complex dispersal networks Michael Bode, University of Melbourne - - PowerPoint PPT Presentation

Modelling the ecological implications of complex dispersal networks

Michael Bode, University of Melbourne

Population dynamics on a single patch

In the absence of dispersal:

Population dynamics on a single patch

Recruitment limitation:

Doherty (1991) Ecology of Fishes on Coral Reefs

Metapopulations are populations of populations linked by dispersal

Connectivity is interesting, complex and novel

Dispersal is essentially a linear driver of a multidimensional, nonlinear system

• Dispersal is defined by connectivity matrix C
• Matrix element cij is the proportion of larvae

from reef i that travel to reef j

Metacommunity models = Local processes (dynamically & temporally complex) + Connectivity (spatially & temporally complex)

Metacommunity models = Local processes (dynamically complex) + Connectivity (spatially complex)

The role of mathematics is to provide some insight into what the result might look like Not necessarily prediction

How does dispersal interact with :

• Population ecology
• Evolution
• Community dynamics

How does this affect ecosystem dynamics and conservation management?

THREE COMMUNITY ECOLOGY EXAMPLES Small scale community dynamics

• 1. Asymmetric dispersal
• 2. Different dispersal abilities

Large scale community dynamics

• 3. Dispersal differences on the GBR

Prologue: Competition in a single population

Prologue: Competition in a single population

These two species cannot stably coexist “Gause’s exclusion principle”

Population dynamics on a connected patch

a b c d

Competition across two patches

Patch 1 Patch 2

Invasibility criteria

2 2

Invasibility criteria

The two patches are saturated, allowing us to express Linearise the system of equations around the two extinction points: 2 2

Invasibility criteria

If the dominant eigenvector of the Jacobian at both extinction points is greater than 1, coexistence is possible

Example 1: Asymmetric dispersal patterns

Coexistence via asymmetric dispersal

• What ecological mechanisms could drive different

dispersal patterns for different species?

• How does this manifest in larger metapopulations?
• Is the coexistence robust to reasonable variation?

• Two species, identical at a local scale
• Larval dispersal stages of

slightly different lengths.

• Three identical patches

Example 2: dispersal differences and coexistence

dij

Dispersal differences and coexistence

Dispersal differences and coexistence

Coexistence is possible if each species is a superior disperser over

• ne of the inter-patch

distances However, this is neither necessary nor sufficient.

Dispersal differences support coexistence that:

• Is simple and intuitive
• Can create quite complex patterns
• Does not depend on local competitive advantage
• Creates stable geographic replacement
• Driven by common factors

Williams (1991) Patterns and processes in the distribution of coral reef fishes. In:The Ecology of Fishes on Coral Reefs (Ed. P.F. Sale)

Example 3: GBR dispersal differences

Theoretical proof involves drastic simplifications:

• Simple, three-patch landscape
• Deterministic, isotropic dispersal
• No temporal variation

Interannual variation Interspecific variation

Coexistence is still possible when dispersal involves:

• Realistic patch distributions
• Multiple species
• Biophysical drivers
• Temporal stochasticity

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