Bio 171 Lecture 3: Population Ecology I

Ecology:

Study of how organisms interact w/ one another and w/ their physical environment.

Emigration:

Individual organisms moving away from population’s geographic range.

Exponential growth (r):

Pop. grows at rate proportional to N.

Geographic range:

Area over which a pop. is spread. Partly reflects range of climates a pop. can tolerate and determines amount of other species pop. encounters.

Geometric rate of increase (lambda):

Type of discrete n growth. Where pop. changes after certain amount of time under ideal conditions.

Immigration:

Individual organisms entering pop.’s geographic range.

Maximum per capita growth rate (rmax):

Max rate of increase of pop. given set of abiotic condition. Possible when b is at highest value, d is at lowest value.

Lambda (λ):

base # of individuals in organism to predict N in discrete/geometric growth models.

Per capita growth rate (r):

Observed continous rate of pop. growth at every pt. in time for every individual contribution. Equals change in N. r=B-D/N.

Population:

All the individuals of a given species that live and reproduce in a particular place; one of several interbreeding groups of organisms of the same species living in the same geographical area.

Population size (N):

# individuals of all ages alive at a specific time in a specific place.

Vital rates:

Probability of any given stage class either reproducing (b), dying (d), emigrating (e), or immigrating (i).

Describe how birth, death, immigration, and emigration influence population growth rate and population size, and how absolute numbers of births, deaths, immigrants, and emigrants relate to birth, death, immigration, and emigration rates, respectively.

NEED

Define the geometric rate of increase, λ, and per capita growth rate, r. Describe how geometric rate of increase, λ, and per capita growth rate, r can be used to understand how populations change over time. (NOTE: The formulas you need to know are listed below.)

NEED

Explain the relationship between lambda (λ) and r.

In pop. r determines what lambda will be at discrete time pts.

Apply the geometric (discrete) and exponential equations to predict population growth rate and population size in the future. (Note: we will give you equations on the exam, but you will have to recognize which is which and know how to apply them.)

NEED

Explain why population growth rate is constant under exponential growth.

Constant rmax and lambda. Limiting factors (density-independent/dependent factors).

Identify an exponential growth curve. Give an example of a conservation or management situation in which exponential growth is relevant.

NEED

Contrast rates of change in populations with per capita rates of change in population size (e.g., dN/dt vs. r, B(t) vs b, D(t) vs. d)

dN/dt vs. r: r is the per capita vital rates to understand per capita growth rate and dN/dt is the absolute vital rates to understand the rate of change of N over a unit of time.

What sorts of problems do ecologists work on?

Theoretical work and applied problems (invasive species, infectious diseases, fisheries, effects of pollutants on pops, and climate change).

What four things can change the size of a population?

Births, deaths, immigration, emigration.

What do changes in population size reflect?

Predict the number of organisms that will occur in a particular location at a time point in the future. Reflect sum of BIDE.

What does t represent

Unit of time.

What does it mean if lambda is greater than, less than, or equal to 1?

<1: pop. decreased. ~1: pop. stayed the same. >1: pop. increased.

What does it mean if r is greater than, less than, or equal to 0?

>0:pop. increased . <0: pop. decreased. ~0: pop. stayed the same.

How can we predict population size one time step into the future?

Use lambda. N(t+1)=lambda*N(t).

How can we predict population size more than one time step into the future?

N(t)=lamda^t * N(0).

Why should you be careful predicting very far into the future?

Initial equation wouldn’t account for external factors and lambda is often inconsistent.

How does lambda relate to the percent increase in the population?

lambda=1+c, c=% increase in decimals. % increase is another form of the geometric growth equation using lambda. However you need to know N at the prev. time point.

What is the difference between discrete and continuous growth?

Discrete Growth: Pop. changes in distinct intervals. Continuous Growth: Pop. changes in a continuum.

What is dN/dt?

Rate of change in N over a unit of time.

How are λ and r max related?

lambda=e^r; Inversely, ln(lambda)=r. Used if assume r is constant over the time interval.

What is the difference between capitalized vital rates and lower case?

bide: Finding r in a closed pop. # per unit time (e.g. b: births per individual). BIDE: # of individuals.

What does "per capita" mean?

Per indvidual.

What is the relationship between r and r max?

r is almost always <rmax. r is never > rmax

How can you calculate the change in population size for a population that is growing exponentially?

(Bt+It-Dt-Et)/Nt=b+i-d-e=r=(dN/dt)/Nt OR Nt=N0 e^(rmaxt)

If given information on births, deaths, immigration, emigration, and population size — or if given b, i, d, and e — how can you calculate r?

r = b + i - d - e

When a population has a constant r max or λ, what happens to the number of individuals added to the population per time step?

# of individuals added = # of individuals removed from the population.