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sodininkystė ir daržininkystė 25(4)

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extremely high frequency as though all membranes were destroyed; τ is a generalized<br />

time constant of the tissue; ψ is a distribution factor of the time constant<br />

(Repo et al., 1993); ψ is a complex number operator [(-1) 1/2 ] and ω is angular<br />

frequency of the alternate current. The ô and ø parameters characterize the whole<br />

system and describe the distribution of cell sizes. Impedance parameters were<br />

normalized to values for 1 cm 3 of tissue. In this report, all data are normalized and<br />

all resistances are expressed as ohm·cm -1 .<br />

For the seedling experiment, mortality tests were conducted on the plants once<br />

they were removed from cold storage, moved to the greenhouse, defoliated with<br />

scissors, and regrown for four weeks. Plant viability was measured as percent seedling<br />

survival. This was collected as binomial data with each plant given a rating of<br />

either 1 or 0. Only plants that had a ≥ 50% stem death were recorded as 0. Percentages<br />

of plant population mortality were then calculated by dividing the number of<br />

plants given a rating of zero over the total number of seedlings per tray per selection<br />

population.<br />

Statistical analysis. With the f<strong>ir</strong>st method, the mortality of apple cultivars was<br />

related to a series of freezing temperatures by logistic regression, from which the<br />

temperature that 20% of trees died was determined (i.e., LT 20<br />

). The predicted values<br />

for LT 20<br />

were obtained from a mixed model (REML) analysis, with year and cultivar<br />

as fixed factors. The morbidity of the surviving trees, which were planted in the<br />

field, was assessed by the increases in root volume and trunk diameter and reduction<br />

in shoot growth. The increase in root volume was calculated for each individual tree.<br />

Both root volume and trunk diameter increases were regressed on the log scale for<br />

each group of cultivar and replicate trees; the percentage increase was calculated<br />

from the ratio of the mean final to mean initial measurements. This ratio of the<br />

means is a more precise estimate of the fractional increase than from the mean of the<br />

ratios from individual trees. To calculate the temperature at which 50% regrowth<br />

occurred a “linear divided by linear” functional relationship was used, i.e., Y = a + (b /<br />

(1 + c t)), where t = temperature, and from which the temperature at RT 50<br />

was<br />

calculated using the estimated parameters. A hardiness index was computed by averaging<br />

the results of the four regrowth attributes. Correlations between our results<br />

(root volume RT 50<br />

) and the Champlain Valley field results (% survival) were used to<br />

validate our findings.<br />

With the second method, unit weighting statistical procedures were used for all<br />

impedance spectral analyses. In most analyses, the full range impedance data (100<br />

Hz to 800 KHz) were used. Please refer to Privé and Zhang (1996) for details.<br />

With the last method, the survival of the three genotypes to freezing was analysed<br />

as a General Linear Model (GLM), (SAS Institute Inc., Cary, N. C.) with the<br />

number of plants surviving as a binomial variant with a logistic link function (McCullagh<br />

and Nelder, 1983). The data were back-transformed [y = 100×exp(p)/(1 +<br />

exp(p))] in order to express the data as percentages.<br />

Results. The whole-plant controlled freezing experiments followed by regrowth<br />

measurements provided a good segregation of the cold hardiness of various<br />

apple rootstocks (Table 1). In the subsample of rootstocks presented in this<br />

manuscript, KSC28 had the highest (-14.3°C) while M.4 had the lowest (-8.1°C)<br />

98

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