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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 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 ] |