Comprehensive Notes on Population Growth

Population Growth

Key Terms

  • Population: All individuals of the same species living in the same place at a certain time.
  • Community: All species that occupy a given area.
  • Ecosystem: Includes both biotic (living) and abiotic (nonliving) components of a specific area.
  • Ecologists can describe:
    • How a population interacts with another (interspecific competition).
    • How individual members of one species relate to each other (intraspecific competition).
    • How a population interacts due to environmental change.

Fundamental Characteristics of Populations

  1. Population Density: The number of individual organisms in a given area or volume.
  2. Population Distribution: Describes how organisms are distributed in a given area or volume.

Population Density (Dp)

  • The number of individual organisms (N) in a given area (A) or volume (V).
  • Formula: Dp = \frac{N}{A} or \frac{N}{V}

Example 1:

  • A sample of Richardson’s ground squirrels was taken to be 12 gophers living in an area of 10.0 m^2.
    • Calculate the population density of the gophers.
    • If the field was 200.0 m^2, estimate the size of the population.

Example 2:

  • A 200.0 mL sample of stagnant pond water contains 54 wrigglers (mosquito larvae).
    • Calculate the population density of the wrigglers.

Example 3:

  • A count was taken on the endangered Banff Springs Snails (Physella johnsoni). They calculated that there are 2500 snails/m^2.
    • The study area is 9.0 m^2. Calculate the population size of the snails in the given study area.
  • Researchers noted that they were not evenly distributed throughout the habitat; instead, they were clumped in certain areas. Therefore, the actual size of the snail population is lower than calculated.

Theoretical Distribution Patterns

  1. Clumped Distribution
  2. Random Distribution
  3. Uniform Distribution
  • Diagram showing uniform, random, and clumped dispersion.

1. Clumped Distribution

  • When individuals are grouped in patches or aggregations.
    • Individuals group together in an area where food, water, or shelter is abundant.
    • Examples:
      • Plants that reproduce asexually
      • Banff Snail near spring water
      • Schools of fish
      • Salamanders clumped under logs

2. Random Distribution

  • Occurs when resources are very abundant, and population members do not have to compete with one another.
    • Not very common.
    • Biotic and abiotic factors have little effect.
    • Examples are trees of some species in tropical rain forests.

3. Uniform Distribution

  • Individuals are evenly spaced over a defined area.
    • This is seen due to competition among individuals for space, resources, light, nutrients.
    • Some plants secrete chemicals that inhibit the growth of nearby plants.
    • Seen in birds of prey and other organisms that behave territorially to defend their resources and protect their young.

Measuring and Modeling Population Change

  • Population size directly depends on how much and how fast it grows.
  • Four processes that can change the size (# of individuals) of a population (\Delta N = change in population size):
    1. Births (b)
    2. Immigration (i) – movement into a population
    3. Deaths (d)
    4. Emigration (e) – movement out of a population
  • Equation: \Delta N = [b + i] - [d + e]

Rate of Population Growth

  • The speed at which the change occurs is just as important as the size of population growth.
    • Population Explosion – spreads before it can be contained.
    • Population Crash – population decreases so rapidly.
  • Change in the number of individuals in a population (\Delta N) over a specific time frame (\Delta t) is known as the population’s growth rate (gr).
  • Equation: gr = \frac{\Delta N}{\Delta t}

Growth Rate Example:

  • In Jan 1997, the population of Banff Springs snails was estimated to be 3800. Two years later, the population was estimated to be 1800. What was the change in population size?

Per Capita Growth (cgr)

  • The growth rate equation does not take into account the initial size of the population.
    • Larger populations have more individuals that can sexually reproduce than smaller populations.
  • To compare populations that are different sizes or live in different habitats, the change can be expressed as the rate of change per individual, known as per capita growth rate (cgr).
    • As long as nothing limits the growth of either population.
  • Per Capita Growth (cgr): Change in the number of individuals (\Delta N) relative to the original number of individuals (N).
    • Equation: cgr = \frac{\Delta N}{N} or \frac{N_{final} - N}{N}
    • cgr: per capita growth rate
    • \Delta N: change in the number of individuals
    • N: original number of individuals
    • Per capita growth rate can be a negative number if deaths and emigration outnumber births and immigration.

Practice Problem 1:

  • Suppose that in a town of 1000 people, there are 50 births, 30 deaths, 30 immigrating and 60 emigrating. What would be the cgr?

Practice Problem 2:

  • A population of 26 Caribou was introduced onto a predator-free island in Alaska in 1910. For the next 25 years, the per capita growth rate of the population was 75.9. In about 1935, resources became limited, and the population crashed. Calculate the number of caribou on the island just before the population crashed. (ans: 1999)

Practice Problem 3:

  • Over 2 years, a population of 900 experienced 66 births and 14 deaths. Five individuals left the population, and 13 individuals joined the population. Using this information, determine
    • a) the population change
    • b) the new population size
    • c) the growth rate
    • d) the per capita growth rate

Practice:

  1. Complete Table 1 by calculating the missing values.
    • Table 1 Measured and Calculated Factors Describing Four Different Populations
      • Columns: Initial Population (N), Time period (At) ,Births (n), Deaths (m), Immigrants (i), Emigrants (e), Population change ($\Delta$N),Growth rate (gr), Per capita growth rate (cgr)
  2. The human population has a per capita growth rate of approximately 0.012 per year.
    • If the human population is 6 billion, determine
      • (a) the change in population per year
      • (b) the change in population per day

Factors That Affect Population Growth

  • Consider a single bacterium that can reproduce by fission every 20 minutes under ideal laboratory conditions. After 36 hours, there would be enough bacteria to form a layer a foot deep over the entire Earth! Thankfully, in the real world, this does not occur. This is because there are biotic and abiotic factors that affects growth.

Factors That Affect Population Change

  • The previous scenario doesn’t happen because there are biotic and abiotic factors that affect growth.
    • Biotic limiting factors includes the physiological and physical characteristics of a species that determines how fast and how often it can reproduce.
    • The ability of a habitat to support a population, due to biotic and abiotic factors, also limits the size of a population.

Biotic Potential (r)

  • Every species has an intrinsic rate of growth that is possible, given there are unlimited resources and ideal living conditions.
  • BIOTIC POTENTIAL (r): The highest possible per capita growth rate for a population.
  • Factors to determine a species’ biotic potential:
    1. Number of offspring per reproductive cycle
    2. Number of offspring that survive long enough to reproduce
    3. Age of reproductive maturity and number of times that the individual reproduces in a life span
    4. Life span of the individuals

Exponential Growth Pattern

  • When a population is growing at its biotic potential, then we would expect to see exponential growth; this is called the EXPONENTIAL GROWTH PATTERN.
    • You will notice a brief lag phase, followed by a steep increase.
    • Can be observed in the laboratory using microorganisms like bacteria under ideal conditions.
    • Can be described as a J-shaped curve.

Stationary Phase & Logistic Growth Pattern

  • In a small population, the growth rate is slow because there are only a few individuals to reproduce – this is called the LAG PHASE.
  • As the numbers increase, the population experiences an exponential growth rate (GROWTH PHASE).
  • In nature, the rapid growth rate cannot continue forever – this is called the STATIONARY PHASE.
    • Competition for resources and other limiting factors will slow the growth rate. This also limits the amount of energy for reproduction (births decline).
    • At this phase, the birth rate and death rate is equal.
  • An S-shaped curve (sigmoidal) is seen. This is also known as the logistic growth pattern.

Carrying Capacity (K)

  • Due to competition and other limiting factors, there is a maximum population size that the environment can sustain over an extended period of time – this is called the CARRYING CAPACITY (K).
    • It represents the number of individuals that can live in a given environment without depleting the resources they need or harming their habitat or themselves.
    • The carrying capacity also changes due to the season.
    • Over time, population size may fluctuate around the carrying capacity of the habitat in stable equilibrium.
  • Figure 20.5: Graph showing the effect of environmental resistance on population growth. Limiting factors such as disease, predation, and competition for limited resources reduce the amount of energy that is available for reproduction which causes the growth rate of the population to decrease.

Environmental Resistance

  • The combined effects of various, interacting limiting factors is described as the environmental resistance to population growth.
    • Prevents a population from growing at its biotic potential and determines the carrying capacity of the habitat.
    • What is the environmental resistance for human population growth?
    • What kind of growth pattern does the world human population exhibit?

Factors Limiting a Habitat’s Carrying Capacity

Density-Dependent Factors

  • Biotic factors that influence the growth of the population due to the density of the population.
    • Examples:
      • Diseases
      • Competition among species
      • Predation
      • Waste accumulation

Density-Independent Factors

  • Any abiotic factors that will affect the population regardless of the population size.
    • Examples:
      • Draught
      • Wildfires
      • Volcanic eruptions
      • Hurricane
      • Deforestation

Reproductive Strategies

r-Selected

  • (maximum growth rate, below carrying capacity)
  • In an unstable environment, it can be advantageous to expend energy in order to reproduce while conditions are favorable
    • Early reproduction age
    • Short life span
    • High mortality rate
    • Little or no parental care
    • Large investment in producing large numbers of offspring
    • Below carrying capacity
    • Examples:
      • Bony fish
      • Grasshoppers

K-Selected

  • (maximizes population size near carrying capacity)
    • Late reproduction age
    • Long life span
    • Low mortality rate
    • Extensive parental care
    • Greater investment in maintenance and survival of adults
    • At or near carrying capacity
    • Examples:
      • Sharks
      • Elephants
  • Table comparing characteristics of r-selected and K-selected species including homeostatic capability, maturation time, lifespan, mortality rate, # offspring per reproductive episode, # of reproductions per lifetime, age at 1st reproduction, size of offspring, and parental care.

Check Your Understanding

  1. Define biotic potential and give its symbol
  2. Name four factors that determine the biotic potential of a species
  3. What is an exponential growth pattern? What is its shape in a graph?
  4. Explain how biotic potential and exponential growth are related.
  5. Define carrying capacity and give its symbol
  6. What are two differences between density-dependent and density-independent factors?
  7. What is environmental resistance? How does it affect populations?