Delayed feedback and multiple attractors in a host–parasitoid system

 Continuous-time, age structured, host–parasitoid models exhibit three types of cyclic dynamics: Lotka–Volterra-like consumer-resource cycles, discrete generation cycles, and “delayed feedback cycles” that occur if the gain to the parasitoid population (defined by the number of new female parasitoid offspring produced per host attacked) increases with the age of the host attacked. The delayed feedback comes about in the following way: an increase in the instantaneous density of searching female parasitoids increases the mortality rate on younger hosts, which reduces the density of future older and more productive hosts, and hence reduces the future per head recruitment rate of searching female parasitoids. Delayed feedback cycles have previously been found in studies that assume a step-function for the gain function. Here, we formulate a general host–parasitoid model with an arbitrary gain function, and show that stable, delayed feedback cycles are a general phenomenon, occurring with a wide range of gain functions, and strongest when the gain is an accelerating function of host age. We show by examples that locally stable, delayed feedback cycles commonly occur with parameter values that also yield a single, locally stable equilibrium, and hence their occurrence depends on initial conditions. A simplified model reveals that the mechanism responsible for the delayed feedback cycles in our host–parasitoid models is similar to that producing cycles and initial-condition-dependent dynamics in a single species model with age-dependent cannibalism. Received: 24 October 1997 / Revised version: 13 June 1998     

Pollen availability,seed production and seed predator clutch size in a tephritid—thistle system

Summary We develop a simple model explaining clutch size behaviour ofOrellia ruficauda on its principle host in North America,Cirsium arvense. Offspring of flies feed solely on thistle seeds and seed production is pollen-limited. Thus, female flies risk reduced offspring fitness when committing large clutches to hosts (female flower heads) occurring in localities where male plants are locally absent. We therefore predict that attacked hosts will contain fewer eggs in such localities, a prediction that is consistent with data obtained in the field: large clutches are never laid in flower heads in low-pollination localities. However, larvae reared from such low-quality hosts are significantly smaller on average and will therefore carry smaller egg loads as adults. Small clutches in poor-quality hosts may thus be an expression of lower per-adult fecundity. Nevertheless, sufficient numbers of large, fecund flies are produced in low-pollination localities to make this last explanation less convincing.     

Models for pest control: Complementary effects of periodic releases of sterile pests and parasitoids

Four host-parasitoid models that incorporate the simultaneous or sequential release during each generation of sterile hosts and parasitoids for control or eradication of host species are presented. The models are based on two modifications of the Nicholson-Bailey model which incorporate density regulation either in the host larvae or via parasitoid oviposition. Parasitization of host larvae and adults forms another comparison. The models indicate that the release of sterile hosts alone is more efficient than release of parasitoids alone in controlling the hosts if population regulation is in the parasitoids; otherwise, the release of parasitoids alone is more efficient. The release of both steriles and parasitoids is much more efficient than the release of either alone for either suppressing or eradicating the hosts. This greater efficiency in combination rather than separately appears to be a special case of a more general principle, which is that two pest control methods will mutually complement each other if their optimal actions in reducing host numbers are at very different host densities. This is the case for sterile releases (optimal at low host densities) and parasitoid inundation (optimal at high host densities).     

Diadegma mollipla parasitizing Plutella xylostella: host instar preference and suitability

Oviposition decisions (i.e., host selection and sex allocation) of female parasitoids are expected to correspond with host quality, as their offspring fitness is dependent on the amount and quality of resources provided by a single host. The host size model assumes that host quality is a linear function of host size, with larger hosts believed to contain a greater quantity of resources, and thus be more profitable than smaller hosts. We tested this assertion in the laboratory on a solitary larval–pupal parasitoid Diadegma mollipla (Holmgren) (Hymenoptera: Ichneumonidae) developing on three instars (second–fourth) of one of its hosts, the diamondback moth, Plutella xylostella (L.) (Lepidoptera: Plutellidae). In a no‐choice test, parasitism levels and sex ratio (i.e., proportion of female progeny) were significantly high in hosts attacked in the second instar followed by third then fourth instars. However, the few parasitoids that completed a generation from the fourth instars did so significantly faster than conspecifics that started development in the other two instars. In direct observations, however, the parasitoids (i) randomly attacked the various host instars, (ii) spent a similar period examining the various host instars with their ovipositors, (iii) subdued all three host instars with about the same effort, and (iv) no statistical differences were observed in the attack rates on the three host instars. In a choice test, the females parasitized significantly more third instars followed by second then fourth instars. However, total parasitism in this experiment was 43% lower compared to parasitism of only second instars in the no‐choice test. No significant differences were detected in progeny sex ratios. In both choice and no‐choice tests, significantly more fourth instars died during the course of the experiments than second instars, while third instars were intermediate. The higher parasitism of third than second instars in the choice test indicates that the females perceived larger hosts as higher quality than smaller hosts, despite their lower suitability for larval development.     

Relic behaviours, coevolution and the retention versus loss of host defences after episodes of avian brood parasitism

Most previous studies of brood parasitism have stressed that host defences, such as egg recognition, are lost in the absence of parasitism. Such losses could result in coevolutionary cycles in which parasites shift away from well-defended hosts only to switch back to them later at a time when these hosts have lost much or all of their defences and the parasite's current hosts have built up effective defences. However, the alternative 'single trajectory' model predicts that parasites rarely switch back to old hosts because ex-hosts retain egg recognition for long periods in the absence of parasitism. If true, egg recognition by the host may be a 'relic behaviour', because in the absence of parasitism its adaptive value is close to neutral. Using artificial nonmimetic eggs, I tested for egg recognition in two populations that are currently unparasitized but that are descended from lineages likely to have been parasitized in the past: the grey catbird, Dumetella carolinensis, on Bermuda and the loggerhead shrike, Lanius ludovicianus, in California. Both of these populations showed long-term retention, ejecting nonmimetic eggs at rates of nearly 100%. Because potential present-day selection pressures, such as conspecific parasitism, do not explain this egg recognition, Bermuda catbirds apparently retain recognition from North American conspecifics that were cowbird hosts before colonizing Bermuda and shrikes retain recognition from Old World congeners that were hosts of cuckoos. Retention is also indicated by passerines in California and the Caribbean that had high rejection rates of nonmimetic eggs before coming into contact with cowbirds. These new data suggest that both the coevolutionary cycles and single trajectory models have importance and that rejection behaviour can have insignificant costs, which is consistent with evolutionary lag explanations for the acceptance of parasitic eggs shown by some cuckoo and many cowbird hosts. Copyright 2001 The Association for the Study of Animal Behaviour.     

Host switching vs. host sharing in overlapping sylvatic Trypanosoma cruzi transmission cycles

ABSTRACT

The principle of competitive exclusion is well established for multiple populations competing for the same resource, and simple models for multistrain infection exhibit it as well when cross-immunity precludes coinfections. However, multiple hosts provide niches for different pathogens to occupy simultaneously. This is the case for the vector-borne parasite Trypanosoma cruzi in overlapping sylvatic transmission cycles in the Americas, where it is enzootic. This study uses cycles in the USA involving two different hosts but the same vector species as a context for the study of the mechanisms behind the communication between the two cycles. Vectors dispersing in search of new hosts may be considered to move between the two cycles (host switching) or, more simply, to divide their time between the two host types (host sharing). Analysis considers host switching as an intermediate case between isolated cycles and intermingled cycles (host sharing) in order to examine the role played by the host-switching rate in permitting coexistence of multiple strains in a single-host population. Results show that although the population dynamics (demographic equilibria) in host-switching models align well with those in the limiting models (host sharing or isolated cycles), infection dynamics differ significantly, in ways that sometimes illuminate the underlying epidemiology (such as differing host susceptibilities to infection) and sometimes reveal model limitations (such as host switching dominating the infection dynamics). Numerical work suggests that the model explains the trace presence of TcI in raccoons but not the more significant co-persistence observed in woodrats.     

The role of epistasis on the evolution of recombination in host-parasite coevolution

Antagonistic coevolution between hosts and parasites is known to affect selection on recombination in hosts. The Red Queen Hypothesis (RQH) posits that genetic shuffling is beneficial for hosts because it quickly creates resistant genotypes. Indeed, a large body of theoretical studies have shown that for many models of the genetic interaction between host and parasite, the coevolutionary dynamics of hosts and parasites generate selection for recombination or sexual reproduction. Here we investigate models in which the effect of the host on the parasite (and vice versa) depend approximately multiplicatively on the number of matched alleles. Contrary to expectation, these models generate a dynamical behavior that strongly selects against recombination/sex. We investigate this atypical behavior analytically and numerically. Specifically we show that two complementary equilibria are responsible for generating strong linkage disequilibria of opposite sign, which in turn causes strong selection against sex. The biological relevance of this finding stems from the fact that these phenomena can also be observed if hosts are attacked by two parasites that affect host fitness independently. Hence the role of the Red Queen Hypothesis in natural host parasite systems where infection by multiple parasites is the rule rather than the exception needs to be reevaluated.     

The population biology of parasite-induced changes in host behavior

The ability of parasites to change the behavior of infected hosts has been documented and reviewed by a number of different authors (Holmes and Bethel, 1972; Moore, 1984a). This review attempts to quantify the population dynamic consequences of this behavior by developing simple mathematical models for the most frequently recorded of such parasite life cycles. Although changes in the behavior of infected hosts do occur for pathogens with direct life cycles, they are most commonly recorded in the intermediate hosts of parasites with complex life cycles. All the changes in host behavior serve to increase rates of transmission of the parasites between hosts. In the simplest case the changes in behavior increase rates of contact between infected and susceptible conspecific hosts, whereas in the more complex cases fairly sophisticated manipulations of the host's behavioral repertory are achieved. Three topics are dealt with in some detail: (1) the behavior of the insect vectors of such diseases as malaria and trypanosomiasis; (2) the intermediate hosts of helminths whose behavior is affected in such a way as to make them more susceptible to predation by the definitive host in the life cycle; and (3) the behavior and fecundity of molluscs infected with asexually reproducing parasitic flatworms. In each case an expression is derived for R0, the basic reproductive rate of the parasite when first introduced into the population. This is used to determine the threshold numbers of definitive and intermediate hosts needed to maintain a population of the pathogen. In all cases, parasite-induced changes in host behavior tend to increase R0 and reduce the threshold number of hosts required to sustain the infection. The population dynamics of the interaction between parasites and their hosts are then explored using phase plane analyses. This suggests that both the parasite and intermediate host populations may show oscillatory patterns of abundance. When the density of the latter is low, parasite-induced changes in host behavior increase this tendency to oscillate. When intermediate host population densities are high, parasite population density is determined principally by interactions between the parasites and their definitive hosts, and changes in the behavior of intermediate hosts are less important in determining parasite density. Analysis of these models also suggests that both asexual reproduction of the parasite within a host and parasite-induced reduction in host fecundity may be stabilizing mechanisms when they occur in the intermediate hosts of parasite species with indirect life cycles.(ABSTRACT TRUNCATED AT 400 WORDS)     

Pathogen-Driven Outbreaks in Forest Defoliators Revisited: Building Models from Experimental Data

Models of outbreaks in forest-defoliating insects are typically built from a priori considerations and tested only with long time series of abundances. We instead present a model built from experimental data on the gypsy moth and its nuclear polyhedrosis virus, which has been extensively tested with epidemic data. These data have identified key details of the gypsy moth-virus interaction that are missing from earlier models, including seasonality in host reproduction, delays between host infection and death, and heterogeneity among hosts in their susceptibility to the virus. Allowing for these details produces models in which annual epidemics are followed by bouts of reproduction among surviving hosts and leads to quite different conclusions than earlier models. First, these models suggest that pathogen-driven outbreaks in forest defoliators occur partly because newly hatched insect larvae have higher average susceptibility than do older larvae. Second, the models show that a combination of seasonality and delays between infection and death can lead to unstable cycles in the absence of a stabilizing mechanism; these cycles, however, are stabilized by the levels of heterogeneity in susceptibility that we have observed in our experimental data. Moreover, our experimental estimates of virus transmission rates and levels of heterogeneity in susceptibility in gypsy moth populations give model dynamics that closely approximate the dynamics of real gypsy moth populations. Although we built our models from data for gypsy moth, our models are, nevertheless, quite general. Our conclusions are therefore likely to be true, not just for other defoliator-pathogen interactions, but for many host-pathogen interactions in which seasonality plays an important role. Our models thus give qualitative insight into the dynamics of host-pathogen interactions, while providing a quantitative interpretation of our gypsy moth-virus data.     

Successful colonization, reproduction, and new generation emergence in live interior hybrid spruce Picea engelmannii×glauca by mountain pine beetle Dendroctonus ponderosae

1 Although mountain pine beetle Dendroctonus ponderosae Hopkins are able to utilize most available Pinus spp. as hosts, successful colonization and reproduction in other hosts within the Pinaceae is rare.
2 We observed successful reproduction of mountain pine beetle and emergence of new generation adults from interior hybrid spruce Picea engelmannii × glauca and compared a number of parameters related to colonization and reproductive success in spruce with nearby lodgepole pine Pinus contorta infested by mountain pine beetle.
3 The results obtained indicate that reduced competition in spruce allowed mountain pine beetle parents that survived the colonization process to produce more offspring per pair than in more heavily-infested nearby pine.
4 We also conducted an experiment in which 20 spruce and 20 lodgepole pines were baited with the aggregation pheromone of mountain pine beetle. Nineteen pines (95%) and eight spruce (40%) were attacked by mountain pine beetle, with eight (40%) and three (15%) mass-attacked, respectively.
5 Successful attacks on nonhost trees during extreme epidemics may be one mechanism by which host shifts and subsequent speciation events have occurred in Dendroctonus spp. bark beetles.     

Population Processes at Multiple Spatial Scales Maintain Diversity and Adaptation in the Linum marginale - Melampsora lini Association

Host-pathogen coevolution is a major driver of species diversity, with an essential role in the generation and maintenance of genetic variation in host resistance and pathogen infectivity. Little is known about how resistance and infectivity are structured across multiple geographic scales and what eco-evolutionary processes drive these patterns. Across southern Australia, the wild flax Linum marginale is frequently attacked by its rust fungus Melampsora lini. Here, we compare the genetic and phenotypic structure of resistance and infectivity among population pairs from two regions where environmental differences associate with specific life histories and mating systems. We find that both host and pathogen populations are genetically distinct between these regions. The region with outcrossing hosts and pathogens that go through asexual cycles followed by sexual reproduction showed greater diversity of resistance and infectivity phenotypes, higher levels of resistance and less clumped within-population spatial distribution of resistance. However, in the region where asexual pathogens infect selfing hosts, pathogens were more infective and better adapted to sympatric hosts. Our findings largely agree with expectations based on the distinctly different host mating systems in the two regions, with a likely advantage for hosts undergoing recombination. For the pathogen in this system, sexual reproduction may primarily be a survival mechanism in the region where it is observed. While it appears to potentially have adverse effects on local adaptation in the short term, it may be necessary for longer-term coevolution with outcrossing hosts.     

Adaptive host preference and the dynamics of host-parasitoid interactions

Models of two independent host populations and a common parasitoid are investigated. The hosts have density-dependent population growth and only interact indirectly by their effects on parasitoid behavior and population dynamics. The parasitoid is assumed to experience a trade-off in its ability to exploit the two hosts. Three alternative types of parasitoid are investigated: (i) fixed generalists whose consumption rates are those that maximize fitness; (ii) "ideal free" parasitoids, which modify their behavior to maximize their rate of finding unparasitized hosts within a generation; and (iii) "evolving" parasitoids, whose capture rates change between generations based on quantitative genetic determination of the relative attack rates on the two hosts. The primary questions addressed are: (1) Do the different types of adaptive processes stabilize or destabilize the population dynamics? (2) Do the adaptive processes tend to equalize or to magnify differences in host densities? The models show that adaptive behavior and evolution frequently destabilize population dynamics and frequently increase the average difference between host densities.     

Developmental variability and stability in continuous-time host-parasitoid models

Insect host-parasitoid systems are often modeled using delay-differential equations, with a fixed development time for the juvenile host and parasitoid stages. We explore here the effects of distributed development on the stability of these systems, for a random parasitism model incorporating an invulnerable host stage, and a negative binomial model that displays generation cycles. A shifted gamma distribution was used to model the distribution of development time for both host and parasitoid stages, using the range of parameter values suggested by a literature survey. For the random parasitism model, the addition of biologically plausible levels of developmental variability could potentially double the area of stable parameter space beyond that generated by the invulnerable host stage. Only variability in host development time was stabilizing in this model. For the negative binomial model, development variability reduced the likelihood of generation cycles, and variability in host and parasitoid was equally stabilizing. One source of stability in these models may be aggregation of risk, because hosts with varying development times have different vulnerabilities. High levels of variability in development time occur in many insects and so could be a common source of stability in host-parasitoid systems.     

Body-size scaling in an SEI model of wildlife diseases

A number of wildlife pathogens are generalist and can affect different host species characterized by a wide range of body sizes. In this work we analyze the role of allometric scaling of host vital and epidemiological rates in a Susceptible-Exposed-Infected (SEI) model. Our analysis shows that the transmission coefficient threshold for the disease to establish in the population scales allometrically (exponent = 0.45) with host size as well as the threshold at which limit cycles occur. In contrast, the threshold of the basic reproduction number for sustained oscillations to occur is independent of the host size and is always greater than 5. In the case of rabies, we show that the oscillation periods predicted by the model match those observed in the field for a wide range of host sizes.The population dynamics of the SEI model is also analyzed in the case of pathogens affecting multiple coexisting hosts with different body sizes. Our analyses show that the basic reproduction number for limit cycles to occur depends on the ratio between host sizes, that the oscillation period in a multihost community is set by the smaller species dynamics, and that intermediate interspecific disease transmission can stabilize the epidemic occurrence in wildlife communities.     

Do yearly temperature cycles reduce species richness? Insights from calanoid copepods

The metabolic theory of ecology (MTE) has explained the taxonomic richness of ectothermic species as an inverse function of habitat mean temperature. Extending this theory, we show that yearly temperature cycles reduce metabolic rates of taxa having short generation times. This reduction is due to Jensen’s inequality, which results from a nonlinear dependency of metabolic rate of organisms on temperature. It leads to a prediction that relatively lower species richness is found in habitats with larger amplitudes of yearly temperature cycles where mean temperatures and other conditions are similar. We show that metabolically driven generation time of a taxon also relates functionally to species richness, and similarly, its yearly cycles reduce richness. We test these hypotheses on marine calanoid copepods with 46,377 records of data collected by scientific cruise surveys in Mediterranean regions, across which the temperature amplitudes vary dramatically. We test both bio-energetic and phenomenological effects of temperature cycles on richness in 86 1° × 1° latitudinal and longitudinal spatial units. The models incorporated the effect of both periodic fluctuations and mean temperature explained 21.6% more variation in the data, with lower AIC, compared to models incorporated only the mean temperature. The study also gives insight into the basis of energetic-equivalence rule in MTE determining richness, which can be governed by generation time of taxon. The results of this study lead to the proposition that amplitude of yearly temperature cycles may contribute to both the longitudinal and the latitudinal differences in species richness and show how the metabolic theory can explain macro-ecological patterns arising from yearly temperature cycles.     

Adaptive Host Preference and the Dynamics of Host–Parasitoid Interactions

Models of two independent host populations and a common parasitoid are investigated. The hosts have density-dependent population growth and only interact indirectly by their effects on parasitoid behavior and population dynamics. The parasitoid is assumed to experience a trade-off in its ability to exploit the two hosts. Three alternative types of parasitoid are investigated: (i) fixed generalists whose consumption rates are those that maximize fitness; (ii) “ideal free” parasitoids, which modify their behavior to maximize their rate of finding unparasitized hosts within a generation; and (iii) “evolving” parasitoids, whose capture rates change between generations based on quantitative genetic determination of the relative attack rates on the two hosts. The primary questions addressed are: (1) Do the different types of adaptive processes stabilize or destabilize the population dynamics? (2) Do the adaptive processes tend to equalize or to magnify differences in host densities? The models show that adaptive behavior and evolution frequently destabilize population dynamics and frequently increase the average difference between host densities.     

Warning Signal Efficacy: Assessing the Effects of Color,Iridescence, and Time of Day in the Field

Warning coloration deters predators from attacking distasteful or toxic prey. Signal features that influence warning color effectiveness are not well understood, and in particular, we know very little about how effective short‐wavelength and iridescent colors are as warning color elements in nature and how warning signal effectiveness changes throughout the day. We tested the effect of these factors on predation risk in nature using specimens of the distasteful pipevine swallowtail butterfly, Battus philenor. B. philenor adults display both iridescent blue and diffusely reflecting orange components in their warning signal. We painted B. philenor wings to create five different model types: all‐black, only‐iridescent‐blue, only‐orange, iridescent‐blue‐and‐orange (intact signal), and matte‐blue‐and‐orange. We placed 25 models in each of 14 replicate field sites for 72 h and checked for attacks three times each day. Model type affected the likelihood of attack; only‐orange models were, the only model attacked significantly less than the all‐black model. Iridescence did not enhance or decrease warning signal effectiveness in our experiment because matte‐blue‐and‐orange models were attacked at the same rate as iridescent‐blue‐and‐orange models. Time of day did not differentially affect model type. Video recordings of attacks revealed that insectivorous birds were responsible. The results of this experiment, when taken with previous work, indicate that the response to blue warning coloration is likely dependent on predator experience and context, but that iridescence per se does not affect warning signals in a natural context.     

Host-pathogen interactions, insect outbreaks, and natural selection for disease resistance

The theory of insect population dynamics has shown that heterogeneity in natural-enemy attack rates is strongly stabilizing. We tested the usefulness of this theory for outbreaking insects, many of which are attacked by infectious pathogens. We measured heterogeneity among gypsy moth larvae in their risk of infection with a nucleopolyhedrovirus, which is effectively heterogeneity in the pathogen's attack rate. Our data show that heterogeneity in infection risk in this insect is so high that it leads to a stable equilibrium in the models, which is inconsistent with the outbreaks seen in North American gypsy moth populations. Our data further suggest that infection risk declines after epidemics, in turn suggesting that the model assumption of constant infection risk is incorrect. We therefore constructed an alternative model in which natural selection drives fluctuations in infection risk, leading to reductions after epidemics because of selection for resistance and increases after epidemics because of a cost of resistance. This model shows cycles even for high heterogeneity, and experiments confirm that infection risk is indeed heritable. The model is very general, and so we argue that natural selection for disease resistance may play a role in many insect outbreaks.     

Single generation cycles and delayed feedback cycles are not separate phenomena

We study a simple model for generation cycles, which are oscillations with a period of one or a few generation times of the species. The model is formulated in terms of a single delay-differential equation for the population density of an adult stage, with recruitment to the adult stage depending on the intensity of competition during the juvenile phase. This model is a simplified version of a group of models proposed by Gurney and Nisbet, who were the first to distinguish between single-generation cycles and delayed-feedback cycles. According to these authors, the two oscillation types are caused by different mechanisms and have periods in different intervals, which are one to two generation times for single-generation cycles and two to four generation times for delayed-feedback cycles. By abolishing the strict coupling between the maturation time and the time delay between competition and its effect on the population dynamics, we find that single-generation cycles and delayed-feedback cycles occur in the same model version, with a gradual transition between the two as the model parameters are varied over a sufficiently large range. Furthermore, cycle periods are not bounded to lie within single octaves. This implies that a clear distinction between different types of generation cycles is not possible. Cycles of all periods and even chaos can be generated by varying the parameters that determine the time during which individuals from different cohorts compete with each other. This suggests that life-cycle features in the juvenile stage and during the transition to the adult stage are important determinants of the dynamics of density limited populations.     

寄主龄期对可疑柄瘤蚜茧蜂寄生及其后代适合度的影响

采用单选试验,观察了可疑柄瘤蚜茧蜂（Tysiphlebus anbiguus）对不同发育时期黑豆蚜的寄生选择及其后代生长发育适合度相关特征,以检验寄主大小与其质量是否存在正相关关系。结果表明,黑豆蚜（Aphis fabae）1～4龄和成蚜均被寄生,但对2龄若蚜的寄生率最高（35．25％）,对成蚜寄生率最低（14．75％）;寄生低龄蚜虫的羽化率显著高于高龄若蚜和成蚜。寄生2龄若蚜的发育历期（8．4d）最短,而寄生1龄若蚜最长（9．3d）;寄生2～4龄蚜虫的后代蜂体型显著大于寄生1龄和成蚜;寄生4龄若蚜的后代中,雌蜂比例（75．74％）显著高于1龄若蚜（62．89％）和成蚜（65．19％）,但与寄生2～3龄若蚜无显著差异。寄主黑豆蚜的质量从高至低依次为2龄〉3龄=4龄〉成蚜〉1龄,因此,对可疑柄瘤蚜茧蜂而言。寄主大小与其质量并非存在正相关性。