biotic factors affecting population growth.__

### Dispersion

**Dispersion** describes the geographic distribution, or clustering, of the individuals in a population (Fig. 2).

This property is like density, but subtly distinct. For example, a woodpecker living in beech-maple forest lives in the entire forest, but may cluster around the location of maple trees because of their soft bark.

### Sex distribution

**Sex distribution** is used to describe the quantity of individuals in a population who are male and female.

In population dynamics, counting individuals of each sex are in a population can help determine the maximum potential birth rate. By extrapolating the number of breeding females, population growth can be predicted.

Sex distribution is succinctly described by using a **sex ratio**, which is a fraction representing the number of individuals of one sex (e.g., females) to individuals of the other sex (e.g., males).

### Age distribution

**Age distribution** is used to describe the quantity of individuals of a population within a specific age group, as sorted in classes, or cohorts. A **cohort** is a group of individuals in a population born within the same time frame. Population dynamics uses cohorts to observe whether a population is young or old, booming or busting.

## Population Dynamics Models

### Age-Structure Diagrams

During population growth studies, you may see age-structure diagrams. **Age-structure diagram****s** (Fig. 3) are vertical histograms representing the cohorts of a population, separated by age group and sex.

Often, the shape of this model is indicative of a population growth trend. For example, a pyramid shaped age structure diagram shows a boom of young individuals, whereas another model that is narrowest at the base is indicative of an aging population with low population growth.

### Survivorship Curve

Survivorship curves are another model which efficiently displays population dynamics. **Survivorship curves** plot a population's number of (surviving) individuals on the y-axis and the age of the individuals on the x-axis (Fig. 4).

Population growth in survivorship curves tend to follow **one of three trends**:

**Type I**: A population with a high mortality rate in old age. Type I species are typically associated with strong parenting.**Type II**: A population with similar mortality throughout its life span.**Type III**: A population with a high mortality rate in young age. Type III species typically perform little to no parenting, preferring instead quantity over quality. Species that lay multiple eggs, like frog populations, are an example of a Type III species.

### Growth Rate Curves

Population size can either increase, through **birth** or **immigration**, or decrease, through **death** or **emigration**.

When discussing *population dynamics*, the observations are being made with a sense of time as a scale. These four factors are known as the **vital rates **of population dynamics. Therefore, we can calculate population growth using these vital rates:

**Birth rate**is the number of individuals entering a population by birth, per unit time.**Death rate**is the number of individuals exiting a population by death, per unit time.**Immigration rate**is the number of individuals entering a population geographically, per unit time.**Emigration rate**is the number of individuals exiting a population geographically, per unit time.

The general equation to find the population growth rate, symbolized by a lowercase **r**, is:

** $growthrate=(birthrate+immigrationrate)\hspace{0.17em}-(deathrate+emigrationrate)$**

or

$r=(B+\hspace{0.17em}I)-(D+E)$

In population dynamics, graphing the size of a population over time is an efficient model for displaying the biotic potential of a population. **Biotic potential** is the idealized maximum population growth rate, with little to no death or emigration. The resulting population dynamics model is a “J-shaped” graph representing the **exponential growth curve **(Fig. 5). In equation form, the exponential growth curve is expressed as such:

$\frac{dN}{dt}=rN$

where N = size, t = time and r = growth rate.

Realistically, a population will reach such a large size that the population's ecosystem can no longer support it. The maximum population size is limited by an ecosystem's abiotic and biotic factors, called the **carrying capacity (K). **

**Carrying capacity** (K) is the maximum population size an ecosystem can sustain, as imposed by limiting abiotic and biotic factors.

In population dynamics, there is a model of population growth rate that takes carrying capacity into consideration. The **logistic growth curve** (Fig. 6) is a population dynamics model with an “S-shaped” curve, where the carrying capacity (K) is represented as the population's ceiling, or maximum population growth rate.

In equation form, the exponential growth curve is expressed as such:

$\frac{dN}{dt}=rN\left[\frac{\left(K-N\right)}{K}\right]$

where N = size, t = time and r = growth rate, and K = carrying capacity.

## Population Dynamics in Ecology

Population dynamics has many practical applications in ecology. Fish and game departments monitor populations to ensure healthy and fishing and hunting. Agricultural organizations track pest populations to protect their crops. Environmental protection groups ensure the survival of endangered, threatened or vulnerable species by observing shifts in population sizes.

For populations to be able to survive in their ecosystems, they have to adapt to the biotic and abiotic factors in their environment. When population and community density is high, then there is a lot of competition, and resources are scarce. Some species excel at winning when competing for resources. They spend a lot of energy doing so, and spend less energy reproducing. Thus, they experience slow population growth and rarely exceed the carrying capacity. A **K-selected** species carry fewer offspring and experiences slow population growth that follows the logistic growth curve. Elephants, tortoises, and bears are examples of K-selected species.

On the other hand, some species aren't good competitors. To compensate, these species have developed rapid population growth during periods of abundant resources, when competition is less necessary. These **r-selected** species carry large numbers of offspring and experience fast population growth in the shape of an exponential growth curve, exceeding the ecosystem's carrying capacity temporarily. The r-selected species typically experience population growth events known as booms, and then crashes. Swarms of mice during bountiful growing seasons or salmon spawning during the breeding season are examples of r-selected species.

## Human Population Dynamics

The concepts of population dynamics extends to every species, even human populations! **Demography** is the application of population dynamics to the human species. In fact, demographics are extensively used in many other sciences, such as sociology, political science, anthropology, or geography. Demography uses its unique terminology when describing population dynamics.

**Crude birth rate (CBR)**: Total number of birth per 1000 individuals.

**Crude death rate (CDR)**: Total number of death per 1000 individuals.

**Total fertility rate (TFR):** Average number of birth per woman of child-bearing age.

Demography uses a **demographic transition model **(Fig. 7) to observe how human population growth patterns over long periods of time. Most often, these graphs are used to compare the human populations of two or more countries.

## Population Dynamics Worksheet

Recall the following equations for population growth rates curves.

$\frac{dN}{dt}=rN$ $\frac{dN}{dt}=rN\left[\frac{\left(K-N\right)}{K}\right]$The two population dynamics models being represented by these equations are the exponential growth curve and the logistic growth curve, respectively. In this worksheet, we will explore how a population dynamics model can be extracted from population size data. For 12 weeks, a population dynamics scientist counted the population of two species of insects, Study Bugs and Smarter Bugs. The data is compiled in the table below. From this data, you will derive a population growth rate (r).

This worksheet may be easier to complete if the table is printed out, or copied to a spreadsheet application.

Time (t) (weeks) | Study Bug Population # (N) | $\frac{dN}{dt}$ | Growth Rate (r) | Smarter Bug Population # (N) | $\frac{dN}{dt}$ | Growth Rate (r) |

0 | 20 | — | 5 | — | ||

1 | 63 | 26 | ||||

2 | 177 | 128 | ||||

3 | 534 | 669 | ||||

4 | 1 583 | 3 300 | ||||

5 | 4 695 | 16 911 | ||||

6 | 13 501 | 84 352 | ||||

7 | 35 353 | 422 777 | ||||

8 | 68 375 | 2 189 299 | ||||

9 | 64 800 | 10 546 547 | ||||

10 | 68 500 | 51 734 594 | ||||

11 | 68 356 | 263 672 108 | ||||

12 | 68 734 | 1 318 359 564 |

1) Calculate the change in population (N) over the change in time (t), or *d*N/*d*t. Fill out the corresponding column. Can you determine which population whose population growth rate is affected by the carrying capacity (K)? Why?

Hint: For week 1, *d*N_{1} = N_{1} - N_{0} = 63 - 20 = 43, and *d*t_{1} = t_{1} - t_{0} = 1 - 0 = 1.

2) For the species in question 1, can you determine what the carrying capacity (K) appears to be?

3) Do Study bugs appear to follow a population dynamics model in the shape of an exponential growth curve or a logistic growth curve?

4) Do Smarter bugs appear to follow a population dynamics model in the shape of an exponential growth curve or a logistic growth curve?

5) Using the equation from your answer to question 4, determine the population growth rate (r) and fill out the corresponding column. (Note: the answer for "r" will not be exactly equal in each row, but all resulting calculations should be close to a single value)

Hint: If rN_{0} = *d*N_{1 }/ *d*t_{1}, then r = ( *d*N_{1 }/ *d*t_{1 }) / N_{0}

6) A separate experiment in population dynamics determined the true value of K at 10 000 individuals. Using the equation from your answer to question 3, determine the population growth rate (r) and fill out the corresponding column. (Note: again, the values for "r" will diverge slightly.)

Hint: If r * [ (K-N_{0}) / K ] = *d*N_{1}/*d*t_{1}, then r = (*d*N_{1}/*d*t_{1}) / [ (K-N_{0}) / K ]

### Worksheet answers:

1) Study bug. The population growth *d*N/*d*t decreases and approaches zero as time increases.

2) The maximum population appears to slow down at about 70000 individuals.

3) Logistic growth curve

4) Exponential growth curve

5) r = 4

6) r = 3

## Population Dynamics - Key takeaways

Population dynamics is the study of the fluctuations of a population’s size over time, as observed through rates of birth, death, immigration, and emigration.

Important characteristics of a population are size, density, dispersion, sex distribution and age distribution.

The four vital rates of population dynamics for measuring population growth are birth, death, immigration, and emigration.

Carrying capacity (K) is the maximum population size an ecosystem can sustain, as imposed by limiting abiotic and biotic factors.

Species' life strategies can be classified as r-selected, with numerous offspring and rapid growth, or K-selected, with few offspring and slow, steady growth.

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##### Frequently Asked Questions about Population Dynamics

What is population dynamics?

Population dynamics is the study of the fluctuations of a population's size over time as observed through rates of birth, death, immigration, and emigration.

What are the 3 characteristics of population dynamics?

The 3 main characteristics of population dynamics are birth rate, death rate, and migration rate.

What is the importance of population dynamics?

Population dynamics are important because it can demonstrate whether a population is growing or shrinking.

What are the major components of population dynamics?

The major components of population dynamics, called the vital rates, are birth rate, death rate, immigration rate and emigration rate.

How does population dynamics affect the environment?

Population dynamics is used to observe if a population is growing at a rate that would exceed its carrying capacity. A population above carrying capacity would be indicative of an unsustainable ecosystem because it is being drained of its resources.

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