Dynamics of the Scale and Its Natural Enemies in a Citrus Grove at Ceiba, Cuba

Aim: Research was conducted to study the population dynamics of a citrus scale, and its parasites in “Empresa de Citricos de Ceiba”, Havana Province, Cuba. Orange trees, Glover’s scale Lepidosaphes gloverii (coccidae, homoptera), and four of its natural enemies including three fungi and a parasitic wasp, were studied in their distributions in space and time, and their interactions, in order to understand why this scale is not a serious pest in Cuba. Methodology: The study consists of observations made bi-weekly on the site during an entire year. Various statistical analyses including Taylor regression and new probabilistic methods that were developed for this study were used to explore the mechanisms of natural regulation of the pest. Major findings: The results of the analysis showed that the scale population was kept in check by seasonally varying recruitment and by mortality that was density dependent through gradual parasitization by several species with distinct spatial preferences and some overlapping. The findings also showed that the first natural enemy to settle on the scale did so independently of the number of scales on the leaf; but ones this happens there was contagion within the scales on the leaf. Conclusion: The study demonstrates that the pest can be regulated within an ecological context of community dynamics. A general theoretical result based on loop analysis demonstrates that using pesticides to control agricultural pests where they co-exist with their natural enemies would actually have counterproductive results, in fact increasing the pest.


Introduction
Community ecology is increasingly dynamic.It has to deal with the changing populations of species where both the impact of the external physical environment and the impact of the mutual interactions are essential.This is particularly relevant in agriculture where the crop and its invading pests become part of the natural ecosystem.Thus, research was conducted to study the population dynamics of the Glover's scale Lepidosaphes gloverii (coccidae, homoptera) (Metcalf & Flint, 1962) and its parasite on citrus leaves.The orange trees, the scales themselves at their developmental stages, and four natural enemies including three fungi and a parasitic wasp were studied in their distributions in space and time, and their interactions in order to determine the mechanisms of population regulation in the context of a multi species community.
among micro-habitats and therefore the environments to which species are exposed.The availability of resources as influenced by density and the physical environment can determine the nutritional status of organisms, body size and therefore how they respond to the physical environment and how mobile they are.The environment may determine the outcomes of aggressive and competitive interactions.Environmentally sensitive "weak determination" (Strong, 1989) still reflects the interaction pattern and is quite different from autonomous responses to the environment.Even when conditions become extremely harsh and resources dry up or freeze independently of the species densities, the probabilities of survival of individuals are inf1uenced by the previous interactions, and the total survival responds to the numbers.
The citrus scale is useful for the study of community dynamics.After the brief crawler stage, the subsequent stages (except for the adult males) are sessile, so that different trees and sections of trees can be examined as distinct populations in distinct microhabitats.The long generation time (more than two months) (Metcalf et al., 1962) allows us to track populations with biweekly observations.Broken scales are retained on the leaf as evidence of predation while parasitized scales can be identified as to parasite.The number of scales in different life stages, their distribution over seasons and microhabitats, the intensity of aggregation and the correlated spatial-temporal variation of the natural enemies allow us to interpret the observed pattern both as density-dependent (non-linear) and environmentally responsive.
Biodiversity is considered essential for maintaining the health of agroecosystems (Altieri, 1999).The expansion of agricultural land led to the loss of non-crop habitats resulting in a decline of biodiversity needed to preserve natural enemies of agricultural pests (Bianchi, Landis, & Wilby, 2006).
For the first time a holistic ecological analysis is developed to demonstrate that control of agricultural pests takes place within a context of a community of natural enemies that share they prey by invading at different seasons and differing in their spatial distribution.Moreover this work presents novel mathematical approaches to understand the mechanisms of regulation.

The Site and the Environment
The field work was carried out at the Empresa de Citricos de Ceiba, located 17.5 km northeast of Artemisa, Havana Province, Cuba at an average elevation of 80 meters.The average temperature was 24.9 o C, ranging from an average minimum of 14.6 o C in the coldest month (February) to an average maximum of 31.2 o C in the hottest month (July).Annual precipitation averaged 1505 mm over a ten-year period.The region has karst topography with protrusions of bare limestone and a red ferralitic soil varying from depths of less than 2 cm to 100 cm.The yield of oranges averaged 113.3 kg/tree.The major pests of citrus on this farm were rust mites and two species of curculionid, with thrips, aphids, and a few other coccids and mites having minor importance.

Data Collection
Biweekly observations were made on five trees of Valencia oranges following flushes during 1986, resulting in a collection of 4740 data points which enabled the study of scale dynamics through many cycles of population growth.Five trees were selected and numbered as follows: trees 1-4 were located at the corners of a field and tree 5 was in the middle.For each tree, branches were selected at each of four different cardinal points (N, S, E, W) and three different strata defining levels of height above the ground (1, 2, 3).Two leaves from a recognizable flush were chosen at random from each tree, at each cardinal point and at three strata levels, resulting in a minimum of 120 leaves examined on each date.As the season progressed and more leaves developed, then the other leaves in that flush were also identified and examined.On each branch, leaves were numbered starting at 1 for the one closest to the trunk.Leaves numbered "0" are leaves without scales and their location along the stem was not recorded.The upper and lower surfaces of each leaf were examined for scales and natural enemies.The scales were counted on the leaf and classified visually as to stage of development: crawlers, nymphs or seconds, pre-adult females, females with eggs, and males.Parasitized scales were identified as having infections of Sphaerostilbe auranticola (HR), Podonectria cocciola (HB), a third unspecified internal fungus (HI), and the wasp Aspidiotiphagus sp (chalcid) (PI).Infected scales could not be identified as to stage.

Analytical Methods
Data were analyzed using EPI Info version 6, a non-proprietary program prepared by the Center for Disease Control (A.Dean, J. Dean, Burton, & Dicker, 1990) and Lotus 1-2-3 (Lotus Development Corp., 1988).

Distribution of Leaves in Space and Time
Contingency tables were constructed to compare the numbers of leaves on different trees, strata, and cardinal points and over time; chi-square statistics were used to test statistical significance.The number of collected leaves is an indicator of the condition of the tree since numbers above the basic 24 per tree reflect the balance between new leaves on a twig and leaf fall.

Distribution of Scales and its Natural Enemies in Space and Time
Distribution of scales and its four natural enemies, across leaves at the various positions along the branch, was determined by calculating the mean number of scale per leaf for a particular position.Contingency tables were constructed to compare the numbers of scales on different trees, strata, cardinal points, upper and lower leaf surfaces over time; chi-square statistics were used to test statistical significance.

Taylor's Regression to Study Aggregation
Taylor (Taylor, Woiwod, & Perry, 1978) proposed that aggregation of living organisms be described by the exponent b in the relationship: where M and V are the mean and variance of the numbers in different sites.A random distribution would show the Poison value of b = 1; a more uniform distribution would have b < 1 while aggregation would show up in values of b > 1.This method was previously used to compare aggregation in other scale populations in Israel (Nestel, Cohen, Saphir, Klein, & Mendel, 1995).The following logarithmic form was used for the analysis: The estimates of M and V over time and space were obtained from data analysis carried out with Epi-Info.The parameter b was estimated with linear regression based on equation (2) using Lotus 1-2-3.

Crawler Migration
The crawlers are the first developmental stage after the eggs hatch and the only immature one which is not sessile.Indeed, many of the crawlers are found on leaves without females with eggs.A model to assess migration was developed as follows: suppose that movements were at random, and that the fraction pc of the crawlers exit from the leaf on which they were born.Since the fraction pl of the other leaves has females with eggs, p c p l of the crawlers would move to other leaves with females with eggs and (1-p l ) p c would reach leaves without them.Then p c could be estimated by: where x is the fraction of the crawlers found on leaves without fecund females and an average of 1-pc of the crawlers remain on their birth leaves.This calculation does not take into account migration from leaves to stems or fruit.

Reproduction
It is not possible to measure fecundity directly by counting eggs.Therefore crawlers were counted as the first stage of life.Since crawlers live for only a day, the ratio of crawlers to fecund female (with eggs) it approximately estimates fecundity.This may not be a true fecundity since the crawlers experience high mortality during their one day of life (Greathead, 1990).In the analysis the ratio of crawlers to fecund females was used as a measure of reproduction.
Another estimate of reproduction can be obtained taking advantage of the knowledge of migration: Let p c be the fraction of the crawlers that exit from the leaf on which they were born, as previously defined.The probability that all n crawlers that were born to a particular female leave the site of birth is p c n , and to k females is p c kn .Let r be the probability that no crawlers enter the site of fertile females.Thus the probability of finding no crawlers on a leaf with one fertile female is q 1 = r p c n , and for k females is q k = r p c kn .The ratio q k / q k-1 = p c n and can be estimated from the data.Knowing p c enables the estimation of n, the number of crawlers born to one female: n = [log (q k / q k-1 )]/log p c (4)

Probability of Infection
Let p i1 be the probability that a propagule of a fungus, or a foraging wasp from outside a leaf finds a host on a leaf with non-parasitized scales.Suppose that there are n uninfected scales on the leaf.Then the probability y, of missing all of them is (1-p i1 ) n and the probability p i1 of a unit propagule finding a scale is estimated by where y is Let p i2 be same leaf.other scale where z is estimating infected sc

Leaf D
The numb The five tr tree numb number: 2 ranked in i the center number: R perhaps th There was = 3.10, df points: 26. 3, P-value

Spatia
The scales along a bra   On the upper surface there were more observations than on the lower surface of the leaves which might have changed the overall distribution.Thus, dates were examined where the number of observations was the same on both surfaces (May 6 and 20) and found that there was no difference in scale distribution between these two dates and all other dates, indicating that the different number of observations will not alter the overall results.
The upper surface of a leaf is preferred by scales.The ratio of the number of scales per leaf between the upper and lower surface of the leaf is highest for crawlers, and decreases as the scale progresses through the stages (Table 3).On the upper surface there are more fungi per scale than in the lower surface of the leaf.However there is a slight preference by the wasp to choose the lower surface.In general there is a higher parasitization rate on the upper surface (Table 4).

Distribution of Scales Over Strata
There was no significant differences in the mean number of live scales per leaf across strata (1.4,1.2 and 1.3 for strata number 1, 2, and 3, Kruskal-Wallis H P-value = 0.074).However there was a statistically significant difference if parasitized scales were included in the analysis (2.1, 1.7 and 1.8 for strata number 1, 2, and 3 respectively, Kruskal-Wallis H P-value = 0.026).This small differences in means while statistically significant might not be biological meaningful.Parasitization rates are different across strata: HB and HI prefer the middle section, HR prefers 1 and the wasp prefer 3 (Table 5).

Distribution of Scales Over Cardinal Point
The scales start their lives as crawlers preferring to settle in some directions over others (mean numbers per leaf: 0.459, 0.388, 0.423, and 0.237 for North, South, East and West respectively, Kruskal-Wallis H P-value = 0.000013).The location of the scale foci is determined by the crawlers because the subsequent stages are sessile.
There was a significant difference in the mean number of live scales per leaf across cardinal point (1.6, 1.3, 1.4 and 1.0 for North, South, East, West respectively, Kruskal-Wallis H P-value = 0.000023).This has the same ordering as the one for crawlers.
However no significant difference was found when parasitized scales were included in the analysis along with the live ones (2.2, 1.8, 2.0 and 1.6 for North, South, East and West respectively, Kruskal-Wallis H P-value =0.11).While scales themselves might not prefer one location over the other, as they get parasitized more survivors will be found on the North surface and fewer on the West side of the tree.An analysis of parasitization rate on each of the directions found that in general the fungi preferred scales on the west side while this side was least preferred by wasps and the scales themselves as determined by the crawlers (Table 6).

Emerg
The forma immature to start up   Pi3 -probability of third infection； *The numbers were too small for the calculations.
The probability that a second parasite infests scales, pi2, given that a first infection already exists was calculated using equation ( 6).Table 9 shows that although this probability is higher than the probability of infection with the first parasite it is also independent of scale density.The same can be said for pi3.In summary: it was observed that pi3 > pi2 > pi1.It seems that pi is random and once the first parasite settles it needs just an adjacent scale to propagate and not the entire foci.
The estimate of pi2 includes both external infection probabilities pi1 and the additional probability due to sharing a leaf.Therefore the additional probability is estimated by pi2 -pi1.This is equivalent to the increased risk for a scale when it shares its leaf with other scales.A similar argument can be used to ask about the conditional probability of infecting a third scale given that two are already infected on a given leaf.A separate analysis for Sphaerostilbe auranticola, the most prevalent fungus shows a similar pattern (Table 10) and the same was observed for the wasp (Table 11):

Survival Through the Stages
The number of scales in each life stage reflects the duration of that stage, survival from previous stages, and survival during that stage.As the scale progressed through the various developmental stages there was a decrease in abundance as seen from the ratios among the stages as presented in Table 12 (the calculations takes into account that a crawler lives for one day and the other stages last approximately 20 days).The greatest loss happens at the transition between crawlers to the nymph stage.Once the scale survived through the nymph stage there was good survival to the adult one.Half of the nymphs would expect to become females and the observed ratio of .49means that there was a 98 % survival.Of those, 58% survived and became fertilized.The above results indicate the most of the loss occurs in the crawler and nymphal stages.Past the nymphal stage there is almost un-interfered progression to completion of the life cycle.
The data in Table 12 served as the basis for comparing the daily survival probabilities of the scale at its different developmental stages.For the calculations it was assumed that scales exist as crawlers for only one day, and that it takes twenty days to progress from one stage to another in the subsequent stages (Metcalf & Flint, 1962).Thus, accounting for the different average length of survival, the twentieth roots of the ratios female/nymph and fertile/female were taken (Table 13).

Discussion
If a population varies greatly during the annual cycle and yet remains within bounds over the years, then some processes of regulation must be at work.Either fecundity decreases or mortality or emigration increases with density.Although reproduction does depend on seasonal conditions, no evidence of it varying across locations was found despite density differences.
The coccid scale Lepidosaphes gloverii is common on orange trees, with 61% of the leaves having one or more scale insect.The distribution on leaves was not uniform across microhabitats.The patterns were somewhat different when only live scales or total scales (live scales plus parasitized scale) were examined.Total scales did not differ among cardinal points, but because of uneven parasitization the live scales were not equally abundant.
On the other hand, total scales differed among strata in the tree, but after uneven parasitization the difference disappeared.There was variation among trees, with the number of scales per leaf being correlated with the vigor of growth of new flushes, providing better nutrient conditions.Scales were more abundant on the upper than the lower surface of leaves and there was a tendency to prefer the middle leaves of a flush.
The population dynamics of the scale depended on its interaction with its environment.There was marked seasonal variation in recruitment (fecundity times crawler survival), associated with the seasonal cycle of the trees.The mineral content of the leaves varies seasonally and young leaves are produced in a few flushes peaking in late autumn (Figure 1); although no physiological data was collected for the trees their condition can be inferred from the number of leaves counted in each observation period.The seasonal distribution of scales coincided with that of the scales (Figure 3).New foci are formed by the crawlers, the only mobile stage in the life cycle of the scale.In fact results show that 80% of the emerging crawlers leave the site of birth preferring the upper side of the leaf over the lower one, by four folds.The parasitic species differ among themselves in microhabitat locations (Table 14).This, both, reduces potential competition among the natural enemies of the scale and increases the coverage of the microhabitats in the orchard.In particular the two most abundant parasites the fungus Sphaerostilbe auranticola and the wasp Aspidiotiphagus sp.prefer to inhabit different locations.Furthermore, they are introduced and reach their peaks at different times, again to minimize competition and increase the likelihood of parasitization.In accordance mathematical models have predicted that biological control is most effective when natural enemies are heterogeneous in their spatial distribution (Beddington, Free, & Lawson, 1978).
Infection by fungi or parasitoids can occur in two ways.The first is introduced from the outside.A spore drifting in the air can land on a leaf and germinate, penetrating a scale.Similarly a wasp searching for a host in the foliage may find a leaf with scales and deposit her eggs in the scale.
The second type of infection occurs within a leaf.If a scale is infected, crawlers can drag spores around the leaf surface infecting other scales.Or a wasp finding a host on a leaf may be encouraged to continue looking.Therefore the probability of a second scale becoming infected on a leaf once a first scale has been infected may be greater.
The observation from Table 9, that pi3 > pi2 > pi1, indicates that pin is random and once the first parasite settles it needs just an adjacent scale to propagate and not the entire foci.The estimate of pi2 includes both external infection probabilities pi1 and the additional probability due to sharing a leaf.Therefore the additional probability is estimated by pi2 -pi1.This is equivalent to the increased risk for a scale when it shares its leaf with other scales.
A similar argument can be used to ask about the conditional probability of infecting a third scale given that two are already infected on a given leaf.
Indeed the mortality due to parasitization of a scale increases with the number of scales on the same leaf.However, aggregated scales do not attract parasites; that is, the probability of the first scale on a leaf being infected by a fungal spore or parasitized by the wasp is independent of the number of scales on the leaf (Tables 10,11,12).But once one scale is parasitized the risk to the others increases linearly with the number of scales (Figure 6). www.ccsen The scale aggregatio aggregatio parasitizat with the nu mechanism Scale inse heavy rain the upper s between th survival th The nymph adults.Thi Table 13).a fertilized in studies w the crawle Fernandez (except for Table 13).operative simultaneously as proposed by others (Levins & Schultz, 1996;Price, 1991).The mechanisms of pest regulation in the context of a multi species community as presented in this paper explains the overall theoretical result obtained through loop analysis of a complex system which also includes the addition of pesticides (Figure 7).According to this analysis, the use of pesticides might be counter productive and perhaps the best intervention as not to intervene (Awerbuch, Kisezewski, & Levins, 2002).

Fi
st likely to be nd 54.6%.This er leaf was high undance: 1.97, was observed le and leaf abu Figure 3 sh leaves of V fungi and t fungi Sphaerostilbe auranticola and the wasp.The number of observations for the other two fungi was too small to carry out a similar analysis.

Table 2 .
Mean number of scales across leaf position

Table 3 .
Mean number of scales per surface of leaf

Table 4 .
Mean number of parasites per scale on upper and lower surfaces MD = Myrianguium duriaei Monty Berk and the wasp; SA = Sphaerostilbe auranticola; ASPI = Aspidiotiphagus sp.

Table 9 .
Probability of sequential infection as a function of scale number

Table 10 .
Probability of sequential infection by Sphaerostilbe auranticola *The numbers were too small for the calculations.

Table 11 .
Probability of sequential infection by the wasp

Table 12 .
Survival ratios through the stages across trees

Table 13 .
Daily survival of the scale stages

Table 14 .
Parasites preferred location