coexistence with stochastic dispersal in a nearshore multi-species fishery heather berkley &...
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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. (Volterra-Gause)
• 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
If they are put together, species B becomes extinct,species A thrives
Note: this is what eddy-diffusion model predicts
On their own, both species can persist
Time (years)
IC’s: A = 100, B = 100
Packet Model
• Larval settlement as arrival of N packets
• L = domain size• l = eddy size (50 km)• T = Spawning time• t = eddy turnover rate (14 d)
⎟⎠
⎞⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛=t
T
l
LN
eddy size (l)
N larval packets
Packet model case
IC’s: A = 100, B = 100
Generations
• Completely different spawning timing leads to coexistence
Time-space variationsSpecies A Species B
Coexistence with Species A more abundant at most (but not all) locations
Generations
Generations
Alongshore Location (km)
Alongshore Location (km)
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
• 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
Species A Species B
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
Correlation between Connectivity Matrices for Sp A & B
Correlation between Connectivity Matrices for Sp A & B
Mea
n C
orre
latio
n C
oeff
icie
nt
# 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 timeSpecies A Spawning Window
Species B Spawning Window
TIME
Species A Species B
Tsp = 30 days Tsp = 30 days
Species A Species B
Tsp = 30 days Tsp = 36 days
Species A Species B
Tsp = 30 days Tsp = 42 days
Species A Species B
Tsp = 30 days Tsp = 48 days
Species A Species B
Tsp = 30 days Tsp = 54 days
Species A Species B
Tsp = 30 days Tsp = 60 days
Species A Species B
Tsp = 30 days Tsp = 66 days
Species A Species B
Tsp = 30 days Tsp = 72 days
Tsp = 30 days Tsp = 78 days
Species A 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