Competition. Not until we reach the extreme confines of life, in the arctic regions or on the borders of an utter desert, will competition cease

Transcription

1 Competition Not until we reach the extreme confines of life, in the arctic regions or on the borders of an utter desert, will competition cease Darwin 1859 Origin of Species

2 Competition A mutually negative interaction among spp at the same trophic level directly or indirectly resulting in reduced fitness How might competition take place (2 main classes)?

3 Cameos of competition (mechanisms cf Schoener 1983) Consumptive: Ants and rodents (Brown and Davidson 1977) Pre-emptive: Barnacles (Connell 1961) Overgrowth: Tree seedlings, (Chapman 1945) Chemical: Allelopathy (Lankau et al. 2009) Territorial: Birds (Manorina) (Loyn et al. 1983) Encounter: Beetles (Park et al. 1965)

4 Consumptive competition between seed-eating rodents and ants in Sonoran Desert Strong resource limitation - seeds are primary food of many taxa (rodents, birds, ants, beetles) Almost complete overlap in the size of seeds consumed by ants and rodents Long-term exclosure experiments - fences to remove rodents, insecticide to remove ants. Recensuses of ant and rodent populations. What do you predict? Remove rodents: number of ant colonies increased 70 % Remove ants: rodent biomass increased 24 %

5 Chemical interference competition in garlic mustard Garlic mustard produces gylcosinolates that kill mycorrhizas in the soil and inhibit seed germination of neighboring native plants

6 Glucosinolate production declines as garlic mustard populations age. Why? Competing native plants recover as glucosinulate concentration declines (walnut in this case).

7 Territorial competition Bell miners vs. the rest Flocks of Australian Bell Miners defend patches of Eucalyptus forest against other (larger birds) BM territories are often full of sick eucalyptus trees - covered in lerps (secretions of the red gum lerp psyllid, Glycaspis brimblecombei (Homoptera: Psyllidae)

8 Experimental Test: First remove the BMs Methods: Count the birds, measure foliage Results: Invasion by guild of 11 spp of insectivorous birds 3-fold increase in lerp removal rate 15 % increase in epicormic foliage

9 Descriptive competition models When would competition lead to species coexistence or species local extinction (exclusion)? Non-mechanistic - competition modeled as direct influence of the abundance of one species on another. Assume: population growth is dependent on pop size, N, and limited resources ensure that there is a max. pop. size, K (i.e., carrying capacity) dn/dt = rn(k-n/k) where r = per capita rate of increase

10 Single species logistic growth curve dn/dt = rn(k-n/k) What about the N of other spp??

11 Competition coefficients (Gotelli 2001) K species 1 Proportion of species 1 resources used by individual of sp 1 (=purple) or sp 2 (=green) Individuals of species 2 (green) consume 4 times as much of the resources available to the purple species as does species 1 (purple) itself. Competition coefficient α purple, green = 4 Read α 1,2 as effect of species 2 on species 1

12 Lotka (1925) and Volterra (1926) used the logistic equation to describe competition between two species Species 1: dn 1 /dt = r 1 N 1 ((K 1 -N 1 -α 12 N 2 )/K 1 ) Species 2: dn 2 /dt = r 2 N 2 (( K 2 -N 2 -α 21 N 1 )/K 2 ) Where α ij = competition coefficient for the effect of species j on species i Overall: Proximity of each species i to its carrying capacity, K is dependent upon its current population size, N i, and the population size of its competitor, N j, weighted by the competition coefficient, α ij If α ij = α ji = 1, then effect of individuals of each species are the same, and species are

13 Competitive interactions need not be symmetrical: If α ij <1, and α ji <1, then interspecific competitors have a weaker effect than intraspecific competitors What conditions lead to stable coexistence for two species? Same as asking under what conditions will the growth rates (dn/ dt) of both species = 0 for population sizes (N>0)? Set differential equation to zero 0=(K 1 -N 1 - α 12 N 2 ) Gives us zero-growth isoclines: So Equilibrium N 1 = K 1 - α 12 N 2; Then, equilibrium N 2 = K 2 - α 21 N 1

14 Can we calculate equilibrial N 1 without knowing equilibrial N 2? Example of N 1 Substitute: N 1 = K 1 - α 12 (K 2 - α 21 N 1 ) rem: equilibrial N 2 = K 2 - α 21 N 1 Multiply out: N 1 = K 1 - α 12 K 2 /1- α 12 α 21 For N 1 to have an equilibrium population size >0, the denominator must be >0 (ie product α 12 α 21 is <1). MUCH CLEARER USING STATE SPACE GRAPH!

15 Competition coefficients (Gotelli 2001) K species 1 Proportion of species 1 resources used by individual of sp 1 (=purple) or sp 2 (=green) Individuals of species 2 (green) consume 4 times as much of the resources available to the purple species as does species 1 (purple) itself. Competition coefficient α purple, green = 4 Read α 1,2 as effect of species 2 on species 1

16 Zero growth isoclines - combination of abundances of N 1 and N 2 at which growth of one species is zero =1000/0.6 + ve - ve K 1 =1000 a 1,2 = 0.6

17 Zero growth isoclines - combination of abundances of N 1 and N 2 at which growth of one species is zero =1000/0.6 + ve - ve K 1 =1000 a 1,2 = 0.6 No competitor (N 2 ) so population Of N 1 will stop growing at K 1

18 Zero growth isoclines - combination of abundances of N 1 and N 2 at which growth of one species is zero =1000/0.6 + ve - ve K 1 =1000 a 1,2 = 0.6 No N 1 so N 2 will grow to a maximum size determined by how much of K 1 each individual of N 2 uses.

19 Zero growth isoclines - combination of abundances of N 1 and N 2 at which growth of one species is zero =1000/0.6 + ve - ve

20 For any starting value of N 1 and N 2 what is the predicted equilibrium population sizes??

21 Predicted popn sizes

22 What is the outcome of competition now? K 1 /a 1,2 =1000/0.5 a 12 =0.5 a 21 =1.2 K 1 = 1000 K 2 = 1000

23 K 2 /a 21 =1000/1.2 =833

24 (here we just switched the comp coefficients around) a 21 =1.2 a 12 =0.5 K 1 = 1000 K 2 = 1000

25 a 1,2 ~ 1.1 a 2,1 ~ 1.2

26 Competitive exclusion principle Volterra model predicts that species can only coexist if intraspecific competition is stronger than interspecific competition. (i.e. both competition coefficients < 1 for similar K) Volterra models had a major influence through 1930 s and beyond on concept of the niche However Volterra leaves unanswered: How different do species need to be to coexist, or is there a limit to similarity of competitors for coexistence?

27 Multispecies Volterra Can generate a multispecies Volterra model with growth equations for each species Each species growth is determined by the additive effects of a i,j competition coefficients Assumes no higher order interactions (ie competition coefficients are fixed).

28 Volterra model Paradox of the plankton Hutchinson (1961) How do spp of plankton in temperate lakes coexist when they all compete for the same resources? Still a paradox today this is the Grail of community ecology