Lecture 10. Chapter 7: Species Interactions/Competition Chapter 8: Mutualisms

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1 Lecture 10 Chapter 7: Species Interactions/Competition Chapter 8: Mutualisms

2 Terminology -/- Competition -/+ Predation and other associations where one species benefits and the other is harmed +/0 Commensalism +/+ Mutualism Facultative Obligatory Carnivorous predators Parasitoids Parasitism: Ectoparasites Endoparasites Herbivores Seed predation

3 7.1: Concept of Niche Joseph Grinnell (1917) Charles Elton (1927) G. E. Hutchinson (1957) Robert Ricklefs (1997) Informal and Formal definitions Fundamental Niche Realized Niche

4 7.2: History of Interspecific competition Tansley (1917) : context dependent competitive exclusion Galium saxitale Galium sylvestre

5 7.2: History of Interspecific competition Gause (1934) The struggle for existence Yeast Protozoans, Paramecium caudatum and P. aurelia Fig. 7.1 in text and original (Chapter 5: Fig. 21) shown here:

6 Gause s results (1934) Competitive Exclusion Principle No two species can occupy the same ecological niche

7 7.3: Lotka (1925) - Volterra (1926) competition equations Based on Logistic equation (intraspecific competition) Assumed growth rate of each species would be decreased as the population of its competitors increased. Therefore impact of spp2 on growth rate of spp1 is expressed as a modification of logistic equation and vice versa. Wrote 2 simultaneous equations, one for each species And include a competition coefficient α ij Equations 7.1 and 7.2 (pg. 163)

8 7.3: Lotka (1925) - Volterra (1926) competition equations Equation 7.1 dn 1 /dt = r 1 N 1 [K 1 -N 1 -α 12 N 2 /K 1 ] Equation 7.2 dn 2 /dt = r 2 N 2 [K 2 -N 2 -α 21 N 1 /K 2 ] Where: N 1, N 2 = number of individuals per species r 1, r 2 = intrinsic rate of each species K 1, K 2 = carrying capacity of each species α 1 2 = competition coefficient effect of species 2 on species 1 α 21 = competition coefficient effect of species 1 on species 2 t = time (pg. 163)

9 Competition coefficient Competition coefficient: α ij Value normally ranges between 0 and 1 If = 0, indicates no competition between two species. No reason to pursue further since no competition. If coefficient is negative, then each species benefits growth of one another, ~ mutualistic interaction If = 1, indicates intraspecific competition Thus interspecific competition is usually less intense than intraspecific competition and is noted by 0> α <1 value Lots of parameters to estimate (r, K, α ) but can simplify with: Equilibrium Analysis equate popln growth to zero dn 1 /dt = 0 and dn 2 /dt = 0

10 Popln of species 2 Lotka-Volterra cont. Competition coefficients determined by ratio of two species carrying capacities α 12 = K 1 /K 2 (eq: 7.10) Fig. 7.2 Zero isocline for pop 1 (0,K 1 /α 12 ) N 2 = (K 1 -N 1 )/α 12 (K 1,0) Popln of species 1 See also: Fig. 7.3 Zero isocline for species 2

11 Lotka-Volterra cont. Competition coefficients determined by ratio 2 spp. carrying capacities Recall: α 12 = K 1 /K 2 (eq: 7.10) By placing zero isoclines (Saturation levels) on same graph 4 combo s possible: 1) Fig. 7.4 Species 1 wins K 1 /α 12 >K 2 with K 1 >K 2 /α 21 2) Fig. 7.5 Species 2 wins K 2 >K 1 /α 12 with K 2 /α 21 >K 1 3) Fig. 7.6 Unstable equilibrium (S) or competitive exclusion with indefinite winner K 1 >K 2 /α 21 with K 2 >K 1 /α 12 4) Fig. 7.7 Coexistence of both species at stable equilibrium, E K 1 /α 12 >K 2 with K 2 /α 21 >K 1

12 7.4: Laboratory competition experiments Table 7.1 Thomas Parks (1954) Flour beetles pg 169 Temp % Rel.Humidity Climate T confusum T castaneum Hot-moist Hot-dry Warm-moist Warm-dry Cold-moist Cold-dry 100 0

13 7.5 Resource-based competition theory Fig. 7.8 Per capita growth as a function of resource availability (Pg 171) Fig. 7.9 Per capita growth as a fn of resource availability, BUT with constant mortality. R* = dn/dt = 0: amt of resource producing a per capita growth rate equals zero, thus R* growth rate balances death. K Ri = supply rate R i = resource quantity q = consume resource at rate q b = efficiency individual converts resources to new individuals. dr i /dt = k Ri (Eq. 7.11) In form of logistic equation: dn/dt = bk Ri N(1-qN/k Ri ) (Eq. 7.13) Fig Popln size and resource dynamics

14 7.5 Resource-based competition theory Michaelis-Menton Enzyme Kinetics equation Monod Revision via bacteria work R* = mk i /b-m (eq. 7.18) Allows prediction of R* (resource level at which growth stops) If know half-saturation constant ( K i ) and max growth rate (b) and mortality rate (m) ADVANCE over Lotka-Volterra => If resource identified then a variable R* can be derived from simple experiments!

15 7.5 Resource-based competition theory R* Rule = for any given resource (R), if determine R* value for each species grown alone in same environment, then spp with lowest R* should competitively exclude all other species when grown together given enough time in same constant environment. NOT Predicted by Lotka-Volterra: A species with high affinity for a resource can still LOSE if it has a low growth rate (r) & high death (m). See Table 7.2 R* Rule calculations R* < R 0 or all species die out because of lack of resources

16 Spatial competition hypothesis: generalized for multiple species interactions. Proposes stable coexistence for inferior competitors in a diverse community. 7.6 Spatial competition and the competitioncolonization trade off Multiple species can coexist within a community without resulting into one species yielding to the other idea is foundation of competitioncolonization trade-off idea 1 st proposed by Levins and Culver (1971) dp/dt = cp(1-p)- εp (Eq. 7.21) P = 1- (ε/c) (Eq. 7.22) c = ε/ (1- P) (Eq. 7.23) c 1 > ε 1 Eq. 7.29a c 2 > c 1 (c 1 + ε 2 - ε 1 )/ ε 1 Eq. 7.29b

17 7.7 Evidence for competition in nature Connell s barnacles Ant succession: opportunists extirpators insinuators Literature Review of field studies of competition

18 7.8 Indirect Evidence for competition & natural experiments Ghost of Competition Past Jared Diamond (1983) & 3 advantages of natural experiments 1) Gather data quickly 2) Assess situations where experimental manipulation is unlikely 3) Allows assessment of long term ecological and evolutionary pressures end result

19 7.8 Indirect Evidence for competition & natural experiments Five types of indirect evidence from natural experiments: Jared Diamond (1983) & 3 advantages of natural experiments 1) Ecological release 2) Contiguous allopatry 3) Niche partitioning 4) Character displacement 5) Historical replacement

20 Chap. 7: Highlights Competition The ecological niche The competitive exclusion principle The Lotka Volterra competition equations Resource-based competition theory Spatial competition and the competition colonization trade-off Evidence for competition from nature Indirect evidence for competition and natural experiments

21 Mutualisms: Chapter 8

22 8.1 Mutualism or Parasitism +/+ Mutualism +/- Parasitism Facultative Obligatory Mutualism are complex and do not often fit into a neat category of facultative or obligatory May be context dependent and exist in only under a unique set of conditions Some mutualisms more common in tropical vs. temperate regions Examples?

23 Ant Acacia mutualisms

Obligate Mutualisms - Yucca and Yucca moth http://4.bp.blogspot.

24 Obligate Mutualisms - Yucca and Yucca moth A/TdZsCDd3TcI/AAAAAAAAAEM/4Hg5PSXiyp4/s1600/Yucca%2Bfilame ntosa.jpg

25 Fig Fig wasp obligate mutualism

26 8.2: Modeling mutualism Back to the Lotka-Volterra equation orgy of mutual benefaction (Robert May 1981) Mutualism coefficients, c 1 and c 2, replace competition coefficients c 1 = measures rate an indiv. of N 2 benefits from growth rate of N 1 c 2 = measure rate an indiv. of N 1 benefits from growth rate of N 2 dn 1 /dt = r 1 N 1 [K 1 + c 1 N 2 -N 1 ]/K 1 Eq. 8.1 dn 2 /dt = r 2 N 2 [K 2 + c 2 N 1 -N 2 ]/K 2 Eq. 8.2

27 8.2: Modeling mutualism dn 1 /dt = r 1 N 1 [K 1 + c 1 N 2 -N 1 ]/K 1 Eq. 8.1 dn 2 /dt = r 2 N 2 [K 2 + c 2 N 1 -N 2 ]/K 2 Eq. 8.2 Perform equilibrium analysis by setting dn 1 and dn 2 to zero Results in the population of each species being increased beyond its carrying capacity w/ additional individuals of its partner species. The more intense the mutualism, (>er benefits to partner spp.) the larger the equilibrium popln becomes: N 1 = K 1 + c 1 N 2 Eq. 8.3 N 2 = K 2 + c 2 N 1 Eq. 8.4

28 8.2: Modeling mutualism N 1 = K 1 + c 1 N 2 Eq. 8.3 N 2 = K 2 + c 2 N 1 Eq. 8.4 The interaction is stable when only one partner benefits from the interaction. If c 2 = 0, then N 2 cannot exceed K 2 and N 1 stabilizes at K 1 + c 1 K 2 Another approach: substitute carrying capacity after mutualism & note as K* 1 and K* 2 Eq. 8.5 K* 1 = K 1 + c 1 N 2 Recall: c = mutualism coefficient Eq. 8.6 K* 2 = K 2 + c 2 N 1 Eq. 8.7 dn 1 /dt = r 1 N 1 [K* 1 -N 1 / K* 1 ] = r 1 N 1 [K 1 + c 1 N 2 -N 1 /K 1 +c 1 N 2 ] Eq. 8.8 dn 2 /dt = r 2 N 2 [K* 2 -N 2 / K* 2 ] = r 2 N 2 [K 2 + c 2 N 1 -N 2 /K 2 +c 2 N 1 ]

29 8.2: Modeling mutualism Lotka-Volterra approach is phenomenological in design Mechanistic approach needed: Based on actual rates of exchange of relevant resources between 2 mutualisms Since each interaction is unique, complex, and context dependent, model generalizations are hard to arrive at that have any meaning. No standard approach to modeling mutualism Assess the following points: 1) Mutualism involve costs and benefits 2) Costs set limits on evolution of mutualism 3) Conflict of interest exists between mutualists 4) Organisms that cheat often receive the benefits 5) Related or similar organisms may benefit by acting as parasites 6) Mutualisms may evolve toward parasitism 7) Continuous coevolution is needed to maintain mutualism

30 Chap 8: Highlights Mutualisms Mutualism or parasitism? Modeling mutualism The costs of mutualism

Page # Effect of high adult mortality on amount of early reproduction: Effect of high adult mortality on larval development time:

Page # Effect of high adult mortality on amount of early reproduction: Effect of high adult mortality on larval development time: FROM Wednesday - end of lecture on comparative life histories: A laboratory evolution experiment - effects of different rates of adult mortality on life history traits in Drosophila (fruit flies) Question: