Exam review

Question 1

What is demographic stochasticity?
Why is it that some simulation runs result in extinction while others result in exponential growth?

Answer 1

Demographic stochasticity describes individual variability of probability of birth and death, these events are random. (someone gets hit by a car, fallen tree etc.) This usually has a larger impact on smaller populations. Because these event are random, some simulation runs will inevitably go extinct (especially with a small initial population). It is random whether the next event is a birth or a death, and so it could take only a few deaths in a row to put a population on the road to extinction.

Question 2

What is environmental stochasticity? Why is it that some simulation runs result in extinction while others result in approximately exponential growth?

Answer 2

Refers to unpredictable temporary spatiotemporal fluctuations in environmental conditions, that causes changes in population growth rates. Such as floods, droughts, availability of resources. Usually has as large of an effect on both small and large populations. Again, since they are random, it can lead to extinction in some simulation runs, and exponential growth in others.

Question 3

Give the formula that can be used to calculate the probability of extinction due to demographic stochasticity.

Answer 3

Pext = N0*(1-b/d)

Question 4

How is the proportion of simulation runs resulting in population extinction affected if (A) b is increased, (B) d is increased, (C) N is increased?

Answer 4

A. If b is increased, fewer simulation runs result in extinction
B. If d is increased, a larger prop of simulation runs will result in extinction.
C. If N is increased, each population has room for larger fluctuations and fewer simulation runs will go extinct.

Question 5

How do you calculate a population x time steps into the future using lambda?

Answer 5

For example, 3 time steps into the future.
N1 = N0lambda
N2 = N1lambda
N3 = N2*lambda

Question 6

What does geometric mean growth rate mean?
How can it be used to examine two different conservation strategies?

Answer 6

it is also known as “stochastic growth factor”. The number we are interested in, in population growth in a temporally fluctuating environment. A population has decreased in the end of a time series if geo.mean is < 1, and has increased i geo.mean > 1 (however, it might have techniqually been extinct sometime during the time series if there exists an extinction threshold.

The geometric mean can be used to estimate if the population will grow or shrink.

For example: lambda during four time steps are: 0.5, 2, 1.5, 0.7
Geometric mean:
0.5 * 2 * 1.5 * 0.7 = 1.05
λ^4 =1.05
λ = fourth root of 1.05
Geometric mean = fourth root of 1.05 = 1.01227

If we use these calculations on hypothetically increased lambdas (from a conservation strategy), we can estimate if a strategy will make a population grow.

Question 7

What is the Allee effect? Name two biological mechanisms that can result in this effect.

Answer 7

The phenomenon that population growth is negative at low densities and turns positive only after a certain threshold has been passed.

Mate limitation, the difficulty of finding a compatible and receptive mate for sexual reproduction at lower population size or density.

Organisms with cooperative defence or that hunt in groups might do worse when their density is low because of limited group formation.

Question 8

Imagine a plot of dynamics of logistic growth with Allee-effect. How do you determine the stability of each equilibrium?

Answer 8

Equilibriums are where N = 0, and where population growth rate dN/dt “crosses zero”, crosses the x-axis with N.

Alternating between the equilibriums, the growth rate is negative at low densities (from N1 to N2) and becomes positive after reaching the threshold N2. After reaching the threshold N3, it becomes negative once again. So it alternates between positive and negative.

If our starting population size is between N1 and N2, the growth rate is negative and pop will decrease until equilibrium N1.
If our starting population size is between N2 and N3, the growth rate is positive and pop will increase until equilibrium N3.
If it is larger than N3, it will decrease until reaching N3.

N1 and N3 are stabile equilibria and N2 is unstable. These always alternate.

Question 9

What is the difference between local attractors and global attractors (Allee effect)

Answer 9

Equilibrias that are attractors of the dynamics for only a subset of initial conditions are called local attractors. For example N1 is the attractor of the interval 0 to N2.

Equilibrias that are attractors of the dynamics of all possible initial consitions (except unstable equilibria) are called global attractors. N3 is a global attractor with the interval N2 to infinity.

Question 10

What is the implication of an Allee effect for the conservation of rare endangered species?

Answer 10

If there exists a threshold of population density such as under that threshold the population is destined for extinction without help, this of course has big implications for conservation. Knowing which direction a species is going in, which equilibria it is approaching and whether this is stable or unstable can be huge help in knowing where conservation efforts should be made.

Question 11

Explain asymmetric competition

Answer 11

Asymmetric competition is an unequal division of resources among competing species.

Question 12

Explain “ghost of competition past”

Answer 12

A term proposed to describe a possible reason for observed differentiations in niches. Two competing species might be less fit than a species that occupies a niche that does not overlap with other species, and therefore avoid competition. This way, natural selection might favor the non-competing species: it’s population increases while those of the competing species decrease.

The then observed differentiation in population sizes are a result of past competition, “a ghost of competition past”.

Question 13

Which are the four conditions for classical metapopulation dynamics.

Answer 13

1. The suitable habitat for a certain species occurs in discrete patches.
2. Even the largest local populations have a substantial risk of extinction (if not, we have an island-mainland metapopulation)
3. Habitat patches are not too isolated to prevent recolonizations (if they are too isolated, we have a non-equilibrium metapopulation)
4. Local populations do not have completely synchronous dynamics (if they do, the metapopulation will not persist much longer than the local population with the smallest extinction risk)

Question 14

How does the incidence function model improve our ability to understand metapopulation
dynamics as compared to Levins (or general) metapopulation model?

Answer 14

DONT KNOW!!

Question 15

Rapoports rule.

explain the pattern in 1-2 sentences.

provide 2-3 sentences on one or more potential mechanisms thought to generate the pattern.

Answer 15

The tendency for species living at higher latitudes to have larger range sizes.

At higher altitudes there is greater climatic variability, which selects for broader environmental tolerances and makes species able to become more widespread in different environments. It is also hypothesised that species from higher altitudes with restricted ranges went extinct due to glaciation and climate change, leaving only those with larger ranges.

Question 16

The latitudinal diversity gradient.

explain the pattern in 1-2 sentences.

provide 2-3 sentences on one or more potential mechanisms thought to generate the pattern.

Answer 16

The fact that there is higher diversity with lower latitude, closer to the equator and the tropics, while habitats in higher latitudes generally have lower diversity.

This is thought to be because of higher productivity in the tropics, more sun and higher temperatures gives more food, conditions for reproduction all year round, which can in turn give higher speciation rates. More stable climates can also mean that there is and has been lower extinction rates at lower latitudes.

Question 17

The very basic version of Lotka - Volterra predator-prey model is:
dN/dt = rN – αNP and
dP/dt = fαNP-qP

How is predators functional response included in this model?

Answer 17

The predators functional response is the relationship between the per capita rate of consumption and the number of prey.

aN in this model is the capture efficiencynumber of prey.

Question 18

How can predator functional response be modified to add more realism in the Lotka-Volterra model?

Answer 18

It becomes more realistic if we add handling time (type 2) or searching time (type 3). That way the predator cannot consume infinitely many prey as the prey population grows, because eventually the number of prey that can be consumed is limited by the handling time.

The diagram…

Question 19

The very basic version of Lotka - Volterra predator-prey model is:
dN/dt = rN – αNP and
dP/dt = fαNP-qP

How is preys carrying capacity included in this model?

Answer 19

It’s not. To include prey carrying capacity the first part of the model would be:

dN/dt = rN (1-N/K) - aNP

By doing this the prey population would not be able to grow forever, which is important if we want to understand the cycles of predator and prey.

Question 20

During the food web part, we talked about three different approaches to construct food webs, what are they?

Answer 20

• Connectedness web
• Energy flow web
• Functional web

Question 21

Discuss the differences between these three approaches and include what type of estimates the webs are based on.

Answer 21

• Connectedness web - shows the presence of an interaction between species.
• Energy flow web - measures and demonstrates the amount of energy moving between species
• Functional web - shows the strength of interaction between species.

When looking at them, they can all include the same species (species in a lake for example.

In connectedness, there is a line or arrow between all species that interact with each other.
In energy flow, the same arrows are present but the thickness depends on the amount of energy (ex. yearly biomass) that goes from one species to the other.
In functional, all arrows might not be present as all species and interactions are not equally important for the food web function.

Question 22

What is the meaning of “common garden experiments”?

Answer 22

Common garden experiments are indoor or outdoor plantings of species or populations collected from multiple distinct geographic locations, grown together under shared conditions.

A central question for all common garden experiments is to what extent the local environment drives expression of traits such as growth and phenology

Transplant experiments are designed to prove local adaptation, common gardens are designed to study the genetic bases of traits, regardless if adaptive or not.

Question 23

What is the biological interpretation of the right eigenvector?

Answer 23

The right eigenvector gives the stable state distribution.

Question 24

What is the biological interpretation of the left eigenvector?

Answer 24

The left eigenvector is the vector of reproductive values.

Question 25

What is the dominant eigenvalue?

Answer 25

Lambda is the dominant eigenvalue of the matrix L.

Question 26

The sensitivity matrix

Answer 26

Each entry of the matrix contains the sensitivity of λ with respect to the corresponding entry in the population projection matrix.

You can use it to estimate what change in lambda is given from a certain conservation strategy. For example: an increase of 0.2 for the survival of adults (in position 3-3).

We take the value from the sensitivity matrix in position 3-3 and multiply it with 0.2. So always multiply with the increase, even if its for example increase of 100 in fecundity.

The value you get from sensitivity*increase (or decrease) you then add on to the original lambda and see if the conservation strategy can get lambda up to over 1. Or under 1 if you are looking at an invasive species.

“By how many units does lambda change if we change the matrix entry by one unit?”

Question 27

The elasticity matrix

Answer 27

The sensitivity matrix gives the absolute change in λ based on the demographic parameters. It does not take into account that survival probabilities and fecundities are generally on very different scales. To correct for this, we can compute the elasticity matrix.

It gives us the proportional change in λ given a proportional change in the demographic parameters. Basically, the entries with the highest values in the elasticity matrix are those that we want to focus on for conservation strategies. There, the changes have the biggest effect.

Answers “by what percentage lambda changes in response to a change in the matrix expressed in percent”

“If i change the matrix entry by one percent, by what percent does lambda change?”

Question 28

Mass effect

Answer 28

Environmental heterogeneity is common in nature and most species experience a world that is both patchy and heterogeneous. This causes individuals to disperse within and across
communities causing shifts in local and regional species richness, which is often also called
mass effects.

Question 29

Metacommunities:
What is alpha, beta and gamma diversity?

Answer 29

Alpha diversity = local diversity (within a patch or habitat)
Beta diversity = difference in diversity between patches or habitats
Gamma diversity = regional diversity (or the entire landscape)

Question 30

Metacommunities:
How and why may alpha, beta and gamma diversity change at low, intermediate and high dispersal of individuals

Answer 30

The graph…

Question 31

Arithmetric and geometric mean

Answer 31

Arithmetric mean is the one we are more used to, mutliplying the numbers and dividing them by how many numbers there are. But it is not suitable to predict the fate of a population with fluctuating values of lambda.

Instead we want to use the geometric mean: multiplying the lambdas and then taking the x’th root out of that. For example if we multiply four lambdas, we take the fourth root out of that value to get the geometric mean lambda.

Question 32

How do you interpret the geometric mean growth factor (lambda)?

Answer 32

If it is smaller than 1, the population will go extinct.
If it is larger than 1, it could survive, but could also go extinct due to the environmental stochasticity.

Question 33

What is amensalism?

Answer 33

A typ of interaction between two species, where one is effected negatively and one is not effected at all.

For example: foragers that step on an insect or a birds nest when foraging.

Question 34

What is commensalism?

Answer 34

A typ of interaction between two species, where one is effected positively and one is not effected at all.

For example: a bird living in a pre-existing hole in a tree, or a tree-frog using a tree for protection.

Question 35

Keystone species

Answer 35

A species that hold together the complexity of a food web. By controlling the abundance of certain species, their presence increase diversity, benefits weaker competitors, stops one competitor from outcompeting all others.

Question 36

Plastic vs constitutive defenses.

Answer 36

Plastic defense: defense that is not always expressed, in habitats with variable predation risk.
Constitutive defense: in habitats with continuous high predation risk.

Defense mechanisms have costs, like reduced reproduction, and therefore defense mechanisms are not always developed and constantly expressed for all individuals at all times.

Question 37

Landscape of fear

Answer 37

continuous spatial variation due to an animal’s perception of predation risk. Prey learn where and when predators are active, and tend to avoid these areas. This can have important effects on other species, for example the plants that are eaten by the prey.

In yellowstone: deer and elk avoided valleys because it is harder to escape the wolf in there, then the trees could establish more around the rivers in the alleys, the rivers stabilized with the increased vegetation, then the beavers came back to the rivers…. etc.

Question 38

TMI and DMI

Answer 38

TMI = trait mediated interactions. Fitness costs of defensive strategies and predator mediated stress (=non-consumptive effects)

DMI = density mediated interactions. Mortality due to direct consumption by predators (=consumptive effects)

Studies show that both can be equally as strong in affecting prey-predator interactions

Question 39

What are the two distinctions in interspecific competition?

Answer 39

• Exploitative/scramble competition: depletion over shared resource
• Interference/contest competition: direct interactions between species (for example over territory)

Question 40

Which six mechanisms effect interspecific competition?

Answer 40

• consumption (direct consumption of prey)
• preemption (competition over a physical resource (space, breeding spot)
• Overgrowth (one species grows so much that it covers other species, suffocates it)
• Chemical interactions (one plant releases chemicals that harm other species/ stops them from growing)
• Territoriality (competition over territory)
• Encounter competition (interference in nonterritorial encounters that results in negative effects)

Question 41

What is required for two species to co-exist?

Answer 41

Two species can coexist only if they show trade-offs in consumption of two resources

Coexistence is possible when both species consume proportionally more of the resource that most limits its own growth.

Intraspecific competition has to be stronger than interspecific competition.

Question 42

Character displacement

Answer 42

Evolutionary change that occurs when two similar species inhabit the same environment. Natural selection favors divergence in the characters - morphology, ecology, behavior, or physiology - of the organisms. This to lessen competition between them.

Question 43

SLOSS

Answer 43

Single large or several small?

A debate during the 70s and 80s about whether a single large or several small areas are better for conservation purposes.

larger means: larger pop sizes, less edge effects
smaller means: more habitat diversity, if one patch is damaged in flood or fire etc. the other ones are still fine.

A good end to the debate is that we rarely get to choose, conservation is more about taking whatever you can get.

Question 44

Bergman’s rule

Answer 44

a macroecological pattern.

the tendency for species at higher latitudes to have larger body mass.

possible explanations: small body mass associated with low dispersal, increased heat conservation in large bodies, increased starvation resistance in large bodies.

Question 45

What challenges are there to constructing food webs?

Answer 45

• impossible to assign specific species to trophic levels due to omnivory
• predictions are limited with respect to how many and which species you have within a trophic level.
• there is a trade-off between keeping as much info about species as possible and at the same time simplifying and make less complex

Question 46

How can we deal with complexity when constructing food webs?

Answer 46

The major goal is to find general “laws” that explain the structure and dynamics of natural communities.
Two approaches:
- construct theoretical food webs and compare with real food webs, or to make predictions for real food webs
- identify important traits for explaining network structure.

Question 47

what can structured population models be used for?

Answer 47

• Assessing extinction risk, time to extinction
• comparing populations, which should be focused on for conservation?
• identifying key life stages, which life stage should be focused on for conservation?
• maximum sustainable yield
• efficient reintroduction, how many are needed for viable population?
• minimum reserve size, what is the minimum size of nature reserve to minimize extinction risk?
• pest control

Question 48

irreducible

Answer 48

a population projection matrix can be irreducible or reducible. It is irreducible if there exists a path from any state to any other state. By traveling along the arrows an individual (or its offspring) can end up in any other state regardless of the state of origin. If it is not irreducible it is reducible. Reducible life cycles are organisms with post-reproductive age classes (humans, killer whales etc.) or for systems with geographical boundaries, where migration only goes one way.

Irreducible matrices can be either imprimitive or primitive.

Question 49

Imprimitive or primitive.

Answer 49

an irreducible matrix is called primitive if there exists a natural number k such that M to the power of k > 0 (all numbers in the matrix are positive, no zeros left, when raising M to k). A matrix that is not primitive is called imprimitive.

Shortcuts to recognize a primitive matrix:
- any irreducible matrix that contains a self-loop somewhere or…
- any irreducible matrix where at least two adjacent age-classes both have fertility (has to be an age-structured Leslie matrix)

If a matrix is primitive, the pop will reach a unique stable state distribution and will from then on grow by a fixed unique factor lambda. Unique here means that the stable state distribution and lambda are independent of N0.

We have the tools to investigate this type of matrix!

Question 50

Leslie matrix

Answer 50

A discrete, age-structured model of population growth.

Question 51

Reproductive value

Answer 51

a females current and future contribution to the population through reproduction. The highest value belongs to those in the beginning of their reproductive period. They have both survived until the start of reproduction, and have “all of their fertility left”.

The formula for reproductive values is true only for a population at equilibrium (lambda = 1). If the population is growing, offspring produced early in life are more valuable than offspring produced early in life. The situation is reversed for lambda < 1.

Question 52

What is a non-equilibrium metapopulation?

Answer 52

no migration between the subpopulations, with time the system will vanish, go extinct