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Figure 4 Akaike weights of models plotted against the week up to which cumulative vector pressure was calculated. Filled triangles: using vectors only (inoculum and resistance effects excluded) and using the best relative efficiency factor (REF) set (nho80, based on van Hoof, 1980); open triangles: using Aphis fabae only; filled squares: using vectors only, but with all REF sets; open circles: based on all models containing vector pressures, that is including those models containing inoculum and resistance effects. The vertical line indicates the average time of opening of the first flowers [Biologische Bundesanstalt, Bundessortenamt and Chemical industry (BBCH) growth stage 60] in the potato crops.

Figure 4 Akaike weights of models plotted against the week up to which cumulative vector pressure was calculated. Filled triangles: using vectors only (inoculum and resistance effects excluded) and using the best relative efficiency factor (REF) set (nho80, based on van Hoof, 1980); open triangles: using Aphis fabae only; filled squares: using vectors only, but with all REF sets; open circles: based on all models containing vector pressures, that is including those models containing inoculum and resistance effects. The vertical line indicates the average time of opening of the first flowers [Biologische Bundesanstalt, Bundessortenamt and Chemical industry (BBCH) growth stage 60] in the potato crops.

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*Upper infection threshold (%) for Potato virus Y (PVY): A-clone = 0; B-clone = 0; SE = 0; E1 = 0.2; E2 = 0.5; E3 = 1; B = 10; FOS = Farm’s own seed (not certified). 609 = plant emergence at 9 + 4 days; 60 = opening of the first flower in population at 60 + 4 days. SR: PVY resistance level of cultivar (www.europotato.org); |: initial PVY level as set by the classification of seed lots used in the field (upper infection threshold); L: initial PVY level of the seed potatoes as measured by a leaf test after emergence of the plants; Y: final PVY level measured by tuber tests after harvest; D: absolute increase of PVY level from initial to final level during the growing season. 4The level of resistance to PVY was not available from the database for this cultivar; resistance level was set to 4. °Seed lot was not certified; initial virus level was determined based on a leaf test after emergence. Table 1 Experimental conditions of the trial sites in 2007-09
*Upper infection threshold (%) for Potato virus Y (PVY): A-clone = 0; B-clone = 0; SE = 0; E1 = 0.2; E2 = 0.5; E3 = 1; B = 10; FOS = Farm’s own seed (not certified). 609 = plant emergence at 9 + 4 days; 60 = opening of the first flower in population at 60 + 4 days. SR: PVY resistance level of cultivar (www.europotato.org); |: initial PVY level as set by the classification of seed lots used in the field (upper infection threshold); L: initial PVY level of the seed potatoes as measured by a leaf test after emergence of the plants; Y: final PVY level measured by tuber tests after harvest; D: absolute increase of PVY level from initial to final level during the growing season. 4The level of resistance to PVY was not available from the database for this cultivar; resistance level was set to 4. °Seed lot was not certified; initial virus level was determined based on a leaf test after emergence. Table 1 Experimental conditions of the trial sites in 2007-09
Figure 1 (A) A colony of black bean aphids (Aphis fabae) on the winter host (snowball tree, Viburnum opulus) in the Tyrnava-Liminka area. (B) Yellow pan traps set up next to a potato field.
Figure 1 (A) A colony of black bean aphids (Aphis fabae) on the winter host (snowball tree, Viburnum opulus) in the Tyrnava-Liminka area. (B) Yellow pan traps set up next to a potato field.
Table 2 List of variables, indices and abbreviations used in modelling
Table 2 List of variables, indices and abbreviations used in modelling
PVY, Potato virus Y. Table 3 The average number per field of aphids considered as vectors of PVY (van Hoof, 1980) obtained from yellow pan traps in the potato fields of the high-grade seed potato production zone in Finland
PVY, Potato virus Y. Table 3 The average number per field of aphids considered as vectors of PVY (van Hoof, 1980) obtained from yellow pan traps in the potato fields of the high-grade seed potato production zone in Finland
Figure 2 Log-transformed weekly counts of winged aphids per field detected using yellow pan traps in the Tyrnava-Liminka area (high-grade seed potato production zone, HG zone) during 2007 (dotted lines), 2008 (dashed lines) and 2009 (solid lines). Counts of the most common vector species, (A) Aphis fabae and (B) Rhopalosiphum padi, were singled out, whereas (C) the counts of other species with documented ability to transmit Potato virus Y (PVY) (Acyrthosiphon pisum, Aphis pomi, Aulacorthum solani, Capitophorus hippophaes, Macrosiphum euphorbiae, Metopolophium dirhodum and Myzus persicae) (van Hoof, 1980) were combined. The vertical line indicates the approximate week in which the potato crops under study emerged [Biologische Bundesanstalt, Bundessortenamt and Chemical industry (BBCH) growth stage 09] in a total of 19 fields in 2007-09.
Figure 2 Log-transformed weekly counts of winged aphids per field detected using yellow pan traps in the Tyrnava-Liminka area (high-grade seed potato production zone, HG zone) during 2007 (dotted lines), 2008 (dashed lines) and 2009 (solid lines). Counts of the most common vector species, (A) Aphis fabae and (B) Rhopalosiphum padi, were singled out, whereas (C) the counts of other species with documented ability to transmit Potato virus Y (PVY) (Acyrthosiphon pisum, Aphis pomi, Aulacorthum solani, Capitophorus hippophaes, Macrosiphum euphorbiae, Metopolophium dirhodum and Myzus persicae) (van Hoof, 1980) were combined. The vertical line indicates the approximate week in which the potato crops under study emerged [Biologische Bundesanstalt, Bundessortenamt and Chemical industry (BBCH) growth stage 09] in a total of 19 fields in 2007-09.
Table 4 Comparison of model structures with different sets of explanatory variables used for modelling D (i.e. the difference between final and initia virus incidence)? @Shown are the corrected Akaike information criterion values (AIC,), and Akaike weights (w), the best REF set (REF’) and the best (x’) where applicable Q: all vector species considered; A: only Aphis fabae included; L: inoculum based on leaf test; |: inoculum based on seed grade. Models are sorted b increasing AIC, for V = QandZ =L. Maximum Akaike weights are indicated in bold.
Table 4 Comparison of model structures with different sets of explanatory variables used for modelling D (i.e. the difference between final and initia virus incidence)? @Shown are the corrected Akaike information criterion values (AIC,), and Akaike weights (w), the best REF set (REF’) and the best (x’) where applicable Q: all vector species considered; A: only Aphis fabae included; L: inoculum based on leaf test; |: inoculum based on seed grade. Models are sorted b increasing AIC, for V = QandZ =L. Maximum Akaike weights are indicated in bold.
Table 5 Parameter estimates of (A) the individual models and (B) those based on multimodel inference (for abbreviations, see Table 2)
Table 5 Parameter estimates of (A) the individual models and (B) those based on multimodel inference (for abbreviations, see Table 2)
Figure 3 Importance of explanatory variables for modelling the increase of Potato virus Y (PVY) (D) over the growing season. The importance was calculated as cumulative Akaike weights, that is the figures sum up probabilities of all tested models which contain a given explanatory variable. The importance values were calculated for two sets of models, containing two alternative measures of initial inoculum: either the initial leaf test (L), black columns; or the seed grade (I), striped columns. The columns show the importance of ‘Vectors’, that is the cumulative vector pressure Q; the ‘inoculum’, that is the initial leaf test or seed grade; and ‘Resistance’, that is PVY resistance of the cultivar (R) (see also Table 2).
Figure 3 Importance of explanatory variables for modelling the increase of Potato virus Y (PVY) (D) over the growing season. The importance was calculated as cumulative Akaike weights, that is the figures sum up probabilities of all tested models which contain a given explanatory variable. The importance values were calculated for two sets of models, containing two alternative measures of initial inoculum: either the initial leaf test (L), black columns; or the seed grade (I), striped columns. The columns show the importance of ‘Vectors’, that is the cumulative vector pressure Q; the ‘inoculum’, that is the initial leaf test or seed grade; and ‘Resistance’, that is PVY resistance of the cultivar (R) (see also Table 2).
Figure 6 The effect on model fit of the removal of various vector species from the data set, as measured by changes in Akaike’s information criterion (AIC). Models predicting the absolute increase of Potato virus Y (PVY) incidence during the growing season (the difference of incidence between the yield and the seed potatoes) were either based on a full cumulative vector pressure (CVP) data set or on a reduced data set from which individual vector species were removed. Cumulative vector pressure was calculated based on the relative efficiency factors of van Hoof (1980). Lines depict the change in AIC that occurred after removal of Aphis fabae (filled squares), Aulacorthum solani (open circles) or Rhopalosiphum padi (filled triangles). Increases in AIC mean decrease of model fit, that is the strongest loss of predictive ability of the model occurred when A. fabae caught in weeks 26, 27 and 28 were removed from the data set. Note that the absolute contribution of vectors to PVY spread is displayed in Fig. 4, while this figure shows the deterioration of the model with the removal of the vector species, that is for the later weeks (after week 31), the increase of the AIC occurs on a much lower level of model fit than for the earlier weeks. Figure 5 Akaike weights for the sets of relative vector efficiency factors. ho80: van Hoof (1980); ha83: van Harten (1983); si84m: Sigvald (1984); si84p: proposed by Sigvald (1984) but not based on direct measurements; hr89: Harrington & Gibson (1989); bo90: De Bokx & Piron (1990); feO9: FERA (2009); ve10n: Verbeek etal. (2010) for PVY"; ve10Ontn: Verbeek et al. (2010) for PVY™"; count: unweighted number of aphids.
Figure 6 The effect on model fit of the removal of various vector species from the data set, as measured by changes in Akaike’s information criterion (AIC). Models predicting the absolute increase of Potato virus Y (PVY) incidence during the growing season (the difference of incidence between the yield and the seed potatoes) were either based on a full cumulative vector pressure (CVP) data set or on a reduced data set from which individual vector species were removed. Cumulative vector pressure was calculated based on the relative efficiency factors of van Hoof (1980). Lines depict the change in AIC that occurred after removal of Aphis fabae (filled squares), Aulacorthum solani (open circles) or Rhopalosiphum padi (filled triangles). Increases in AIC mean decrease of model fit, that is the strongest loss of predictive ability of the model occurred when A. fabae caught in weeks 26, 27 and 28 were removed from the data set. Note that the absolute contribution of vectors to PVY spread is displayed in Fig. 4, while this figure shows the deterioration of the model with the removal of the vector species, that is for the later weeks (after week 31), the increase of the AIC occurs on a much lower level of model fit than for the earlier weeks. Figure 5 Akaike weights for the sets of relative vector efficiency factors. ho80: van Hoof (1980); ha83: van Harten (1983); si84m: Sigvald (1984); si84p: proposed by Sigvald (1984) but not based on direct measurements; hr89: Harrington & Gibson (1989); bo90: De Bokx & Piron (1990); feO9: FERA (2009); ve10n: Verbeek etal. (2010) for PVY"; ve10Ontn: Verbeek et al. (2010) for PVY™"; count: unweighted number of aphids.
Figure 8 The numbers of winged (striped columns) and unwinged morphs (black columns) of Aphis fabae observed on the winter host Viburnum opulus in the Tyrnava-Liminka area during the potato-growing seasons (A) 2008 (n = 4) and (B) 2009 (n = 6), respectively. Error bars indicate standard deviation. Figure 7 Potato virus Y (PVY) increment over the growing season (response variable D) plotted against the total counts of Aphis fabae up to week 28 (explanatory variable A), both In(y + 1) transformed.
Figure 8 The numbers of winged (striped columns) and unwinged morphs (black columns) of Aphis fabae observed on the winter host Viburnum opulus in the Tyrnava-Liminka area during the potato-growing seasons (A) 2008 (n = 4) and (B) 2009 (n = 6), respectively. Error bars indicate standard deviation. Figure 7 Potato virus Y (PVY) increment over the growing season (response variable D) plotted against the total counts of Aphis fabae up to week 28 (explanatory variable A), both In(y + 1) transformed.
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