Jo Albers of OSU visited UC Davis’ Agricultural and Resource Economics department to speak about her work on optimal management on invasive species management. The work is also part of Kim Hall’s dissertation research and was completed in conjunction Majid Taleghan, Tom Dietterich, and Mark Crowley from OSU Engineering.

These are my rough notes from Dr. Albers’ talk talk. Any errors or misrepresentations are my own.

Economics of invasive species

Need to bring the biology back into bioeconomic modeling.

  • Invasives are economically costly
  • Ecologically costly
  • Most previous literature has been on
    • Dispersal via trade
    • Stochastic-dynamic programming looking at timing of control of species
    • Steady-state spatial work
  • Recent ecological work in species competition, and non-trade dispersal pathways

  • Invasion as spatial and dynamic process
    • Management of the frontier
    • Deterministic or steady state analyses typical

Computational issues

  • Analytical solutions for stochastic systems in space and time are difficult or not useful
  • But dimensional issues make computing difficulty

Overview

  • Economic optimization decision framework
  • Spatial representation in a river network
  • Ecological model of species dispersal and competition
  • Computational methods

Ecological model

  • Metapopulation
  • Each reach of a river is native, invasive, or empty
  • In each time period
    • Natural death
    • Propogule production
    • Dispersal
    • Site-competition, colonization, establishment
    • Death, dispersal, and competition is stochastic
    • Propogules compete to establish, and then just one species establishes

Economic model

  • Minimize expected discounted costs
    • sum of cost of invasive and cost of management
    • choose timing and location of
      • doing nothing
      • eradication
      • eradication and restoration
  • Subject to an annual dispersal rate

# Dispersal model

Propogules flow up and down stream, but more likely downstream:

\[K_{ij} = Cu^{NU_{ij}}d^{ND_{ij}}\]

  • \(C\): constant
  • \(u\): upstream propogule survival rate
  • \(d\): downstream propogule survival rate
  • \(NU_{ij}\): number of reaches between \(i\) and \(j\)

This follows @MekirioXXXX ecology paper on river dispersal.

\[ p_{wins} = \frac{\beta g_k}{\beta g_k + g_0}\]

  • \(p_k\): probability species \(k\) wins
  • \(\beta\): “competitive advantage of invader over the native
  • \(g_k\): number of propogules of species \(k\)
  • \(g_0\): number of propogules of other species (not \(k\))

Solution method

  • Markov decision process - no state variable representing the condition of the habitat
  • But even with this, there are 14 billion different combinations
  • Estimate transition probabilities matrix by drawing samples from stochastic ecological simulation model

Results

  • Native species
    • Provide propogules to compete with invaders
    • Make habitat sites unavailable for invasives
  • So, if you have more native species in the system, then eradication is better, because it’s likely that natives will regrow
  • If you have fewer native species, you should restore
  • As directionality of flow is stronger, optimum is to eradicate and restore downstream

Dispersal mechanisms

If there is no long-distance dispersal, you eradicate more than restore, focusing on the center connected reach. But if there is long distance dispersal, you do more restoration, and do it farther upstream.

Ecology

When invasives are good site competitors, treat upstream and mostly eradicate

When invasives are swamping with propogules, restore to get more propogules of natives, and block invasion of a reach. Restore in the central reaches.

Rule of thumb v. optimal

Some traditional rules of thumb:

  • Triage - treat the most invaded reach
  • Treat leading edge
  • Treat the most connected

These are all somewhat more costly than optimal