Population Growth Notes

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.
Interspecific Competition: How a population interacts with another.
Intraspecific Competition: How individual members of one species relate to each other.

Fundamental Characteristics of Populations

Population Density ( $D_p$ ): The number of individual organisms ( $N$ ) in a given area ( $A$ ) or volume ( $V$ ).
- Formula: $D<em>p = \frac{N}{A}$ or $D</em>p = \frac{N}{V}$
- Example 1:
  - 12 gophers in an area of 10.0 $m^2$ , $D_p = \frac{12}{10.0 m^2} = 1.2$ gophers/ $m^2$
  - If the field was 200.0 $m^2$ , estimate is $1.2 \frac{gophers}{m^2} * 200.0 m^2 = 240$ gophers
- Example 2:
  - 200.0 mL sample of pond water contains 54 wrigglers: $D_p = \frac{54}{200.0 mL} = 0.27$ wrigglers/mL
- Example 3:
  - 2500 snails/ $m^2$ in a 9.0 $m^2$ study area. Population size: $N = D_p * A = 2500 \frac{snails}{m^2} * 9.0 m^2 = 22500$ snails.
  - If snails are clumped, the actual population size may be lower than calculated.
Population Distribution: Describes how organisms are distributed in a given area or volume.

Theoretical Distribution Patterns

Clumped Distribution: Individuals are grouped in patches or aggregations.
- Occurs where food, water, or shelter is abundant.
- Examples: Plants that reproduce asexually, Banff snails near spring water, schools of fish, salamanders under logs.
Random Distribution: Resources are abundant, and population members do not compete.
- Not very common.
- Biotic and abiotic factors have little effect.
- Examples: Trees of some species in tropical rain forests.
Uniform Distribution: Individuals are evenly spaced over a defined area.
- Due to competition for space, resources, light, and nutrients.
- Some plants secrete chemicals that inhibit the growth of nearby plants.
- Seen in birds of prey and other territorial organisms.

Measuring and Modeling Population Change

Four processes change population size ( $\Delta N$ ):
1. Births ( $b$ )
2. Immigration ( $i$ ) – movement into a population
3. Deaths ( $d$ )
4. Emigration ( $e$ ) – movement out of a population
Equation: $\Delta N = [b + i] - [d + e]$
Population's Growth Rate ( $g_r$ ): Change in the number of individuals in a population ( $\Delta N$ ) over a specific time frame ( $\Delta t$ ).
- Equation: $g_r = \frac{\Delta N}{\Delta t}$
- Population Explosion: Spreads before it can be contained.
- Population Crash: Population decreases rapidly.
Example: Banff Springs snails, Jan 1997: 3800 snails, Two years later: 1800 snails. $\Delta N = 1800 - 3800 = -2000$ . $g_r = \frac{-2000}{2} = -1000$ snails/year.

Per Capita Growth Rate

The growth rate equation does not account for initial population size.
Larger populations have more individuals that can reproduce.
Per Capita Growth Rate ( $cgr$ ): Change in number of individuals ( $\Delta N$ ) relative to original number of individuals ( $N$ ).
- Equation: $cgr = \frac{\Delta N}{N} = \frac{N_{final} - N}{N}$
- Can be negative if deaths and emigration outnumber births and immigration.
Practice Problem 1: Town of 1000 people, 50 births, 30 deaths, 30 immigrating, 60 emigrating.
- $\Delta N = [50 + 30] - [30 + 60] = -10$
- $cgr = \frac{-10}{1000} = -0.01$
Practice Problem 2: 26 Caribou introduced, $cgr$ = 75.9 for 25 years. What is the number of caribou before the population crashed.
Practice Problem 3:
- Initial population: 900
- Births: 66
- Deaths: 14
- Immigrants: 13
- Emigrants: 5
- Population change: $\Delta N = [66 + 13] - [14 + 5] = 60$
- New population size: $900 + 60 = 960$
- Growth rate: $g_r = \frac{60}{2} = 30$
- Per capita growth rate: $cgr = \frac{60}{900} = 0.067$

Factors Affecting Population Growth

A single bacterium can reproduce by fission every 20 minutes under ideal conditions: After 36 hours, there would be enough bacteria to form a layer a foot deep over the entire Earth!

Factors Affecting Population Change

Biotic and abiotic factors affect growth.
Biotic limiting factors: Physiological and physical characteristics of a species that determine 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 population size.
Biotic Potential ( $r$ ): The highest possible per capita growth rate for a population.
- Factors: Number of offspring per reproductive cycle, number of offspring that survive, age of reproductive maturity, and lifespan of individuals.
Exponential Growth Pattern: When a population is growing at its biotic potential, there will be a brief lag phase, followed by a steep increase. Can be described as a J-shaped curve.
Lag Phase: The growth rate is slow because there are only a few individuals to reproduce.
Growth Phase: As the numbers increase, the population experiences an exponential growth rate.
Stationary Phase: Competition for resources and other limiting factors will slow the growth rate.
- Birth rate and death rate are equal.
- An S-shaped curve (sigmoidal) is seen. This is also known as the logistic growth pattern.
Carrying Capacity ( $K$ ): Maximum population size that the environment can sustain over an extended period.
- Number of individuals that can live in an environment without depleting resources or harming the habitat/themselves.
- Changes due to the season.
Environmental Resistance: The combined effects of various, interacting limiting factors.
- Prevents a population from growing at its biotic potential and determines the carrying capacity.

Factors Limiting Carrying Capacity

Density-Dependent Factors: Biotic factors that influence the growth of the population.
- Examples: Diseases, competition among species, predation, and waste accumulation.
Density-Independent Factors: Any abiotic factors that will affect the population regardless of population size.
- Examples: Drought, wildfires, volcanic eruptions, hurricanes, and 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, short lifespan, high mortality, little parental care, large investment in offspring numbers, below carrying capacity.
- Examples: Bony fish, grasshoppers.
K-Selected: Maximizes population size near carrying capacity.
- Late reproduction, long lifespan, low mortality, extensive parental care, greater investment in adults, at or near carrying capacity.
- Examples: Sharks, elephants.

Check Your Understanding

Define biotic potential and give its symbol: The highest possible per capita growth rate for a population, symbol (r).
Name four factors that determine the biotic potential of a species: Number of offspring per reproductive cycle, number of offspring that survive, age of reproductive maturity, and lifespan of individuals.
What is an exponential growth pattern? What is its shape in a graph? A brief lag phase, followed by a steep increase. Can be described as a J-shaped curve.
Explain how biotic potential and exponential growth are related. When a population is growing at its biotic potential then we would expect to see exponential growth.
Define carrying capacity and give its symbol: Maximum population size that the environment can sustain over an extended period, symbol (K).
What are two differences between density-dependent and density-independent factors? Density dependent are biotic factors, Density independent are abiotic factors.
What is environmental resistance? How does it affect populations? The combined effects of various, interacting limiting factors which Prevents a population from growing at its biotic potential and determines the carrying capacity of the habitat.