Tipos de violencia familiar 1 Violencia física

Comparison with laboratory feeding trials

In the laboratory study of Baker et al. (1999) fresh, new season’s leaves of each of

E. nitens and E. regnans were harvested and fed to replicate cohorts of each C. bimaculata larval instar. Leaves were weighed before and after feeding when

replacing leaves every two days. The difference in leaf weight resulting from feeding were adjusted for moisture loss and wet leaf weights were converted to green leaf area using the specific leaf area (SLA) for a sample of E. nitens leaves typical of those fed to the larvae. The average wet area of the leaves fed to L1 to L4 larvae ranged from 9.44 to 35.9 cm2 respectively but the corresponding SLAs were similar for leaves fed to L1 to L3 instars with mean of 28.5 while the SLA dropped slightly to 27.4 cm2 g-1 for L4 larvae. Overall, the SLA averaged 28.05 cm2 g-1. The total consumption per surviving larva (i.e. the total for L1 to L4 stages) was 0.2345 and 0.3158 g larva-1 for E. nitens and E. regnans respectively.

These green weights and leaf areas consumed per larva were calculated as the total consumed for the cohort divided by the number of surviving individuals at the end of each feeding period. The total larval mortality was 22.8% and 69.1% for E. nitens and E. regnans respectively so that the individual weight and leaf area consumed per larva is inflated by the amount eaten by individuals that died during the feeding period similarly to the estimate of total apparent defoliation given by κˆ .

For E. nitens, given the above SLA, this corresponds to 6.6 cm2 of green leaf area consumed per surviving larva. This corresponds to C

( )

tp where C

( )

tp =NpC

( )

tp

and C

( )

tp is total consumption for the cohort given in model (4.5). Using the total

consumption of the 10 cohorts fed on E. nitens leaves in the Baker et al. (1999) laboratory trial the 95% confidence interval for C

( )

t_p , ignoring variability in SLA, was calculated here as 6.0 to7.2 cm2 larva-1.

Elek and Beveridge (1999) report a laboratory trial to measure mortality and consumption by C. bimaculata L1, L2 and L3 larvae when fed E. nitens foliage sprayed with the biotic insecticide Bacillus thuringiensis subsp. tenebrionis. For the unsprayed (i.e. control) foliage, consumption from L1 to the end of L4 stages averaged 3.4 cm2 (95% confidence limits of 2.6 to 4.1 cm2) per surviving larva. Control survival was 33%, which is substantially lower than that obtained here (Table 4.2) and that obtained by Baker et al. (1999), and is attributed to the poor quality of the foliage (N.Beveridge FT, pers. comm.).

The average leaf area loss per larva, excluding the effect of disbudding, was estimated here as κ =ɵ 12 6 cm. 2 larva-1 which is almost double the loss estimated from the study of Baker et al. (1999) of C

( )

t_p =6.6 cm2 larva-1.

The above laboratory study of Baker et al. (1999) gave relatively precise estimates of green leaf weight and area consumed by each larval instar for a wide range of leaf sizes but narrow range of leaf toughness as measured by SLA. However, to obtain an estimate of leaf area loss at the shoot level, notwithstanding the problem of

estimating potential losses, these results would need to be applied to typical shoots and development times for each larval instar in combination with models of feeding behaviour. Also the impact of disbudding cannot be estimated by applying the laboratory results to the field.

The estimate of ELAL obtained here is applicable for shoots similar to the sample of shoots used here, with their inherent distribution of leaf size and leaf phenology, and for actual larval feeding behaviour using a reasonably close approximation to the natural environment. Therefore, although the laboratory trial of Baker et al. (1999) gives an accurate estimate of consumption rate it does not provide by itself realistic data on overall feeding impact. In contrast, the feeding observed in the caged-shoot trial is a realistic representation of feeding effects. However, because growth impact was only measured at the aggregate shoot level rather than the individual leaf level, development of a more realistic simulation model was not possible. Instead the

estimate of ELAL as κ =ɵ 12 6 cm. 2 larva-1 is a compromise taking into account actual, but unobserved, feeding behaviour on existing leaves and assumed disbudding

behaviour both aggregated to the shoot level. Even after excluding the impact of disbudding on growth, the value of * =κˆ =12.6

C is almost double that of

consumption C =6.6 cm2 larva-1 so that loss of potential leaf area is significant and needs to be incorporated in prediction of defoliation as in Valentine’s (1980)

‘apparent defoliation’.

Comparison of predictions of growth impact using the ANOVA/response surface and process/simulation models

Excluding the effect of disbudding, both the linear model (4.11) fitted to the batch- size means and the process/simulation model with the estimated value of ELAL applied to the sample of shoots, give similar relationships between growth loss and population size (Figs. 4.18 and 4.19). The main difference between model (4.11) is that the process/simulation model gives a greater absolute growth loss at the early treatment due to the impact of disbudding. The disbudding effect accounts for the greater apparent defoliation at low population levels than that predicted from (4.11).

An indication of the effect of disbudding on shoot growth can be obtained from Fig. 4.18 using a population size of five. After feeding mortality of some 40% [i.e.

) 4 . 0 1 ( 0 − =N

Np ] the remaining three larvae consume on average 3x12.6=37.8 cm 2

green leaf area. Therefore, from Fig. 4.18 and a loss of leaf area of approximately 134 and 66 cm2 for early and late times respectively, the corresponding losses due to disbudding alone are 96 and 28 cm2 per shoot.

Direct comparison of κˆ and τˆ is complicated by the indirect incorporation of the pooled (i.e. across times) disbudding effect in τˆ as well as the different definitions of

N used in each case. If τˆ (Table 4.6) is scaled by multiplying by N /0 Np (i.e. using

average survival given in Table 4.2 as 60%) then the value obtained is 17.5 cm2 larva-1. However, this value also includes the pooled, disbudding effect.

The direct incorporation of the effect of disbudding in the process/simulation model is a more robust method than that implied by either model (4.11) or the nonlinear

model (4.12). Although the disproportionate growth loss at the 10-batch size was predicted by model (4.12) (Fig. 4.11), no distinction was possible between this effect at the early compared to late time due to the necessity of pooling the two times. Note also that the process model gives better predictions of batch means that model (4.11) especially for the early time as seen in Figs. 4.18 and 4.19. For the early time the process model predicts the growth loss for the 10-batch size as intermediate between models (4.11) and (4.12) (i.e. compare Figs. 4.11 and 4.18). Since model (4.12) is purely an empirical, nonlinear interpolation of the means in Fig. 4.11 the generality of this model is limited.

A further difference is the increasing size of the confidence bounds on predictions with population size, seen in Figs. 4.18 and 4.19, as a result of applying the

confidence bounds obtained for κˆ in the simulation algorithm. These ‘proportional’ bounds are more ‘natural’ than the fixed-size confidence intervals for the REML means (Figs. 4.11, 4.18, and 4.19).

For the above reasons, the economic analyses described in Chapter 7 apply the regression of growth loss or equivalently apparent proportional defoliation, P/100, on population size using the coefficients based on the process/simulation model given in Table 4.7.

Generalisations of the process/simulation model

Different feeding behaviour, particular with respect to disbudding, will give different growth impacts. Since the impact of disbudding is considered independently of growth losses for existing leaves as quantified using ELAL, if different assumptions on the prevalence and degree of disbudding are made then the above simulation model can be re-run with these assumptions and growth impacts re-estimated. For example it may be assumed or predicted that a given proportion of browsed shoots are not disbudded and/or a given proportion of buds on browsed shoots are left intact.

Apart from the way disbudding is incorporated, the extra generality possible in application of the above process/simulation model resides mainly in its ability to predict shoot growth in the absence of browsing using steps (C1) to (C9). Growth of leaves and thus shoots can be simulated for any part of a growing season using the

day-degree-driven leaf expansion model and the initial phenology of the shoot’s leaves. However, more general models of leaf recruitment need to be incorporated in step (C8). These leaf recruitment models would need to predict not only recruitment of new leaf buds but also natural bud mortality where this is mortality due to the physiological process of shedding buds rather than removal by invertebrate browsing. Observations suggest that natural mortality of leaf buds is highly variable and can be substantial (J. Elek FT, pers. comm.).

4.6SUMMARY

Apparent defoliation was modelled as the sum of two components : (a) the combined total of leaf area lost directly from consumption and indirectly from consumption of actively expanding leaves, and (b) loss of potential leaf area due to removal of buds (i.e. disbudding). A general dynamic model of leaf expansion and larval feeding was used to provide a framework for the development of empirically models of apparent defoliation calibrated using data from a caged-shoot feeding trial. Two models were used : (i) an ANOVA/linear response surface model which gave a combined estimate of losses due to (a) and (b), and (ii) a process/simulation model which estimated (a) and (b) separately.

The caged-shoot trial used 9 replicate shoots of each nominal egg batch sizes of 10, 20, and 30 eggs with each replicate located on a different tree. Visually matched control shoots, a caged-control and an uncaged (sprayed) control, were also allocated to each of the 27 sample trees. The 27 sample trees in the trial were divided across two times, 18 trees in December (early) and 9 in February (late). The two times were pooled for the ANOVA/response surface method. This method compared treatment to control shoot growth to estimate apparent defoliation.

Estimation using the linear mixed model was used to extract the maximal amount of information in the trial on the contrast of treatment and control growth in order to estimate the mean apparent defoliation for each batch size. Unfortunately,

imprecision in these estimates due to variation in growth between matched shoots, variation in feeding success, and the small number of replicates meant that

predictions from the linear response surface model were subject to a large amount of uncertainty.

The process model was used to estimate apparent defoliation by comparing growth of the treatment shoots both with (actual) and without (predicted) feeding using the leaf expansion models described in Chapter 3. Growth losses were estimated using a profile log-likelihood to estimate ‘effective leaf area loss per larva’ (ELAL) for existing leaves, combined with the observed number of surviving larvae, and the loss of potential leaf area due to the loss of newly recruited leaves (i.e. disbudding). The use of the process/simulation model overcame some of the difficulties mentioned above for the ANOVA method but the estimate of ELAL was also subject to considerable uncertainty.

The two methods gave similar estimates of losses for late (February) but for the early (December) population the process/simulation model predicted greater losses at low population levels (<20 eggs per shoot) due largely to the explicit modelling of losses due to disbudding. Even after excluding the impact of disbudding, apparent

defoliation estimated using an ELAL of 12.6 cm2 larva-1 (95% confidence interval=9,16 cm2 larva-1) for larvae successfully completing development (i.e. mean=60%) was almost double the green leaf area consumed in a laboratory feeding trial. Therefore, the loss of potential leaf area was significant and was incorporated in prediction of defoliation as a function of population size.

Percent defoliation, including the effect of disbudding, for populations at or above 5 eggs per shoot was predicted from simulation of defoliation in December using the process model and the sample of 54 shoots. Defoliation was estimated at 8.7% plus 0.6% for each unit increase in number of eggs per shoot above 5. The corresponding figures for late (February) defoliation using the sample 27 shoots were 7.6% and a 1% increase per unit increase in population size above 5. Simulating populations below 5 eggs per shoot was not considered since these are well below any possible economic threshold.

CHAPTER 5

MODELS OF THE IMPACT OF SIMULATED BROWSING ON

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