ONLINE SUPPORTING INFORMATION
Appendix S1-Detailed description of the model
(a) Parameters
The model discussed here has 14 parameters; three govern mortality, five relate to small-scale factors and six to large-scale factors. A summary of all chosen parameter values is given in Table 1 of the main paper. Recall from the main text of this paper that parameters are termed ‘small-scale’ because they relate to local mortality which is governed by factors spatially encompassing the crop and its immediate margins, and temporally within the period of pollen shed. By contrast ‘large-scale’ parameters drive global mortality which is governed by factors averaged over an entire landscape or regional scale and over a whole growing season. All parameters have assumed values except for the two principal mortality parameters denoted g and h, which are estimated.
Mortality parameters
Regarding the three mortality parameters, the parameter g(E) represents the 'worst-case' probability that a given larva will suffer mortality from ingesting Bt maize pollen deposited onto its host plant located in the field margin at distance E from the nearest edge of the Bt maize crop. Here, the term 'worst-case' refers to potential mortality, as measured in the laboratory or under controlled experimental conditions, before allowance for factors such as physical effects and temporal coincidence, which reduce this mortality to realistic values observed in the field (see below). The parameter g represents an average probability over factors such as whether the margin is on the upwind or downwind side of the field, or time of day. The parameter h represents the 'worst-case' probability that a given larva will suffer mortality from ingesting Bt maize pollen deposited onto its host plant located within the Bt maize crop. The third mortality parameter, m, represents the sensitivity of the assumed species to pollen of the particular Bt maize variety being considered. Sensitivity is expressed by the LC50, i.e. the lethal concentration value that kills on average half of the larvae of the instar considered, measured in units of pollen grains cm-2 leaf area of the host-plant. Obviously, the smaller is m, the more sensitive is the species.
The parameters g(E), h and m are specific to the host plant, lepidopteran species and larval stage modelled, but generic across regions.
Small-scale parameters
Two small-scale parameters are specific to regions, host plants and species; parameters e and f measure, respectively, the density of the host plant within the maize crop and in the field margins, in plants m-2. For simplicity it is assumed that host plants occur spatially at random within crops and field margins. Two further small-scale parameters relate to field size and are therefore specific to regions but generic across host plant and species. For simplicity it is assumed that Bt maize fields are square. The parameter C represents the average size of a maize field in hectares and the parameter D represents the average width of a field margin in metres. When parameterizing the model for specific regions, allowance may have to be made for possible bimodal distributions of field margins, because fields in a region may often have margins that are several metres wide or have no margins at all. The final parameter, w, is the width in metres of the non-Bt maize strips which represent the simulated mitigation measures studied in this paper, and which are assumed to be planted around each of the four field edges.
Large-scale parameters
Two large-scale parameters model effects that reduce exposure. The parameter x represents the proportion of larvae that remains exposed, after allowance for a set of physical effects that include: any degradation of pollen toxicity or palatability; rain washing pollen off leaves; larvae feeding on the underside of leaves where pollen densities are smaller; larval avoidance of leaf midrib area where pollen densities tend to be aggregated; larvae feeding on lower leaves on which less pollen has been deposited through the shading effect of leaves above them, etc.
The parameter a represents the proportion by which exposure is reduced due to lack of temporal coincidence between the susceptible larval stage concerned and the period over which Bt maize pollen is shed. For simplicity, the model considers a single larval instar. The quantification of temporal coincidence is conceptualised as follows. Lepidopteran larvae do not enter instars synchronously; it is assumed that there is a bivariate distribution for the days on which larvae enter and leave the particular susceptible instar modelled. Regarding anthesis, similarly, the period within the flowering of maize when pollen is shed is asynchronous between individual crop plants and it is assumed that there is a bivariate distribution for the days on which plants begin and end shedding pollen. Consider the ellipsoids that represent the 95th percentiles of these two bivariate distributions. This model assumes that the full exposure of larvae to pollen is reduced proportionately by the degree to which the overlap between these two ellipsoids is incomplete. Specifically, the parameter a measures the proportion of the ellipsoid that represents the 95th percentile for instar development that is not overlapped by the ellipsoid that represents the 95th percentile for pollen shed. Note that the expected actual mortality rate for an individual larva is therefore xag(E) within the field margin and xah within the crop.
The parameters x and a are assumed to be specific to the geographic region, host plant, lepidopteran species and larval stage modelled.
The other three large-scale parameters of the model control aspects of large-scale demographic aspects of exposure and are all specific to regions but generic across host-plant and species. The parameter z represents the proportion of arable fields that are cropped with maize in any given year in the defined region. The parameter v represents the proportion of maize sown within the defined region that is the particular variety of Bt maize under consideration. The parameter y represents the proportion of the lepidopteran host plant that is found within arable crops and in their margins (as opposed to gardens, woodlands, non-arable fields, etc., which are too far from Bt maize fields for pollen deposition to present any quantifiable risk). Note that the proportion of the population potentially exposed, after allowance for reduction due to these large-scale demographic factors is then yzv. Note further that, in this paper, the value of the product yzvxa is denoted by the parameter L.
(b) Estimates of individual (local) mortality
Overall strategy
In the next stage of the model construction two relationships are defined and these are then integrated. Firstly, an established mortality-dose relationship, for the particular instar and species being considered, is expressed on appropriate scales. In particular, this first relationship is reformulated as a linear regression of logit-transformed probability of mortality on logarithimically-transformed dose in units of pollen grains cm-2 host-plant leaf area.
Secondly, an established pollen deposition-distance relationship for Bt maize pollen, which defines the decline in pollen deposited on the host-plant concerned within the margins of the field, on appropriate scales, with increases in E, the distance from the Bt maize crop. In particular, this second relationship is reformulated as a linear regression of logarithmically-transformed dose in units of pollen grains cm-2 on E, the distance to the nearest source of Bt maize pollen.
These two relationships are then integrated to remove the variable dose, to yield field margin mortality-distance relationships for individual larvae of the chosen larval/host plant combinations. This new relationship is a regression of logit-transformed probability of mortality on distance, E, and effectively defines the parameter g(E). The logit relationship facilitates a simple closed solution for values of g for any given value of E.
The average mortality within a margin of any particular width, say D, in denoted by μ=μ(D). The estimated value of μ(D) is found by numerical integration of g(E), over all the possible values of E from 0 ,…, D, within the margin.
Estimates of the within-crop mortality, denoted by parameter h, may then be derived by noting that pollen deposition within a maize crop is approximately 2.7 times that at the edge.
Effect of maize MON810 pollen on larvae of Inachis io (from Perry et al., 2010)
As an example, for maize MON810 pollen, Perry et al. (2010) estimated the LC50 as 5800 pollen grains cm-2 leaf area for first instars of Inachis io. However, quantification of the mortality-dose relationship through a logit-regression relationship requires information concerning not only the intercept (effectively given by the LC50) but also the slope (the rate of change of mortality with change of concentration).
Perry et al. (2010) noted that their calculated estimates of mortality were highly sensitive to the slope, measuring the rate of change of mortality with concentration, but accurate estimates of such slopes are rarely available for non-target Lepidoptera. Perry et al. (2010) adopted a value for the slope of 2.473 found by Saeglitz et al. (2006) in preference to another due to Felke et al. (2010), because it gave a worst-case estimate that would not underestimate mortality; they noted that had the latter value been used, then the mortality rates reported would have been about 8 × 10-7 smaller. (Note that since the slope is invariant under change of scale for logit regression in bioassay, the estimated slope would apply equally both to concentrations expressed in units of pollen grains cm-2 leaf area and to doses in units of ng of truncated toxin used by other authors.)
Hence, if pB represents the proportion of I. io individuals that suffer mortality as a result of a concentration, d, expressed as the number of Bt maize pollen grains cm-2, then:
logit(pB) = -9.30 + 2.47log10d
(Note that at the LC50, m = d = 5800, then 2.47log10d = 9.30, so logit(pB) = 0, as required.)
The concentration, d, of pollen grains adhering to the leaves of host plants declines rapidly with increasing distance in metres, E, from the maize source as noted by several authors. Perry et al. (2010) allowed for the fact that Urtica dioica, the host-plant of I. io, has hairy leaves that retain a surfeit of pollen. The relationship used was:
log10d = 2.346 – 0.145E
The above two equations are combined to express mortality within the field margin directly in terms of distance from the edge of the crop, thus yielding the parameter denoted g(E) above:
logit(pB) = -3.504 - 0.359E, so
g(E) = pB = exp(–0.359E) / [33.25 + exp(–0.359E)]
Note that at the very edge of a Bt maize crop, where E=0, the estimated mortality rate is g(0) = pB = 0.0292 (equivalent to 1 individual in every 34.25) and that 2m into the margin this rate itself is approximately halved.
The average mortality within a margin of width D = 2m, μ(2), was estimated by numerical integration to be 0.0209. As a rough guide, the value of μ(D) is about double the value for small values of D (very narrow margins) than for D = 5, and there is a further approximate halving of μ(D) at D = 10.
The estimated value of the parameter h was derived from 2.7g(0) = h = 0.0805
Effect of maize 1507 pollen on larvae of the five hypothetical species considered in this paper
The mortality-dose relationship assumed here has the same slope, 2.473, as that assumed by Perry et al. (2010) (see above), so
logit(p) = α + 2.473log10d
Here, the intercept, α, in equation 1 is determined by the sensitivity of the species to the Cry1F protein, expressed through m, the LC50, for which logit(p)=0. There are five LC50 values considered here (Wolt et al. 2005 and see Table 1), that form a geometric series with 11.4-fold increments: m = 1.265, 14.36, 163.2, 1853 and 21057. These represent values for the larvae of five hypothetical species with differing sensitivities, denoted, respectively, as ‘worst-case, extreme’, ‘very high’, ‘high’, ‘above-average’ and ‘below-average’; the rationale for these values is provided in Appendix S3 (Supporting Information). The five values of α corresponding to these different sensitivities are found from the equation above, by substituting the relevant value of m into the equation α=-2.473log10m. This mortality-dose relationship is then integrated with a field-derived regression of logarithmically-transformed dose, d, on distance, E, from the nearest source of the pollen: log10d =2.346–0.145E, (the same relationship used by Perry et al. (2010), to derive a linear mortality-distance relationship for mortality of larvae in the margin, on the logit scale. Backtransformed to the natural scale, the estimated probability of mortality, g(E), for a larva at distance E into the margin from the nearest source of pollen at the edge of the field (Figure 1), is given by:
g(E) = exp(–0.35853E)/[β + exp(– 0.35853E)],
where values of β for different sensitivities are calculated as, respectively: 0.003893, extreme; 0.05290, very high; 0.7190, high; 9.774, above-average; and 132.9, below-average (Figure 2). The estimated proportion of all the larvae in the 2m-wide margin that suffer mortality is denoted by µ, and is obtained by averaging the value of g(E) over the margin, using numerical integration of equation (2). The estimated probability of mortality, h, for a larva within the Bt crop (Figure 1), is calculated, as in Perry et al. (2010) from:
h = 2.757g(0) = 2.757/(β +1) (and see Figure 2 of main paper).
Calculating overall local mortality