HostParasite - Host—ParasntOId Interactions Arthropod...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Host—ParasntOId Interactions Arthropod predator—prey and host~parasitoid interactions are ex- ceptionally well studied for several reasons. These are systems that can often be studied on a relatively small spatial scale. These also are interactions that can be reasonably thought ,of as rep- resenting tightly coupled systems of two species. Finally, these are systems of great economic importance, because often the hosts are significant pests of crops, and the parasitoids may act as control agents. the host that leads to a tight coupling between hosts and para- sitoids; often a parasitoid must lay its eggs in only one species of host, to which it is adapted. The typical dynamics of the host— parasitoid interaction are similar to predator—prey dynamics, as illustrated in Figure 9.1. In this brief chapter, We examine some of the most striking features of host—parasitoid dynamics. Because the interaction is 182 This is the same Nicholson who performed the classic experiment with blowflies that we examined earlier. Discrete time is used because hosts often have one or a small fixed number of generations per year, and parasitoids must time their generations to match their hosts. 9. Host—Parasitoid Interactions 1 000 800 60.0 - 4:. C) O Papulation density 200 Generations FIGURE 9.1. Dynamics of the host parasitoid interaction between a wasp, Heterospilus pros— pidis, and its host, the bean weevil, Callosobruchus chinensis (data are from Utida 1957). —o—-- Parasitoid; ----0— Host so similar to the predator—prey interaction, an extensive treatment is not needed, and only some of the differences between the two interactions are stressed. It is important to emphasize that the host—parasitoid interaction is not rare —- parasitoids represent about 8.5% of described insect species, and estimates of the true fraction of insects that are parasitoids run as high as 25% (Godfray, 1994). 9.1 Nicholson—Bailey model Once again, our goal is to determine what allows host and par—' asitoid to persist. The starting point for our discussion is a basic model introduced to ecology in a classic paper by Nicholson and Bailey (1935). Many models of host—parasitoid interactions take this model and its modifications as their starting point. i We begin our analysis by looking at a general model for a host— parasitoid system in discrete time. Let N, be the number of hosts at time t and P, be the number of parasitoids at time t. We assume that, the host population grows exponentially (geOmetrically) in 9.1 NicholsOn—Bailey model 1 83 M the absence of the parasitoid at a per capita rate A per year. Let f (M,P,) be the probability that a host egg laid in year t, with host pOpulation size N, and parasitoid population size Pt, escapes being parasitized. The number of hosts next year is then given by the product of the per capita growth rate of the population, the number of hosts this year, and the probability of escaping parasitism. The model basically assumes that we count given by the product of the number of parasitoids emerging from “the eggstage'”theh°5‘5?°‘herw'5“ . 0 would appear in the equation for the each parasrtlzed host, the number of hosts this year, and the prob- parasitoids. ability of a host being parasitized. The model we begin with is thus If the probability of not being parasitized is f, what is the probability of being [VH1 == AN‘fUVh Pt) (9,1) parasitized? PH] = CM“. _f(1V:,Pt)]. distribution, which is f .___ e—aP, , (9.3) where a is a parameter (with units of 1 over parasitoid num- bers) that measures the efficiency of the parasitoid. With this assumption our model becomes the classical Nicholson—Bailey model 184 First find P from the equation for NH and then find N from the equation for PM . is there another, trivial equilibrium? Part of the reason that the stability analysis is more difficult here is that the condition that a matrix have both eigenvalues less than one (in magnitude) is more complex than the condition that both eigenvalues have a negative real part. A second reason for the complexity of this analysis is simply the presence of exponentials in the Nicholson-Bailey model. 9. Host—Parasitoid Interactions 10000 _ 1000 100 {’3 8 E 10 :3 C :9 1 3 3 0.1 (U o. 0.01 10 100 1000 104 Host numbers FIGURE 9.2. Dynamics ofthe Nicholson—Bailey model with A = 11.61 = 0.001,and c = 3. Note the log-log scale, and that when the simulation was stopped the parasitoid population size had dropped approximately seven orders of magnitude. The dynamicsare clearly unstable. We first find the equilibria of the model by setting N = N, = NH; and P = P, = PM. We obtain the equilibrium _ ' A In A N ‘ m (96) A P -= 131—. (9.7) a We can immediately see that if this equilibrium is to make bio- logical sense the growth rate of the host in the absence of the predator, A, must be greater than 1. Also, as the efficiency of the parasitoid goes up —- as or increases — the equilibrium level of both Species goes down. But what is the biological implication of the equilibrium of this model? Is the equilibrium stable? We could then proceed with a stability analysis of this model. However, the algebra, is, shall we say, formidable. Thus, rather than go through the steps in the analytical techniques in this chap- ter, we instead just present the results of stability analyses, and illustrate the behavior of the models with numerical solutions. The results of the stability analysis (which we have omitted) of the Nicholson—Bailey model are unequivocal: the nontrivial 4-._._.._._. __. .. ... 9.2 Simple stabilizing features 185 EN ls it really enough to present results for one . . . . . . . ? illustrated in Figure 9.2, not only 18 the equ111br1um unstable but semfpa'ame‘e'va'm‘ We are now left with a quandary. Experimental host—parasitoid Before reading on, think of stabilizing systems, and natural systems such as the interaction between fea‘"’°‘°fa “°“”p‘"a"‘°'d mm” that could be included. red scale (Aon idiella dammit) and its parasitoid Apbytis meli- nus, show that long-term coexistence of host and parasitoid is possible. Thus, important stabilizing biological features must be missing from our simple model. 9.2 Simple stabilizing features There have been numerous suggestions of potential stabilizing mechanisms for host—parasitoid systems. We begin by listing a few of the mechanisms that might stabilize the host—parasitoid interaction. 0 Density dependence in the host species (Beddington et al., 1975). o Interference among parasitoids (Beddington et al., 1978). If female parasitoids avoid each other, or avoid laying eggs where others have laid eggs, then the rate of parasitism rises more slowly with the number of parasitoids than assumed in the Nicholson—Bailey model. Can you think of other ways to include density dependence? 1.86 9. Host—ParaSEtoid Interactions 1 0000 1 000 Parasitoid numbers 100 1 00 1000 Host numbers FIGURE 9.3. Dynamics ofthe Nicholson—Bailey model modified to include density dependence, with A = 1.1, a = 0.001, c: = 3,,and K = 1000. Here host and parasitoid coexist in a stable cycle. NM = lMeKI—Nr/KFaPJ (98) 10,.1 = cN,[1 —- (“3]. (9.9) The stability of this model can again be determined analytically, but we do not do so here. We note that with this modification there is a wide range of reasonable parameters for which the model allows the host and parasitoid to persist, as shown in Fig- ures 9.3 and 9.4. Depending on the parameters, the persistence can either be cyclic (Figure 9.3) or approach a stable equilibrium (Figure 9.4). Thus, the model can lead to the cyclic coexistence illustrated for the laboratory population in Figure 9.1. From the figures one can see that the parasitoid still does have an effect on the density of the host — the equilibrium (or the av— era ge population level for the cyclic persistence) is below the population level the host would reach in the absence of the From your experience with predator-er parasitoid. What might 5°” destabilizing Similar numerical analyses show that the other two stabilizing features we have listed also can produce stable equilibria. 9.3 What stabilizing features operate in nature? 1000 92 (D .0 E 2 E 100 .9. '5 e (U 0. 10 . 100 , 1000 Host numbers FIGURE 9.4. Dynamics ofthe Nicholson—Bailey model modified to include density dependence. with A = 1.1, a = 0.001.c = 3, andK == 750. Here host and parasitoid coexist at a stable equilibrium. 9.3 What stabilizing features Operate in nature? Models can be used to determine potential stabilizing influences One of the best long-term studies attempting to understand what allows host and parasitoid to persist at a stable equilibrium has been that of red scale (Aom'diella aurantz’z‘) and its parasitoid Apbytis melz'nus, conducted by Murdoch and his colleagues (sum— marized in Murdoch, 1994). A large number of potential stabilizing mechanisms have been proposed, including many beyond what we have discussed here, but careful experimental examination of all these mechanisms has failed to show that any single one of them is in fact responsible for producing the apparently stable equilibrium observed in the field. 188 9. Host—Parasitoid Interactions W regulating, or regulated by the parasitoid? Justify your an- swer, and discuss how you would answer this question for a field system. 2. Host—parasitoid systems are used to look at biological con- trol, where a parasitoid is introduced to reduce the host population of a pest on a crop. How would the models developed here help to choose a parasitoid to use for bi- ological control, and what qualities should be looked for? What are some potential pitfalls? - a 3. By numerically solving the model with density dependence, equations (9.8) and (9.9), for the values of a, c, and A used in the chapter, but varying K, determine the effect of density dependence on stability. ' Suggestions for further reading A summary Of host—parasitoid models is contained in Hassell’s 1978 book The Dynamics of A n‘bropod Predator—Prey Systems. A recent, extremely comprehenswe revrew of parasrtord biology IS Applications of Nonlinear Dtfierence Equations to Population Biology 79 Host Infected host Adult female Parasitoid Figure 3.2 Schematic representation of a ‘ host. Infected hosts die, giving rise to parasitoid host-parasitoid system. The adult female parasitoid progeny. Uninfected hosts may develop into adults deposits eggs on or in either larvae or pupae of the and give rise to the next generation of hosts. PM = number of hosts parasitized in previous generation X fecundity of parasitoids (c). Noting that 1 - f is the fraction of hosts that are parasitized, we obtain NM =~i AN.f(N., R). (140) PM = cN,[1 — f(N., 11)]. (14b) TheSe equations outline a general framework for host—parasitoid models. To proceed further it is necessary to specify the term f(N,, P.) and how it depends on the two. populations. In the next section, we examine one particular form suggested. by Nicholson and Bailey (1935). ...
View Full Document

This note was uploaded on 02/09/2011 for the course EEP 115 taught by Professor Waynem.getz during the Fall '10 term at University of California, Berkeley.

Page1 / 9

HostParasite - Host—ParasntOId Interactions Arthropod...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online