BIOL 304: Midterm 2 Guide Flashcards
Covers Lecture 9-16
Lincoln Peterson Formula:
π = MC/R
Logistic Equation of Population Growth:
ππ/ππ‘= ππ (1 βπ/πΎ)
What does each letter represent in the logistic equation of population growth?
-dN/dt= instant growth rate in a population
-r= intrinsic growth rate
-N= population size
-K= carrying capacity
Geometric Equation of Population Growth:
ππ‘ = π0ππ‘
What does each letter represent in the geometric equation of population growth?
-N(t)= population size at time of t
-N(0)= initial population size
-π= finite growth rate/ rate of increase
-t= time
Exponential Equation of Population Growth:
ππ‘ = π0πππ‘
What does each letter represent in the exponential equation of population growth?
-N(t) = population size at time t
-N(0)= initial population size
-r= intrinsic growth rate
-e= Eulerβs number
-t= time
Basic Model of Meta Population Dynamics Formula:
πΜ= 1 β π/π
What is the relationship between r and Ξ»:
Ξ» = er
r = loge Ξ»
The intrinsic rate of increase (r) and the finite rate of increase (Ξ») are directly related to each other.
Ξ» relates to r: calculates Ξ» based on intrinsic growth rate
r relates to Ξ»: calculates r based on finite rate of increase
What are the three models of population growth that we have discussed, and how do they differ?
- Geometric
- Exponential
- Logistic
The Geometric Population Growth Model:
Appropriate for organisms that reproduce at discrete time intervals (annually, seasonally, etc)
The exponential and geometric models express essentially the same thing: with one describing continuous reproductive events, and the other describing periodic reproductive events (exponential curve)
The Exponential Population Growth Model:
Appropriate for organisms that reproduce a seasonally or continuously
Unlike the geometric model, the exponential models gives a continuous estimate, which is represented with a J curve
The Logistic Population Growth Model:
More realistic model that takes into account carrying capacity (k). It predicts an S curve where growth slows down as the population approaches carrying capacity and eventually levels off.
What is carrying capacity and what factors affect it?
(K) is the maximum population size that can be supported by a given environment.
(K) differs for a given species as a function of environmental variables and is affected by factors such as:
-Resource availability (food, water, shelter)
-Habitat quality (space and changing abiotic or biotic conditions)
-Predation
-Disease
What is delayed density dependence and how does it impact population growth patterns?
Occurs based on a population density at some time in the past / situations where the negative effects of high population density take time to impact the population
What is overshoot?
When a population grows beyond its carrying capacity
Ex: Sudden increase in birth/death rates or decrease in K
What is die off?
Follows overshoot, represents a significant decline in population in a given area
Resource depletion and increased competition take hold, causing populations to crash back below the carrying capacity
What are stable limit cycles?
Population size continues to exhibit large oscillations overtime following a perturbation
Think of a constantly spinning gear, with consistent ups and downs
What is damped oscillation?
Population size initially oscillates following change, but the magnitude of the oscillation declines over time, eventually stabilizing
Think of a pendulum gradually coming to rest
Compare stable limit cycles and damped oscillations:
-Both involve fluctuations around an equilibrium point
-Driven by ecological interactions
-Modeled by mathematical equations
Contrast stable limit cycles and damped oscillations:
Stable Limit Cycles:
-Constant amplitude fluctuations
-Perpetual oscillations
-Specific conditions promoting self-sustaining cycles
Damped Oscillations:
-Decreasing fluctuations
-Reaches stable population level
-Factors return population to equilibrium
What are the three models of metapopulation dynamics?
- Basic Metapopulation Model
- Source-Sink Model
- Landscape Model
The Basic Metapopulation Model:
Uses extinction and colonization rates to predict the average probability of patch occupancy
-Equal patch quality
-Suitable patches embedded in uninhabitable matrix
-Some patches are unoccupied at any given point in time
The Source-Sink Model:
Relaxes the assumption of equal patch quality; High quality patches produce disproportionately more dispersers (source populations); Low quality patches produce disproportionately fewer dispersers (sink populations)
-Patches vary in quality: refinement of the basic model
-High quality patches produce more than low quality patches
-Low quality patches depend on immigrants to maintain a viable subpopulation (sink subpopulations)