1. Mutualistic Interactions and Symbiotic Relationships Mutualism (obligate and facultative) Termite endosymbionts Commensalisms (Cattle Egrets) Examples: Bullhorn Acacia ant colonies (Beltian bodies) Caterpillars “ sing ” to ants (protection) Ants tend aphids for their honeydew, termites cultivate fungi Bacteria and fungi in roots provide nutrients (carbon reward) Bioluminescence (bacteria) Endozoic algae (Hydra), bleaching of coral reefs (coelenterates) Nudibranch sea slugs: Nematocysts, “ kidnapped ” chloroplasts Endosymbiosis (Lynn Margulis) mitochondria & chloroplasts Birds on water buffalo backs, picking crocodile teeth Figs and fig wasps (pollinate, lay eggs, larvae develop)

2. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages

3. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages bees —> clover

4. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages bees —> clover

5. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages bees —> clover

6. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages mice —o bees —> clover

7. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages cats —o mice —o bees —> clover

8. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages cats —o mice —o bees —> clover —> beef

9. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages cats —o mice —o bees —> clover —> beef —> sailors

10. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages cats —o mice —o bees —> clover —> beef —> sailors —> Britain ’ s naval prowess

11. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages spinsters —> cats —o mice —o bees —> clover —> beef —> sailors —> Britain ’ s naval prowess

12. Indirect Interactions Darwin — Lots of “ Humblebees ” around villages spinsters —> cats —o mice —o bees —> clover —> beef —> sailors —> naval prowess Path length of seven! Longer paths take longer (delay) Longer paths are also weaker, but there are more of them —————————————————>

13. Indirect Interactions Trophic “ Cascades ” Top-down, Bottom-up Minus times minus = Plus

14. Competitive Mutualism

15. Interspecific Competition leads to Niche Diversification Two types of Interspecific Competition: Exploitation competition is indirect, occurs when a resource is in short supply by resource depression Interference competition is direct and occurs via antagonistic encounters such as interspecific territoriality or production of toxins

16. Verhulst-Pearl Logistic Equation dN/dt = rN [(K – N)/K] = rN {1– (N/K)} dN/dt = rN – rN (N/K) = rN – {(rN 2 )/K} dN/dt = 0 when [(K – N)/K] = 0 [(K – N)/K] = 0 when N = K dN/dt = rN – (r/K)N 2

17. Inhibitory effect of each individual On its own population growth is 1/K Linear response to crowding No lag, instantaneous response r max and K constant, immutable

18. S - shaped sigmoidal population growth

19. Lotka-Volterra Competition Equations Competition coefficient  ij = per capita competitive effect of one individual of species j on the rate of increase of species i dN 1 /dt = r 1 N 1 ({K 1 – N 1 –  12 N 2 }/K 1 ) dN 2 /dt = r 2 N 2 ({K 2 – N 2 –  21 N 1 }/K 2 ) (K 1 – N 1 –  12 N 2 )/K 1 = 0 when N 1 = K 1 –  12 N 2 (K 2 – N 2 –  21 N 1 )/K 2 = 0 when N 2 = K 2 –  21 N 1 Vito Volterra Alfred J. Lotka

20. N 1 = K 1 –  12 N 2 if N 2 = K 1 /  12, then N 1 = 0 N 2 = K 2 –  21 N 1 if N 1 = K 2 /  21, then N 2 = 0

21. N 1 = K 1 –  12 N 2

23. Zero isocline for species 1

24. Four Possible Cases of Competition Under the Lotka–Volterra Competition Equations ______________________________________________________________________ Species 1 can contain Species 1 cannot contain Species 2 (K 2 /  21 K 1 ) ______________________________________________________________________ Species 2 can containCase 3: Either species Case 2: Species 2 Species 1 (K 1 /  12 K 2 ) always wins can contain the other; stable coexistence ______________________________________________________________________ Alfred J. Lotka Vito Volterra

26. Saddle Point Point Attractor

27. Lotka-Volterra Competition Equations for n species (i = 1, n): dN i /dt = r i N i ({K i – N i –  ij N j }/K i ) N i * = K i –  ij N j where the summation is over j from 1 to n, excluding i Diffuse Competition Robert H. MacArthur

28. Alpha matrix of competition coefficients  11  12  13...  1n  21  22  23...  2n  31  32  33...  3n.......  n1  n2  n3...  nn Elements on the diagonal  ii equal 1.

29. More realistic, curvilinear isoclines

30. Competitive Exclusion in two species of Paramecium Georgi F. Gause

31. Coexistence of two species of Paramecium Georgi F. Gause

32. Coexistence of two species of Paramecium Georgi F. Gause Two equations, two unknowns

33. Mutualism Equations (pp. 234-235, Chapter 11) dN 1 /dt = r 1 N 1 ({X 1 – N 1 +  12 N 2 }/X 1 ) dN 2 /dt = r 2 N 2 ({X 2 – N 2 +  21 N 1 }/X 2 ) (X 1 – N 1 +  12 N 2 )/X 1 = 0 when N 1 = X 1 +  12 N 2 (X 2 – N 2 +  21 N 1 )/X 2 = 0 when N 2 = X 2 +  21 N 1 If X 1 and X 2 are positive and  12 and  21 are chosen so that isoclines cross, a stable joint equilibrium exists. Intraspecific self damping must be stronger than interspecific positive mutualistic effects.

36. Outcome of Competition Between Two Species of Flour Beetles ____________________________________________________________________ Relative Temp. Humidity Single Species (°C) (%) Climate Numbers Mixed Species (% wins) confusum castaneum ____________________________________________________________________ 34 70 Hot-Moistconfusum = castaneum 0 100 34 30 Hot-Dryconfusum > castaneum 90 10 29 70 Warm-Moistconfusum castaneum 87 13 24 70 Cold-Moistconfusum castaneum 100 0 ________________________________________________________

38. Evidence of Competition in Nature often circumstantial 1. Resource partitioning among closely-related sympatric congeneric species (food, place, and time niches) Complementarity of niche dimensions 2. Character displacement 3. Incomplete biotas: niche shifts 4. Taxonomic composition of communities

39. Exploitation vs. interference competition Lotka-Volterra Competition equations Assumptions: linear response to crowding both within and between species, no lag in response to change in density, r, K,  constant Competition coefficients  ij, i is species affected and j is the species having the effect Solving for zero isoclines, resultant vector analyses Point attractors, saddle points, stable and unstable equilibria Four cases, depending on K/  ’ s compared to K ’ s Sp. 1 wins, sp. 2 wins, either/or, or coexistence Gause ’ s and Park ’ s competition experiments Mutualism equations, conditions for stability: Intraspecific self damping must be stronger than interspecific positive mutualistic effects.

40. Alpha matrix of competition coefficients N, K Vectors  11  12  13...  1n N 1 K 1  21  22  23...  2n N 2 K 2  31  32  33...  3n N 3 K 3.........  n1  n2  n3...  nn N n K n Elements on the diagonal  ii equal 1. N i * = K i –  ij N j Matrix Algebra Notation: N = K – AN

41. Lotka-Volterra Competition Equations for n species dN i /dt = r i N i ({K i – N i –  ij N j }/K i ) N i * = K i –  ij N j at equilibrium Alpha matrix, vectors of N ’ s and K ’ s Diffuse competition –   ij N j summed over all j = 1, n (but not i) N 1 * = K 1 –  12 N 2 –  13 N 3 –  14 N 4 N 2 * = K 2 –  21 N 1 –  23 N 3 –  24 N 4 N 3 * = K 3 –  31 N 1 –  32 N 2 –  34 N 4 N 4 * = K 4 –  41 N 1 –  42 N 2 –  43 N 3 Vector Notation: N = K – AN where A is the alpha matrix Partial derivatives ∂N i / ∂N j sensitivity of species i to changes in j Jacobian Matrix of partial derivatives (Lyapunov stability)

42. Evidence of Competition in Nature often circumstantial 1. Resource partitioning among closely-related sympatric congeneric species (food, place, and time niches) Complementarity of niche dimensions 2. Character displacement 3. Incomplete biotas: niche shifts 4. Taxonomic composition of communities

43. Major Foods (Percentages) of Eight Species of Cone Shells, Conus, on Subtidal Reefs in Hawaii _____________________________________________________________ Gastro- Entero-Tere- Other Species pods pneusts Nereids Eunicea belids Polychaetes ______________________________________________________________ flavidus 4 64 32 lividus 61 12 14 13 pennaceus 100 abbreviatus 100 ebraeus 15 82 3 sponsalis 46 50 4 rattus 23 77 imperialis 27 73 ______________________________________________________________ Alan J. Kohn

44. Major Foods (Percentages) of Eight Species of Cone Shells, Conus, on Subtidal Reefs in Hawaii _____________________________________________________________ Gastro- Entero-Tere- Other Species pods pneusts Nereids Eunicea belids Polychaetes ______________________________________________________________ flavidus 4 64 32 lividus 61 12 14 13 pennaceus 100 abbreviatus 100 ebraeus 15 82 3 sponsalis 46 50 4 rattus 23 77 imperialis 27 73 ______________________________________________________________ Alan J. Kohn Resource Matrix Niche Breadth Niche Overlap

45. Resource Matrix (n x m matrix) utilization coefficients and electivities Resource Consumer Species State123...n 1 u 11 u 12 u 13... u 1n 2 u 21 u 22 u 23... u 2n 3 u 31 u 32 u 33... u 3n........................ m u m1 u m2 u m3... u mn

46. Cape May warbler Bay-breasted warbler

47. MacArthur ’ s Warblers (Dendroica) Robert H. MacArthur

49. John Terborgh

51. Time of Activity Seasonal changes in activity times Ctenophorus isolepis Ctenotus calurus

52. Active Body Temperature and Time of Activity