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