Organisms as resources and consumers
Part 2
Overarching questions in Consumer–resource dynamics
- What allows persistence of consumers and resources in the long term?
- Are there conditions in which consumers “over-consume” and engineer their own demise?
- How does perturbation of the system (e.g. removal of a “top predator”) affect the network as a whole?
Historical inspiration
Resource dynamics (R):
dRdt=exponential growth - loss to consumer
Consumer dynamics (C:
dCdt=growth from consumption - energy loss
dRdt=rR−aRC
dCdt=eaRC−mC
- This model features tightly coupled dynamics
- Changes in one population immediately cause feedbacks onto the other population
- In-built “delay”: peaks in resources lead to peaks in consumers
Recall the original motivation for this model
Without any additional complexity, this model can provide an explanation for changes in proportion of prey:predator caught and sold at fish markets
Let’s think about the “equilibrium” in this model
Is this system at equilibrium?
Do the population dynamics always reach the same cycles?
Let’s perturb the system by slightly reducing R
The populations always cycle, but the amplitude of the cycle depends on the initial size of the populations
“Neutral oscillations” - a different type of equilibrium
Amplitude of cycles change, but average remains the same!
The oscillations happen around a central equilibrium point
Review of equilibrium stability
Equilibrium happens whenever dNdt=0.
Stability of an equilibrium reflects what happens if a system is “pushed”
Stable equilibrum: System comes back to the original point
- e.g. Carrying capacity
Unstable equilibrium: System keeps moving away from the original point, in the direction of the “push”
Neutral equilibrium: Once pushed, the system doesn’t return to the origina point, but doesn’t keep “moving away”
Challenge question: What is the equilibrium condition for this model?
dRdt=rR−aRC
dCdt=eaRC−mC
- Solve the dRdt equilibrium with respect to C (i.e. C=? for dRdt=0?)
- Solve the dCdt equilibrium with respect to R (i.e. R=? for dCdt=0?)
Challenge: Draw the Zero Net-Growth Isoclines for the predator–prey model.
Dicrostonyx torquatus - Northern collared lemming
Mustela erminea - Stoat/“ermine”
Organisms as consumers and resources
Recall the canonical model for consumer–resource dynamics:
dRdt=rR−aRC
dCdt=eaRC−mC
How do we find the equilibrium conditions of this model?
Resource equilibrium (dRdt=0) happens at C=ra
Consumer equilibrium (dCdt=0) happens at R=mea
Trophic networks in ecological systems
What are the consequences of perturbing a whole network?
Let’s start by considering a tri-trophic interaction network.
“Enemy of my enemy is my friend”
Origins of this idea
But, trophic networks can get further complicated
Let’s draw a schematic of this trophic network
Consumer–Resource wrapup and mid-semester checkin
Importance of consumers in maintaining ecosystems
Source: Status and Ecological Effects of the World’s Largest Carnivores, Ripple et al. 2014
Source: Trophic rewilding can expand natural climate solutions, Schmitz et al. 2023
Mid-semester retrospective
Overview of the past eight weeks
Population ecology
- Questions that we asked:
- How can population sizes be estimated?
- Under what conditions do populations grow, shrink, or stay constant?
- dNdt>0, dNdt<0, dNdt=0
Population ecology
- Estimating population sizes through Mark–recapture approaches
Population ecology
How do populations grow and shrink?
A simple model with no population structured; constant reproduction rate and death rate
Expand to structured populations (not all individuals have the same rates of reproduction/mortality)
What if birth/reproduction rates respond to population size?
Assumes closed populations - no migration
Population ecology
Introduced the concept of equilibrium and stability
- Equilibrium: dXdt=0; stability = system at equilibrium returns to equilibrium
- Carrying capacity is a stable equilibrium
Overview of the past eight weeks
Community ecology
Overview of past eight weeks
Reductionism as an approach to study ecological communities
Often times, we see lots of “similar” species coexisting
Multiple herbacious plant species; multiple trees; multiple seed-eating birds, multiple predatory birds, etc.
Key question: What determines diversity of coexisting species that compete for shared resources?
Overview of past eight weeks
Key question: What determines diversity of coexisting species that compete for shared resources?
- Expand from dNdt to dN1dt and dN2dt
- Introduced a new form of graphical analysis: state-space analysis
- Coexistence requires stronger competition within species than between species
Overview of past eight weeks
- What about interactions among consumers and resources?
Consumer–resource interactions
Reductionist approach: start with one consumer and one resource
Analysis: Again, through isocline analysis
Insight: population cycling is likely – thus, oscillating equilibrium
Consumer–resource interactions
Complexity of trophic networks can generate unexpected causal links
Unexpected causal links
Consumer–resource interactions
What escapes the eye, however, is a much more insidious kind of extinction: the extinction of ecological interactions
- Dan Janzen, 1976
Next steps in the course
Patterns of diversity across space
- Why are some regions of the world more diverse than others?
- How do we quantify change in biodiversity over space and time?
Next steps in the course
Ecosystems ecology
- What governs the movement of energy and nutrients through ecological communities?
- How do human disruptions of ecological systems impact ecosystem processes?
Next steps in the course
Ecology and human societies
- What are ecological patterns in human systems (e.g. cities)?
- How can lessons from ecology shape human societies, and vice-versa?
Organisms as resources and consumers Part 2