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)

Indirect Interactions Darwin — Lots of “ Humblebees ” around villages

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

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

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

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

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

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

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

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

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

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 —————————————————>

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

Competitive Mutualism

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

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

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

S - shaped sigmoidal population growth

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

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

N 1 = K 1 –  12 N 2

Zero isocline for species 1

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

Saddle Point Point Attractor

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

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

More realistic, curvilinear isoclines

Competitive Exclusion in two species of Paramecium Georgi F. Gause

Coexistence of two species of Paramecium Georgi F. Gause

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

Mutualism Equations (pp , 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.

Outcome of Competition Between Two Species of Flour Beetles ____________________________________________________________________ Relative Temp. Humidity Single Species (°C) (%) Climate Numbers Mixed Species (% wins) confusum castaneum ____________________________________________________________________ Hot-Moistconfusum = castaneum Hot-Dryconfusum > castaneum Warm-Moistconfusum castaneum Cold-Moistconfusum castaneum ________________________________________________________

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

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.

Alpha matrix of competition coefficients N, K Vectors  11  12   1n N 1 K 1  21  22   2n N 2 K 2  31  32   3n N 3 K  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

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)

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

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 lividus pennaceus 100 abbreviatus 100 ebraeus sponsalis rattus imperialis ______________________________________________________________ Alan J. Kohn

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 lividus pennaceus 100 abbreviatus 100 ebraeus sponsalis rattus imperialis ______________________________________________________________ Alan J. Kohn Resource Matrix Niche Breadth Niche Overlap

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

Cape May warbler Bay-breasted warbler

MacArthur ’ s Warblers (Dendroica) Robert H. MacArthur

John Terborgh

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

Active Body Temperature and Time of Activity