Midterm 2 Study Guide
Population Distribution Lecture Notes
-Geographic range: total area
-Species Niche: range of conditions
-Fundamental Niche: whole range a species COULD occupy
-Realized Niche: Range a species ACTUALLY occupies
Patterns of distribution suggest species niches. So how do we test whether species are really limited to particular conditions?
2 species of monkey flowers occur at different elevations
-Lewis monkey flower resides in higher elevations
-Scarlet monkey flower resides in lower elevations
Are these two species limited by competition or can they only survive at specific elevations?
-Scarlet was placed in high elevation
-Lewis was placed in low elevation.
-Lewis could not survive in low elevation, so it was distribution limited. -Scarlet grew a little at high elevation, so it was limited by competition
It is important to know the fundamental and realized niches of species for conservation
-Understand the spread of invasive
-Understand that it may be a rare species with already low numbers -Understand how climate change will affect these niches.
Ecological Niche Modeling predicts where to find species
1. Map locations where individuals have been found (usually use GIS) -Gather data from…
Don't forget about the age old question of What is article 19 of the universal declaration of human rights?
-Museums and herbariums
2. Identify ecological envelope
-predicted range of suitable conditions
-what variables are important? We also discuss several other topics like Where is australia located?
3. Map the locations where these conditions occur.
Characteristics of population distribution
Population Abundance – number of individuals per sample or ecosystem Methods to estimate abundance
-vegetation quadrats and extrapolate data
Size, height, DBH, decomposition
-Mark and recapture
Not great for territorial animals
I-Click question We also discuss several other topics like What is the meaning of codependence?
You collect 100 arthropods. You mark them all. 2 weeks later you capture 200 and 20 were marked. What is the total population?
100 x 10=1000 is the total population
Population Density – number of individuals per unit area
-May be uneven
Populations are most dense near center of geographic range (Kirk Batrick and Barton)
-limited at edge by environmental tolerance limits
-doesn’t adapt well to edges due to gene flow
-they are best adapted in the middle We also discuss several other topics like What is the symbol for angular velocity (radians/sec)?
If you want to learn more check out What is the cycle of managers?
-more genes in middle that aren’t adapted to edges
I-Click: What would be better adapted to local conditions?
-Individuals at core of range and from regions with high population density
Dispersion: How individuals spread locally
-Random: Null model
-Evenly spaced/ over dispersed Don't forget about the age old question of What is the meaning of static in biometrics?
-measure distance to nearest neighbor and if number is higher than you expect then it is evenly spaced
-due to social reasons, low dispersal, resources, etc
Dispersal: affects changes in geographical range
Populations may live in distinct habitat patches
Habitat may be patchy at multiple scales
-Patches may vary in quality at small scales
Population densities should be different in patches of different quality
Dispersal affects the spatial behavior of populations.
One population: if individuals can disperse freely among patches Subpopulation: fluctuate more independently and dispersal is rare Conceptual models describe spatial structure of sub populations Metapopulation Models
-Lots of elaborations on the metapopulation model
-describes behavior of multiple subpopulations
Levins Metapop Model
-assume equal quality
-look at one species at a time
-how do colonization/extinction rates affect patchy occupancy?
Equilibrium occupancy rate
-Assume no differences in patch quality or subpopulation size
p=fraction of occupied patches
e=rate of extinction of occupied patches
c=rate of propagule generation by occupied patches (colonization rate)
Slope tells how quickly p changes in respect to t
-if the slope is zero, then dp/dt is zero
dp/dt increases as new patches are added and decreases when patches go extinct
If colonies are added or
If you let colonization and extinction happen, you can reach equilibrium
Each patch has a 10% probability of going extinct each step. The probability of being colonized is 20%. What is the equilibrium occupancy rate?
p= 1- .1/.2= .5
.5 x 100= 50%
How does Levin’s model predict that you could increase patch occupancy rates? -Justifies use of corridors
-if you increase c, you make it easier for colonization allowing movement increases colonization
c>e size increase
e>c size becomes zero
But in real life, patches aren’t equal
Patchy occupancy is sensitive to quality
Source-Sink Model: differences in patch quality
-Prediction-some patches are more important to population persistence High population growth is more important for x
Sources: send colonists which increases population
Sinks: move in but don’t send colonists out
-Some patches are important to population persistence
-Variation may be important
-suboptimal patches may act as reserves
-source-sink may fluctuate
Bay Checkerspot butterfly
-during dry conditions, some patches persist while others don’t -during good years, the large patch acts as a sink for the butterfly -during bad years, like drought, large patch acts a source for the butterfly
Landscape model: effects of patch arrangement and surrounding landscapes -isolated and small patches are likely to be unoccupied
-connected and large patches are likely to be occupied
Implication for conservation
-Long term persistence may depend upon maintenance of many potential habitat patches
-connectivity important but also increases the spread of predators and pathogens
-patch sources change
Every patch has a risk of extinction
-may need to reintroduce species into several habitats
-Focus on increasing c and decreasing e
Quantifying Population growth Ch12 Lecture Notes
Is the population stable, increasing, or decreasing?
How do abiotic and or biotic factors affect population growth?
Which demographic rates most influence population growth?
Take measurements at regular time intervals
Models overall population trajectory
Discrete time Equation
Predict N in the future
Population size at time t=N
If per capita birth and death rates are constant, if population growth is proportional to population size.
Lambda=Nt+1 /Nt Nt+1= Ntlambda
If N is constant every year, you can estimate population size.
If Lambda = 1, the population size does not change
If lambda is >1, the population increases
If lambda is <1 then population decreases
Continuous time Equations
Time steps shrink to small intervals calculate the slope
dN= change in numbe3r of individuals
dt= per change in time
r=rate of growth
N= number of individuals in a population
r intrinsic rate of population growth, equals per capita instantaneous birth rate (b) - per capita instantaneous death (d)
lambda= er r=ln(lambda)
Discrete= Nt=N0ert Continuous= Nt=N0lambdat
Lambda will never be negative
If a population of 1000 mice has an intrinsic rate of increase of .5, how many mice will be in the population after 6 months?
You may want to compare poulation growth between populations Easier to compare slopes of lines than curves
So using a log graph is easier to compare populations
The graphs below are the same graphs (conceptually). The first is an exponential graph, and the second is a log graph.
Exponential and geometric equations
Describe density-independent population growth
R and lambda are intrinsic population growth rates, birth rates, and death rates
Population growth is limited
Ex temperature, fire, hurricane, etc
The growth of some populations is determined by density-independent factors
Population density mostly determined by rain and temperature
Population growth can be limited due to population density
Effect proportional to population size
Negative density dependence: population growth declines ad density increase. (Pretty common)
Ex diseases, predation, food limitation, nesting sites
Imposes a carrying capacity
Example of negative density dependence
The Northern Gannet
There was data collected on its historic and current colony size
Small colonies grew faster than large colonies because large colonies have a longer feeding flights in order to find more fish. So the large colonies had an increase in food scarcity.
Not everything has a negative effect
Allee effects= cause positive correlation between density and population growth rates
More density=more chances to meet and mate
- Reintroducing a fish species into Lake Eerie (or any large lake)
Difficult to find mates
Failure of group defense
Cowslip Plant Allee Example
The graph shows that as population size increases, the Cowslip plant produces more seeds and as the population size decreases, the plant produces fewer seeds
Allee effects can make recovery difficult
Fisheries when a population crashes, it can’t recover because they need density to grow.
Density dependent population growth is modeled using logistic equation Add a term to slow growth ad density increases
As population growth gets slower, N gets larger
dN/dt N k/ Inflection
If N>K, it is a negative slope
If the population is small, it is influenced by rN
If the population is large, it is influenced by (K-N)/(K)
As N gets bigger it gets closer to K and the slope gets smaller till it levels off at zero
All these models have assumed demographic equivalence. In real life, populations differ in age structure and have different demographic rates
In the U.S, the age is fairly even from 0-50. This means that the population size is stable and won’t change a lot
In Germany, there are more post-reproductive people than pre-reproductive. This means that there will be fewer people in the future and the population is on the decline.
In India, there are more pre-reproductive people than post-reproductive, which means that the population is increasing.
Normal age distribution for a species is affected by survivorship patterns
Type I: survival rate high at a young age and most mortality occurring at an old age (humans)
Type II: Constant rate of death. (Lizards)
Type III: High mortality in earliest age and survivorship increases as they mature(Sequoia trees)
Age structure reflect conservation status
A Juniper in Spain is in trouble because it produces very few seedlings and juveniles.
Summarize demographic grates
Usually females only
nx= number of individuals in each age class immediately after the population has produced offspring
sx= survival rate from one age class to next age class
bx= number of offspring produced by each individual
Number of surviving to the next age class= (nx)(sx)
Number of new offspring produced= (nx)(sx)(bx)
Age/Stage based models
Use matrix models
Need to know demographic rates (arrows)
The arrows represent the probability of going onto the next stage or staying at current stage.
1= Small Juvenile
2= Large Juvenile
Building a stage-based model
Express membership in size class at (t+1) with equation
n1, t+1= n1P11+n3+F
n2, t+1= n1P21+n2P22
n3, t+1= n2P32+n3P33
Calculate the size of each class for 2 time steps. Start with 100 individuals in every class
There si a probability rate for every arrow
Put probabilities and starting class sizes into your equations
Calculate nt+1 for every stage class
Total population is sum of all stage class
(I’m tired of subscripts)
F = .561 P11=.672 P21=.018 P22=.849 P32=.138 P33=.969 t=0 t=1 t=2 t=3
N1 100 123.3 144.9 164
N2 100 86.7 75.8 66.9
N3 100 110.7 119.2 126
N1=(100 x .672)+ (100 x .561)= 123.3
N2= (100 x .018) + (100 x .849)=86.7
N3=(100 x .138) + (100 x .969)=110.7
N1, t+2= (123.3 x .672) + (110.7 x .561)= 144.9603
Projecting a population over time
Iterate until population reaches stable stage distribution and a stable per capita growth rate (lambda)
Stable Stage Distribution (SSD)
Eventually evens out
Ration of classes stays the same
Determined by arrows
Shows which class will be more at the end
Settle at a constant growth rate
Initial stage structures are not affected by SSD or final intrinsic growth rate lambda SSD and lambda are determined entirely by transition probabilities
To calculate SSD wait until population growth rate stabilizes then calculate the size of each class a percentage of total population size.
The population will not grow after a few time steps (lambda=1) How could we increase per capita growth if we want populations to persist? need to change arrows to change lambda
How do you know which arrow to change? Through a perturbation analysis Perturbation Analysis
Reveals how changes in demographic rates would or could affect lambda
Sensitivity= absolute change in lambda given a small absolute change in demographic rate (P)
Simple sensitivity equation: change in lambda/ change in P
Can be calculated for every demographic rate, which causes the biggest change Example
If P32 is big, then changing it will affect the growth rate a lot because P32 would be sensitive
Sensitivity is useful in conservation when determining the budget and where to allocate resources.
Some vital rates are in different units
Changing fecundity by 0.1 is often different than changing survivorship by 0.1 Might want to know the relative effect of a certain proportional change (change in lambda/ lambda)/(change in P/P)
Proportional rather than absolute change
High elasticity value population growth rate is sensitive to changes in that demographic rate
In cheetahs, which life stage is most important to population growth? Hollow= sensitivity Blue= Elasticity
Because the elasticity is higher in adults, you would want to increase adult survivorship to affect population survivorship
Elasticity Application Considerations
change in lambda/change in Pji
-usually calculated in matrix models
(change in lambda/lambda)/(change in P/P)
Population viability Analysis
Use stage-based models to predict risk of extinction
Usually use stochastic models changes in variable stochastically
Run several times (sometimes up to 1,000 times) to see how long it took for a species to go extinct gives an idea how vulnerable populations are
Example of using population viability analysis
Guanaco were reintroduced to Argentina
Their populations where not increasing very much so population modeling was used
Ecologists created different models with different conditions to compare what management practices would decrease the probability of extinction in 100 years.
Population Dynamics Chapter 13 Lecture
How populations respond to environmental conditions
Some populations are intrinsically stable, unstable, or fluctuate a lot
Stability is affected by…
Body size and homeostasis How resistant an organism is to environmental changes
Demographic rates intrinsic properties of the population
Life span, reproduction, etc
Whether it’s a K or r selected species
Example Phytoplankton in Lake Erie
Very stochastic, they are not constant or stable
Plankton are really small which plays a part in their instability
Environmental changes tend to be
Stochastic, NOT periodic
Populations may track environment challenges. However most population dynamics are periodic.
Intrinsic Population Dynamics
Steady, so no oscillations
Some of these patterns can be predictable
Example Gyrfalcons population cycles every 10 years
Why do oscillations occur in population dynamics?
Some density dependent exceed their carrying capacity, which cause a crash. How do they exceed their carrying capacity?
1. There is a delay in their density dependent responses
2. They experience rapid population growth so they approach carrying capacity very quickly.
A metaphor to explain this is a new golfer. The hole is the carrying capacity, and the new golfer hits the ball so hard it goes past the hole. (The population has now exceeded their carrying capacity and are at their peak) To compensate going past the hole, the new golfer hits the ball back to the whole with the same amount of force. Once again, it goes past the hole (This is when the population crashes)
What causes delayed density-dependence responses?
Discrete generations, such as ones that have annual reproduction Slow responses to feedback mechanisms
Ex A species of Daphnia stores energy in times of abundance, so they exceed their carrying capacity when resources are low
Ex pulse of resources leads to higher quality offspring being produces, so the effects of the resource pulse are not apparent until next generation
Ex Predators take time to reproduce. This is one reason why when you see cycling of a predator and prey relationship (like snowshoe hare and lynx) the prey starts to decline before the predator and also increase before the predator
Modeling delayed density dependence
Make logistic equation responsive to population size in the past dN/dt=rN[(K-Nt-tal)/(K)]
tal= time delay in response to population density
The length of the delay (tal) and the rate of increase (r) determine pattern Large tal or r can lead due to oscillations
If you have no delay and/or reached r there will be no oscillations Damped oscillation
overshoot K a little but eventually level off
-Similar to the metaphor of the beginner golfer, but instead think of an intermediate golfer.
If r x tal is small, then there is no oscillation
If r x tal is intermediate, then there is damped oscillation
If r x tal is large, then there is a cycle and chaos
Can you predict risk of outbreaks?
Cycles can lead to periods when N > K (When the population exceeds carrying capacity)
Populations of parasites and pests may cycle, so it would be useful to predict and prevent cycles
Interrupting chaos cycles
Ex Flour beetles
r selected species, so it has a large boom and bust cycle
If we were to disrupt the cycle, it could cause the cycle to level out
If individuals were added at the peak of a cycle, it caused the cycle to level out