BIOS 6150: Ecology Dr. Stephen Malcolm, Department of Biological Sciences
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1 BIOS 6150: Ecology Dr. Stephen Malcolm, Department of Biological Sciences Week 7: Dynamics of Predation. Lecture summary: Categories of predation. Linked prey-predator cycles. Lotka-Volterra model. Density-dependence. Interference. Functional response. Aggregation of risk. Click on picture BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 1
2 2. Categories of Predation: Predators: Kill & completely consume many prey items during their life. Parasitoids: Free-living adult insects that lay eggs in or on their single host ( prey ) in which the larva (or larvae) develops into a new freeliving adult. The host is always killed. Parasites: Most of their life is spent in close association in or on a single host and usually do not kill the host. Herbivores: Most only partially consume individual plants, but they include a range of plant feeders that act like: true parasites (e.g. aphids) parasitoids (e.g. fig wasps) predators (e.g. mice and seed beetles). BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 2
3 3. Prey - predator cycles: Dynamics of change in numbers through time: Prey-predator, hostparasitoid and plantherbivore interactions (Fig. 10.1). Coupled oscillations How do we describe these dynamics? BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 3
4 4. Snowshoe hare - lynx cycles: Snowshoe hare-lynx cycling is a famous example (Fig. 10.1c [10.1a, 4 th ed.]). But is it the interaction, or other factors such as prey food availability, and induced defense, that generates the cycles? Hare-plant interactions appear to generate a time-lag that in turn generates the cycles that are simply tracked by the predatory lynx and not generated by lynx. BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 4
5 5. Other factors can influence apparently coupled oscillations: Other interactions may influence the dynamics of trophic and competitive interactions among plants, hares, grouse and predators (Fig. 10.5, 3 rd ed.). A system much like that for the snowshoe hare-lynx interaction of Fig. 10.1c. Here lynx may fine-tune the cycles. BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 5
6 6. Population Dynamics of Predation Two modeling approaches: (1) Based on the discrete, difference equations of Nicholson & Bailey (1935): As in Begon, Mortimer & Thompson (1996). (2) Based on the continuous, differential equations of Lotka (1932) & Volterra (1926): As in Begon, Townsend & Harper (2006). Without logistic limitation of prey or predators. This is a mass action model to which logistic limitation can be added. BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 6
7 7. The Lotka-Volterra model of prey-predator dynamics: For prey, dn =rn-consumption rate of prey, or, dt dn =rn - apn dt Where N = prey population, P = predator population, and a = attack rate. For predators (consumers), dp =predator births-qp(deaths), or, dt dp =fapn -qp dt Where q = predator mortality rate (starve exponentially in absence of prey, so dp/dt = -qp). Predator birth = consumption rate of prey (apn) x efficiency f of turning this into offspring births). BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 7
8 8. Zero isoclines for the Lotka-Volterra model: The prey zero isocline occurs when: dn dt =0, or rn =apn, and so P =r a The predator (consumer) isocline is at: dp =0, or fapn =qp, or N = q dt fa These isoclines are shown together in Fig.10.2: Model generates coupled oscillations (10.2d) that are unrealistically 'neutrally stable' as opposed to a more realistic set of 'stable limit cycles' with a tendency to return to the original cycle after disturbance. BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 8
9 9. Prey-predator cycles: Coupled oscillations (Fig ) may or may not be a product of preypredator interactions alone, but may already exist in absence of predators BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 9
10 10. Bottom-up & top down influences: Bottom-up (from food) and topdown (from natural enemies) influences on population cycling in the North American community of plants, hares, grouse and predators (Fig. 10.5, 3 rd ed.). Trophic level BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 10
11 11. Delayed density-dependence: Cycles can also show delayed density dependent mortality (Fig. 10.6) in which mortality appears to be density independent. But when plotted as a time series (k-value against log host density) spirals inwards for damped oscillations. If plotted against log host density-t then gives straight line relationship. This regulates a host-parasitoid model with different degrees of density dependence: under- (b<1), exactly- (b=1), or over-compensating (b>1). BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 11
12 12. Self-limitation: Inclusion of intraspecific competition or mutual interference in the Lotka-Volterra model: Can include a logistic term in the basic model! Intraspecific effects change the unrealistically vertical and horizontal zero isoclines of Fig. 10.2, which are density-independent, to more realistic, density-dependent shapes (Fig. 10.7). These prey and predator isoclines are constrained by intraspecific competition (self limitation), assuming a linear functional response*: Shape of curve of prey eaten as prey density increases. Oscillations are no longer neutrally stable! BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 12
13 13. Change in predator efficiency: Decrease in predator efficiency dampens oscillations, decreases predator abundance & increases prey abundance E.g. Fig. 10.7d (i) & (ii). BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 13
14 14. Strong predator self-limitation: Strong intraspecific competition can eliminate predator-prey oscillations completely. E.g. Fig. 10.7d (iii). BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 14
15 15. Functional responses and the Lotka-Volterra predation model: Predator functional responses to prey density also modify the model. Type 3 functional response (sigmoidal): Predators inefficient at low prey density stabilizes interaction (Fig ai), but decrease in efficiency (e.g. interference) increases oscillations (Fig aii). BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 15
16 16. Effect of switching: If a predator switches effectively from prey to prey then its abundance may be independent of prey density (Fig b). BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 16
17 17. Effect of a type 2 functional response or an Allee effect: For type 2 functional responses (decelerating rise to asymptote) the prey isocline is humped (Fig ). At low prey density this can lead to instability and extinction (unlikely because predator handling times have to be very long). But at high prey density this leads to damped oscillations and stability. Allee effect Disproportionately low rate of recruitment at low population density also generates a humped prey isocline. Important in conservation and resource management. BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 17
18 18. Effect of predator efficiency combined with environmental heterogeneity: Efficient predation with an aggregative response in heterogeneous environments can generate stability as in Fig BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 18
19 19. Spatial heterogeneity: Aggregated prey, or prey occurring in crevices or other refuges, show spatial heterogeneity (clumped distributions): E.g. prey mites in Huffaker s orange experiment. The prey isoclines can look like those in Fig which tends to generate stable equilibria quickly. Hence the coexistence of the prey and predator mites. BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 19
20 20. Pseudo-interference: Also generates an aggregation of risk among hosts of parasites because at high parasitoid density, attacked hosts are more likely to have been parasitized already (like Fig 10.7d iii). BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 20
21 21. Aggregation of risk: Aggregative responses of parasitoids to hosts can either be the same at all host densities (Fig a) or, Density dependent (Fig b & c) or, Density independent (Fig d). BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 21
22 21. The CV 2 >1 rule: Such aggregations of risk led Pacala, Hassell and May to generate the CV 2 >1 rule: If the coefficient of variation (standard deviation/ mean) of the risk of being parasitized is greater than 1 then the interaction is more likely to be stable. Especially when aggregated risk is host density independent (as in Fig d). BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 22
23 Prey isocline Predator isocline Figure 10.2: Lotka-Volterra predator-prey model: (a) Prey and (b) predator zero isoclines; (c) cycling, (d) neutral stability through time, and (e) effect of disturbance. BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 23
24 Figure 10.6 (3 rd ed.): Delayed density dependence in (a) hostparasitoid model, (b, c, d) plots of k mortality against log density to show delayed density dependence, and (e) field data. BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 24
25 Figure 10.7: Influence on both (a) predator, and (b) prey, zero isoclines subject to crowding and (c) effects on stability. BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 25
26 Figure 10.12: Influence of a humped prey isocline on stability for (i) efficient predator, and (ii) inefficient predator. BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 26
27 BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation Slide - 27
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