Population Ecology and Interspecific Interactions Lecture 7

1. Population Ecology and Interspecific InteractionsLecture 7 EbenGoodale College of Forestry Guangxi University

2. Review • What’s a population? • What characteristics do populations have? • What factors influence how a population grows?

3. Review • How does a population grow in the absence of limiting factors（限制因子）? Nt = Noλt Geometric growth When breeding is periodic N Log N Nt = Noer(t) Exponential growth When breeding is continuous

4. Exponential/geometric growth • When does this happen in nature? • Unlimited food (bacteria in dish) • Population released from some restriction (elephants after hunting ban) • Population colonizing（殖民） new area

5. Review • How do we include limitations（边界） into models of population growth? Why do you think this real example doesn’t fit the model well? Today, we’re going to look more At this model with a time lag（时间间隔）. And with two competing species.

6. Today’s class • A little more population ecology • Population cycles caused by delayed density dependence. • Extinctions in small populations • Metapopulations. • Species Interactions: competition • Some time to think about exam

7. Fluctuations common in populations • May be like sheep example, K keeps shifting up and down. • Predators and prey also can make each other’s populations cycle. We will explore this after exam.

8. The logistic equation and time lags The idea of “overshooting （过辐射)” K 0 < rτ < 0.368 Robert May (1976) 0.368 < rτ < 1.57 If a big lag (τ), Or fast growth (r), Can get oscillations rτ > 1.57

9. The logistic equation and time lags Nicholson 1957: Negative effects of adult high densities Only felt some time later, when many fly larvae hatched (all die because too many)

10. Fluctuations can be dangerous in small populations When λ goes up and down (is variable– 变量), small populations can go extinct.

11. Other reasons for small populations being extinction-prone • Genetic drift: • What is it and why is it important in small populations? • Inbreeding • The “Allee effect”: in some populations λ gets lower when population is low. • Animals can have trouble finding mates

12. Metapopulation（集合种群） theory Some metapopulations are successful and send out colonizers. They are “sources（起源）”. Other metapopulations are less successful and are called “sinks（减少）”. A large population is actually broken into many small populations, linked by dispersal (传播). The small populations continually go extinct or are colonize.

13. Metapopulation theory • A model of metapopulations (Levin 1969, 1970) dp/dt = the change in the amount of patches over time. What happens if this is 0? p = Proportion of habitat patches occupied at time t c = Patch colonization rate e = Patch extinction rate 0 = cp(1-p) – ep ep = cp(1-p) ep = cp – cp2 e = (cp – cp2) / p e = c – cp cp = c-e p = (c-e)/c p = 1 – e/c If c > e, p is positive and dp/dt is positive. But if e > c, dp/dt is negative and the meta- population will go extinct. You don’t need to be able to solve this. I just emphasize how equations can be solved using 0’s.

14. Metapopulation theory • When forests are fragmented（变成碎片）, c gets less because it is harder for animals to move between patches. • e also increases because the patches are smaller and cannot sustain large populations. • Hence e/c might become greater than 1 and the whole meta-population may go extinct. This argument has been used to preserve forest from fragmentation, especially in the case of the northern spotted owl.

15. Metapopulation theory Patches that are large and nearby other patches are colonized first.

16. Today’s class • A little more population ecology • Population cycles caused by delayed density dependence. • Extinctions in small populations • Metapopulations. • Species Interactions: competition • Some time to think about exam

17. Competition: a definition • Competition occurs between two individuals that use the same resources. • Resources（资源）are anything that can be depleted such as food, water, light (because it can be shaded), and space (because it can be used up). • Both individuals are harmed (an - / - interaction) Space can be a limiting resource Give an example of a + / - interaction. A + / + interaction.

18. Intraspecies（种内） competition Biomass Young birch stand # individuals Self Thinning Older stand

19. Intraspecific competition # males without territories # males with territories # offspring per female Song Sparrow # females Juvenile survival # adults

20. Resource competition All individuals get smaller amount of common resource Interference（干扰） competition Some individuals get resource and exclude(排除) others from it 2 different kinds of competition

21. Resource competition All individuals get smaller amount of common resource Interference competition Some individuals get Resource and exclude others from it: tends to be aggressive（好斗的） 2 different kinds of competition Cattle grazing– As more cattle all will be thinner Terrioriality（领土权） in birds – Some get the territories, some don’t

22. Intraspecific competition Is controlling population growth Population

23. And now we are starting to talk about species interactions（种间相互作用), starting with interspecific（种间的） competition. The niche（生态位） is a characteristic Of the species Species Population Intraspecific competition Is controlling population growth

24. The niche The set of environmental requirements of the species. “N-dimensional hypervolume” N = all the environmental variables Important to survival and reprodution Fundamental niche: The abiotic environmental variables G. Evelyn Hutchinson Realized niche: Actual niche where biotic interactions are also considered.

25. What does this “N-dimensional hypervolume” look like? Ecologists then Measure overlap（重叠） In niches

26. Interspecific competition: competitive exclusion（排斥）principle • 2 species can not share the same niche indefinitely Gause’s 1934 experiments

27. Interspecific competition: competitive exclusion principle • 2 species can not share the same niche indefinitely Gause’s 1934 experiments: P. aurelia and P. caudatum eat the same resource and one goes extinct. P. bursaria eats a somwehat different resource. Notice K when 2 species co-exist is low.

28. Lotka-Volterra theory of competition • This model developed in the 1920’s by two scientists independently. • It looks at two populations that are competing with each other, and how they effect each other’s population size. • We will look at the model graphically（生动的） and try to understand it’s major ideas, not the details.

29. A note on mathematics • Ecology is mathematical in nature, so presenting it without math is not really letting you see the science. • My favorite experiences in ecology have been in understanding at a basic level the idea of an equation. • Equations are valuable not only for their conclusions, but understanding assumptions. • Working with equations is like reading a primary literature paper: scary, but if know tricks doable. • Use “0”s and “1”s to simply equations. • Look at trends graphically • I will be specific about what you need to know for tests.

30. rmax (N2) rmax (N1) (K1 – N1) (K2 – N2) K2 K1 dN dN2 dN1 dt dt dt = = Adjusting the logistic equation for interspecific competition N ) = rmax (N) (1 - K These are the growth rates Of the two species. We want to know: under what conditions can the two species co-exist?

31. rmax (N2) rmax (N1) (K2 – N2) (K1 – N1) K2 K1 dN2 dN dN1 dN1 dN2 dt dt dt dt dt = = rmax (N1) rmax (N2) (K2 – N2 – α21N1) (K1 – N1 – α12N2) = = K2 K1 Adjusting the logistic equation for interspecific competition N ) = rmax (N) (1 - K We are saying that the population growth of one species is dependent on（取决于） the other species. Where α12 is the competitive effect of species 2 on 1, and α21 is the competitive effect of species 1 on 2.

32. rmax (N2) rmax (N1) (K2 – N2) (K1 – N1) K2 K1 dN2 dN1 dN dt dt dt = = Adjusting the logistic equation for interspecific competition N ) = rmax (N) (1 - K rmax (N1) (K1 – N1 – α12N2) rmax (N2) (K2 – N2 – α21N1) 0 0 = = K1 K2 (K1 – N1 – α12N2) = 0 (K2 – N2 – α21N1) = 0 N1 = K1 - α12N2 N2 = K2 – α21N1 Again notice we solve for 0. We are looking at conditions where growth is 0.

33. Drawing the isocline（等斜线） K1/ α12 In these series of graphs we are looking at initial numbers of N1 and N2. Over time they change. N2 N1 = K1 - α12N2 If N2 = 0, N1 = If N2 = K1/ α12, N1 = N1

34. dN1 dN1 dN1 dt dt dt rmax (N1) (K1 – N1 – 0 )) = K1 rmax (N1) (K1 – N1 – α12N2) Is positive = K1 Putting dN/dt on the graph If N2 is 0, and N1 < K1 What happens? N2 N1

35. dN1 dN1 dN1 If N1 is 0, and N2 < dt dt dt K1 X α12 α12 Where X < K1 rmax (N1) (K1 – N1 – α12N2) Is positive = K1 rmax (N1) (K1 – 0– X) = Where X < K1 K1 Putting dN/dt on the graph What happens? N2 N1

36. Putting dN/dt on the graph In fact, when the initial conditions are to the left of this line, N1 will increase. Using the same arguments, when initial conditions are to the right of this line, N1 will decrease. N2 N1

37. Putting dN/dt on the graph Now we could make a similar graph for N2

38. Putting dN/dt on the graph Things get really complicated When we put both dN1/dt and dN2/dt on the same graph But let’s take a point In the lower left corner What’s dN1/dt doing? What’s dN2/dt doing? We can combine their motion like this

39. Putting dN/dt on the graph Now let’s take a point In between the lines What’s dN1/dt doing? What’s dN2/dt doing? We can combine their motion like this

40. Putting dN/dt on the graph Finally, pick a pint in upper right corner What’s dN1/dt doing? What’s dN2/dt doing? We can combine their motion like this

41. Putting dN/dt on the graph The whole picture looks like this What does this mean? In this case, N2 will go extinct

42. Putting dN/dt on the graph There are other scenarios, too Note that now N2’s isocline is on top of N1’s What’s the outcome here? In this case, N1 will go extinct

43. Putting dN/dt on the graph A third scenario（方案） Compare to the first we did What’s the outcome here? In this case, N1 or N2 will go extinct, depending on the initial numbers

44. Putting dN/dt on the graph And a fourth scenario Compare to the third… What’s the outcome here? In this case, the two populations can co-exist

45. What does this mean Also note that the point of equilibrium（平衡点） for species is smaller than K1 and K2. The only situation When these 2 Species can Co-exist（共存) when: K1 /α12 > K2 That means α12 is small At the same time K2 /α21 > K1 So α21 is small, too Overall when the effects of the interspecific competition are less than intraspecific competition, two species can co-exist

46. Lotka-Volterra theory of competition • In most cases in which two species compete, one will go extinct. • But an equilibrium can be reached when interspecific competition is low (niches are somewhat different) • And at that equilibrium the carrying capacity for both species is lower than when they are by themselves: same as Gause’s results.

47. But does competition happen in real communities? • Review articles（综述） show that competition was found in most cases in the field. • For example, Schoener (1983) looked at 164 papers studying 390 species and 76% of species showed some effect of competition. • Let’s look at some examples…

48. Barnacles（藤壶） in the intertidal zone（潮间带） Joseph Connell removed Balanus and looked at response of Chthamalus. Chthamalus moved down, proving that it is not in this area due to competition with Balanus.

49. Barnacles in the intertidal zone

50. Rodents（啮齿动物） in the desert Brown and colleagues