Midterm 2 Flashcards
Advantages of matrices over exponentila/logistic growth models
Sensitivety analysis
Elasticity analysis
Can model a greater diversity of life historie
Age structure exists
Explicity based on assumptions of variation in lxand bx(fx) among age classes
Finite rate of increase
Lambda=R+1
Main goal of leslie matrix?
Calculate finite rate of increase
What is a vector and a scalar?
Vector: matrix with only one row of column
Scalar: is a single number
Primary subDiagonal?
Top row of leslie matrix?
Top row: fecundity of each age class
Primary subdiagonal: age specific survivorship
Fx in regards to a matrix?
Per capita output of new young by age class. Called fertility (px*bx)
How do you convert a life table to a leslie matrix?
Explain post and pre breed differences.
Need to calculate px and fx
Post breed:
px=lx+1/lx
fx=(px)(bx+1)
Pre breed:
px=lx+1/lx
fx=(p0)(bx)
Output of a leslie Matrix?
- Population size at each successive time step
- Age class structure
- Calculation of lambda=Nt+1/Nt
- Continued calculation of lambda using the matrix, b/c assumes unchanging lxand fx, generates eventually the Lambda in Nt+1=lambdaNt Known as asymptotic growth rate
- Once AGR is attaine lambda does not change, pop attains SAD.
What is a Lefkovich Matrix?
Identical to Leslie matrix except:
- idividuals can stay within an existing stage or transition forward or backward
- lambda is still calculated but SSD is attained insteas
- boasts small data sets.
What do the various rows in a Lefkovich matrix mean?
What are Px and Gx in relation to a Lefkovich matrix?
Px= probability that in individual will survive and remain in the same stage or size class in the next time unit.
Gx= probability that an individual will survive and move up to the next stage or asize class in the next time unit.
Quick way to calculate mortality in Lefkovich matrix?
mortality= 1-(probability of advancing+probability of remaining)
What are sensitivity and elasticity analyses?
Sensitivity determines how very small changes in each variable, while holding all others constant, affect lambda
Elasticity scale sensitivity to units. Proportional sensitivities scaled so that they are dimensionless and directly comparable.
Describe methods for calculating sensitivity an elasticity analyses.
<span>Determine right eigenvector (w)= run matrix till SAD, then calculate proportion of each age class…this is (w)</span>
<span>Next determine left eigenvector (v) this is reproductive value measurement. </span>Transpose original matrix and complete normal matrix analysis. Represent each age class as a proportion. Standardize by dividing each element by p’o.
Sensitivty (viwi)/ (
See image 1
Elasticity
What are some properties that same species regularly exhibit
- variation in Neq among sites
- stable numbers at anyone site when viewed on the short-term
- long term change not uncommon
Describe the difference between regulation and limitation.
Limitations are typicall phycial factors. Otherwise known as a cap
Regulation is typically biotic factors.
what are the two principles of basic model of population regulation?
No population stops growing unless percapita B or D rates decline with density
Differences in density can arise from variation in D-D or per capita B and D. (emigration and immigration is important)
What is a sink?
a population that persists over long periods of time despite contradicting birth and death rates (BIDE models). due in part to immigration from other populations.
What is ideal-free?
Ideal free is a distribution pattern that individuals distriubte themselves across a resource gradient that is proportionate to the amount of resource per area. Greater resource= more animals. This is a way to minimize resource competition for resources and to maximize fitness.
What does Ideal-despotic distribution mean?
distribution occurs when hab selection is controlled by territorial behavior
elements need to determine reproductive rate?
of bouts
number/bout
Annual frequency
%breed-cost of reproduction
Age specific effects
Estimate “apparent mortality”?
Apparent mortality= Pdeath +Pemigration+Psighting
What does Zigive in a statistical mark-recapture model??
Zi=number marked before time i, not caught in i, but are caught at a later time.
Calculated by summing rows i+1
What does φ signify?
φ is apparent survival
φ=[Mi+1]/[Mi-mi+Ri]
Prop. survive = (# marked from time period 2 alive before current sample [3]), divided by (# marked from time period 1 & alive at start of period 2, less # marked in time period 2, plus # released in sample 2 after marking)
How many years of data do you need to perfom a Cormack Jolly-seber model?
- Interested in annual survival, robust design has shorter time intervals built into a large time frame.
How do you estimate survival from age class composition?
Calculate finite annual survival
Assumes: survival rate constant for each age class, all year-classes recruited at same abundance, all classes sampled equally
S=(T)/R+T-1
R=ΣNt T=N1 + 2N2 + 3N3 + ….
What are catch curves?
Often used in fisheries. Blue box is estimation of mortalit, overall measurement of adult survival. Multiple assumptions.
How do calculate S from a catch curve?
S=eslope
what is the Kaplan-Meier estimate of survival?
It is a known fate model: allows for (a) multiple sample intervals, (b) staggered entry, (c) right censoring of data. RT good example
How do you calculate S in a Kaplan-Meier model?
St+1=St(1-(#dead/#@risk))
Can also multiply probabilites of times leading up to year wanting to calculate
Can convert long term survival rates to daily survival rate. How do you do this?
Can populations be regulated?
The is inherent variability introduced by a) environmental stochasticity, b) demographic stochasticity, c) internal biotic limitations (time lags) and an uncertainty over appropriate scale of mearsurement. It is essential distinguish between limitation and regulation.
Is regulation a DD response?
Yes!
How do you establish if and how regulation is occurring?
a) do B and D rates vary with N, and, do patterns differ among age/sex groups?
b) identify causes for variation in B and D rates, what are mortality agents?
c) Does population show negative feedback?
Why is DD difficult to determine?
(a) analyses of populations in which N is to low to detect it,
(b) conducting studies for to brief a period
(c) failure to include non-breeders in estimates of N
(d) inappropriate measures of density (#/area vs. #/food supply)
(e) difficulty of separating biotic and abiotic factors (e.g. severe winter weather and food)
(f) inherent difficulty of estimating population size and survival rates (g) need to view populations on larger spatial scales (metapopulations)
(e) density responses due to numbers of other species
Explain additive mortality
Additive mortality is when mortality agent acts independently of other sources of mortality and thus increases the rate of mortality when added to the system, such as predation.
Explain compensatory mortality.
When one source of mortality replaces another and a population stabilizes.
What is a Key-Factor Analysis?
An extension of a life table. Best used on species with discrete life stages life insects. Calculation of (Kx) which is total mortality, or generation mortality.
How do you calculate Kx?
K=Σki=ki=log(Ni)-log(Ni+1)
sum of k values equals K.
How do you test to see if mortality is DD in a Key factor analysis model?
Plot K vs N across years, increase if indicator of DD.
With what organisms is a KF analysis best used?
Best applied to organisms without overlapping generation, key factor driving pop change no always DD and doesn’t always result in regulation, Plots of key factors against N can yield useful information on strenght of DD, time lags and other phenomena.
What do different slopes of key factor analyses mean? example when b>1? etc..
1=b perfect compensation
b>1 over compensating
b< under compensating
-b inverse density dependence
circular=delayed density dependence
scatter=density independent
what is self-thinning?
Reduction in density (through mortality) as a consequence of the increased mean weight of individuals when growth is constrained at high densities.
What is reproductive suppression?
Largely associated with mammals. As density increases greater proportion of females stops breeding. Likely hormornally induced. Found that food influences rate at which nonparous is exhibited.
Name the 7 types of interactions between species
Competition, Parasitism, Mutualism, Predation, Disease, Facilitation, Herbivory
Explain interspecific competition
Competition for the same resource between different species
Explain intraspecific competition
Competition between individuals within the same species
What is exploitative and interference?
Exploititive competition is when one species is better adapted at utilizing a resource than the other.
Interference is when a species actually physically interfers with a competitor ability to utilize a resource.
What is competitive exclusion?
Guase 1934: One species ultimately excludes the other in a closed setting with limited resources and at constant pop values.
Autoecological vs. synecological?
auto is single organism level and syecological is population level.
What is a niche?
Widely defined.
Hutchinson–>fundamental vs. realized
Elton–> Where the species fits in the environmental web.
Has evolved over time.
Where should we find competition to be potentially most common?
Closely related species (similar size, morphology, physiology, and activity patterns).
What is resource partitioning?
The division of a resource between two competitors in order to reduce competition. Example tropical lizards.
What is character displacement?
This is a result of resource partitioning. Character displacement is when a species co-occur in distribution their differneces are extenuated but when they are isloated differences are not as prominent. Due to competition of same resource.
What did Hutchinson say about species coexisting with one another?
He said that if species differed in size with a ratios of at least 1.3 they could coexist. Leads to exploitation of differend resource. Avoidance of competition.
What is the unutilized portion of the environment?
(K-N)/K
Lotka-Volterra Equations
N1 =K1 –αN2
N2 = K2 – βN1
Explain unstable equilbrium
Alpha and beta values are > 1.0 therefore interspecific competition is stronger than intraspecifc.
Stable equilibrium is?
Alpha and beta are both <1.0 therefore interaspecific competition is stronger than interspecific
What do L-V competition models assume?
1) all assumptions inherent to the logistic model
DD is linear, all individuals are exactly alike, K constant, no time lags, closed pop, no abiotic sources of mortality
2) Resources are limited
3) Competition coefficients are constant
δ γ represent what in L-V competition models?
Interaction coefficients
What is intraguild predation?
Two competing species who also interact as predator and prey.
An indirect affect of competition between A and C due to the competition between C and B.
Prey switching. What is it? Provide an example.
Prey switching is when a predator utilizes a certain species at a particular density and then switches prey when density drops too low. Example is the Arctic fox, arctic goose an the lemmings.
What types of predators are there?
Carnivores, parasites, herbivores, cannibals, parasitoids. Easily observed and quatified.
What does predation have impacts on?
community structure, evolutionary force, weak and sick animals,
What is bottom up regulation? What is top down regulation?
Bottom up regulation refers to limits in abundace of species due to low trophic factors such as food supply
Top up is the negative affect of predators and/or parasites and competition.
What is the equation for prey continuous generation model? What do each variable stand for?
dN/dt=rN-aNP
r=growth
N=pop size
a=efficiency of search and attack by predator
NP=encouter rate between the two.
What is the equation for predators in a continuous generation model? what does each variable mean?
dP/dt=f(aNP)-qP
q=per capita starvation rate
f=converting prey into new predators
aNP=rate of food consumption always<1.0
a=efficiency of search and attack by predator
How do prey and predators respond to each other? How do we show this graphically?
Create state space diagrams using P=r/a N=q/fa (P=predator, N=prey)
what does r/a and q/fa represent?
r/a=ratio of growth rate of prey to capture efficiency of predator
q/fa=ratio of death rate of predators to efficiency of capturning (a) and turning prey into predators(f)
q is per capita starvation rate
Draw a modified prey isocline as described by Rosenzwig and MacArthur. What did it add to the idea?
It adds realism. All along the curve dN/dt=zero.
What is a refuge? and what does it look like graphically?
Area where a prey species can persist in the presence of the predator indefinetly.
What is a time lag in regards to predator prey models?
Time lags-logistic assumes instantaneous response on part of populations to changes in resources. Creates instability, leads to probable extinction for one or both species.
What is the difference between an “efficient” and “inefficient” predator?
“Efficient” predator keeps prey well below K
“Inefficient” predator results in prey regulating near K
What does the term “paradox of enrichment” mean?
Rosenzweig 1971 coined the term to describe the instability of predator populations caused by an added influx of food to prey populations. Lynx and the hare is a good example, an added abundance of rabbits causes the lynx populations to grow to an unstable number and will lead to eradication or a significant drop in numbers.
Why do refuges exist?
a)true spatial refuge, b)aggressive behavior of prey, c) a strong type III response, d) a fixed number of immigrants (pseudo refuge)
Describe each of the curves shown.
1=standard L-V
2=predator population increases w/prey
3=self limitation due possibly to interference
4=predator population limited by own predators or other factors
When does a predator exist completely independently of prey? What does the isocline look like?
When intraspecific competition and prey switching are prevalent.
Cycling behavior leads to what in LV predator prey models?
Clockwise fashion cycling typically leads to stabilization
Counter clockwise tend to be de stabilizing.
The more independent the predator and prey are of one another the more stable the system’s dynamics.
Predator responses to changes in prey density. What are the two types of responses, and what do these responses entail?
Numerical- Immigration and reproduction
Functional- Change in prey consumption patterns:
Type 1 Linear rise in consumption rate as prey density increases
Type II A decelerating rise in consumption rate, eventually asyptotes slope of line =a from LV equation. (invertabrate curve)
Type III Sigmoidal shape that also attains an asymptote (vertebrate curve)
What kind of predator response does this graph show?
Numerical
what response does this graph represent?
Type II functional response
What type of response does this graph show?
Type III functional response
Is this a numerical or functional response?
Numerical, because of the linear relationship.
Is this a functional or numerical response?
Functional type III response
Describe each type of functional responses.
Type I: effective at all population densities of prey
Type II: effective at low densities, but unable to limit prey at high densities (destabilizing)
Type III: effective at low densities, but ineffective at high densities (destabilizing)
