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Definitions & Data Collection

Experimental Designs For Life Tables

Kinds of Data in Life Tables

Natural Enemies Other Than Parasitoids

Use For Biological Control Systems


Assessing Quantitative Impact of Natural Enemies

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Ecological Roles For Natural Enemies





          The subject of life tables and their value in evaluation of the role of natural enemies in biological control has been recently discussed by Bellows & van Driesche (1999). These authors pointed out that several approaches exist for evaluating the impact of natural enemies in biological systems. One method is the construction and analysis of life tables. Other approaches include manipulative experiments and construction of system or simulation models. A thorough examination of a particular system may require more than one approach to fully address questions regarding interactions among the species. After almost 30 years of intensive life table investigation, however, it is now clear that the usefulness of such tables is limited, and the construction of thorough tables requires an enormous amount of cost. Numerous assumptions need to be made during the acquisition of data, so that life table studies are still suited primarily to academic pursuits. Funding for biological control projects being generally limited, rather precludes the diversion of funds to construct life tables. Unfortunate as it may be, it is nevertheless a reality that is not apt to change in the near future. There are, however, possibilities in the construction of life tables that do not include all mortality in the population, but which can show valuable trends and give clews to future lucrative areas of research.

          Life table analysis strives to evaluate natural enemies to provide answers to two basic questions: (1) the quantitative impact of natural enemies. Net reproductive rates of pest populations (Ro) must be reduced to below unity for a population to decrease. Life table analysis permits assessment of the degree to which particular natural enemies contribute toward reaching this goal. (2) the ecological role of natural enemies, and life table analysis in this context is used to determine the degree to which natural enemies contribute to stabilizing pest populations (Bellows & Van Driesche 1999). Construction of life tables for the evaluation of natural enemies requires accurate estimates of numbers entering stages and numbers dying within stages due to specific causes. Methods to obtain such estimates include stage-frequency analysis, recruitment, growth rate analysis and death rate analysis. These approaches vary in both the types of data required for their use and in the types of information they can provide. Measurement of recruitment is the most direct method for obtaining the data required for life table construction. Regardless of the data collection procedures utilized, sampling programs must avoid potential biases caused by behavioral changes of parasitized hosts and by host patchiness.

Several measures for expressing mortality caused by natural enemies may be contained in life tables. Principal among these are apparent mortality, real mortality and marginal death rate. The relative contributions of different natural enemies in reducing population growth may be evaluated by considering their impact on the net reproductive rate of the host population. Analyses of life tables for evaluating the ecological role of natural enemies have focused on the issue of natural enemy contributions to population stability. Current methods are capable of detecting spatial density dependence, but do not provide statistically sound tests for temporal density-dependence and related, potentially stabilizing, effects of natural enemies.

One approach for the evaluation of natural enemies is the combination of life table analysis and manipulation of host-natural enemy populations. Studies which construct life tables for populations both with and without the natural enemy can provide exceptional opportunities for defining the quantitative level of natural enemy impact in a system. In addition such studies allow questions concerning ecological roles to be addressed in a comparative way, avoiding many of the statistical difficulties which frustrate the detection of density dependence and regulation in studies of single populations. In a broad sense, the use of life tables in the evaluation of natural enemies is part of the iterative process of the scientific method of hypothesis development, data collection, analysis and use of analytical results to pose further, more developed hypotheses. Viewed in the larger context of the scientific method, life table analysis can be used, either alone or in combination with such other forms of natural enemy evaluation as experimental manipulation, to address fundamental questions of population dynamics and regulation as well as practical problems of natural enemy utilization.

Bellows & van Driesche (1999) discussed natural enemies of all types, but much of the detail is presented with reference to insect parasitoids. The following discussion is divided into five sections: (1) type of life tables and data necessary for their construction; (2) measuring the quantitative impact of natural enemies on their target populations (how much mortality is caused by natural enemies?); (3) how may life tables be employed to assess the ecological role of natural enemies (what type of impact is the natural enemy having on the dynamics of the system, e.g., stabilizing, destabilizing, neutral); (5) a general framework for the experimental use of life tables in the study of host-natural enemy systems is proposed and (6) how the topics developed in this division should be applied to pathogens, predators and beneficial herbivores.

Definitions and Data Collection

Types of Life Tables.--Life tables, first applied to the study of animal populations by Deevey (1947), are organized presentations of numbers of individuals surviving to fixed points in the life cycle together with their reproductive output at those points. Mortality usually is assigned to specific causes. Such information can be organized by either age or stage, but age of individual insects rarely is known with precision in field populations, whereas developmental stages can usually be determined. Therefore this information for arthropods most often is organized by stage, producing stage-specific rather than age-specific life tables. Inspection of such tables allows determination of stage survival rates and comparisons of the degree of mortality contributed by agents acting at differing points in the life cycle or in different populations.

There are principally two kinds of life tables. In the first data are collected which present the fate of a real group or cohort, typically a generation of individuals, whose numbers and mortalities are determined over the course of time for each of a series of stages; this method has been referred to as a horizontal life table. The second kind, more applicable to continuously breeding populations than those breeding in discrete generations, is to examine the age structure of a population and infer from it the mortalities occurring in each stage. Such an approach requires assumptions that the population has reached a stable age distribution, and mortality factors acting on the population are constant. Theoretically age distribution may be stable if the population is either expanding or declining exponentially or remaining at an unchanging density. In practical terms, life tables of this type reflect only the type and magnitude of mortality acting in a short time period immediately preceding the sampling date. As such, one life table will present an incomplete picture of the total pattern of mortality across the whole season, which may undergo major changes if specific factors act more strongly at some times than others. Life tables developed in this way are referred to as vertical life tables. Southwood (1978) provides a description of the terminology and conventional organization of both types of life tables. Both types of construction have application in the evaluation of natural enemies in insect life tables. Horizontal construction is most typical for insects breeding in discrete generations. Both horizontal and vertical construction are applicable for continuously-breeding populations.

The purpose of constructing life tables for evaluating the impact of natural enemies is to obtain quantitative estimates of the mortality caused by each. These estimates are typically measured as rates, the per capita number of individuals dying from a particular cause. Caution must be employed to distinguish between sequentially-acting and contemporaneously-acting factors. When collecting data, the sampling program must permit factors which act contemporaneously to be distinguished. Subsequently, suitable analytical procedures may be employed to calculate correctly the mortality caused by each. These matters are discussed more fully as follows:

Kinds of Data in Life Tables

Initially life tables require estimates of numbers entering successive stages in a life history. These may be obtained in two basically different ways. The first way is to measure the density of each stage several times during the generation or study, providing stage-frequency data. These data may then be analyzed by a variety of techniques to provide estimates of numbers entering successive stages (Southwood 1978, McDonald et al. 1989). The data do not, however, provide information on the causes of death in the separate stages. Assignment of causes of death must come from additional information collected during the study, such as dissections to determine parasitism or disease incidence, or by exclusion experiments.

An alternative method for obtaining estimates of the numbers entering successive stages is to measure the recruitment to each stage of interest (Van Driesche & Bellows 1988, Bellows et al. 1989a). This approach provides direct assessment of the processes which contribute to stage densities, and thus permits intermediate construction of the life table without recourse to stage-frequency analysis (Bellows & Van Driesche 1999). The recruitment approach is particularly important because methods of stage-frequency analysis for two-species coupled systems (e.g., host-parasitoid systems) have yet to be developed.

The objective of life table construction usually is to assess the mortality rate assignable to a particular agent. The way in which the data are collected regarding the action of natural enemies can affect the accuracy of the estimates. Losses from parasitism must be assessed at the time of attack, in the host life stage in which the attack occurs. Attempts to score parasitism in a subsequent stage which is not the stage attacked but is the stage from which the parasitoid emerges will lead to incorrect estimates because losses potentially will have been obscured by subsequent mortality from other factors. Additionally scoring parasitism at emergence is further flawed because mortality levels are incorrectly associated with the host density in the more mature stage, rather than with the density of the earlier stage which was actually attacked.

Mortality rates can, in some circumstances, be estimated in the absence of stage density information without the formal construction of a life table. Gould et al (1990a) and Elkinton et al (1990a) have described an approach where groups of individuals are collected at frequent intervals (but without density information), and these individuals are then held at field conditions and their death rates during specific intervals observed. The cause of death of each individual dying during the interval is recorded, and by a mathematical process the original mortality rates assignable to each cause are calculated. The process is repeated for samples collected throughout the season, and the interval-specific mortality rates may then be used to calculate the total mortality assignable to each cause during the study. When density information also is available, this approach is applicable to most mortality factors. In cases where density information is not available, the method is applicable to many, but not all, factors (Elkinton et al. 1990a).

Some mortality due to natural enemies (e.g., host-feeding) is not readily quantifiable using the approaches discussed above. For these factors, experimental methods may be employed to provide rate estimates. This is usually accomplished by measuring, either in the laboratory or the field, the frequency of occurrence of these factors relative to some other, more readily quantifiable, event such as parasitism. Once this relative frequency is known, extrapolation from the frequency of the observed event (e.g., parasitism) to the frequency of the unobserved event is possible (Van Driesche et al. 1987).

Use For Biological Control Systems

In the construction of life tables for assessment of the magnitude or role of mortality from natural enemies, three considerations of importance are (1) accurate determination of total numbers entering successive stages and those dying from natural enemies and from all other sources of mortality, (2) assessment of all additional natural enemy caused mortality other than parasitism or predation, as, e.g., host-feeding by adult parasitoids, and (3) correct focusing of the sampling regimen in relation to the spatial and temporal scale of host distribution and natural enemy attack.

Determining Total Numbers Entering Stages.--Life table construction requires that estimates be obtained for numbers entering successive stages. More detail is required, however, to provide an evaluation for specific natural enemies. Estimates must be obtained for the numbers dying due to specific causes in each stage. These causes might be specific natural enemies, or for general action of groups of natural enemies (e.g., parasitism) (Carey 1988). Several approaches to obtaining these estimates are available.

Stage-frequency Analysis.--Usually methods for quantifying numbers entering a stage have made use of stage-frequency data, and a variety of techniques have been developed for treating such data to extract estimates of numbers entering stages (Southwood 1978, McDonald et al. 1989). These methods are not immediately applicable for use in quantifying processes in joint host-parasitoid or other natural enemy systems (Bellows et al. 1989a,b) but must be modified to permit analysis of the multispecies system.

An exception to this case is where the natural histories of the species under study cause all members of the generation to be present in a single stage at a single moment of time, for example due to diapause at the end of the stage, and in these cases a single sample at that time may be an accurate estimate of total losses to parasitism provided significant losses have not occurred due to mortality from other factors. However, the more usual case is for recruitment, molting and mortality to overlap broadly. In such cases no single sample provides an accurate estimate of total generational losses to parasitism (Simmonds 1948, Miller 1954, Van Driesche 1983). Several approaches have attempted to rectify the biases inherent in sample percentage parasitism, and recommendations have included scoring parasitism after parasitoid oviposition in the host population is complete (Miller 1954), mathematical formulae for adding successive levels of parasitism (Smith 1964), and estimating parasitism from pooled samples of larvae in instars too old for parasitoid attack and too young for parasitoid emergence (Hill 1988). None of these approaches provides an accurate estimate for the numbers dying due to a specific natural enemy for populations where recruitment, molting and mortality overlap (Van Driesche 1983).

Methods developed for determining numbers entering a stage of one species (Southwood 1978, McDonald et al 1989) may be adapted to the problem of estimating total entries simultaneously for two species, the host and the parasitoid (Bellows et al. 1989a,b). The graphical technique of Southwood & Jepson (1962), e.g., may be used with certain modifications. Because the accuracy of this technique is strongly affected by mortality, and because parasitism is a significant source of mortality, the application of the technique is limited. Bellows et al. (1989b) show seven variants of the method applicable to different life histories and sampling requirements. The method appears to be suitable primarily for cases where independent estimates of host recruitment are available or where total mortality in the system is less than 20%, although specific cases discussed by Bellows et al. (1989b) permit its application in other situations. A modification of Richards & Waloff's (1954) second method may be used to estimate mortality for a stage where parasitism is the source of mortality (Van Driesche et al. 1989). Further work in extending single-species analytical techniques to the case of two interacting species will probably add to the methods available for analyzing systems in this manner. These modifications appear to be applicable to both populations breeding discretely and continuously.

Recruitment.--An important alternative to the stage-frequency approach is to measure directly the numbers recruited into each stage (Birley 1977, Van Driesche & Bellows 1988, Van Driesche 1988a,b; Lopez & Van Driesche 1989). In this case the total numbers entering the stage are found by adding together recruitment for all time periods during the study or generation. Total numbers dying in each stage from parasitism also must be estimated in some manner. For parasitism this may be achieved by direct measurement of recruited individuals into the "parasitized host" category (Van Driesche & Bellows 1988, Van Driesche 1988a,b, Lopez & Van Driesche 1989). Total parasitoid recruitment divided by total host recruitment then gives the proportion of hosts in the generation killed by the parasitoid. When applied to systems with discrete generations, this approach provides estimates of mortality per generation. When applied to systems with overlapping generations, this approach provides estimates of total mortality during the course of the study.

If recruitment cannot be directly measured for the stages of interest, it may be estimated from data on recruitment to a previous stage together with density estimates for the stage of interest (Bellows & Birley 1981, Bellows et al. 1982). Van Driesche et al (1990) review in greater detail the subject of recruitment.

Growth Rates.--For continuously breeding populations, methods additional to those just discussed may be applied. These have as a unifying theme the use of population growth rates as predictors of population increase between samples, with the difference between observed and expected population sizes being an estimate of the numbers dying between sampling times. They differ in the method used for calculating the growth rates.

One approach by Hughes (1962, 1963) for such continuously breeding insect species as the cabbage aphid, Brevicoryne brassicae (L.), estimates the growth rate from the age-class distribution of a population in the field. An assumption of the method is that a stable age distribution, required for the estimation of the growth rate parameter rm has been attained when the population is studied. Carter et al. (1978) criticized the validity of this assumption and stated that instar distribution in the field should not be used to calculate rm.

Caged cohorts of the pea aphid, Acrthosiphon pisum (Harris) were used by Hutchinson & Hogg (1984, 1985) to determine survival and fertility schedules and from these estimated the population growth rate rm. Use of this estimate for comparison to field population growth rates still involves the assumption that the field population has reached a stable age-class structure. The difference between observed densities and those projected from the estimated population growth rates represent the aggregate effects of all causes of reduced reproduction, including mortality and reduced fertility of diseased or parasitized individuals. Quantifying the effects of separate factors is not possible in this method.

An alternative approach which avoids the general limitations of the other methods is to measure directly in the field the per capita reproduction (e.g., recruitment) of adult females chosen randomly from the population over a short interval (Lopez & Van Driesche 1989) and derive population rates of increase from these data. Such estimates of recruitment, together with density estimates of adult females, allow projections of population growth for comparison to actual population levels on subsequent sample dates. This approach has the advantage of not making any assumptions concerning age structure and does not compound the effects of mortality and reduced fertility of parasitized and diseased individuals.

Death Rates.--The quantification of mortality rates may be estimated without first constructing the life table (Gould et al. 1989a). The method consists of scoring the death rates of individuals in the population at intervals throughout the study and analyzing the observed rates to provide estimates of the independent, or marginal, mortality rates assignable to each cause (Royama 1981a). This is accomplished by collecting samples of the stages of interest at frequent intervals and rearing the collected individuals under field conditions. These individuals are reared only until the next sampling date and, during the intervening period, the numbers of individuals in the sample dying from specific causes are recorded. The proportions of individuals dying are used to calculate the marginal mortality rates for each cause or factor using the equations given by Gould et al. (1990a) and Elkinton et al. (1990). The aggregate losses in the population to a specific factor are calculated from the losses in each sampling interval during the study.

This method may be applied to a population provided that all hosts have entered the susceptible stage before the first sample (i.e., there is no recruitment to the population during the study). It has the particular advantage that population density data are not required to obtain estimates of mortality rates. The method is capable of providing estimated rates for factors which act contemporaneously. The method does not, however, provide the traditional stage-specific estimates of loss due to a particular factor if a factor can affect more than one developmental stage, because all stages are treated together during the study. The method does provide interval-specific loss rates, and calculates aggregate loss rates from these rather than from stage-specific loss rates. It is applicable to many, but not all, types of natural enemy-host interactions (Elkinton et al. 1990).

Method Comparisons.--Measuring directly the recruitment in both hosts and parasitoid populations is preferable for most situations (Van Driesche & Bellows 1988). It has the advantages of quantifying the events of interest (e.g., parasitism), avoids compounding sequential and contemporaneous factors, and does not require complicated analytical techniques to construct the life table. It is applicable to both discrete-breeding and continuously-breeding populations.

If recruitment measurement is not possible, stage-frequency analysis provides a potential solution for obtaining estimates of numbers entering stages. A suitable stage-frequency analysis must be selected to extract estimates of numbers entering stages from the stage frequency data. Although several techniques are available for use with single-species populations, few have been extended to incorporate the special considerations necessary for application to multispecies, host-parasitoid systems (Bellows et al. 1989a,b, Van Driesche et al. 1989).

Two other approaches, growth rate and death rate analysis, do not estimate numbers entering the stages but r4ather estimate numbers or proportions dying. Growth rate analysis may be applied specifically to continuously breeding populations and provides a measure of total mortality during specific time periods. Separating this aggregate measure into component rates for specific factors requires additional information. Death rate analysis provides a method for estimating mortality rates for specific time periods without the need for data on stage density and allows the contributions of contemporaneous factors to be quantified separately.

Additional Parasitoid-Caused Mortality.--Host deaths are not always obviously attributable to a natural enemy. This is particularly the case with insect parasitoids. Such losses may be difficult to quantify directly in field populations. They may resemble predation in that mortalities of these types usually result in missing individuals that leave no traces or artifact such as empty leafmines. Such mortality is typically assigned to predation or another category by default. Levels of these mortalities may not be trivial and they may equal or exceed losses attributed to demonstrable parasitism (DeBach 1943, Alexandrakis & Neuenschwander 1980). They may be critical in explaining biological control successes in which observed levels of parasitism are low (Neuenschwander et al. 1986).

Host Feeding.--Host feeding has been recorded in over 20 families of Hymenoptera (Jervis & Kidd 1986) and is nearly ubiquitous in such important genera as Tetrastichus and Aphytis as was previously discussed (Bartlett 1964). Hosts killed in this manner may or may not have previously received an oviposition. The role of host feeding in field populations has received little study because the process usually does not leave easily identifiable remains. Field levels of host feeding of Sympiesis marylandensis Girault could be noted in life tables of Phyllonorycter crataegella (Clemens) as a distinct mortality factor because leafmines preserved recognizable cadavers (Van Driesche & Taub 1983). DeBach (1943) used field exclusion techniques to infer the level of mortality due to host feeding on the black scale, Saissetia oleae (Bern), by the parasitoid Metaphycus helvolus (Compere), and concluded that of the 70-97% mortality typically caused by this parasitoid, 45-77% was due to host feeding rather than parasitism. In a field study of Aspidiotus nerii Bouché, host feeding by Aphytis chilensis Howard was found to contribute half of all host mortality based on field counts of dead and parasitized scales (Alexandrakis & Neuenschwander 1980). For mobile hosts where cadavers neither adhere to plant surfaces nor are retained in galls or leafmines, individuals killed by host feeding disappear and cannot be scored directly. In such cases laboratory data may be used to estimate losses from parasitism/host feeding ratios and, together with levels of field parasitism, to estimate host feeding losses (Legner 1979, Chua & Dyck 1982, Van Driesche et al. 1987). Use of laboratory data must take into account such complexities as selective host feeding on hosts of ages different from those usually parasitized (Chua & Dyck 1982), host feeding in habitat zones not suitable for oviposition (Legner 1977 ), or changing host feeding/parasitism ratios at varying host densities (Collins et al. 1981).

Mortality From Oviposition and Envenomization.--Piercing with the ovipositor may also cause hosts to die from mechanical trauma. This process is distinct from host feeding, and younger hosts may suffer this mortality more than older hosts (Rahman 1970, Neuenschwander & Madojemu 1986, Hammond et al. 1987, Neuenschwander & Sullivan 1987, Van Driesche et al. 1987). Deaths unrelated to parasitism also occur in species which paralyze their hosts, where host death occurs in paralyzed hosts in which no oviposition takes place (e.g., S. marylandensis). (Van Driesche & Taub 1983).

Susceptibility to Other Factors.--Parasitism may make hosts more susceptible to predation (Godwin & O'Dell 1981, Jones 1987) or disease (Godwin & Shields 1984). Such events, occurring after parasitoid attack, do not change actual parasitoid-caused losses. Such factors may, however, obscure the actual rate of parasitoid attack, with deaths of parasitized hosts later eaten by predators being assigned in life tables to secondary agents of mortality rather than to parasitism. These deaths can be assigned correctly to the original cause (parasitism) by careful design of the sampling scheme, particularly measuring recruitment, as discussed earlier. A more complicated situation arises in evaluating natural enemies of plants, as death may result from several factors acting together. In some cases, the presence of one factor can enhance the detrimental effect of another (Huffaker 1953, Andres & Goeden 1971, Harris 1974). One approach to quantifying the relative contributions and interactions of these multiple factors is to use field experimental plots with different combinations of natural enemies (McEvoy 1990a,b).

The presence of parasitoids in systems can lead to healthy individuals experiencing greater mortality from other factors. For example, Ruth et al. (1975) noted that when greenbugs, Schizaphis graminum (Rondani), were exposed to the braconid Lysiphelebus testaceipes (Cresson), 41.0-62.0% of the aphids left their feeding sites, often falling to the soil. Such aphids were more likely to die due to high soil temperature before reestablishing themselves on plants than undisturbed aphids. Pea aphids also leave their host plants when disturbed by parasitoids (Tamaki et al. 1970).

In addition to effects on individual hosts, the presence of parasitoids may cause changes at population levels in other mortality factors. For example, introduction of exotic parasitoids suppressed winter moth, Operophtera brumata (L.), in British Columbia (Embree & Otvos 1984), but apparently did so by making ground inhabiting pupal predators more effective (Roland 1988).

While the just mentioned types of losses are properly assigned in a life table to the actual cause of death, it is important to be aware of any enhancement in levels of mortality caused by the presence of a natural enemy. This enhancement may be significant and must be considered when evaluating the overall impact of a natural enemy in a system

Missing Natality.--Host population growth may be limited by parasitoids suppressing natality through several mechanisms, including sterilization, reduced daily fertility or reduced longevity. Some euphorine braconids sterilize host adults shortly after parasitoid attack (Smith 1952, Loan & Holdaway 1961, Loan & Lloyd 1974). For example, Microctonus aethiopoides Loan attacks and sterilizes reproductively mature female alfalfa weevils (Loan & Holdaway 1961, Drea 1968), causing a rapid degeneration of already developed eggs. This results in a 50% loss in total population natality (Van Driesche & Gyrisco 1979). Parasitism of Nezara viridula (L.) by the tachinid Trichopoda pennipes (F.) reduces lifetime but not daily fecundity by 74% (Harris & Todd 1982) by reducing adult life span. Dipteran parasitism (e.g., the sarcophagid Blaesoxipha hunteri (Houg)) of the grasshopper Melanoplus sanguinipes (F.) reduced both the proportion of females producing egg pods and the number of pods per laying, producing an overall reduction in natality of 76% (Rees 1986). The myrmecolacid strepsipteran Stichotrema dallatorreanum Hofeneder reduced numbers of mature eggs in field-collect adults of the tettigoniid Segestes decoratus Redtenbacher in Papua, New Guinea by 67% (Young 1987). Parasitism of the sowthistle aphid Hyperomyzus lacticae (L.) by the aphidiid Aphidius sonchi Marshall reduced total fertility by a variable amount depending upon the age of the host when parasitized. Aphids parasitized in the third, fourth or adult stages suffered 92.4%, 85.5% and 77.8% loss of lifetime reproductive capacity (Liu Shu-Shen & Hughes 1984). Similar relationships have been reported for pea aphid when parasitized by Aphidius smithi Sharma and Subba Rao (Campbell & Mackauer 1975) and for green peach aphid, Myzus persicae (Sulzer), when parasitized by Ephedrus cerasicola Stary (Hagvar & Hofsvang 1986). Such effects appear to derive mainly from reduced adult longevity, but may also involve a reduced daily rate of progeny production prior to adult death. Polaszek (1986) showed that parasitized aphids experienced reductions in embryo number and length within three days after parasitoid attack. When life tables are constructed for such continuously breeding species as aphids, lost fecundity may be listed as a type of mortality (Hutchinson & Hogg 1985).

Sample Design.--The sampling design used to score mortality caused by a natural enemy must ensure adequate and unbiased sampling of both parasitized and unparasitized individuals. Sampling schemes also must use spatial and temporal scales appropriate to the species studied.

Behavioral Biases.--Unparasitized hosts may behave differently than parasitized hosts in ways which render them ore or less vulnerable to detection. Healthy individuals may also occupy different habitats than when parasitized. Many of these behaviors result from differences in mobility between parasitized and healthy individuals, and these differences are more likely to affect relative rather than absolute sampling regimes.

Parasitized and healthy individuals may respond differently to traps. Yano et al. (1985) reported that levels of parasitism in the leafhopper Nephotettis cincticeps Uhler were distinctly higher (13% vs. 3%) in individuals taken in sweep nets than in those collected at the same date and location in light traps because parasitism damaged thoracic muscles and weakened the insect's flight ability. Wylie (1981) reported that levels of parasitism of flea beetles, Phyllotreta striolata (F.) and P. cruciferae (Goege), by the euphorine braconid Microctonus vittatae Muesebeck were lower in beetles collected in traps baited with allyl isothiocyanate than in beetles collected with a vacuum suction device, but only when beetles were reproductively active. Parasitized beetles are sterilized and reacted like nonreproducing beetles, which are less attracted to host plant odors.

Parasitism also may influence movement of hosts between habitats. The potato aphid, Macrosiphum euphorbiae (Thomas) when parasitized by diapause-bound Aphidius nigripes Ashmead leaves its habitat (Brodeur & McNeil 1989), while those bearing parasitized parasitoids not bound for diapause do not. Wylie (1982) reported that flea beetles, Phyllotreta cruciferae and P. striolata, parasitized by Microctonus vittatae emerged from overwintering sites earlier than unparasitized beetles. Consequently, samples of beetles in the crop exhibited a steady decline in percentage parasitism over a 10 day emergence period, unrelated to changes in parasitism in the entire population. Ryan (1985) attributed decrease in percentage parasitism of larvae of the larch casebearer, Coleophora laricella (Hübner), on larch foliage to selective drop of parasitized larvae to the undergrowth, an unsampled habitat zone.

Host movement can also be affected by parasitism, making hosts more likely to be seen and collected. The Isopod Armadillidium vulgare Latreille moved farther and rested less often when parasitized by the acanthocephalan parasitoid Plagiorhynchus cylindraceus (Schmidt & Kuntz), making parasitized individuals more easily detectable in its habitat (Moore 1983).

Most of the difficulties posed by these behaviors can be avoided by using absolute, rather than relative, measures of population density during sampling. Care must be taken to sample all occupied habitats and, where necessary, subsample different portions of the population to provide relative rates of parasitism in each. These partial rates may be weighted by the densities in each habitat to provide an overall estimate of numbers dying from parasitism in the population as a whole. Studies evaluating predation rather than parasitism may need to take into account similar effects.

Biases Affecting Detection of Density Dependence.--Finding density-dependence can be difficult if either the spatial scale or timing of the sampling regime are inappropriate. If hosts are strongly clumped and clumps are distributed on a spatial scale that is meaningful to parasitoids, their activity may be concentrated on dense clumps, either from aggregation of foragers or greater progeny production and retention in locally host-rich areas. In such cases, the sampling program must provide samples from patches of different densities, and each sample must consist of individuals from a given density rather than a mixture of hosts from high and low density patches (Heads & Lawton 1983). If samples are based on mixtures of individuals from patches of strongly differing densities, any density-dependency can be obscured (Hassell 1985a, 1987, Hassell et al. 1987, Bellows & Van Driesche 1999). Pooling os samples from high and low density periods in a time series may have the same effect as pooling high and low density samples collected at one time from several locations, obscuring temporal density dependence.

Finally, it should be emphasized that parasitoid-caused mortality acts upon hosts selected for oviposition, not hosts from which parasitoid adults emerge. Nevertheless, estimates of parasitism often are based on rearing parasitoids from host instars or stages subsequent to the one attacked. Mortality levels are then associated incorrectly with the density of the host at the time the samples were collected rather than with the density of the host when it was actually attacked. Density dependency of a mortality factor will only be detectable if its level is measured accurately and correctly associated with the host density upon which its acts (Bellows & Van Driesche 1999).

Assessing Quantitative Impact of Natural Enemies

With one or several well constructed life tables for a host population affected by a natural enemy, questions regarding the amount of mortality (both in absolute terms and relative to other sources) in the host's life system can be examined.   Nevertheless, obtaining this kind of data is often too time-consuming for most projects, but alternatives may be substituted (Please see Legner et al. 1970, 1992, 1973,  1983, 1983, 1975, 1980).

Parameters in the Life Table.--The objective of life table analysis for natural enemy evaluation is to estimate the attack rate of specific natural enemies to permit comparisons between agents or populations. Some of the methods discussed above under life table construction (such as measurement of recruitment) yield these rates directly and do not require further calculations from a life table. Where these methods have been used, construction of a life table and further analysis to determine the quantitative impact of the natural enemy may not be necessary. Construction of a life table in these cases may be useful if additional analyses, such as those relating attack rates to population densities, are desired. Other methods described above will require that density and mortality information be subjected to further calculations to arrive at attack rates for the different factors in the life table.

The components of a life table typically include the numbers entering each of several life stages (lx) in an insect's life cycle, numbers dying within each stage (dx) due to specific factors, together with estimates of rates of lose in each stage (Southwood 1978). Mortality rates are typically expressed in proportions. Several different types of mortality rates have been included in life tables, such as real mortality, apparent mortality, indispensable mortality, marginal attack rates and k-values.

More than one mortality factor may act contemporaneously at some point in the life table. It is appropriate, therefore, when seeking an index for assessing the impact of natural enemies, to select one which will have the same meaning when describing both contemporaneous factors and those which act alone within a stage. Real mortality, apparent mortality, and indispensable mortality are only of value when considering factors which act alone in a stage. Marginal rates are applicable to both sequentially and contemporaneously acting factors.

Real mortality is the ratio of the number dying in a stage (dx) to the number initially entering the first stage in a life table (lo): real mortality = dx/lo (Southwood 1978).

Apparent mortality (qx) is the ratio of the number dying in a stage to the number entering the stage, or the number dying from a factor to the number subject to that factor: qx = dx/lx. When only one mortality factor occurs in a stage, or where more than one occurs and they act sequentially, then the apparent mortality (the proportion of animals dying from a factor, (qx = dxi/lxi), is the same as the proportion initially attacked by the factor (the marginal attack rate). Southwood (1978) suggested that this measure may be used for comparison of independent, noncontemporaneous, factors or with the same factor in different life tables. Apparent mortalities, because they are calculated on a stage or factor specific basis, are not additive in any sense, but the product of their associated stage survival rates (1 - stage apparent mortality) yields the total survival in the life table.

Indispensable mortality has been little used. It is described as "that part of the generation mortality that would not occur, should the mortality factor in question be removed from the life system, after allowance is made for the action of subsequent mortality factors" by Southwood (1978), who also described its calculation. This type of calculation entails an assumption that subsequent mortality factors in the life history act in a density-independent manner. Huffaker & Kennett (1966) suggested that indispensable mortality may be used to assess the value of a factor in a biological control program, but this applies primarily to comparisons within a life table, rather than among several life tables, as its value depends on the quantitative level of other mortalities in the life table, which may vary in different systems.

The proportion of individuals entering a stage which are subject to attack by an agent is termed the marginal attack rate (Royama 1981, Elkinton & Bounaccorsi 1990, Elkinton et al. 1990a,b). It is the measure of mortality that has the most consistent interpretation among life tables or among factors within a life table; it is the only measure whose calculation permits correct interpretation of the impact of contemporaneous mortality factors. The details of its calculation depend somewhat on the nature of a specific factor (Elkinton et al. 1990b). For factors which act alone in a stage, the apparent mortality is the marginal attack rate. When two or more factors act contemporaneously, the apparent mortality will be different from (and smaller than) the marginal death rate. For such contemporaneous factors, determining the number attacked by a factor must account for those which receive attacks from more than one agent. Two general approaches are available in these cases, either (1) assessing the attack rate as it occurs (e.g., measuring recruitment by dissection for parasitism), which directly estimates the marginal attack rates, or (2) calculating the attack rate from the observed death rates of individuals succumbing to the various factors (Gould et al. 1990b). The equations employed in calculating marginal attack rates from observed numbers dying vary for different categories of natural enemies. Equations for contemporaneous parasitism differ slightly from those used when predation and parasitism occur together (Elkinton et al. 1990b). The product of 1 - marginal rates) for all factors is equal to the overall survival rate for the life table.

In addition to these measures of mortality, k-values may also appear in life tables. These values are survival rates on a logarithmic scale, and are the negative logarithm of the (1 - the marginal rate) for a factor. Although equivalent in principle to the marginal rate, their calculation has been a source of difficulty in cases of contemporaneous factors. The explicit calculation of a k-value requires the number of attacked individuals and the number of individuals initially subject to the factor (Varley & Gradwell 1960, 1968, Varley et al. 1973), the same information necessary for calculating marginal rates. Use of the numbers observed dying due to a factor can only lead to correct calculation of a k-value if factors act strictly sequentially in a stage or in successive stages. K-values for contemporaneous factors cannot be calculated from the number observed dying because the action of each factor is obscured by the action of others. A lack of appreciation of this crucial distinction has led to the incorrect calculation of k-values in many studies. Because k-values are logarithms of survival rates, their sum (when each has been properly calculated) is equal to the logarithm of total survival, in the same way that the product of survival rates for separate factors yields the overall survival in the life table.

Evaluation of the effects of natural enemies in a life system must be made with respect to some standard of host population growth potential. An appropriate standard is the population net rate of increase Ro, which is the ratio of population sizes in two successive generations. Calculation of Ro from a life table requires data on fertility of the population, which often can be measured or estimated. The product of overall proportion survival and fertility yield an estimate of Ro. When Ro = 1, the population is neither increasing nor decreasing. Values greater than unity imply an increasing population, while values of less than unity imply than the population is decreasing in density. In the context of biological control programs, a value of Ro greater than unity implies a need for greater natural enemy action in order to reduce the population.

Comparisons among factors and life tables is most easily accomplished with reference to marginal rates, the values of which are independent of the presence of additional, contemporaneous factors in the system (this is not true for either apparent or real mortality). Marginal rates assigned to a particular factor are directly comparable among different life tables, even when those life tables contain differing numbers or quantitative levels of other factors. When correctly quantified, k-values may be used equivalently.

Interpreting Life Tables.--Some examples will serve to illustrate the relationships among life table parameters together with their interpretation. The simplest case for a life table is when each factor acts independently and sequentially, so that no overlap occurs among stages subject to individual factors. In this case the marginal death rate and the apparent mortality for each factor are the same. In this example, where 50% of the individuals die in each of two successive stages, real mortality declines from stage 1 to stage 2, as only 25 individuals die in stage 2.

When two factors act contemporaneously, marginal rates and apparent rates differ. The proportion actually attacked by factor 1.1 are also attacked by factor 1.2. Because some animals may be attacked by both factors contemporaneously, but can die from only one, the total number of animals attacked exceeds the total number dying. This underscores an important feature of marginal rates which renders them so particularly valuable for comparison: the marginal rate is the proportion which would die due to that factor in the absence of other independent factors or when that factor is acting alone (Elkinton et al. 1990b). This feature is constant for marginal rates in any combination with other factors. No other measure of mortality has this uniformity of representation or meaning across different life tables.

It may be observed that factors with large apparent mortalities add only a small amount of additional real mortality to systems in which there is already substantial mortality (Bellows & Van Driesche 1999). The contributions of a specific mortality agent may be additionally evaluated by removing it from the life table and recalculating the survival and reproduction parameters. Comparisons between tables with and without the action of the natural enemy provide an index of its contributions to the system. However, evaluating the specific contribution of any particular factor in a life table requires the careful selection of an appropriate index. Because apparent mortality in a stage can rise only to 1.0, the value of addition of further mortality agents for a stage is not well reflected by rises in apparent mortality. In general, the higher the level of mortality from a preexisting factor, the smaller will be the rise in apparent mortality from the addition of another factor. Thus, increases in apparent or real mortality in a stage due to the addition of a new mortality agent do not adequately reflect the contribution of the new mortality agent. In contrast, the marginal death rate of any factor in a system is a direct reflection of its impact on reducing the numbers entering the final stage in the table, and therefore its contribution in reducing host densities. Of the available methods of expressing mortality in life tables, marginal rates best allow an accurate expression of the individual contributions of particular factors, particularly when two or more factors act contemporaneously.

The overall contribution of specific mortality agents in life tables can be examined by addition or subtraction of such factors, manipulating numbers in the life table to reflect their absence or presence. Such manipulations allow hypotheses to be formulated concerning the impact of specific agents. Such hypotheses can be formulated in terms of changes in the net reproductive rate of the population. Ro is a particularly suitable index because it expresses the ability of the population to reproduce itself given the state of all sources of mortality in the system.

The percentage mortality due to parasitism or other biotic agents, observed in populations is relatively meaningless in the absence of quantitative values for all mortalities acting in the parasitized stage. These additional mortalities are nearly always essential for estimating the marginal death rate due to parasitism, the parameter which best quantifies the impact of a natural enemy on a population (Royama 1981b, Elkinton et al. 1990b). The relative importance of a mortality factor is most effectively expressed with respect to the reproductive dynamics of the insect it attacks, that is, the fertility of the host and a full quantitative description of all mortalities. Even if any given natural enemy does not cause the population of the host to decline immediately, it may be valuable if it increases the overall mortality, because Ro may become less than unity after the addition of some additional factor or natural enemy (e.g., Aphytis paramaculicornis DeBach and Coccophagus utilis Compere on olive scale as noted by Huffaker & Kennett (1966)).

Ecological Roles For Natural Enemies

A basic precept of biological control is that effective natural enemies will contribute to a reduced and stable pest density. Both of these features are relative terms-- the new pest density would be lower relative to the previous density and exhibit fewer fluctuations than the population without the natural enemies. Thus, natural enemies may play one or more of a variety of roles in the ecology of a natural enemy-pest system. Most of the features desired in natural enemies fall into one of two categories: (1) the natural enemy will reduce the pest density and (2) the natural enemy will aid in stabilizing the pest density. Life table data can contribute to testing hypotheses concerning these and related roles for natural enemies (Bellows & Van Driesche 1999).

Several life tables must be examined for trends in the impact that natural enemies have on pest populations in order to test such hypotheses. Consequently, where in the previous sections we were concerned with the proper construction of, and quantification of factors in life tables, here we will deal with the analysis of such features where several life tables are available for the same system. These might arise from sequential sampling of the same population over several generations, from contemporaneous sampling of several populations in different areas, or both. The types of questions which can be addressed depends somewhat on which type of data are available.

Natural enemies may play either or both of the above mentioned roles in an ecological system, which leads to several possibilities in the structure of natural enemy-pest interactions. The classical interaction envisaged by many authors is the situation where both roles are embodied in the same species, so that the natural enemy contributes quantitatively to the suppression of survival or reproduction (so that Ro<1 or rm<0 at high densities) and also contributes to stabilizing the system at the new, reduced density. Such an outcome would indeed be optimal and desirable, as no further contributions to the system are needed for success in either the context of reducing population density or in maintaining stability. Two additional situations also are possible. The natural enemy may contribute to reductions in survival or fertility (thus contributing mortality in the life table so that Ro will be reduced) without contributing to stability per se. In such a situation the system may be stabilized by some other factor in the life table (e.g., Harcourt et al. 1984), or may be relatively unregulated. Finally, the natural enemy may contribute to stability or regulation without increasing the total level of mortality in the life table, perhaps by replacing an existing factor with a new one which causes an equivalent level of mortality but acts with an increased level of density dependence.

To identify the role of natural enemies in a particular system may not provide a comprehensive answer to the question of what features are significant in shaping the dynamics of pest and natural enemy populations. Addressing that question may of necessity require an evaluation of the role of several or all of the factors operating in the system.

Many of the available theories concerning host and parasitoid dynamics (Beddington et al. 1978, May 1978, Hassell 1985b) employ some density-related property as a stabilizing mechanism. These appear in various forms and can all be considered under the general heading of density-dependence. These theories generally provide testable hypotheses regarding the role of natural enemies, although conducting the tests in a statistical sense can be problematical. Four cases regarding density-dependence in a life-table may be distinguished: (1) there may be no density dependence in the system, (2) density dependence may be attributable to a natural enemy under investigation, (3) density dependence may be due to some other factor in the life table or (4) density-related factors may exist but may be masked by stochastic factors. In addition, more than one factor may be density dependent, which necessitates careful consideration in constructing tests of hypotheses. Hypotheses regarding density dependence are usually tested against the null hypothesis that no density-dependence is present in the system.

Other theories have proposed dynamics of pest-natural enemy systems which are not characterized by density-dependent stabilizing mechanisms (Murdoch et al. 1987). The hypotheses provided by such theories are not as readily testable by analyzing life table data, as they are characterized by dynamics which do not have deterministic relationships between measured variables (such as density and mortality). These theories may provide more readily testable hypotheses following further development.

Ecological Roles and Hypotheses.--It is helpful to review some terms and their meanings before considering in detail some specific role questions and techniques for addressing their related hypotheses. Simply, it is implied here by the term regulation, the tendency of a population to move towards some mean value. This does not imply a reduction in density, which will be termed suppression.

Bellows & Van Driesche (1999) considered that regulation is often regarded as due to the action of some density-related factor. In general, density relatedness may be viewed as falling into one of three categories: (1) density dependence (where proportional mortality increases as density increases), (2) inverse density dependence (where proportional mortality decreases with increasing density, and (3) density independence (where proportional mortality neither increases nor decreases with mortality). Density dependence may further be defined as direct density dependence, where the factor is related to the density of the generation in which it acts, or delayed density dependence, where the factor is related to the density of the generation prior to the one in which it acts. Density-relatedness may be expressed among portions of a population in different locations (over space) or between successive generations of the same population (over time), or both. A key factor is the mortality factor more closely related to, or responsible for, change in total generational mortality among several generations in the population. This term does not imply either that the factor is regulatory or that it is the factor more responsible for determining the mean density of the population. Natural enemies may be important either as sources of mortality or as regulating factors without being the key factor in a system.

The role question most suitably addressed by the examination of several life tables primarily deals with whether or not the natural enemies function as regulating factors. Such regulation usually is reflected in hypotheses as density dependent mortality, and consequently life tables are often examined to determine whether the mortality imposed by a natural enemy acts in a demonstrably regulating, or density dependent, manner. Several mechanisms have been proposed that fall into this category (Bellows & Van Driesche 1999). In each case the proportion of pests dying due to the natural enemy increases with pest density. Inverse density dependence also can act, in some cases, as a stabilizing factor (Hassell 1984).

Important when considering relationships between density and mortality, is to quantify correctly the proportional losses assigned to a factor and to associate this mortality with the density and stage upon which the factor acts. For example, parasitoids attacking only young larvae are acting on a population whose density may be very different than the late larval population from which the parasitoids emerge (Van Driesche & Bellows 1988). Similarly, when not all individuals in the population are susceptible to natural enemy attack, the proportional mortality must be related to the density of susceptible individuals. A less rigorous approach will confound the underlying relationships by associating mortality rates with unrelated densities from inappropriate stages in the life table.

The possible alternative hypotheses related to natural enemies acting as a regulating factor are twofold: (1) they may act in a destabilizing manner (i.e., they are acting in either a destabilizing inverse density dependent manner or in a delayed density dependent manner), or (2) they may not contribute to regulation, but serve solely as an additional density independent mortality in the life table. In this second case the density independent mortality may have a small variance, or have a larger variance and be catastrophic in nature.


Population and life table data are analyzed for the purpose of detecting stability and regulation. Two distinct approaches are (1) to address general questions of population stability with reference solely to density counts in successive generations, and (2) to be concerned with density relatedness of specific factors in life tables. Although the overall objective of the two are similar, they employ somewhat different analytical techniques.

Population Stability Tests.-- These tests focus on the general question of dynamical behavior of a population over several generations, without reference to causal mechanisms. The general framework for this question arises from Morris's (1959) proposal for the detection of stability in a population. In this context stability is the tendency of a population to grow in a manner which moves it toward an equilibrium value (= steady density of Nicholson, 1935), and increase when below the value. Such populations are in contrast to those which either grow or decline exponentially and those which exhibit a random undirected trajectory through time. In this sense if a population is characterized by the logarithm of its density in generation t, Xt, then the dynamics of an unstable population may be expressed by

Xt+1 = r + Xt + et                               (1)

where r is the growth rate between generations and et is a stochastic error term representing random deviations in r. Stable populations may be represented, in contrast by

Xt+1 = r + BXt + et

where B takes values between -1 and 1 and represents density dependent restrictions on population growth (Bellows & Van Driesche 1999).

Several analytical tests for detection of stability by examining series of population censuses have been developed. Most of this work has followed Morris (1959). The original proposal involved regressing Xt+1 against X and testing the slope of the regression for significant difference from 1, the null hypothesis value for no regulation. The general concept has been widely accepted, but its application to hypothesis testing has been doubtful. The first order autocorrelation in the time series of equation (1), together with the presence of sampling errors in the abscissal values Xt, create such significant biases in the regression slope that the test is generally inadequate (Varley & Gradwell 1968, Bulmer 1975, Pollard et al. 1987) because it rejects the null hypothesis in a large proportion of cases when the null hypothesis is the true case (i.e., it has a large liklihood of a Type I error). A number of parametric as well as simulation tests have been proposed to overcome this difficulty.

The first parametric test proposed was that of Varley & Gradwell (1968), who outlined a modification of the criteria for rejecting the null hypothesis by suggesting that double regressions be performed, and the slope estimates b (for the regression of Xt+1 on Xt) and slope estimate bxy (for the regression of Xt on Xt1) be performed. The null hypothesis would be rejected only when both regression slopes differed significantly from unity and both b and 1/bxy are less than unity. This test is overly conservative, and simulation studies have indicated that, while it has a low likelihood of a Type I error, it also has relatively poor power (that is, it fails to reject the null hypothesis in a large proportion of cases when the population is stable); as a statistical test it is overly conservative.

Other parametric tests have been proposed. Bulmer (1975) introduced a test statistic based on the reciprocal of Von Neuman's ratio for time series analysis, and a modification of this statistic for cases when there are errors in sample estimates of population counts (the usual case). Slade (1977) suggested using two other statistics developed previously for estimating slopes of relationships where error occurs on both axes, the major axis (Deming 1943) and the standard major axis (Ricker 1973, 1975). A number of simulation studies have been conducted to assess the error rate (for Type I errors) and the power of these various statistics (Slade 1977, Vickery & Nudds 1984). The general conclusions of these and other workers (Gaston & Lawton 1987) are that these tests are not robust and that they have acceptable error rates and power only in exceptional circumstances. Generally it appears that there is no parametric test generally applicable to testing for stability in a series of counts over several generations. A possible exception is the variation on Bulmer's (1975) statistic proposed by Reddingius & den Boer (1989), although this test has not received the extensive attention of earlier proposals and has not yet been subject to testing by Monte-Carlo simulation, as have the earlier tests.

Alternatives to parametric tests have been developed by several workers using Monte-Carlo techniques. These generally take the form of proposing population models for the two hypotheses under consideration (the null hypothesis of no stability and the alternative hypothesis of stability). The models, which incorporate various components of stochastic variation, are then used to simulate a long series of synthetic populations with parameter values taken from the natural population under study. The dynamics of these synthetic populations are then summarized in one or more statistics, and the same statistic is calculated for the natural population. The distribution of the statistic from synthetic populations is compared to observed values of the statistic from the natural population, and if an observed values lies near the extreme end of the synthetic distribution (usually beyond the 5% most extreme cases), the null hypothesis is rejected. This procedure has provided some very helpful insight into the behavior of parametric tests, and has given "simulation" tests which appear able to distinguish stable from unstable populations. One such test was proposed by Slade (1977) on simulated distributions of the t-value associated with the usual regression slope b. Pollard et al. (1987) found this test insufficient, and developed a test based on likelihood ratios which appears both to have an acceptable Type I error rate and sufficient power to identify stable populations, although the matter of errors in density estimation were not addressed by this technique (Bellows & Van Driesche 1999). Reddingius & den Boer (1989) developed a similar test which does provide for errors in estimation, and gave a fuller examination of its power than have other workers, although they did not provide any information on the error rate of their proposed index under the null hypothesis.

Density Relatedness Tests For Specific Factors.--Both biotic and abiotic factors affect populations, the former showing some form of density relatedness, and the latter is generally density independent. When the variation from year to year in the amount of mortality inflicted by density independent factors is greater than the mortality caused by density dependent factors, the population's dynamical behavior is dominated by these density independent processes and, consequently, may not show stability. This does not preclude the presence of potentially regulatory mechanisms, but makes it very difficult to detect their action by examination of population census data. Therefore, tests have arisen to examine specific factors for attributes which could contribute to stability, even if they are acting in concert with other factors which obscure their effects.

On the view that temporal density dependence (sensu Nicholson 1954) was the primary, or perhaps only, mechanism attributable to a factor which could contribute to regulation of a system, the original approach was predicted. Following this line of reasoning, Varley & Gradwell (1968) suggested plotting survival against density on log scales (the familiar plot of k-value vs log density). Regression analysis was used to determine if the slope of the relationship was significantly greater than 0, implying density dependence because mortality rate was increasing with density. They recognized, however, that the estimate of density was employed on both axes (on the original scale as a component to the k-value), and that errors of estimation occur on both axes. These conditions preclude the application of usual tests for significance of the regression slope, complicating the issue of rejecting the null hypothesis of no density dependence. The issue received considerable attention subsequently, but no completely satisfactory solution has been proposed. Thus the technique of k-value analysis continues to be employed to provide initial assessments of density relatedness, either density dependence, delayed density dependence or inverse density dependence, in long-term studies of populations. Royama (1981a) suggested that an alternative approach might be to attempt to determine a priori what factors in a life table were density independent, identify them and quantify their impact on mortality, and subsequently examine the remaining factors for density relatedness. This proposal appears promising, but Royama does not address issues relating to statistical testing of hypotheses in this context.

Examining data for temporal density dependence in the host population is but one step in the search for regulating features in a life table. Other forms of density relatedness were soon appreciated as potential contributors to population stability, particularly density dependence occurring within a generation but over some spatial scale. These include interference among parasitoids, which is a particular type of temporal density dependence (Hassell & Varley 1969, Hassell 1970), aggregation (Hassell & May 1973, 1974, Beddington et al. 1978), inverse density dependence (Hassell 1984, Hassell et al. 1985), host refuges (Reeve & Murdoch 1986), specific types of natural enemy search behavior such as sigmoid functional response (Hassell et al. 1977, Hassell & Comins 1978), invulnerable life stages or invulnerable fractions of populations (Murdoch et al. 1987), and even simple spatial patchiness or heterogeneity (May 1978). Not all of these features have been found in natural field systems, although many are well known from laboratory systems. Some are known from some field systems and not from others (e.g., lack of aggregation of Aphytis melinus against Aonidiella aurantii by Reeve & Murdoch 1985), but presence of aggregation of parasitoids attacking bivalves (Blower & Roughgarden 1989). Occasionally a particular behavior usually considered to contribute to regulation via density dependence is found to be present, but stabilizing density dependence is not demonstrable (Smith & Maelzer 1986). In some cases the ability to detect certain mechanisms is dependent on the scale of measurement, for example in the cases of aggregation (Hassell et al. 1987) or the assessment of patch sizes as perceived by the natural enemy (Heads & Lawton 1983).

An perception of what types of behavior and qualities of natural enemies and their host populations can enhance stability has advanced rapidly, faster than have statistical developments for handling these very special testing needs. The intricate correlations and interdependencies among variables such as measures of mortality from a life table and the density upon which they act are not completely understood for most of these types of factors. This makes the development of statistical tests that have acceptable error rates and have sufficient power a difficult task requiring considerable development. Many researchers have employed various statistical techniques in efforts to demonstrate the presence or absence of a particular behavior. Most appear rational, but normal statistical assumptions are often breached. In addition linear models relating behaviors to density have been employed when a priori considerations indicate that such models cannot apply and curvilinear models would be more appropriate. This is not to suggest that such studies have failed in their objectives, but only to point out that adequate assessment of the suitability of most statistical techniques for use in the particular circumstances of detecting regulating behaviors is lacking. Hence no standard statistical analytical technique has emerged for the evaluation of these behaviors (Bellows & Van Driesche 1999).

Because of the plurality of properties of biological systems which can affect their dynamics, and the potentially masking effects of random (density independent) factors (Hassell 1985b, 1987), no simple analysis will likely serve to provide definitive answers to questions of density relatedness or the presence of other stabilizing mechanisms in life tables. Carefully planned studies differentiating the behavior of systems both with and without natural enemies may permit simpler comparisons of system behavior and testing of hypotheses.

Experimental Designs For Life Tables

A forceful approach to natural enemy assessment is planned contrasts of life tables for populations having and lacking a natural enemy. Investigators can maximize the power of life table data to reveal both the total mortality contributed by an agent to a system and the qualitative nature of the role of the agent in the system through careful planned use of such contrasts.

Treatments may be organized in one of three general ways: (1) Time can be used to organize the with and without contrast for cases of introduction of new agents where studies of the host population's dynamics can be initiated prior to the introduction (the "without" treatment) and then continued after the agent's establishment (the "with" treatment) (Quezada 1974, Dowell et al 1979). (2) Geography in which plots in one location having the agent are contrasted to plots in similar but separate locations lacking the agent provide the with and without contrast. This is feasible chiefly with new agents that have not yet occupied their full potential range. This approach is less applicable to native or previously introduced agents, as sites having and lacking the agent are likely to differ in some factor of ecological importance to the agent. Life table contrasts between the native home and the area of introduction (after establishment of the agent) can be particularly helpful, e.g., the winter moth in England (Varley & Gradwell 1968, Hassell 1980) versus Nova Scotia (Embree 1966). (3) Exclusion in which some type of barrier is erected to deny the agent access to a portion of the pest population. Methods to create such barriers have been reviewed by Luck et al. (1988). Generally, natural enemies may be excluded from plots by the use of cages, mechanical barriers and plot edges, selective insecticides, hand picking or for certain cases dust or ants, as we discussed in an earlier section.

Each method (time, geography, exclusion) for creating the desired with and without natural enemy condition has certain limitations that may potentially confound the interpretation of results. Contrasts structured on time (i.e., before and after studies) are frequently criticized on the basis that no two years are ever identical in terms of weather, etc., and hence, the results may be due to these other features rather than the presence or absence of the natural enemy. Contrasts based on geography (i.e., here and there studies), similarly, may be criticized because sites that appear similar to the researcher may in fact differ in nonapparent yet important ways. This may be compensated for by utilizing a set of three or more sites for both the "with" and the "without" treatments. However, this may be beyond the resources of many research projects, especially those attempting to construct life tables at each study site. Exclusion-based contrasts are criticized because the means used as barriers often change the physical or chemical environment of the pest population in one treatment group (the "without") but do not do so in the other treatment. Cages, for example, may increase insect development due to within-cage greenhouse effects and also prevent emigration of the pest under study. Selective pesticides may alter reproduction rates of pests in treated plots, either directly or through changes in plant chemistry (Luck et al. 1988, Bellows & Van Driesche 1999).

Generally biases such as these are best controlled by concurrent utilization of two methods of establishing the desired with and without contrast. In such cases each method provides the researcher the opportunity to assess the degree of bias of the other method. The general pattern has been the "with" and "without" contrasts have been evaluated by scoring the pest's density and the rate of mortality inflicted by the agent of interest. These may be determined either once at the termination of the experiment or several times during its progress. The additional construction of life tables for each of the two populations in the contrast provides an improved quantification of the agent's value by allowing marginal rates of mortality from each mortality agent in the system to be calculated, both in the presence and absence of the agent of interest. This in combination with a comparison of Ro for the pest populations both attacked by and not attacked by the agent, provides a clear assessment of the value of the agent in suppressing the pest. Life tables for Phyllonorycter crataegella (Clemens), modified from Van Driesche & Tazub (1983) may be found in Bellows & Van Driesche (1999).

Applications to Natural Enemies Other Than Parasitoids

It was concluded by Bellows & Van Driesche (1999) that although their paper deals explicitly with parasitoids, much of the framework developed can be successfully applied to other cases of mortality agents, such as pathogens and predators. In particular for pathogens, if marginal rates are to be assessed via direct observation of recruitment, two issues are important (1) are all levels of pathogen titer lethal or will some be sublethal infections not ultimately killing the host and (2) can diseased individuals be detected very early after infection. This later may be achieved by use of antigen-antibody technique (McGuire & Henry 1989). If marginal rates for pathogens cannot be assessed via recruitment, the post-facto method of Elkinton et al. (1990) can be used to calculate marginal rates from death rates in reared samples.

As regards predators, in the construction of many life tables some individuals disappear from the population and their disappearance cannot be reliably assigned to a particular factor. Therefore there is often a category employed for such individuals such as residual mortality or missing. The fraction of a population denoted as missing is the marginal rate for this category (Elkinton et al. 1990). It must be ensured, however, that the disappearance of individuals is assigned to the correct stage when constructing the life table (Campbell et 1l. 1982), particularly if intervals between samples are long (Bellows & Van Driesche 1999).

The organisms which are eaten by predators disappear from the population; consequently, mortality due to predation is often combined with other, unspecified sources of disappearance. All disappearance should not be assigned to predation unless abiotic factors can be eliminated. In some cases, predation leaves artifacts, such as exuviae, which can be used to specifically assign deaths to this category (Gould et al. 1990b). When this is possible it permits marginal rates for predation to be separated from the general category of missing individuals. Other techniques have been suggested for quantifying predation rates (Sunderland 1988). These do not usually allow marginal rates for predation to be divided into taxa-specific components, but in some cases this may be approximated by collateral evidence on the composition and relative significance of the numbers of the predator complex (Bellows et al. 1983).

Herbivores and Plant Pathogens require special attention. Plants are rarely treated as a population of individuals whose births (recruitment) and deaths can be counted and assigned rates, although this very natural extension of life tables or actuarial tables would provide excellent quantitative information on effectiveness of natural enemies. The techniques presented here may be applied directly, considering plants as hosts and herbivores as predators or natural enemies whose impact does not directly eliminate entire plants but rather affects their reproduction through effects on their vital rates (such as fertility and death rates) (McEvoy 1990b).

Other significant differences between weeds and insects must be considered when evaluating effectiveness of natural agents via life table analysis. Life tables do not offer any direct way to measure herbivore impact on vigor or biomass except as these are reflected in plant longevity and fertility (i.e., seed set). In some cases a useful approach might be to construct lx/mx lie tables for these systems, both with and without natural enemies (Julien & Bourne 1988), and calculate estimates of population growth parameters from these tables. This would be particularly appropriate for biennial or perennial systems, where differences in fertility might be the major impact of some herbivores, for example flower or seed predators. Comparative life tables for populations with and without the natural enemy of interest are as essential here as they are for insects (Bellows & Van Driesche 1999).

For pathogens of weeds, comparative lx/mx or stage-specific life tables are equally applicable, but quantifying the dynamics of the upper trophic level population (the plant pathogen) may require very different sampling techniques. In some studies the dynamics of the pathogen may be ignored (as for augmentation), but to document the natural effect of an introduced and established pathogen some understanding of the dynamics of the pathogen population will be essential. Constructing life tables for the pathogen is a natural, if not often applied, approach for quantifying the relevant reproduction, recruitment and survival rates. Finally the seed population in the soil of many plants may have a temporal dynamic over a much longer time scale then the plants themselves, an issue which must be considered in the construction of recruitment rates for these populations.


Liberations en masse of natural enemies against pests is common in several cropping systems (Legner & Medved 1981, Frick et al. 1983, van Lenteren & Woets 1988). The use of life tables in these settings can be particularly effective in evaluating the contribution of the released natural enemies. The effects of augmented populations of natural enemies can be treated identically to natural populations using the methods discussed earlier. The construction of a complete life table can provide unambiguous marginal rates for each factor acting on the host population. This permits the impact of released natural enemies to be quantified in relation to the mortality occurring naturally in the system, providing immediate and quantitative evaluation of the effectiveness of the augmentation. The use of life tables to make planned comparisons in augmentation studies is a simple and effective method for natural enemy evaluation. Augmentation studies imply the presence of a population with the natural enemy (the release location). The addition of a non-release location permits the construction of life tables for a population without the natural enemy, and comparative analysis for the "with" and "without" situations may then be conducted.  However, he effectiveness of any augmentative control depends on the continuous availability of specialists who understand the details of using this technique.  Seasons of applications, natural enemy species and strain difference are particularly critical to success.



GENERAL REFERENCES <bc-72.ref.htm>   [Additional references may be found at  MELVYL Library ]