CAPITULO I: ASPECTOS GENERALES 1 Estado, Sociedad y Familia
8. Derechos Fundamentales con respecto a la Violencia Familiar
8.7. Derecho a la no discriminación e igualdad ante la ley
For the following it is simpler to refer to the parameterisation of the model as (5.2) rather than the fitted form of (5.3). As in Candy et al. (1992), the main use of model (5.2) is to determine the economic impact of different levels of defoliation. This requires estimation growth loss as a function of defoliation level (or intensity), as quantified by (5.2), where defoliation level is expressed as the percentage of new foliage removed. Only three levels of defoliation were carried out in the above trials being nominal defoliation intensities of 0, 50, and 100% and corresponding actual intensities of 0, 42.75, and 100%. Model (5.2) allows interpolation to any value of percent defoliation and extrapolation to different ages to that at the final
Figure 5.25 Regression diagnostics for OLS residuals from the fit of model (5.3) to DBH at 1998 for the Arve trial.
Figure 5.25 Regression diagnostics for OLS residuals from the fit of model (5.3) to DBH at 1998 for the Arve trial.
Figure 5.26 Regression diagnostics for OLS residuals from the fit of model (5.3) to Height at 1998 for the Arve trial.
Figure 5.26 Regression diagnostics for OLS residuals from the fit of model (5.3) to Height at 1998 for the Arve trial.
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Figure 5.27 Observed and fitted (OLS) mean (a) DBH and (b) Height at 1998, adjusted for 1993 pre-treatment measurement, showing treatment codes and standard error bars for the Arve trial.
H_L1 L_L1 CONTROL HDL1 CONTROL HDL1 H_L1 L_L1
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Figure 5.27 Observed and fitted (OLS) mean (a) DBH and (b) Height at 1998, adjusted for 1993 pre-treatment measurement, showing treatment codes and standard error bars for the Arve trial.
H_L1 L_L1 CONTROL HDL1 CONTROL HDL1 H_L1 L_L1
To allow extrapolation to other ages Candy et al. (1992) simply defined model (5.1) as the height of defoliated trees relative to that of the control by dividing both sides of (5.1) by the mean control height, yC .
Model (5.2) needs to be modified to allow its general application due to the inclusion of the term λy0 involving initial DBH or Height, y . This modification involves 0 averaging both sides of the equation for trees with same timing, frequency, and level of defoliation and presence or absence of disbudding treatment, and applying the following logical constraint for controls (i.e. D,P=0),
0
C C
C y y
y = θ +λ
where yC0 is the mean of the initial value of DBH or Height for control trees. This gives
C
C y
y 0 =(1−θ)
λ (5.4).
Since, it can be assumed that yT0 = yC0=y0 , when the RHS of (5.4) is substituted for λy0 in the averaged form of (5.2) the following model of relative DBH or height of defoliated to control trees is obtained
(
D P)
(
E R ER)
y y C T 3 2 1 2 1 exp 1−θβ +β τ +τ +τ = γ (5.5).To obtain (5.5) the constraint (5.4) on the parametersλ and θ was imposed and this gives an alternative estimate of λ, λ~, to that obtained from the fit of (5.3) where
0 ) ˆ 1 ( ~ C C y y θ − = λ
and θˆ is the estimate from the fit of (5.3). Given as λˆ the simultaneous estimate from the fit of (5.3) (Tables 5.8 and 5.9), it was found that the OLS fit gave a value for λ~ that was closer to λˆ compared to those from the fit using GLS for each of DBH and Height. That is, for DBH98 and OLS the pair (λˆ,λ~) was (1.499,1.509) while for GLS it was (1.473,1.425). For Height98 the difference between λˆ and λ~ was not as great with values of (1.606,1.586) for OLS while GLS gave (1.496,1.487). The effect of the difference between λˆ andλ~ can be seen for OLS in Figs. 5.23 to 5.24 since the 1:1 line based on λˆ does not pass exactly through the control mean whereas if λ~ is used instead the agreement is exact.
Generally, the GLS parameter estimates would be recommended over the OLS because they are more efficient and standard errors are more reliable (Dielman, 1983). Here the OLS estimates are preferred since : (1) the REP variance is relatively insignificant, (2) model parameters are judged to have a similar degree of
significance (based on t-tests of estimate divided by standard error) whether OLS or GLS is used, and (3) the pair (λˆ,λ~) is more consistently estimated using OLS. It would be possible to incorporate constraint (5.4) into the OLS and GLS fitting procedures but this would worsen the fit and thus make the estimates of the parameters of interest, given in (5.5), less accurate.
Note that the RHS of (5.5) is independent of the initial value of DBH or Height at the age of defoliation. This allows (5.5) to be applied to stands of different age at the defoliation episode and/or stands of different site quality to that of BGK. Note also that, for this reason, it was necessary to provide values of y and re-calibrate model 0 (5.2) for the λ parameter to make the model relevant to the Arve trial. By relevant, it is meant that, given that the model is correct, then re-calibrated it gives unbiased predictions of growth losses due to defoliation. In application of the model for predicting such impacts in stands in which C. bimaculata populations are monitored (Section 7.4) the data required to carry out this ‘re-calibration’ are not available. Therefore, it was necessary to sacrifice some predictive power of (5.2) by eliminating
the term λˆ y0 from the fitted model in order to be able to apply the model in the form of (5.5).
Comparison with model (1) of Candy et al. (1992) for E. regnans
The OLS parameter estimates of β1[=exp(β′1)] and β2 [=exp(β′2)] in model (5.3) for Height98 of 0.046 and 0.066 after scaling by θ=0.486 are considerably smaller than those obtained by Candy et al. (1992) of 0.056 and 0.042 for E. regnans height growth for a model of the form of (5.5) but with θ=1. These parameter estimates for DBH98 of 0.098 and 0.200 respectively, obtained after scaling by θ=0.506, reflect the greater impact of defoliation on DBH growth compared to height growth. Note that with these scaled values for DBH98 the effect of 50% actual defoliation corresponds to very close to the effect of a disbudding. Comparisons of the other terms in the model of Candy et al. (1992) to model (5.6) are complicated by the presence of θ in model (5.5), the significant ER interaction, and the ability to include both an early and late defoliation in the same season in model (1) of Candy et al. (1992).
Comparison of early versus late defoliation
The equivalence of the fixed effect model parameterisations of (5.2) or (5.3) can be seen if the term β′2δP +τ1E in (5.3) is replaced by (β′2 +τ1)δP +τ′1L where L is defined as 1 if timing is ‘late’ and 0 otherwise (i.e. ‘early’) and τ′1 =−τ1. This
corresponds to setting the zero reference, or baseline, level to ‘early’ rather than ‘late’ so that τ1' gives the impact of L relative to the zero effect of E. From the fit of model (5.2) it was determined that the ER interaction was not significant (i.e. the hypothesis
0 3 =
τ was accepted). Model (5.5) can be expressed, after dropping non-significant terms, as
(
D P) ( ) ( )
E R y y C T 2 1 2 1 exp exp 1−θβ +β τ τ =Given the above, a comparison of the relative effect of early versus late treatments can be made using the parameter estimates in Tables 5.8 and 5.9. The late defoliation has a greater negative impact on growth than early defoliation at the same intensity for both DBH and Height since τ1 is negative (i.e. and thus τ′1 is positive) in each case. In contrast, Candy et al (1992) found for E. regnans that a single early
defoliation had a greater impact than a late defoliation. However, given the parameter estimates and their standard errors reported in their Table 7, that difference would not be considered statistically significant.
5.6 DISCUSSION
Accuracy of manual defoliation in simulating defoliation caused by C. bimaculata
The manual stripping of leaves in these trials was carried out for a given tree on a single day while disbudding was carried out over a period of one to two months. This was because it is impractical in an artificial defoliation trial to reproduce the ‘bite-by- bite’ defoliation caused by phytophagous insects. Baldwin (1990) reviewed the ability of artificial defoliation experiments to accurately mimic natural defoliation. The deficiencies in artificial defoliation relate mostly to the inability of the simple manual leaf stripping process to adequately mimic the complex nature of the natural processes involved in feeding. These include the nature of tissue shearing, the amount, timing and spatial distribution of tissue removal, the introduction into the plant tissues of fungi, saliva or other contaminants, and the plant’s response to these damaging processes. Baldwin (1990) concluded that in the absence of the ideal simulated herbivory experiment, ecologists need to proceed with caution since mechanical damage does not adequately simulate true herbivory.
The objective of this study is prediction of the impact of defoliation at a level of accuracy that is adequate for decision-making for the control of monitored populations. Therefore, despite the crudeness of the simulation of the impact of natural defoliation on tree growth using artificial defoliation experiments, the use of model (5.5) should be adequate for this purpose (Section 7.4). However, artificial defoliation studies cannot be sufficiently accurate to be useful for developing an
understanding of the complex processes involved in the interaction of phytophagy and the physiological response of the tree such as the production of manna
(Fig. 4.3c). Fundamental research is required to determine the role of manna as a possible deterrent to browsing and the physiological cost to the tree of its production.
It is not possible here to rigorously determine the level of accuracy of the growth impacts of artificial relative to actual defoliation but some general observations can give some encouragement on the usefulness of the models as follows:
1. Disbudding was carried out progressively as new shoots developed over a period which approximated the feeding period for larvae (1 month) for the early
defoliation and larvae and newly emerged adults (2 months) for the late defoliation.
2. The L3 and L4 instars account for 87% of the total leaf biomass consumed (i.e. green weight) (Baker et al., 1999) by an individual from L1 larval to pre-pupal stages. The total development time for L3 and L4 instars is approximately 9 days assuming an average daily temperature of 15oC and the day-degrees required for development (see Table 6.2). This period is much closer to the single day period for artificial defoliation than the corresponding total period of feeding by an individual, under these conditions, of approximately 28 days.
3. Although disbudding was simulated as an ‘all-or-nothing’ process, observations from the caged-shoot feeding trial (Chapter 4) indicated that when larvae disbud a shoot all buds are eaten or damaged. In addition, since the growth impact of removal of newly emerged leaves should be similar to that for bud removal and these leaves are preferentially browsed, then these leaves are likely to be completely removed during the feeding period if they were not removed at the bud stage.
Simplifying the complex growth responses to defoliation
The split-plot-in-time analyses of all annual measurements, given in Table 5.4 for the BGK trial and Table 5.6 for the Arve trial, demonstrate the complex response of both DBH and Height over time to defoliation treatments as indicated by significant
TREAT x YEAR interaction and covariate effects. However, despite this complexity it was possible to simplify the model by taking advantage of the substantial number of annual measurements taken after the initial defoliation. It was observed that
relative growth for all treatments had recovered to that of the control by the end of, or prior to, three growing seasons subsequent to the season in which the defoliation was carried out. This allowed a simple model of the impact of defoliation to ignore the complex dynamic processes involved in the tree’s response to defoliation over subsequent growing seasons. These processes depend on a number of complex interactions including those examined here of defoliation intensity, timing and frequency. This simplification was achieved by : (a) modelling the cumulative effect of treatments at the end of the third growing season subsequent to the season of the defoliation and (b) representing the treatment mean DBH or Height as a proportion of the control mean.
Linear relationship between growth impact and defoliation intensity
Kulman (1971) in reviewing published artificial defoliation studies (mostly in
northern hemisphere pines, spruces, and hardwoods) found a proportional (i.e. linear) relationship between growth impact and intensity of defoliation. This was also found to be the case here. This can be seen by taking the control mean as fixed and varying intensity, P, in model (5.2) with the nonlinear parameter γ set to unity. Since it was found for both DBH98 and Height98 that the estimate of γ was not significantly different from unity, the hypothesis of the linearity of this relationship is empirically supported here.
Comparison with growth impacts of green pruning and plant compensation for insect herbivory
Considerable research has been carried out on the effects on tree growth caused by green pruning (O’Hara, 1989) (i.e. pruning branches from the ground up into the live crown) though very little of this work has been carried out in eucalypts (Pinkard, 1997). Since green pruning is a form of artificial defoliation it is useful to compare research results for these two forms of defoliation to gain some insights into general
tree responses to defoliation. In 1994 Pinkard (Pinkard, 1997; Pinkard et al., 1998) applied three green pruning treatments to four year old E. nitens trees at two sites, one of which was the Gould’s Block site described in Chapter 4. At these two sites, the number of experimental trees were 60 and 30, respectively, with mean heights of 9.5 m and 7.5 m, mean DBHs of 11.6 cm and 9.7 cm, and mean live crown ratios (i.e. the ratio of length of green crown to total tree height) of 0.95 and 0.97 respectively. The three treatments applied were an unpruned control, removal of 50%, and 70% of green crown height from below corresponding to 0, 55% and 88% removal of foliage biomass.
The major difference between such green pruning and artificial defoliation simulating leaf beetle defoliation is that the majority of the foliage type removed by the green pruning described by Pinkard (1997) was old (>2 years) and mature (< 2 years but fully expanded) leaves while apical foliage was left largely intact. Pinkard’s ‘apical foliage’ corresponds approximately to the majority of the new season edible foliage (NSEL) removed in the artificial defoliation trials at BGK and Arve.
Trumble et al. (1993) noted that arthropod herbivory can change canopy structure resulting in a reduction in the light extinction coefficient. That is, the removal of leaves at the edge of the tree crown will expose the previously shaded inner crown to more light. This inner crown is largely made up of mature (or fully expanded) leaves. Pinkard et al. (1998) showed that it was this foliage class that consistently gave the greatest increase in CO2 assimilation (a measure of photosynthetic activity) after green pruning.
The effect of green pruning on height and DBH growth obtained by Pinkard et al. (1998) are similar to those here with DBH growth exhibiting a greater negative impact of defoliation than height growth and a barely detectable height growth loss for light (i.e. their 50% treatment) defoliation. However, direct comparisons of growth loss as a function of defoliation level is not possible due to the radically different nature of the two types of defoliation. However, their results provide a useful qualitative explanation of the relatively minor impact on growth of low levels (i.e. 50% removal of NSEL) of simulated herbivory observed in this study. The
increase in photosynthetic activity of foliage remaining after defoliation, if
independent of the type of defoliation, will offset to some degree the loss of leaf area from simulated herbivory and the loss of corresponding photosynthate as discussed by Trumble et al. (1993).
Influence of neighbouring trees on DBH and height growth response to defoliation
The prediction of growth impacts of defoliation using models (5.2) and (5.5) consider each tree in the stand independently. Therefore, no account is taken of the effect of the level of defoliation of neighbouring trees on the subject tree. If initial pre- treatment measurement of DBH or height can be taken as a relative measure of tree vigour within the particular stand, then model (5.2) does implicitly incorporate the tree’s competitive position in the stand up to the time the treatments were applied. The large influence of this initial measurement on growth even after severe
defoliation treatments were applied, as quantified by model (5.2), reflects the importance of tree vigour in compensating for defoliation impacts on growth.
However, the applied form of the model, (5.5), does not incorporate this information. Even with this information, the spatial arrangement of neighbours that have been defoliated at different intensities and times may influence the growth of the subject tree.
In the BGK and Arve trials defoliated treatment trees were surrounded by a mixture of undefoliated controls and non-experimental trees. These non-experimental trees were excluded because they were either too tall for treatment, too short compared to the required height range, or did not contain a sufficiently large proportion of adult foliage. Therefore, it is realistic to assume that the treatment trees were surrounded by a range of dominant, co-dominant, and sub-dominant neighbours. Also the full range of defoliation levels, timings, and frequencies were imposed within the area occupied by a REP in the BGK trial. These sources of variation are probably a more realistic, though exaggerated, representation of the spatial variation of natural
defoliation levels compared to that obtained if each treatment had been applied at the REP level. Therefore, if there are important inter-tree components of the effect of defoliation on growth, the data used here should take their average effect into
account. The most obvious inter-tree effects that may arise are : (a) the change in light availability due to the defoliation of a neighbour that is competing for light and (b) the reduced root competition from a defoliated neighbour as it allocates carbon to refoliation at the expense of root development. Vranjic and Gullan (1990) in a study of the effect of infestations of the scale insect Eriococcus coriaceus on glasshouse seedlings of Eucalyptus blakelyi found that the reduction in root dry weight due to sap-sucking by E. coriaceus was greater than that for shoots. Since the stands of interest here are those from age 2 to canopy closure and defoliation is only partial, the effect of variable defoliation on inter-tree competition for light is probably not large.