Population Ecology and Interspecific Interactions Lecture 7 Eben Goodale College of Forestry Guangxi University Review Whats a population? What characteristics do populations have? What factors influence how a population grows? Review How does a population grow in the absence of limiting factors ? Log NN N t = N o t N t = N o e r(t) Geometric growth When breeding is periodic Exponential growth When breeding is continuous 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 new area Review How do we include limitations into models of population growth? Today, were going to look more At this model with a time lag . And with two competing species. Why do you think this real example doesnt fit the model well? Todays 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 Fluctuations common in populations May be like sheep example, K keeps shifting up and down. Predators and prey also can make each others populations cycle. We will explore this after exam. The logistic equation and time lags Robert May (1976) The idea of overshooting ) K 0 < r < < r < 1.57 r > 1.57 If a big lag (), Or fast growth (r), Can get oscillations 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) Fluctuations can be dangerous in small populations When goes up and down (is variable ), small populations can go extinct. Populati on Variabilit y (SD) of Extinctio n after 70 yrs % % % % % % 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 gets lower when population is low. Animals can have trouble finding mates Metapopulation theory A large population is actually broken into many small populations, linked by dispersal ( ). The small populations continually go extinct or are colonize. Some metapopulations are successful and send out colonizers. They are sources . Other metapopulations are less successful and are called sinks . Metapopulation theory A model of metapopulations (Levin 1969, 1970) p = Proportion of habitat patches occupied at time t c = Patch colonization rate e = Patch extinction rate dp/dt = the change in the amount of patches over time. What happens if this is 0? 0 = cp(1-p) ep ep = cp(1-p) ep = cp cp 2 e = (cp cp 2 ) / 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 dont need to be able to solve this. I just emphasize how equations can be solved using 0s. Metapopulation theory When forests are fragmented , 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. Metapopulation theory Patches that are large and nearby other patches are colonized first. Todays 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 Competition: a definition Competition occurs between two individuals that use the same resources. Resources 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) Give an example of a + / - interaction. A + / + interaction. Space can be a limiting resource Intraspecies competition Biomass # individuals Young birch stand Older stand Self Thinning Intraspecific competition # females # offspring per female # males with territories # males without territories Juvenile survival # adults Song Sparrow 2 different kinds of competition Resource competition All individuals get smaller amount of common resource Interference competition Some individuals get resource and exclude ( ) others from it 2 different kinds of competition 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 Cattle grazing As more cattle all will be thinner Terrioriality in birds Some get the territories, some dont Population Intraspecific competition Is controlling population growth Population Intraspecific competition Is controlling population growth And now we are starting to talk about species interactions ), starting with interspecific competition. Species The niche is a characteristic Of the species The niche The set of environmental requirements of the species. G. Evelyn Hutchinson N-dimensional hypervolume N = all the environmental variables Important to survival and reprodution Fundamental niche: The abiotic environmental variables Realized niche: Actual niche where biotic interactions are also considered. What does this N-dimensional hypervolume look like? Ecologists then Measure overlap In niches Interspecific competition: competitive exclusion principle 2 species can not share the same niche indefinitely Gauses 1934 experiments Interspecific competition: competitive exclusion principle 2 species can not share the same niche indefinitely Gauses 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. Lotka-Volterra theory of competition This model developed in the 1920s by two scientists independently. It looks at two populations that are competing with each other, and how they effect each others population size. We will look at the model graphically and try to understand its major ideas, not the details. 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 0s and 1s to simply equations. Look at trends graphically I will be specific about what you need to know for tests. Adjusting the logistic equation for interspecific competition dN dt = r max (N)(1 - K ) N = r max (N 1 )(K 1 N 1 ) K1K1 dN 1 dt = r max (N 2 )(K 2 N 2 ) K2K2 dN 2 dt These are the growth rates Of the two species. We want to know: under what conditions can the two species co-exist? Adjusting the logistic equation for interspecific competition dN dt = r max (N)(1 - K ) N = r max (N 1 )(K 1 N 1 ) K1K1 dN 1 dt = r max (N 2 )(K 2 N 2 ) K2K2 dN 2 dt = r max (N 1 )(K 1 N 1 12 N 2 ) K1K1 dN 1 dt = r max (N 2 )(K 2 N 2 21 N 1 ) K2K2 dN 2 dt Where 12 is the competitive effect of species 2 on 1, and 21 is the competitive effect of species 1 on 2. We are saying that the population growth of one species is dependent on the other species. Adjusting the logistic equation for interspecific competition dN dt = r max (N)(1 - K ) N = r max (N 1 )(K 1 N 1 ) K1K1 dN 1 dt = r max (N 2 )(K 2 N 2 ) K2K2 dN 2 dt = r max (N 1 )(K 1 N 1 12 N 2 ) K1K1 = r max (N 2 )(K 2 N 2 21 N 1 ) K2K2 0 0 (K 1 N 1 12 N 2 ) = 0(K 2 N 2 21 N 1 ) = 0 N 1 = K 1 - 12 N 2 N 2 = K 2 21 N 1 Again notice we solve for 0. We are looking at conditions where growth is 0. Drawing the isocline N1 N2 N 1 = K 1 - 12 N 2 If N 2 = 0, N 1 = If N 2 = K 1 / 12, N 1 = K1/ 12 In these series of graphs we are looking at initial numbers of N1 and N2. Over time they change. Putting dN/dt on the graph N1 N2 = r max (N 1 )(K 1 N 1 12 N 2 ) K1K1 dN 1 dt If N 2 is 0, and N 1 < K 1 What happens? = r max (N 1 )(K 1 N 1 0 )) K1K1 dN 1 dt dN 1 dt Is positive Putting dN/dt on the graph N1 N2 = r max (N 1 )(K 1 N 1 12 N 2 ) K1K1 dN 1 dt What happens? If N1 is 0, and N2 < K1 12 X Where X < K1 = r max (N 1 )(K 1 0 X) K1K1 dN 1 dt Where X < K1 dN 1 dt Is positive Putting dN/dt on the graph N1 N2 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. Putting dN/dt on the graph Now we could make a similar graph for N2 Putting dN/dt on the graph Things get really complicated When we put both dN1/dt and dN2/dt on the same graph But lets take a point In the lower left corner Whats dN1/dt doing? Whats dN2/dt doing? We can combine their motion like this Putting dN/dt on the graph Now lets take a point In between the lines Whats dN1/dt doing? Whats dN2/dt doing? We can combine their motion like this Putting dN/dt on the graph Finally, pick a pint in upper right corner Whats dN1/dt doing? Whats dN2/dt doing? We can combine their motion like this Putting dN/dt on the graph The whole picture looks like this What does this mean? In this case, N2 will go extinct Putting dN/dt on the graph There are other scenarios, too Whats the outcome here? In this case, N1 will go extinct Note that now N2s isocline is on top of N1s Putting dN/dt on the graph A third scenario Whats the outcome here? In this case, N1 or N2 will go extinct, depending on the initial numbers Compare to the first we did Putting dN/dt on the graph And a fourth scenario Whats the outcome here? In this case, the two populations can co-exist Compare to the third What does this mean The only situation When these 2 Species can Co-exist ) when: K1 /12 > K2 That means 12 is small At the same time K2 /21 > K1 So 21 is small, too Overall when the effects of the interspecific competition are less than intraspecific competition, two species can co-exist Also note that the point of equilibrium for species is smaller than K1 and K2. 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 Gauses results. But does competition happen in real communities? Review articles 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. Lets look at some examples Barnacles in the intertidal zone 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. Barnacles in the intertidal zone Rodents in the desert Brown and colleagues And competition can even be between very different kinds of organisms How to avoid competition Organisms can avoid competition by having different niches. Sometimes an inferior competitor can persist because it tolerates disturbance . Sometimes an inferior competitor can persist because predators or herbivores dont like it. This sea palm only lives in areas where waves remove musssels frequently. Otherwise it is out- competed. The ghosts of competition past: Character displacement Often two species are not competing with each other now, but may have had before Character displacement: species are more different when they live in the same place Todays 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 Key concepts Population fluctuations can be caused by time delays in the effect of density- dependent factors. Small populations are more vulnerable to extinction for several reasons. Large populations can actually be thought of as a collection of small populations, that go extinct and are re-colonized. In terspecific competition occurs when individuals of different species both deplete a resource. If the species exact resource requirements (niches) are the same they can not coexist, but they can coexist with some niche overlap. Evidence of interspecific competition has been found commonly by ecologists. Tuesdays exam What to bring: 1) calculator (phone OK) 2) Pen or pencil 3) One A4 piece of paper with your notes (can be front and back). One thing about studying: for lectures 4-7 please check FINAL version on web. What kinds of questions to expect Multiple answer questions (A, B, C, D). Short answer questions One essay question on the primary literature readings (3 choices). For those literature readings, read carefully titles, abstracts and figures, and any more of the article necessary to get the general idea of a) what they did and b) what they concluded. Review questions posted today on website Vocabulary words (underlined in notes or in red in readings) are fair game. Know what these words mean and the ideas associated with them. The review questions will highlight important ideas. I will be at the classroom at 2:00, and between 2:00 and 3:00 will answer any questions. The exam will start at 3:00 and last to 5:00.