Michael Cusack, Teale Fristoe, Cody Kennedy, Louis Bianchi. Co-Evolution in a Flower/Pollinator System
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1 Michael Cusack, Teale Fristoe, Cody Kennedy, Louis Bianchi Co-Evolution in a Flower/Pollinator System
2 Background The co-evolution between flowers and their pollinators is a game which has been played for at least 100 million years. The dynamics of this interaction have generated much of the diversity in the flower/pollinator populations that we see today. In our simplified game we will try to explore this co-evolutionary cycle and examine the forces at work that drive the specialization that we observe in nature.
3 The Goal of the Game is Sex and Food Flowers need bees to spread their pollen to other compatible flowers. Bees want the nectar/pollen reward that flowers offer. As a result bees and flowers have come up with different strategies to reach their goals.
4 Three different bee strategies: -Honesty These bees will prefer one flower and try to go to that same flower type consistently. -Promiscuous The promiscuous bees will go to any flower type that is available. -Cheat This bee type will tear an opening at the rear of the flower in order to access its nectar.
5 Three different flower strategies: -Open A typical flower, its pollen and nectar is left exposed for anything to come in and get it. -Closed This flower has a certain morphology that only allows for one bee type (Honest in this case) to enter. -Protective These flowers have a protective shell that prevents the burrowing caused by cheater bees.
6 The basic interaction: Open flowers lack that specificty needed to assure that their pollen gets to its intended destination. As a result closed flowers can emerge. Closed flowers exclude promiscuous bees from entering but are decimated by an invasion of cheater bees. Protective flowers can defend against cheater bees but cannot compete as well against closed flowers when there are no cheater bees present. This might lead to an RPS like dynamic...
7 Closed Flower VS Cheater Bee Tries to enter... Plan B... Bee: 1 Flower: -1
8 References Darwin, C., The effects of cross and self fertilisation in the vegetable kingdom. Murray, London. Inouye, D., The terminology of floral larceny. Ecology. 61, Irwin, R., Brody, A., Waser, N., The impact of floral larceny on individuals, populations, and communities. Oecologia. 129, Vega-Redondo, F., Pollination and reward: a game theoretic approach. Games and Economic Behavior. 12, Warren, J., Diaz, A, A two-pollinator model for the evolution of floral complexity. Evolutionary Ecology. 15,
9 Simulation - Run a series of steps on a cellular automaton - Each step, do the following for every flower and every bee: Flowers: - Spawn if capable - Age and die - Create nectar Bees: - Spawn if possible - Age and die - Decide what to do - Either: - Move - Visit flower
10 Parameters Simulation driven by several parameters: (red indicates varied, black indicates fixed for our experiment) - Payoff Matrices - Determine payoffs when bees visit flowers - Maximum Populations - Starting Populations - Life Spans - Determine how many steps flowers and bees live - Spawn requirements - Determine how much payoff is required to spawn - Movement Penalty - Perceived cost of moving instead of landing for bees - Flower Refresh Rate - How quickly flowers refresh nectar after being visited
11 Parameterized Payoffs Bee payoff: Open (Y) Honest [bb - bh (P) Promiscu[bB (R) Cheating[bB Specialized, bb + bbs,, bb + bbb Flower payoff: Honest Promiscuous (W) Open [fb, fb (B) Speciali[fB - fcs + fbs, fb - fcs (D) Protecti[fB - fcd, fb - fcd Parameters: bb = Bee Benefit of Pollinated bbs = Bee Bonus for Specialization bbb = Bee Bonus for Burrowing bh = Bee Honesty Factor bcp = Bee Cost of Visiting a Protective Flower fb fcb fcd fcs fbs Protective, bb - bh - bcp ], bb - bcp ], ] Cheating,,, -fcb -fcd ] ] ] = Flower Benefit of Being Visited = Flower Cost of Being Burrowed = Flower Cost of Being Defensive = Flower Cost of Being Specialized = Flower Bonus for Specializing
12 Permutations Population maximums: flowers and 1000 bees flowers and 1000 bees flowers and 2000 bees Cost for bees visiting protective flowers: - No cost - Small cost Bonus for honest bees visiting specialized flowers: - No bonus - Small bonus
13 Understanding the Simulation Bees: - Honest (Yellow) - Promiscuous (Pink) - Cheater (Red) Flowers: - Open (White) - Closed (Cyan) - Protective (Blue) Open Space (Green) nothing
14 Run simulations
15 Results: Baseline. No specialization bonus, protective cost, 1000:3000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.65, 0.00, 1.65, Protecti 0.40] 0.60] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
16
17 Results: Baseline. No specialization bonus, protective cost, 1000:2000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.65, 0.00, 1.65, Protecti 0.40] 0.60] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
18
19 Results: Baseline. No specialization bonus, protective cost, 2000:2000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.65, 0.00, 1.65, Protecti 0.40] 0.60] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
20
21 Results: Specialization bonus, protective cost, 1000:3000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.75, 0.00, 1.65, Protecti 0.40] 0.60] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
22
23 Results: Specialization bonus, protective cost, 1000:2000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.75, 0.00, 1.65, Protecti 0.40] 0.60] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
24
25 Results: Specialization bonus, protective cost, 2000:2000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.75, 0.00, 1.65, Protecti 0.40] 0.60] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
26
27 Results: No specialization bonus, no protective cost, 1000:3000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.65, 0.00, 1.65, Protecti 0.45] 0.65] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
28
29 Results: No specialization bonus, no protective cost, 1000:2000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.65, 0.00, 1.65, Protecti 0.45] 0.65] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
30
31 Results: No specialization bonus, no protective cost, 2000:2000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.65, 0.00, 1.65, Protecti 0.45] 0.65] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
32
33 Results: Specialization bonus, no protective cost, 1000:3000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.75, 0.00, 1.65, Protecti 0.45] 0.65] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
34
35 Results: Specialization bonus, no protective cost, 1000:2000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.75, 0.00, 1.65, Protecti 0.45] 0.65] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
36
37 Results: Specialization bonus, no protective cost, 2000:2000 Area Graph Payoff matrix Bee Payoffs: Open (Y) Honest [0.45, (P) Promiscu[0.65, (R) Cheating[0.65, Speciali 0.75, 0.00, 1.65, Protecti 0.45] 0.65] Flower Payoffs: Honest (W) Open [0.60, (B) Speciali[2.50, (D) Protecti[0.55, Promiscu 0.60, 0.50, 0.55, Cheating -1 Analytics Triangle Graphs
38
39 Future work Improvements for simulation: - More realistic genetics: - Sexual reproduction - Diploid genetics - More genes - Especially preferences - More realistic flower spawing: - Simulate bees carrying pollen - Model bee ignorance: - Bees can't see nectar - Perhaps add learning
40 Conclusion We were able to create a simulation that allows us to explore conditions in which speciation could develop. In the simulations we ran, Specialization Bonus, Protective Penalty, and 1000:2000 population caps proved to offer the best situation for fluctuations and therefore speciation.
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