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128 Cards in this Set

  • Front
  • Back
What is demography?
Study of populations
What does demography involve?
-Involves use of mathematical techniques to predict growth of populations
-Involves intensive study of both laboratory and natural populations
What is the emphasis of demography?
-Emphasis on:
1. Causes of population fluctuations
2. Effects of crowding on birth and death rates
What are the 2 models of population growth?
Exponential Growth Model

Geometric (or Discrete) Growth Model
What are Geometric (or Discrete) Growth Models used?
-When young individuals are added to the population at one particular time interval (coral, lovebugs, etc)
When are Exponential Growth Models used?
When young individuals are added to the population continuously
Which growth model is more common?
Geometric or Discrete Growth Model. But Exponential Growth Model are the basis for every model!
Define the variables:

N
t
Nt
No
N: Population Size
t: Point in time we are interested in
Nt: Number of individuals in a population at time t
No: Population at starting point
Why do we model Population Growth/Decline?
We are interested in predicting the future population size (Nt+1)
What 4 categories cause change in population?
1. Death: Decrease size (D)
2. Birth: Increase size (B)
3. Emigration: Decreasing size (E)
4. Immigration: Increasing size (I)
What is the mathematical expression for population growth?
∆N = B – D + I - E
What defines a closed population?
No immigration/emigration. ONLY births and deaths
∆N = B – D
When are Exponential Growth Models used?
When young individuals are added to the population continuously
What kind of curve demonstrates a closed population?
-Assume continuous growth, described by a smooth curve
Which growth model is more common?
Geometric or Discrete Growth Model. But Exponential Growth Model are the basis for every model!
What is:
r = b-d
Instantaneous rate of increase/intrinsic rate of increase/per capita growth rate. If a negative number, population will crash
Define the variables:

N
t
Nt
No
N: Population Size
t: Point in time we are interested in
Nt: Number of individuals in a population at time t
No: Population at starting point
In a simple model of population growth, what happens if r>0
Population grows!
Why do we model Population Growth/Decline?
We are interested in predicting the future population size (Nt+1)
What 4 categories cause change in population?
1. Death: Decrease size (D)
2. Birth: Increase size (B)
3. Emigration: Decreasing size (E)
4. Immigration: Increasing size (I)
What is the mathematical expression for population growth?
∆N = B – D + I - E
What defines a closed population?
No immigration/emigration. ONLY births and deaths
∆N = B – D
What kind of curve demonstrates a closed population?
-Assume continuous growth, described by a smooth curve
What is:
r = b-d
Instantaneous rate of increase/intrinsic rate of increase/per capita growth rate. If a negative number, population will crash
In a simple model of population growth, what happens if r>0
Population grows!
In a simple model of population growth, what happens if r<0?
Population declines
In a simple model of population growth, what happens if r=0?
Population is stable!
What formula do you use to predict a population size at a given time for a simple model?
Nt = No(e^rt)

-r: Intrinsic growth rate
-e: Base of natural log ~ 2.72
When is Nt = No(e^rt) used?
To predict a population size at a given time.
When predicting a population at a given time for a simple model, how is the curve represented?
-When plotting on curve, always has a “J” shape
-Small population size, growth rate isn’t that high
-Large population, growth rate increases dramatically
What assumptions are made for a simple model of population growth?
-Closed population, no immigration or emigration
-Constant birth and death rates
-No genetic structure
-No age or size structure (sexless and no sex): Immediately reproduce when born
-Continuous growth with no time lags
Explain how seasonal patterns affect Geometric/Discrete Population Growth
-Geometric growth results in seasonal patterns of population increase and decrease
What are the generation types in a Geometric/Discrete Population Growth?
-Population has non-over lapping generations (semelparity, aka salmon)
What is λ?
λ: Ratio of population size at any time to that 1 time unit earlier. Geometric growth rate

λ = N(t+1)/Nt
What is the formula for Geometric/Discrete Population Growth?
Nt = No λt
What is this formula used for?

Nt = No λt
Geometric/Discrete Population Growth
Are Exponential and Geometric Growth related?
Yes!


λ = er r=0.1
log λ = r λ = t λ = Always positive number
When is a population size growing in a Geometric/Discrete Population?
-Growing when λ > 1 or r > 0
When is a population size constant in a Geometric/Discrete Population?
-Constant when λ = 1 or r = 0
When is a population size declining in a Geometric/Discrete Population?
-Declining when λ < 1 (but > 0) or r < 0
What is Intrinsic Rate of Increase Balanced by?
Extrinsic Factors
-Despite potential for exponential increase, most populations remain relatively stable
What are the Consequences of Crowding for Population Growth?
-Results in less food for individuals and their offspring
-Aggravate social strife
-Promotes the spread of disease
-Attract the attention of predators
What are the characteristics of a Logistic Growth Model?
-Relax the assumptions of exponential population growth model
-Size of population affects death and birth rate
-Logistic equation is slightly more complex than the exponential growth model
What is the formula for a logistic growth model?
dN/dt = (b’ – d’)N b’ and d’ = Birth/Death rate with density dependence
What is a simple formula for a decreasing birth rate in a logistic growth model?
b’ = b – aN
b’: Density dependent per capital birth rate
b: Density independent per capita birth rate
a: Strength of density dependence (larger number means sharp drop in birth rate)
What is a simple formula for increasing death rate in a logistic growth model?
d’ = d + cN
d’: Density dependent death rate
d: Density independent death rate
c: Increase in death rate from density dependence
What is the Allee Effect?
-Reality is more complex than the simple models
-b’ and d’ might not decline in a linear manner
-For some organisms, more efficient in groups so birth rate may increase and death rate decreases as population grows
What is K?
Carrying capacity
What is this formula?

dN/dt = rN (1 - N/K)
Expanding Exponential Growth
What is the formual for Expanding Exponential Growth?
dN/dt = rN (1 - N/K)
What is carrying capacity?
-Maximum population size that can be supported (units of number of individuals)
-Encompasses many potential limiting resources including availability for space, food, and shelter
What happens if a population is below K?
It grows!
What happens if a population is above K?
It decreases!
What happens if a population is equal to K?
it remains constant
What is the "unused portion" of the carrying capacity formula?
(1 - N/K)
What is

(1 - N/K)
The "unused portion" of the carrying capacity formula
If the unused portion of the carrying capacity formula is close to 1, what does that mean?
The population is uncrowded, it's growing at a high percentage of the growth rate of an exponentially growing population
If the unused portion of the carrying capacity formula is close to 0, what does that mean?
The population is very crowded and growing at a very slow growth rate.
What is this equation?

Nt = K / 1 + [(K-No)/No] e^rt
The logistic growth equation integrated
What is the formula when you integrate the logistic growth equation?
Nt = K / 1 + [(K-No)/No] e^rt
What kind of graph would a small population in a logistic equation project?
S-shaped, sigmoidal growth
Where is the inflection point in a logistic equation graph and what does it do?
An inflection point at K/2 which separates the accelerating from decelerating phases of population growth
What is the formula when you integrate the logistic growth equation?
Nt = K / 1 + [(K-No)/No] e^rt
What does the logistic equation mean/do?
Simplest equation describing population growth in a resource limited environment
What kind of graph would a small population in a logistic equation project?
S-shaped, sigmoidal growth
What are the assumptions of logistic growth?
-Share assumptions with exponential growth model
-No time lag, migration, genetic variation, or a structure
-Constant carrying capacity (unrealistic)
-Resource availability does not vary over time
-Linear density dependence
-Each individual added to the population causes a decrease in the per capita rate of population growth
Where is the inflection point in a logistic equation graph and what does it do?
An inflection point at K/2 which separates the accelerating from decelerating phases of population growth
What does the logistic equation mean/do?
Simplest equation describing population growth in a resource limited environment
What are the assumptions of logistic growth?
-Share assumptions with exponential growth model
-No time lag, migration, genetic variation, or a structure
-Constant carrying capacity (unrealistic)
-Resource availability does not vary over time
-Linear density dependence
-Each individual added to the population causes a decrease in the per capita rate of population growth
How does age structure determine population growth rate?
-When birth and death rates vary with the age of individuals, contributions of younger and older individuals must be calculated separately
-Age specific schedules of survival and fecundity enable us to project the population size and age structure into the future.
What are these variables?
sx
bx
sx = survival rate of individual in age class x
bx = number of offspring per adult in age class x
What is stable age distribution?
When a population grows with constant schedule of survival and fecundity, the population will eventually reach a stable age distribution
-Each age class represents a constant percentage of total population
What happens under a stable age distribution?
-All age classes grow or decline at the same rate
-Population will grow or decline at a constant rate
What are the 2 types of life tables?
1. Cohort
2. Static
What is a cohort life table?
1. Cohort: Track individuals throughout whole life.
-Based on data collected from a group of individuals born at the same time.
-Better if organism doesn’t move much and has a short life span.
What is a static life table?
2. Static: Survival of individuals of known age during a single time interval.
-Better if organism has a long life span and moves around a lot.
what is lx?
Survivorship
What is the formula for survival rate (sx)
Survival rate (sx): Nt+1/Nt OR lx+1/lx
What is formula for mortality rate (mx)
Mortality rate (mx): dx/lx
What is formula for death rate (dx)?
Death rate (dx): lx-lx+1
What are the 3 types of survivorship curves?
-Type I: High initial survival but drops abruptly with age (humans)
-Type II: Constant survival rate and mortality rate with age
-Type III: High mortality initially but survival is better with age (small invertebrates, fish, plants)
Describe type I survivorship curve.
Type I: High initial survival but drops abruptly with age (humans)
Describe type II survivorship curve.
-Type II: Constant survival rate and mortality rate with age
Describe type III survivorship curve.
-Type III: High mortality initially but survival is better with age (small invertebrates, fish, plants)
What is λ?
λ: Discrete Population Growth Rate
What is the formula for generation time?
T = ∑ x lxbx / ∑ lxbx
What is T?
Average age at which an individual gives birth to its offspring (generation time!)
How do you estimate geometric growth rate?
λ = Ro

(net reproductive rate = Ro)
What are the life table assumptions?
-Shares basic assumptions of the geometric/discrete growth model
-Closed population (no immigration/emigration), no genetic structure, no density dependence
-lx and bx schedules are constant
-Population has reached a stable age distribution
How are fluctuations in populations driven?
-Populations are driven by density dependent factors toward equilibrium numbers
-However populations also fluctuate about such equilibrium because:
-Populations respond to changes in the environment
-Direct effects (temperature, moisture)
-Indirect effects (food supply)
-Populations may be inherently unstable
What is the main intrinsic cause of population cycling?
-The main intrinsic cause of population cycling are time delays in the response of birth and death rates to environmental change
What are the mechanisms for population cycling?
-Populations acquire momentum when high birth rates at low densities cause populations to overshoot the carrying capacity
-Populations then overcompensate with low survival rates and fall below the carrying capacity
What is the formula for the discrete logistic model?
Nt+1 = Nt (1 + rd)
What are the 3 oscillation patterns of discrete models?
-3 patterns depending on rd:
-rd small (< 1): Population will approach K (carrying capacity) and stabilize
-rd exceeds 1 but < 2: Population exhibits damped oscillations
-rd exceeds 2: Population may exhibit limit cycles
-rd is big: Exhibit chaotic cycles
What happens with the population if rd is less than 1?
Population will approach K (carrying capacity) and stabilize
What happens with the population if rd is greater than 1 but less than 2?
Population exhibits damped oscillations
What happens with the population if rd is greater than 2?
Population may exhibit limit cycles
How do time delays result?
Time delays result from developmental period that separates reproductive episodes
What is Tau?
Time delay
What is the equation for population growth with a time lag?
dN/dt = rN [(1-Nt- τ)/K]
What are the 2 factors of the delay differential equation?
1. Length of Time Lag (τ)
2. Response time of population: Inversely proportional to) r (population growth rate
-Populations with fast growth rate have a shorter response time (1/r)
How does the value of r τ relate to population size and oscillations?
-If r τ is small (0< r τ 0.368) then population increases smoothly to K
-If r τ is medium (0.368< r τ 1.57) then population will overshoot then undershoot K. Exhibit damped oscillations.
-If r τ is large (r τ > 1.57) then the population will enter into stable limit cycles
What is amplitude?
-Difference between maximum and average population size (middle of wave to top)
-Units are in number of individuals
-Larger the amplitude, greater the population fluctuations
-If amplitude is very large, population might hit the bottom and go extinct
What is period?
-Amount of time it takes for one complete population cycle (center of top to center of next top)
-Longer period, greater amount of time between population peaks
When a population has a time lag of 1 year, when will is reach peak density?
Every 4 years!

τ is about ¼ of population cycle. 4 τ = one whole cycle!
What is a habitat patch?
Areas of habitat with necessary resources and conditions for populations to persist
What is a metapopulation?
Set of subpopulations interconnected by occasional movement (most useful in wildlife management)
What is a subpopulation?
Individuals living in a habitat patch
What are the 2 kinds of processes in metapopulation dynamics?
1. Growth and regulation of subpopulations within patches
2. Colonization to form new subpopulations and extinction of existing subpopulations
What happens when individuals move frequently between subpopulations?
-Local fluctuations are damped out
What happens at intermediate levels of movement between subpopulations?
-Metapopulation behaves as a shifting mosaic of occupied and unoccupied patches
What happens at low levels of movement between subpopulations?
-Subpopulations behave independently
-If a population goes extinct, it is unlikely they will be reestablished
What are 2 important shifts to study metapopulations
1. Metapopulation models will NOT predict population size, only its persistence
-0: Extinct or 1: Persistent
2. Shiff spatial scale. Other models focused on a single population that persists through time. Focus on multiple subpopulations.
What is local extinction?
One population goes extinct
What is regional extinction?
All subpopulations go extinct
What does it mean if e is 0 in a local extinction?
Persistence is certain
What does it mean if e is 1 in a local extinction?
Extinction is certain
What is the equation for local persistence?
Pn = (1-e)^n
What is the formula to determine regional persistence?
Pn = 1-e^n
What is p in extinction/persistence/colonization formula?
Probability/Fraction of suitable habitat patches that are occupied by a subpopulation.
What does the rate of colonization depend on?
Rate of colonization of empty patches depends on the fraction of patches that are empty (1-p) and the fraction of patches that are sending out colonists p
What is the basic model for metapopulation dynamics (extinction/persistence)?
dp/dt = cp (1-p) – ep (colonization minus extinction)
What happens in a metapopulation if extinction = colonization?
It reaches equilibrium
In a metapopulation model (extinction/persistence) what happens when e = o, p=1 ?
All patches are occupied (extinction rate is 0!)
In a metapopulation model (extinction/persistence) what happens when e = c, p=0?
Whole metapopulation heads towards extinction
In a metapopulation model (extinction/persistence) what happens when 0<e<c ?
A shifting mosaic of occupied and unoccupied patches
What are the assumptions for a metapopulation model?
1. All patches are equal
2. Rates of colonization and extinction for all patches are the same
3. Each occupied patch contributes equally to dispersal (colonization)
4. Colonization and extinction in each patch occur independently
5. Colonization rate is proportional to the fraction of occupied patches
How does the 'Rescue Effect' help a dying metapopulation?
Immigration from a large productive subpopulation can keep a declining subpopulation from going extinct and can be incorporated into metapopulation models by making the rate of extinction decline as the fraction of occupied patches increases