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Michael Bode ARC Centre of Excellence for
Environmental Decisions, University of Melbourne [email protected]
Larval dispersal in reef fishes: biology, ecology, economics
Early research into tropical fish communities
i
Population dynamics on a single patch
Nonlinear dynamics in the absence of dispersal:
Population dynamics on a single patch
Recruitment limitation:
Doherty (1991) Ecology of Fishes on Coral Reefs
Population dynamics on multiple patches
Dispersal is essentially a linear coupling of a multidimensional nonlinear system
• Dispersal is defined by connectivity matrix C • Matrix elements are the proportion of
larvae from reef i that travel to reef j
1
23
Dispersal is essentially a linear coupling of a multidimensional nonlinear system
• Dispersal is defined by connectivity matrix C • Matrix elements are the proportion of
larvae from reef i that travel to reef j
1
23
P. maculatus. Harrison et al. (2012) Current Biology
Measuring dispersal
• Resource intensive • Invasive – individual & species level • Scale limited – (temporal and spatial)
Part 1: Modelling dispersal
Modelling dispersal
Reef fish metapopulations and larval dispersal M. K. James and others 2083
(b)
14 16 18
(d )
14 16 18
18
16
14(c)
latitude (S) of sink reef
latit
ude
(S)
of s
ourc
e re
ef 18
16
14(a)
Figure 3. Images of the seasonal connectivity matrices for (a) 1985 (b) 1989 (c) 1996 and (d ) the matrix averaged over all 20seasons. Axes are labelled in degrees of latitude. Each element aij of the matrix is the proportion of all larval production in aseason on reef i that settles on reef j. These elements are coded by colour (and size) as follows: red, greater than 0.02; blue,between 0.01 and 0.02; green, between 0.005 and 0.01; pink, less than 0.005.
ever, some limited corroboration of the model comes froma comparison with adult distribution data. Williams et al.(1986) conducted a census of fish communities on a tran-sect of the shelf in the Central Section of the Marine Park(on the southern boundary of our study region). Thoseauthors found that for 16 out of 18 species, there was aclose relationship between the distributions of recruits andadults. Recruits tended to be found only in the same cross-shelf location as adults of the same species.
We analysed cross-shelf transport patterns underassumed spawner distributions representing differentspecies. Figure 6 shows the results for our baseline para-meters. Virtual larvae originating from reefs in one of threezones defined by Williams et al. (1986) tend to be trans-ported to reefs within the same zone.
Proc. R. Soc. Lond. B (2002)
4. DISCUSSION
(a) Model predictionsWhen focusing on physical transport processes, the
model predicts that most local populations in our studyregion depend largely on externally supplied larvae. Self-recruiting larvae comprise a smaller fraction of the settlingcohort on most reefs (mean self-recruitment less than 9%of settling cohort on 80% of reefs in the area). Moreover,the model predicts that the total proportion of larvae set-tling back onto their reef of origin is lower than the totalproportion settling on other reefs. These findings contrastwith those from the modelling study of Cowen et al.(2000) of populations on more isolated oceanic reefs inthe Caribbean.
14 16 18
Sour
ce r
eef
Destination reef
Connectivity patterns
Inter-annual variation
Inter-specific variation
Part 2: Dispersal and coexistence
Coexistence needs differences
Reef fish community theory
Metacommunity simulation • Real distribution of reefs (P = 110) • Variable dispersal matrices (t = 1, …, 32 years) • Multiple species (S = 5) – Identical competitors – Identical niches – Different dispersal behaviour
Normally we would expect monodominance
(%)
• Same model • Two species, identical at a local scale • Larval dispersal stages of slightly different lengths. • Three identical patches
Dispersal differences and coexistence
Dispersal differences and coexistence
Dispersal differences and coexistence
Coexistence is possible if each
species is a superior disperser over one of
the inter-patch distances
Coexistence is possible if each species is a superior disperser over one of the
inter-patch distances
Mechanism has high predictive power for
larger simulations
Dispersal differences support coexistence that: • Is simple and intuitive • Driven by common factors • Can create quite complex patterns • Creates stable geographic replacement
Mechanisms are not locally observable.
Part 3: Economic perspectives on dispersal
Measuring dispersal on Manus Island
Plectropomus areolatus. Source: FAO
Timonai Mbunai
Pere Tawi
Locha
Bioeconomic scales on Manus
Bioeconomic scales on Manus
Community tenure areas
Spawning aggregation source areas
Management question • What is the maximum annual equilibrium
harvest rate from each spawning aggregation? • How do dispersal externalities affect the
harvesting decision?
Harvested population model
Plectropomus areolatus. Source: FAO
Harvested population model
Harvested population model
Simulation model Population estimates
Independent communities • Each community chooses: – a harvest rate on each of their
aggregations, – that maximises total equilibrium harvest. – given that other communities act rationally.
Harvests under different coalitions
• Communities are highly heterogeneous • Describe coalition structures using
partitions e.g., C0 = {{1} {2} {3} {4} {5}} C1 = {{1} {2},{3} {4,5}} C2 = {{1,2,3} {4,5}} CG = {1,2,3,4,5}
– 52 unique coalition structures
Harvest coalition size • Non-cooperative groups remove 12-25% / FSA /
yr • Cooperative harvests remove 10-17% • Grand coalition improve overall catch (by 15%)
and equilibrium population levels (by 70%)
Harvest coalition size • The current scale of management on Manus
could lead to undesirable outcomes. • A grand coalition would result in an increase in
catches in every community, for much lower effort
Grand coalition stability Group 2 leaves
coalition
Grand coalition stability • The grand coalition surplus is insufficient for
a set of side-payments to yield rational cooperation.
Smaller coalitions • The coalition between Locha and Pere is the only
Nash equilibrium (internal & external stability). • Almost all the resultant benefits are captured by
the adjacent communities: Tawi and Mbunai
Timonai Mbunai
Pere Tawi
Locha
Economic impacts of larval dispersal
• The scale of larval dispersal creates interconnections between communities
• The dissonant scales causes problems. – Too much dispersal to ignore each other – Too much dispersal to want to cooperate – Not enough dispersal to provide necessary
surplus
Collaborators • Maurice James • Paul Armsworth • Glenn Almany • Lance Bode • Rick Hamilton • Luciano Mason • Geoff Jones • David Williamson