Asymmetric migration decreases stability but increases resilience in a heterogeneous metapopulation

Many natural populations are spatially distributed, forming a network of subpopulations linked by migration. Migration patterns are often asymmetric and heterogeneous, with important consequences on the ecology and evolution of the species. Here we investigate experimentally how asymmetric migration and heterogeneous structure affect a simple metapopulation of budding yeast, formed by one strain that produces a public good and a non-producer strain that benefits from it. We study metapopulations with star topology and asymmetric migration, finding that all their subpopulations have a higher fraction of producers than isolated populations. Furthermore, the metapopulations have lower tolerance to challenging environments but higher resilience to transient perturbations. This apparent paradox occurs because tolerance to a constant challenge depends on the weakest subpopulations of the network, while resilience to a transient perturbation depends on the strongest ones.

Shock corresponds to one cycle with increased dilution factor, D'=750*D. Second row: Shock corresponds to one cycle with reduced growth r'=0.5-r. The increase in resilience is stronger in scale-free networks than in small-world ones. This difference may be due to scale-free networks being more heterogeneous than small-world ones (variance in degree of nodes is 8.9 and 0.84, respectively). Figure 9. Scale-free networks are more resilient to perturbations than isolated populations. Model prediction for survival of a 40-node (A, B) and 60-node (C, D) scalefree networks with daily dilution factor D=750 after a perturbation, as a function of perturbation strength and migration rate. Rest of parameters are as those in Fig. S4. First row: Shock corresponds to one cycle with increased dilution factor, D'=750*D. Second row: Shock corresponds to one cycle with reduced growth r'=0.5-r.

Rationale for the protocol:
In all the experiments in the paper we implement the migration step in parallel with the daily-dilution into fresh media. The protocol can be split into two parts: The dilution factors at each step are chosen such that after taking into account the daily dilution factor, 40% of the cells stay in place. (See next section for calculating dilution factors)

PART 2:
Here we deal with the central and side nodes of star network separately: Central nodes: 1. Here, m=0.6 fraction of cells from the center are split equally between all the 9 neighboring side nodes. To do so, small volume of cells in the central node (from PBS1) is diluted into a reservoir containing fresh media. (We used either 10 ml or 25 ml Integra multichannel reservoirs in all experiments, depending on the volume of fresh media) 2. This reservoir (called CEN) is put on a shaker for at least 30 seconds to ensure that the cells are well-mixed. 3. Then using a multichannel pipette, 100 ul is transferred to the 9 side nodes in the EXP plate.
1. In part 1, we only accounted for 40% of the cells staying in place. For isolated nodes, all the cells must stay in place, so this step takes care of the other 60% cells. 2. Each row (or column) of isolated nodes is diluted twice in rows (or columns) of a 96-well plate containing fresh media (called the NOTCONN) plate using a multichannel pipette. 3. Using a multichannel pipette, 100 ul is transferred from the second dilution in the NOTCONN plate and transferred to the appropriate row (or column) of the EXP Plate

Calculating the dilution factors and volumes: an example
Here, daily dilution factor is D=650, and m=0.6, and N = 10 nodes (i.e. there are 9 side nodes). Say, we perform a 10 fold dilution into PBS. We add 20 ul of the START Plate to 180 ul of PBS in the PBS1 plate. Similarly, we transfer 20 ul from PBS1 to 180 ul of PBS in the PBS2 plate PART 1: • The overall dilution factor in this step is 20(1− ) = 81.25. (The factor of 2 is there because only half of the final volume comes from this part). • The dilution factor for RES1 and RES2 can be sqrt(81.25), which is ~9. If we transfer 20 ul from each plate to the next, then the volume of media in RES1 and RES2 is 160 ul.

PART 2: Isolated nodes
• The overall dilution factor in this step is 20 = 54.17 • The dilution factor (for each step) for NOTCONN can be sqrt(54.17), which is 7.35. If we transfer 30 ul during each dilution, then the volume of media in NOTCONN is 191 ul

Central nodes
• The cells are split between 9 side nodes, so the dilution factor is ( −1) 20 = 487.5.
• If we add 10 ul from the central node of PBS1, then the reservoir should have 4875 ul in the reservoir (round off to 4.9 ml)

Side nodes
• Here, we take cells from every side node and pool into a reservoir.
• The dilution factor in this step is 20 = 54.17 • Say we transfer 50 ul from each side node in PBS1 to the reservoir, using a multichannel. For overall dilution factor to be 54.17 the final volume should be ~2.7 ml. • However, this includes the 50 ul added to the reservoir. For 9 side nodes, we add 450 ul to the reservoir. So the actual volume of fresh media in reservoir is 2.25 mL (round off to 2.3 ml)

Fully connected network
• Here, we take cells from every node in the network and pool into a reservoir.
• If we add 10 ul from each node of the network from PBS1 using a multichannel, then the reservoir should have 4775 ul of fresh media in the reservoir (round off to 4.8 ml) to get a final volume of ~4.9ml.

Experiment 1: Increase in cooperator fraction (for daily dilution factor of 650).
Corresponding to Figures 1 and 2

STEPS:
1. Streak the producer (JG300B) and non-producer (JG210C) strains onto YPD Agar plates 2. Pick four colonies of the producer and non-producer each.
3. Grow them overnight in liquid YNB+ Nitrogen, CSM-his, 2% glucose, and 8 g/mL histidine in a 50-mL Falcon tube at 30C and 50% humidity with shaking at 250 rpm for 24 hours. 4. Mix the two strains at different fractions and dilute them x100 in YNB+Nitrogen + CSM-his supplemented with 2% sucrose, 0.001% glucose and 8 g/mL histidine. 5. Incubate them for 24 hours at 30C and 50% humidity with shaking at 250 rpm (5 mL of culture in 50 mL Falcon tubes). On the first day of the experiment, determine the fraction of each strain in each co-culture with flow cytometry, and mix different co-cultures in order to achieve the desired starting fraction of producers (fp) for the experiment. Desired starting fractions: 0.1, 0.2, 0.3, 0.4 6. Dilute the co-cultures with the appropriate producer fraction 100 times in YNB+Nitrogen + CSMhis supplemented with 2% sucrose, 0.001% glucose and 8 g/mL histidine and add to two 96well plates (one for isolated nodes, another for star and complete networks) 7. Measure OD at 600 nm and incubate for 23 hours at 30C and 50% humidity with 800 rpm shaking. 8. Measure OD the next day at 600 nm. 9. Carry out the transfer protocol as outlined below. 10. Cover the plate with parafilm to limit evaporation. 11. Determine the fraction of producers using flow cytometry after a 100 fold dilution in PBS (make measurements of the PBS2 plate) 12. Measure OD of EXP plate at 600 nm, and incubate the EXP plate at 30C and 50% humidity with 800 rpm shaking. 13. Go to step 8 and repeat till the fraction of producers reaches an equilibrium (should take ~10 days).

NOTE:
While doing the transfers from reservoirs or 96 well plates, they are always kept on a shaker, to ensure that we are sampling from a well mixed solution and transfer the correct number of cells.    3. Grow them overnight in liquid YNB+ Nitrogen, CSM-his, 2% glucose, and 8 g/mL histidine in a 50-mL Falcon tube at 30C and 50% humidity with shaking at 250 rpm for 24 hours. 4. Mix the two strains at different fractions and dilute them x100 in YNB+Nitrogen + CSM-his supplemented with 2% sucrose, 0.001% glucose and 8 g/mL histidine. 5. Incubate them for 24 hours at 30C and 50% humidity with shaking at 250 rpm (5 mL of culture in 50 mL Falcon tubes). On the first day of the experiment, determine the fraction of each strain in each co-culture with flow cytometry, and mix different co-cultures in order to achieve an approximate starting fraction of fp = 0.4. 6. Dilute the co-cultures with the appropriate producer fraction 100 times in YNB+Nitrogen + CSMhis supplemented with 2% sucrose, 0.001% glucose and 8 g/mL histidine and add to three 96well plates (each 96 well plate corresponding to one set of producer and non-producer colony) 7. Measure OD at 600 nm and incubate for 23 hours at 30C and 50% humidity with 800 rpm shaking. 8. Measure OD the next day at 600 nm. 9. Carry out the transfer protocol as outlined below. 10. Cover the plate with parafilm to limit evaporation. 11. Determine the fraction of producers using flow cytometry after a 100 fold dilution in PBS (make measurements of the PBS2 plate) if possible. Measure at the start and end of the experiment at least. 12. Measure OD of EXP plate at 600 nm, and incubate the EXP plate at 30C and 50% humidity with 800 rpm shaking. 13. Go to step 8 and repeat till the fraction of producers reaches an equilibrium (~12-14 days in this experiment).

SIDE reservoirs
• To reservoir SIDE-A, add 1100.0 ul of medium.
• To reservoir SIDE-B, add 1600.0 ul of medium.
• To reservoir SIDE-C, add 2200.0 ul of medium.
• To reservoir SIDE-D, add 2700.0 ul of medium.
• To reservoir SIDE-E, add 3200.0 ul of medium.
• To reservoir SIDE-F, add 3700.0 ul of medium.
• To reservoir SIDE-G, add 4200.0 ul of medium.
• To reservoir SIDE-H, add 4800.0 ul of medium.

RESIDENT DILUTIONS
• Transfer 10 ul from START plate to PBS1 plate.
• Transfer 100 ul from RES2 plate to EXP plate.