Can Packet Larval TransportCreate Favorable Conditions for

the Storage Effect?Heather & Satoshi

“Flow, Fish & Fishing,” UCSB Group MeetingFeb. 21, 2007

Idea

• Can packet model transport amplify the storage effect with small differences in life history between species?

• Different spawning timing?

• Different vertically migrating behavior?

• Different PLD?

• In this talk, we test the role of different spawning timing using the packet model

• Eddy-diffusion model (or dispersal kernel) does not distinguish spawning timing difference; physical connectivity is identical between species A & B

Background

•Storage effect: mechanism that promotes persistence and coexistence between competing species• Buffer against uncertainty in recruitment

• Rapid growth when populations are small

• Slow growth when populations are large

Storage Effect Coexistence Mechanism- Temporal Variability (Chesson papers)

• Buffered population growth • Long-lived adults buffer population against negative impact of variable environment

• Skews variable population growth rates positively because the “bad years” have less of a negative impact

• Allows populations at low density to recover faster

• Species-specific responses to the environment • Each species can respond differently to physical environmental conditions

• Each species can have different biological parameters: Mortality, Fecundity

• Covariance between environment and competition • Favorable conditions for species A

• Larger population A

• Increased intra-specific competition for A

• Species B is less abundant due in these same conditions

• Small population B

• Less impacted by intra-specific competition

Storage Effect Coexistence Mechanism

- Temporal Variability

• Early papers on storage effect showed that as long as recruitment fluctuations were independent between the two species, coexistence occurred (Warner & Chesson ?)

• High variance in recruitment strengthens this result

• F3 Packet model can be used to explore these stochastic dispersal events

Problem setup

• 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

Base case (diffusion case)

• 1-D coast, 256 km, 64 sites, periodic BC’s

Dispersal kernel

On their own, both species can persist

A = 100 B = 97.5

IC’s: A = 100, B = 0 IC’s: A = 0, B = 100

A = 0B = 0

Each species is individually sustained without the other

Carrying capacity is lower due to lower

ability to use resources

Generations Generations

But, they cannot coexistIC’s: A = 100, B = 100

A = 100

B = 0

If they are put together, species B becomes extinct,

species A thrives

Note: this is what eddy-diffusion model predicts

Generations

Packet model case

• A & B catch different eddies, assuming that their spawning periods are a few weeks apart

Given independently by packet model

A & B catch different eddies due to different spawning timing

• Describes larval settlement as arrival of N “larval packets”

Packet ModelPacket Model

L: Domain size

l: Eddy size (~ 50 km)

T: Larval release duration

t: Eddy turn-over time (~ 14 d)

eddy size (l)

N larval packets

•Connectivity is given by determining source & destination statistically in eddy-diffusion range

t

T

l

LN

SIMULATIONS VS. PACKET MODELSIMULATIONS VS. PACKET MODEL

(L = 256 km, l = 50 km, T = 90*n d, t = 14 d)

Circulation simulations Packet model

Destination location (km) Destination location (km)

Sou

rce

loca

tion

(km

)

Sou

rce

loca

tion

(km

)

•Packet model represents heterogeneity & stochasticity without expensive simulations

Packet model case

A = 60

B = 40

IC’s: A = 100, B = 100

Different spawning timing leads to coexistence

Generations

Time-space variationsSpecies A Species B

Coexistence with Species A more abundant at most (but not all) locations

Alongshore Location (km)

Alongshore Location (km)

Gen

era

tion

s

Gen

era

tions

Blue/Red state map

Fraction of species B in a local population =

In general, distribution is purple-ish (co-exist)

Alongshore Location (km)

All Species B

All Species A

# of Species B

# of Species A + # of Species B

Gen

era

tion

s

Parameter study: production ratio

IC’s: A = 100, B = 100

Certain level of productivity ratio (> 0.7 for this case) is

required to achieve coexistence

Generations

Pb/Pa = 0.9, 0.8, 0.7, 0.6, 0.5

Pb/Pa = 0.9, 0.8, 0.7, 0.6, 0.5

Parameter study: # of packets

• Storage effect is more apparent when larval release duration is shorter (i.e. fewer packets are observed)

•More packets:

• Greater packet overlap between species

• Weakens the stabilizing effect of independent recruitment events

IC’s: A = 100, B = 100

Generations

T = 14, 30, 60, 90 days

T = 14, 30, 60, 90 days

Parameter study: IC’s

A = 60

B = 40

IC’s: A = 100, B = 100 IC’s: A = 1, B = 100

A = 60

B = 40

IC’s do not matter

Generations Generations

In parameter space

Coexistence index

Productivity ratio

0

Example 1

1

1

Stochasticity in settlement

0 Example 2

Uncorrelated(few packets)

Correlated(many packets)

Summary

• Turbulent processes can amplify the effect that differences in the timing of spawning can have on species coexistence (through the storage effect)

• Other life history factors (e.g., PLD, behavior) will matter too

• But, less drastic since there are overlaps in eddies for these cases

• Does the scenario shown here fall into the storage effect category suggested by Chesson? (maybe not)

• http://eebweb.arizona.edu/Faculty/chesson/storage_effect.htm

Next Steps?

• Ordering of Recruit arrival. How will this change the competitive relationships?

• More complex competition relationships

• Fishing Mortality

• Fishing only one vs. both species

• Same vs. different magnitude for each species

• Same vs. different methods/patterns of extraction

Comments (Steve)• The role of recruitment variation in coexistence by this mechanism has been explored looking at temporal variation among

species at single spot with an open population model, but I'm not aware of this whole life cycle approach that includes both spatial and temporal variation through the stochastic kernal. Very intriguing.

• Setting a lower carrying capacity for one species versus another would not be an issue of lower productivity, rather it would be lower efficiency at utilizing the shared resources. A: We will vary the the coefficient alpha of the Beverton-Holt equation instead of the fecundity. (Computationally, they are the same thing, but ecologically different.) I believe that, in this way, we are accounting for the difference in ability to utilize the shared resources.

• How are you doing the ordering of broadcasting? Is one species always after the other? (if so, what is the order?) or is spawning random between the two? This may play a role in coexistence if the poorer competitor spawns first and can preempt space. A: We do not specify the order. “First-come, first served” effect is not included. Their competition starts after all settlers show up at a site when they recruit to adults. If species B spawn earlier, then they may be able to increase the chance to get more resources (the coefficient alpha of the B-H equation). What we are saying here is (I guess) that even without this effect, if they use different spawning timing than species A, they can coexist with species A.

• The last thing is that it would be very helpful in interpreting why this pattern of settlement promotes coexistence to look at the dynamics of the two species in different patches. Is the relative constancy across the whole domain masking smaller scale patch dynamics? presumably the likelihood of a packet of recruits from the best competitor landing at a particular site is small enough that significant declines from mortality occur between recruit pulses. A: done.

Comments (Bruce)• You have demonstrated is that differential dispersal timing in a stochastic ocean provides a coexistence mechanism. It is not

necessarily a mechanism that acts according to a "storage effect." I don't remember all the details of what constitutes the storage effect - in your talk you should review these and discuss the extent to which the current mechanism fits into the storage effect framework. A: I need your help on this (for my job interview too). I have been reading Bob and Chesson’s papers, though.

• In the diffusion case, are there any initial conditions for which species B wins? A likely candidate would be lots of B and only a little bit of A. A: done

• Again in the diffusion model, there may be potential for spatial coexistence if the IC is not spatially uniform. This is certainly true if the species are identical, I'm not sure about the case you present. A: done. not shown in the talk, but it did not matter.

• In all the graphs, "generations" is mis-spelled. A: not fixed yet, but when I regenerate the figures.

• Show some more details of the results behind slide 8. What do individual time series look like (I am assuming, because of the error bars, that you are showing means of multiple replicate simulations)? What sort of spatial patterning is there? In what fraction of the replicates do one of the species go extinct? Etc. A: space-time variations are not included in the talk.

• Define the terms in your "coexistence index" on slide 9. A: I did. Not computed yet, though.

Comments (Bruce)• You are assuming that the eddies experienced by the two species are completely independent. (a) Is this consistent with the

flow model (i.e. are connectance patterns a few weeks apart completely independent from one another)? A: I have not checked it yet. But, since the eddy turn-over time scale is about two weeks, if the spawning timing is separated longer than two, three weeks, maybe larvae catch different eddies, hopefully. I will do this experiment. (b) This puts a limit on the total number of species that could be maintained by this mechanism. What happens if there is partial (but incomplete) correlation between the connectance matrices (i.e. the spawning periods partially overlap)? A: The coexistence mechanism will become weaker as the overlaps increase. The difference in PLD or behavior will certainly have overlaps in connectivity. I need to quantify the overlap using the simulations and take it into account in the packet model.

• Another class of coexistence mechanisms is a "competition-dispersal tradeoff" - see Tilman's models of plants, for example. What would happen if species B had a longer PLD (and hence longer mean dispersal distance)? A: see above

• An important parameter in competition models is the ratio of the strength of intra-specific competition to the strength of inter-specific competition, as well as the degree of symmetry in the competition. You have set up all the competitive interactions (inter and intra, for both species) to be equal, which is a very special case. Even within the realm of competition for settling sites, there may be priority effects (the species that spawns first is less affected by interspecific density than is the species the spawns second), only partial overlap in desired substrate (in which case intraspecific density dependence would be stronger than interspecific), or biological differences that create inherent asymmetries in competitive ability. How do you think this (as well as competition in other places in the life cycle) would impact your results? A: something like this? I have no idea how this changes the outcome.... Are there any suggestion for Caa, Cab, Cbb?