Transcript Berkley_02_20_2008

Coexistence with Stochastic
Dispersal in a Nearshore
Multi-Species Fishery
Heather Berkley & Satoshi Mitarai
Competitive Exclusion Principle
• Two species with similar ecological traits
competing for a limited resource cannot coexist
– one will drive the other to extinction. (VolterraGause)
• This does not occur often in nature
• Several different theories explain why
coexistence occurs
– Niche differentiation
– Intermediate disturbance
– Storage effect
• We will focus on temporal & spatial variability in
settlement & recruitment
Simple Two Species Example
• Consider two similar species A & B
– Species A has a slightly better ability to utilize resources
– Recruits compete for limited resources at settlement sites
– Spawning timings are separated by weeks
• Compare cases with i) smooth dispersal
kernel & ii) packet model for connectivity
– Smooth dispersal kernel: spawning timing does not
matter
– Packet model: species A & B “catch” different eddies &
can settle at different sites
Diffusion Case
IC’s: A = 100, B = 100
On their own, both
species can persist
If they are put
together, species B
becomes extinct,
species A thrives
Note: this is what
eddy-diffusion
model predicts
Time (years)
Packet Model
N larval packets
• Larval settlement as arrival of
N packets
 L  T 
N    
 l  t 
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L = domain size
l = eddy size (50 km)
T = Spawning time
t = eddy turnover rate (14 d)
eddy size (l)
Packet model case
IC’s: A = 100, B = 100
• Completely
different
spawning timing
leads to
coexistence
Generations
Time-space variations
Species B
Generations
Generations
Species A
Alongshore Location (km)
Alongshore Location (km)
Coexistence with Species A more abundant
at most (but not all) locations
Spawning Window Overlap
• Specify how many days of overlap
between spawning times for both species
• Makes some packets perfectly correlated
for both species and others independent
Packets will have same
settlement locations
Species A Spawning Window
Species B Spawning Window
TIME
Connectivity
• ~half of packets perfectly correlated
Species A
Species B
Parameters
• Tsp (spawning time) = 30 days for both
– Vary amount of overlap
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Fecundity of Sp.A = 0.5
Fecundity of Sp.B = 0.45
Adult Mortality = 0.09
Run time = 500 yrs;
Patch size = 5 km;
Domain size = 500 km;
Larvae on larvae DD (total # of both sp)
Averaged over 10 simulations
0 days of overlap
Species A
Species B
10 days of overlap
Species A
Species B
20 days of overlap
Species A
Species B
25 days of overlap
Species A
Species B
30 days of overlap
Species A
Species B
Correlation between Connectivity
Matrices for Sp A & B
Mean Correlation Coefficient
Correlation between Connectivity
Matrices for Sp A & B
# of Independent Packets
Spawning Window Overlap
• SpA has its entire spawning window the
same as SpB
• Only Sp B has independent packets
Vary this amount of time
Species A Spawning Window
Species B Spawning Window
TIME
Tsp = 30 days
Species A
Tsp = 30 days
Species B
Tsp = 30 days
Species A
Tsp = 36 days
Species B
Tsp = 30 days
Species A
Tsp = 42 days
Species B
Tsp = 30 days
Species A
Tsp = 48 days
Species B
Tsp = 30 days
Species A
Tsp = 54 days
Species B
Tsp = 30 days
Species A
Tsp = 60 days
Species B
Tsp = 30 days
Species A
Tsp = 66 days
Species B
Tsp = 30 days
Species A
Tsp = 72 days
Species B
Tsp = 30 days
Species A
Tsp = 78 days
Species B
Correlation between Connectivity
Matrices for Sp A & B
Correlation between Connectivity
Matrices for Sp A & B
Spatial Patterns of Adults
• Look at spatial covariance in Adult
densities for SpA and SpB
• Are these spatial patterns Adult densities
strengthening coexistence?
Mean Cov(A,B) through time
Overlap (days)
Species A
Species B
Next Steps
• Compare packet model results with
particle tracking simulations
– Graphs of Correlation vs. Days of overlap in
Tsp for 2 scenarios presented
• Shorten lifespan to see how much is due
to the temporal vs spatial storage effect or
buffering