Population Ecology, part 3

Principles of Ecology Week 4

Reminders

  • Semester Project community list due on Friday
    Please bring a copy to class
  • Weekly Activity and Reflection both due on Sunday this week

Incorporating spatial structure

  • Assumption of closed population when we introduced exponential and logistic growth

  • But nature is patchy, and dispersal (movement from one patch to another) is common

Incorporating spatial structure

  • Each patch holds a population
  • Patches are connected by dispersal
  • Patches are either unoccupied or occupied

Incorporating spatial structure

  • Landscape represents a metapopulation
  • \(P\) is the fraction of occupied patches
  • \(1-P\) is the fraction of unoccupied patches
  • Within each patch, population goes extinct at a rate \(e\)
  • Populations can disperse from an occupied to an unoccupied patch at rate \(m\)

Incorporating spatial structure

Landscape represents a metapopulation
There are a total of \(L\) patches
\(P\) is the fraction of occupied patches
\(1-P\) is the fraction of unoccupied patches
Within each patch, population goes extinct at a rate \(e\)
Populations can disperse from an occupied to an unoccupied patch at rate \(m\)

  • What is the change in patch occupancy (\(P\)) with respect to time?

Incorporating spatial structure

Derive the equation from the principles

Incorporating spatial structure

\[\frac{dP}{dt} = \overbrace{-eP}^{\text{Local Extinction}} + \overbrace{mP(1-P)}^{\text{New patch establishment}}\]

  • What is the Equilibrium patch occupancy?
  • In other words, what fraction of patches should we expect to be occupied at equilibrium?

Incorporating spatial structure

\[\frac{dP}{dt} = \overbrace{-eP}^{\text{Local Extinction}} + \overbrace{mP(1-P)}^{\text{New patch establishment}}\]

\[P^* = 1-\frac{e}{m}\]

  • At equilibrium, species does not occupy all possible patches
  • Species will be extinct from the metapopulation (no patches occupied) if \(e>m\)
  • Total number of occupied patches (\(O\)):

\[O = LP^* = L\bigg(1-\frac{e}{m}\bigg)\]

Implications for populations

Species will be extinct from the metapopulation (no patches occupied) if \(e>m\)

  • Persistence of the species depends on the balance of \(e\) and \(m\)

  • What determines \(e\) and \(m\)?

Implications for populations

What determines \(e\)?




What determines \(m\)?


Implications for conservation

  • Often, when new land is being considered for development, a team of biologists will conduct a biodiversity survey

  • What does it imply if the focal species is not found?

  • Patches that are unoccupied are not unimportant for species persistence

Implications for conservation

  • Consider what happens when absence of a species is used to justify land development:

  • \[O = LP^* = L\bigg(1-\frac{e}{m}\bigg)\]

  • If potentially usable patches are destroyed, \(\downarrow L\)

  • Repeated destruction of habitat that is currently unoccupied will send \(O \to 0\)

Implications for conservation

  • Persistence of the species depends on the balance of \(m\) and \(e\) (\(m>e\) for persistence)

  • Habitat disconnection (\(\downarrow m\)) and/or habitat degradation (\(\uparrow e\)) can drive metapopulation extinction

The power of conceptual thinking

\[\frac{dP}{dt} = \overbrace{-eP}^{\text{Local Extinction}} + \overbrace{mP(1-P)}^{\text{New patch establishment}}\]

  • Small group discussion: How does meta-population dynamics relate to epidemiology?

Principles of ecology
Week 4, Day 2

Reminders

List of potential communities for Semester Project due on Friday before class (Moodle)

Please bring a copy to class.

  • Next week: Review of population dynamics so far (Weekly Activity).

Review of metapopulation dynamics

  • Landscape represents a metapopulation
  • \(P\) is the fraction of occupied patches
  • \(1-P\) is the fraction of unoccupied patches
  • Within each patch, population goes extinct at a rate \(e\)
  • Populations can disperse from an occupied to an unoccupied patch at rate \(m\)

Review of metapopulation dynamics

\[\frac{dP}{dt} = \overbrace{-eP}^{\text{Local Extinction}} + \overbrace{mP(1-P)}^{\text{New patch establishment}}\]

\[P^* = 1 -\frac{e}{m}\]

Persistence of population in the landscape depends on \(e < m\)

Review of metapopulation dynamics

Persistence of population in the landscape depends on \(e < m\)

  • Landscape extinction more likely if \(\uparrow e\) and/or \(\downarrow m\)

  • High patch quality and high connectivity between patches enables persistence

Applications

  • “This is a foundational data and analysis project with ecosystem-level importance that involves the development of an estuary-level oyster metapopulation model that connects larval transport; reef persistence; and oyster growth, mortality, and reproduction in each coastal basin

Applications

Link to paper

Applications

Conceptual thinking practice

How does meta-population dynamics relate to epidemiology?

  • Micro-scale
  • Macro-scale

Meta-population models for epidemiology

Link to paper

Meta-population models for epidemiology

Application at the micro-scale

  • When the focal species is a parasite (pathogen), each host individual can represent a patch

  • Infection of a healthy individual represents migration to a new patch (\(m\))

  • Rate of recovery of an infected host represents local extinction (\(e\))

  • The persistence of the parasite (pathogen) in the landscape depends on low recovery rates (low \(e\)) and high transmission rates (high \(m\))

  • Efforts to increase recovery rates (\(\uparrow e\)) and reduce transmission rates (\(\downarrow m\)) are key epidemiological interventions.

Meta-population models for epidemiology

Application at the macro-scale

  • At larger scales, different geographic areas (jurisdictions) can represent patches
  • Movement of infected individuals across jurisdictions represents migration to a new patch (\(m\))
  • Recovery of infected individuals in a jurisdiction represents extinction (\(e\))
  • More complex, because each jurisdiction (patch) comprises a mix of infected, uninfected, immune, etc. individuals

Meta-population models for epidemiology

This is an imperfect but helpful analogy

  • e.g., acquired immunity of infected hosts breaks assumptions of the simplest meta-population model.

  • In such cases, we can add biological realism.

Link to lecture on Youtube

Applications

  • Meta-population dynamics theory yields insights for species conservation across spatial scales

  • Synthesizing meta-population modeling and epidemiology enables predictions of spatial spread of disease and develop interventions

Review

\[\frac{dP}{dt} = -eP + mP(1-P)\]

Next class

  • Structured group discussion about Semester Project potential communities

Principles of ecology
Week 4, day 3

Structured group discussion

  • Groups of 4, discuss for 25 minutes.

  • Nominate one person as facilitator, one as recorder, one as reporter

  • Facilitator: Manage group discussion time (~5 minutes per person); ensure that everyone gets a chance to speak/ask questions; encourage conversation if things get quiet

  • Recorder: Document the conversations and share notes with relevant individuals (e.g. if we are discussing my idea, Recorder would keep track of the questions that come up and share that with me after the group discussion)

  • Reporter: Share group’s ideas with the class - what is each person’s top choice for ecological community; what are some challenges/questions that arose; what are next steps, etc.

  • Roles switch next week

Structured group discussion

In your groups, please take turns to discuss

  • What idea(s) you had going into this assignment, and why?

  • From your literature search, do you feel that your idea was too narrow/broad/just-right/other?

  • Among the primary literature you are finding (peer-reviewed articles in formal scientific journals), is there a good mix of “basic” ecology and more “applied” environmental/conservation/social science? Or is there a bias towards one or the other?

  • From your searches so far, do you see ways to connect material from class to your semester project? (either material so far, or from future topics)

  • What was one paper/idea/resource that surprised you from your search?

  • What do you think are your next steps for either (a) selecting a focal community from among your options, (b) or getting more information on the community you have decided to focus on?