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LIFE TABLES AND EVALUATION OF NATURAL ENEMIES
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Introduction 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: 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 are 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 . GENERAL
REFERENCES <bc-72.ref.htm> [ Additional
references may be found at MELVYL Library ] |