Ecology Chapter 6

What is a population in ecology?

A group of individuals of the same species that are spatially distinct from other species.

What are the common characteristics shared by all populations?

Distribution, density, and abundance.

What is distribution?

Size, shape, and location of space occupied. 

What is density?

Number of individuals per unit area. How close they live together.

What is abundance? Give example

Total number of individuals or biomass in an area. How many pine trees in a forest

What does higher density and abundance imply about individuals in a population?

Higher fitness or superior performance.

What is a quadrat used for in population studies?

To represent a larger ecosystem by analyzing small areas. An area of exact measure that’s replicate able over and over again.

What equation was used for the daisy counting quadrats problem?

N_total = (A_total/A_sample) x (N_sampled)

What does the variables in N = (nM/m) stand for?

N = total population size, n = second capture, M = total number of marked individuals, m = number of marked and recaptured individuals.

What is the mathematical model for discrete-time population growth? An example question could be an open population, where organisms can move freely back and forth.

N_t+1 = N_t + B_t + I_t - D_t - E_t (where B = births, I = immigration, D = deaths, E = emigration).

What does N_t+1, N_t, B_t, I_t, D_t, E_t stand for?

Number next year, number this year, births this year, immigration this year, deaths this year, emigration this year.

What is a mark-recapture technique?

A method estimating population size by measuring the ratio of marked individuals in a second capture to the total number of individuals caught.

What time populations does lambda only work in?

Discrete time populations. It assumes that all organisms live and reproduce equally through time, and time is once per step (day, week, month, or even your yearrrrr).

State the scale and population relationships in lambda (λ).

The scale is based on 1. If λ > 1 → population increases; if λ < 1 → population decreases; if λ = 1 → population remains stable.

What does λ represent in population studies?

The geometric rate of increase for a population.

There are 100 chupacabras this year. How many will there be next year if λ = 0.85?

Next year's population is expected to be 85, as it indicates a decrease due to a λ less than 1. 100×0.85=85

There are 100 chupacabras this year. How many will there be next year if λ = 1.15?

Next year's population is expected to be 115, indicating an increase as λ is greater than 1. 100×1.15=115.

What assumptions limit the applications of simple population models?

Uniform birth and death rates, equal sex distribution, and no changes in resources or population dynamics year to year.

N_t+1 = N_t λ

N_t+2 = ______

N_t+3 = ______

N_t+2 = N_(t+1) * λ = N_t λ * λ = N_t λ²

N_t+3 = N_t λ³ 

Geometric rate of increase: If we know how many there were this year N_t (stage, month, week, whatever) we can divide the new quantity into it (N_t+1) and get lambda. What is the equation we would use?

λ = N_(t+1) / N_t

What is the λ of El Chupacabra if there are 90 this year and 120 next year?

λ = 120 / 90 = 1.33

Geometric rate of increase: If we know how many there were this year N_t (stage, month, week, whatever) we can divide the new quantity into it (N_t) raised to the power of how many years divided into one and get lambda. What is the equation we would use?

λ = (N_t / N_0) ^ (1/t)

What is the λ of El Chupacabra if there are 90 this year and 180 in five years?

λ = 180 / 90^(1/5) = 1.148

How can environmental DNA (E-DNA) be utilized in studying populations?

To identify species from samples of fur, scat, or slime in aquatic environments.

What technology aids in counting wildlife populations?

High sensitivity microphones, machine learning, audio monitoring, drone footage, and GPS tracking.

When do all organisms breed? How does it change from year to year? What happens to natural resources and carrying capacity?

During discrete time periods. Nothing changes. Natural resources and carrying capacity are not depleted.

Continuous Time Model

A mathematical approach that allows for breeding and population changes at any moment, reflecting ongoing changes in natural resources and carrying capacity.

Allows for overlapping generations and year round offspring. Also allows small changes in populations that accumulate through time. 

Would you rather get 5% interest on upir savings calculated once at the end of each year or have the bank calculate a daily fraction of 5% interest 5% divided by 365 days in the year and deposit that amount in your account every day?

The second option results in higher accumulated interest due to daily compounding, maximizing overall returns over time.

Adding up all the small changes from a starting population, N_0, to an ending population, N_t, will arrive at the following general equation which is ____.

The noert equation. 

What do the variables in the noert equation (N_t = N_0 e^rt) stand for?

N_t = population at time t, N_0 = initial population, e = average rate of logistic growth, r = growth rate, t = time.

What does it mean when dN/dt = 0 and when r<0 and r>0?

When dN/dt = 0, it indicates that the population size is stable, no change, meaning there is no net growth or decline. When r < 0, populations are decreasing, while r > 0 indicates populations are increasing.

Discrete growth is ___, ___, based off __.

Continuous growth is ___,___, based off __.

Discrete growth is geometric growth, lambda (λ), based off one.

Continuous growth is exponential growth, instant rate (r), based off one.

Density dependence

When a population shows a dependence on resources or populations that directly affects birth or death rates (could be anything).

Carrying capacity

The number of individuals that resources in a habitat patch can sustain. Changes often. Ex.) flowers in flower bed. No rain → flower number amount goes down. Rain next day → more flowers.

Example of carrying capacity

Flowers in flower bed. No rain → flower number amount goes down. Rain next day → more flowers.

What does the letter K stand for?

Represents carrying capacity because it comes from the German word Kapazitatsgrenze, which means capacity limit.