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Direct versus Indirect Interactions Exploitation vs. Interference competition Apparent Competition

Direct versus Indirect Interactions Exploitation vs. Interference competition Apparent Competition Competitive Mutualism Facilitation Food Chain Mutualism Trophic Cascades (top-down, bottom up) Complex Population Interactions (Colwell ’ s Plant-Pollinator System) Mutualisms

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Direct versus Indirect Interactions Exploitation vs. Interference competition Apparent Competition

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  1. Direct versus Indirect Interactions Exploitation vs. Interference competition Apparent Competition Competitive Mutualism Facilitation Food Chain Mutualism Trophic Cascades (top-down, bottom up) Complex Population Interactions (Colwell’s Plant-Pollinator System) Mutualisms Euglossine bees and orchids Heliconius butterflies (larval nitrogen reserves) Cattle Egret Commensalism Gause’s competition lab experiments

  2. 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

  3. Competitive Exclusion Georgii F. Gause

  4. Coexistence of two species of Paramecium G. F. Gause

  5. 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-Moist confusum = castaneum 0 10034 30 Hot-Dry confusum > castaneum 90 1029 70 Warm-Moist confusum < castaneum 14 8629 30 Warm-Dry confusum > castaneum 87 1324 70 Cold-Moist confusum <castaneum 71 2924 30 Cold-Dry confusum >castaneum 100 0_______________________________________________________________________________

  6. Recall the Verhulst-Pearl Logistic Equation dN/dt = rN [(K – N)/K] = rN {1– (N/K)} dN/dt = rN – rN (N/K) = rN – {(rN2)/K} dN/dt = 0when [(K – N)/K] = 0 [(K – N)/K] = 0when N = K dN/dt = rN – (r/K)N2

  7. Inhibitory effect of each individual On its own population growth is 1/K Assumes linear response to crowding, instant response (no lag), r and K are fixed constants

  8. S - shaped sigmoidal population growth Verhulst-Pearl Logistic

  9. Lotka-Volterra Competition Equations competition coefficient aij = per capita competitive effect of one individual of species j on the rate of increase of species idN1 /dt = r1 N1 ({K1 – N1 – a12 N2 }/K1) dN2 /dt = r2 N2 ({K2 – N2 – a21 N1 }/K2)Isoclines, set dN/dt = 0 {curly brackets – above}: (K1 – N1 – a12 N2 )/K1 = 0when N1 = K1 – a12 N2 (K2 – N2 – a21 N1 )/K2 = 0when N2 = K2 – a21 N1 Alfred Lotka Vito Volterra

  10. Intercepts: N1 = K1 – a12 N2 if N2 = K1 / a12, thenN1 = 0 N2 = K2 – a21 N1 if N1 = K2 / a21, thenN2 = 0

  11. r1 No competitors / N1 K1 _1 / K competitors 2a \ _ N2 K1 competitors a

  12. Zero isocline for species 1 N1* = K1 – a12 N2

  13. Four Possible Cases of Competition Under the Lotka–Volterra Competition Equations_____________________________________________________________________ Species 1 can contain Species 1 cannot contain Species 2 (K2/a21 < K1) Species 2 (K2/a21 > K1) ______________________________________________________________________ Species 2 can contain Case 3: Either species Case 2: Species 2 Species 1 (K1/a12 < K2) can win always wins______________________________________________________________________ Species 2 cannot contain Case 1: Species 1 Case 4: Neither species Species 1 (K1/a12 > K2) always wins can contain the other; stable coexistence______________________________________________________________________ Vito Volterra Alfred Lotka

  14. Resultant Vectors

  15. Saddle Point Point Attractor

  16. Lotka-Volterra Competition Equations for n species (i = 1, n): dNi /dt = riNi ({Ki – Ni – S aij Nj}/Ki) Ni* = Ki – S aij Njwhere the summation is over j from 1 to n, excluding iDiffuse CompetitionS aij NjRobert H. MacArthur

  17. Lotka-Volterra Competition Equations for 3 species: dN1 /dt = r1 N1 ({K1 – N1 – a12 N2 – a13 N3 }/K1) dN2 /dt = r2 N2 ({K2 – N2 – a21 N1 – a23 N3 }/K2) dN3 /dt = r3 N3 ({K3 – N3 – a31 N1 – a32 N2 }/K2)Isoclines: dN/dt = 0 {curly brackets, above} (K1 – N1 – a12 N2 – a13 N3 )/K1 = 0when N1 = K1 – a12 N2 – a13 N3 (K2 – N2 – a21 N1 – a23 N3 )/K2 = 0when N2 = K2 – a21 N1 – a23 N3 (K3 – N3 – a31 N1 – a32 N2 )/K3 = 0when N3 = K3 – a31 N1 – a32 N2

  18. Lotka-Volterra Competition Equations for n species(i = 1, n): dNi /dt = riNi ({Ki – Ni – S aij Nj}/Ki) Ni* = Ki – S aij Nj where the summation is over j from 1 to n, excluding iDiffuse CompetitionS aij Nj

  19. Alpha matrix of competition coefficients a11 a12 a13 . . . a1n a21 a22 a23 . . . a2n a31 a32 a33 . . . a3n . . . . . . . . . . . . . . an1 an2 an3 . . . ann Self damping elements on the diagonal aii equal 1.

  20. Evidence of Competition in Nature often circumstantial1. Resource partitioning among closely-related sympatric congeneric species (food, place, and time niches) Complementarity of niche dimensions 2. Character displacement, Hutchinsonian ratios 3. Incomplete biotas: niche shifts 4. Taxonomic composition of communities

  21. Resource Matrix (m x n) Major Foods (Percentages) of Eight Species of Cone Shells, Conus, on Subtidal Reefs in Hawaii _____________________________________________________________ Gastro- Entero- Tere- Other Species pods pneustsNereidsEuniceabelidsPolychaetes ______________________________________________________________ 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

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

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

  24. Complementarity of Niche Dimensions, page 276 Anolis Thomas W. Schoener

  25. Prey size versus predator size

  26. Peter R. Grant David Lack

  27. Character Displacement in Hydrobia mud snails in Denmark Snail shell length, mm

  28. Corixid Water Boatman G. E. Hutchinson

  29. Hutchinsonian Ratios

  30. Hutchinsonian Ratios Henry S. Horn Bob May

  31. Hutchinsonian Ratios Henry S. Horn Bob May Recorders

  32. Wind Instruments

  33. Kitchen Knives

  34. Kitchen Pots

  35. Tricycles

  36. Bikes

  37. Hutchinsonian ratios among short wing Accipiter hawks Thomas W. Schoener

  38. Hutchinsonian ratios among Australian Varanus lizards

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