population and community ecology

what is exponential growth

bigger it gets, faster it gets

what is exponential decay

shrinks quick then slows (not reaching 0)

why does exponential growth happen

• birth + deaths are constant

• more births than deaths

• no limiting resources

why does exponential decay happen

• resource depletion

what is discrete time

specific, separate time steps e.g. breeding seasons, generations don’t overlap

what is continuous time

constantly, at every instant e.g. bacteria and overlapping generations

what is the definition of density dependence in population ecology

population growth is influenced by the current population density

what does the carrying capacity (K) represent in population dynamics

the maximum population size an environment can sustain

what’s the equation for logistic growth in continuous time

dN/dt = rN1- N/K)

what happens to population growth when N = K in the logistic growth model

Population growth rate is 0

what is intrinsic growth rate ( r )

the per capita rate of population increase in an ideal environment

what does a bifurcation plot show in population dynamics

how changes in the intrinsic growth rate ( r ) affect population stability

what is the per-capita growth rate (pgr) in logistic growth

pgr = r(1- N/K)

what is the equilibrium density N* I the logistic growth model

N* = K

what is the difference between density dependent and density independent factors

density dependent factors are influenced by population density while density-independent factors are not

what is the transient phase

the initial period of adjustment before reaching equibrilium

what is the Lefkovitch matrix used for

is a way to model population growth for organisms that go through life stages (insects)

what does a lefkovitch matrix show

a table showing

1 who survives to the next stage

2 who stays in the same stage

3 who produces offspring (and how many)

what is a Leslie matrix used for

for age-structured populations

what do the rows of a transition matrix represent

how many individuals enter each stage in the next step

what do the columns of a transition matrix represent

where individuals from each stage go (stay, grow, preproduce))

What is fecundity in a matrix model?

The number of offspring produced by individuals in a certain stage.

why might targeting juveniles in conservation be less effective

because adults often have a larger impact on population growth (reproduction)

What is the meaning of eigenvalues in matrix population models?

they tell us the long-term growth rate of the population

Develop the analytical structure of stage-structured population models using the Lefkovitch matrix. Explain how transitions between stages are represented, including the roles of survival, fecundity, and progression probabilities. Discuss how these models can be extended to incorporate density dependence, and describe how population projections and sensitivities can be analysed using eigenvalues and eigenvectors. Include examples of biological systems that benefit from stage-structured modelling, and outline how such models can be implemented in R.

• introduction introducing population models and explain why age/stage matters in real populations. state focus

• main body - define lefkovitch matrix model and show basic form in diagram

• main body - use a concrete example (insect larvae, nymph, adult) and discuss restraints (no adults = no larvae = 0) clarify assumptions e.g. discrete time steps, individuals can stay or move through stages

• main body - add density dependence so make more accurate and real life examples (seeds, metamorhpis)

• main body - by calculating eigenvalues and eigenvectors we can determine the long term growth rate and distribution of individuals across a life stage

• main body R implementation

• strengths and weaknesses (good for predicting real outcomes, more complex and requires more data)

• conclusion

what would R implementation look like for a stage structured matrix

A <- matrix(c(0, 2, 3,

0.5, 0.3, 0,

0, 0.6, 0.7),

nrow = 3, byrow = TRUE)

what is an isocline

line of equal slope (no change)

what is an eigenvector

the shape/structure of the population when things have stabalized

(percentages)

what is an eigenvalue do

tells you how fast the population grows or shrinks in the long run

what are three main types of species interactions

competition (- -), mutualism (+ +) and predation (+ -)

what is the Lotka-Volterra competition model used for

to describe how two species compete for shared resources and predict outcomes like coexistence or exclusion

what is a functional response in predator-prey models

how the rate of prey consumption changes with prey density

What are the three types of functional responses (Holling)?

• Type I: Linear (constant consumption)

• Type II: Slows down at high prey density

• Type III: S-shaped curve, slow at low prey density, then increases

what is stochasticity in population ecology

random variation in population processes due to environmental or demographic factors

what is the difference between demographic and environmental stochasticity

demographic = random death/birth in individuals

environmental = changes in climate/weather affecting everyone

what is the key difference between deterministic and stochastic models

deterministic models give the same outcome every time; stochastic models include randomness so vary

how do you model environmental randomness in growth

by adding a random term 𝜀 to the growth equation

What does 𝜀 > 0 or 𝜀 < 0 represent in stochastic growth models?

• 𝜀 > 0 = good year (faster growth)

• 𝜀 < 0 = bad year (slower growth or decline)

how can you estimate parameters like r and K from data

using linear regression on population growth rate vs population size

why are multiple simulation runs important in stochastic models

randomness means each run gives a different result. multiple runs can show average trends and variability

Describe how demographic and environmental stochasticity influence population dynamics over time. compare deterministic and stochastic models of population growth highlighting how environmental variability is incorporated mathematically. using examples from real populations, explain the role of random variation in extinction risk ad population persistence. outline how population growth parameters can be estimated using regression techniques in R and illustrate your answer with appropriate equations and plots.

introduction - define population dynamics, introduce stochasticity as unpredictable variation affecting growth. briefly mention deterministic vs stochastic models

main body - demographic vs environmental stochasticity

main body - deterministic vs stochastic models

main body - consequences of stochasticity and estimate parameters (r from the intercept and K from the -r slope)

main body - the importance of multiple simulations and real life examples (magpie parasitism)

conclusion

what are nodes and links in a Network

Nodes - vertices (species, people)

Links/Edges - interactions (trophic, social)

examples of Networks

• WWW

• Freindships

• Airports

• metabolic

why are networks useful

• more synthetic representation of the data

• analyse sub communities, distributions of links and importance of certain vertices and links

• identify key individuals or patterns

describe how ecological networks can be constructed and analysed. include in your answer an explanation of key network metrics such as degree, centrality, modularity and connectence. discuss how network structure influences ecosystem stability and resilience, using examples from real-world or experimental ecological systems.

introduction - dfine an ecological network and state the importance in understanding community structure, function and stability. mention common types e.g. food webs, mutualistic networks

main body - describe how networks are built from field and lab data

main body - describe and interpret key structural measures e.g. degree, centrality, modularity, connectence

main body - robustness to species loss (more connected = more stable), trophic cascades

main body - real life examples

conclusion

what is a degree

number of links per node

example of high degree and low degree

high degree = generalist

low degree = specialist

what is degree centrality

highly connected nodes

what is betweenness centrality

nodes that act as bridges

what is modularity

measures how well a network divides into clusters or communities

what is connectence

proportion of possible links that are realised

Connectance= Actual links/ total possible links

what is a phase-plane diagram

a graph that shows how the population sizes of two species change over time. shows how one species changes with respect to the other