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Using ‘sentinel’ plants to improve early detection of invasive plant pathogens [1]

['Francesca A. Lovell-Read', 'Mathematical Institute', 'University Of Oxford', 'Oxford', 'United Kingdom', 'Stephen Parnell', 'Warwick Crop Centre', 'School Of Life Sciences', 'University Of Warwick', 'Coventry']

Date: 2023-03 

We first considered the effects of implementing a monitoring programme without sentinel plants (the baseline case described in Section 2.2). As expected, lower EDPs were achieved with larger sample sizes N C (inspecting more plants) and smaller sample intervals Δ (inspecting more frequently) ( Fig 2C ). These baseline values provide a point of comparison that we will use to evaluate the relative effects of sentinel-based strategies in subsequent sections. We also performed sensitivity analyses for different baseline parameter values ( S2 Text , S1 Table and S2 and S3 Figs). In every case that we considered, the qualitative behaviour of the baseline EDP as N and Δ were varied was unchanged.

3.2 Introducing sentinel plants–choosing P S and N S carefully is critical

We next considered introducing sentinel plants to the population using the full model described in Section 2.1. This raises two important questions.

How many sentinels should we add to the population (P S )? Although the relatively fast symptom development of sentinels facilitates the rapid detection of disease, this is only beneficial if the faster discovery time corresponds to a lower EDP. Since adding sentinels will also increase the rate of pathogen transmission, including too many sentinels negates the benefits of fast detection, particularly if (as assumed here) sentinel plants are more infectious than crop plants when Undetectable. How many of those sentinels should we include in the sample (N S )? Although a natural choice may be to sample preferentially from the available sentinel population (i.e. to include as many sentinels as possible in the sample), this is not necessarily optimal. For example, if the number of sentinels in the population is close to the sample size, this strategy would lead to frequent repeated sampling of the same set of plants, resulting in a reduction in the information gained per sample (see S1 Text and S1 Fig).

In this section, we demonstrate how choosing P S and N S carefully is critical to avoid the introduction of sentinel plants having a negative effect and instead achieve the maximum possible reduction in EDP for a given sampling effort. For almost all values of P S , N and Δ that we considered, when the number of sentinels included in the sample was optimised (as indicated in Fig 3), a reduction in the EDP compared to the baseline value was achieved (Figs 4A, 4B and 4C). However, when the number of sentinels in the population or the sample was chosen non-optimally, sentinel plants were less beneficial and in some cases detrimental (Fig 3A).

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TIFF original image Download: Fig 3. The optimal number of sentinel plants to include in the sample depends on the sample size, sample interval and the total number of sentinels in the population. A. The effect of varying the number of sentinels included in the sample (N S ) on the percentage change in EDP compared to the baseline level, in the case P S = 50, N = 50, Δ = 30 days. The number of sentinels in the sample for which the reduction in EDP is maximised ( ) is indicated by the green circle. Black dashed line marks the baseline EDP. B. The optimal number of sentinels to include in the sample when P S = 50, as the sample size (N) and sample interval (Δ) vary. Solid black line marks the maximum possible number of sentinels that could be sampled at any time (min(P S , N)). Grey shading marks the unfeasible region in which N S exceeds this maximum. Green circle marks the case considered in A (P S = 50, N = 50, Δ = 30 days). C. The analogous figure to B, but with P S = 100 sentinels added to the population. D. The analogous figure to B, but with P S = 200 sentinels added to the population. https://doi.org/10.1371/journal.pcbi.1010884.g003

As described in Section 2.5, we considered three fixed values for the number of sentinels added to the population (P S = 50, P S = 100 and P S = 200) and a range of sample sizes (N) and sample intervals (Δ). For each combination of (P S , N, Δ) that we considered, we ran the Bayesian optimisation algorithm (see Section 2.5 and S3 Text) to identify the choice of N S corresponding to the greatest reduction in EDP compared to the baseline value for that (N, Δ) pair. We denoted this optimal choice of N S by . For example, in the case P S = 50, N = 50, and Δ = 30 days, the optimisation indicated that the maximum reduction in EDP was achieved when sentinels were included in each sampling round (out of a total possible maximum of 50) (Fig 3A). This choice of sampling strategy (indicated by the green circle) led to a 16% reduction in the EDP compared to the baseline value. When N S was instead chosen to take another of the values considered, smaller reductions (or even increases) in the EDP were achieved. The optimal number of sentinels to include in the sample across the range of sample sizes (N) and sample intervals (Δ) is shown for P S = 50, 100 and 200 in Figs 3B, 3C and 3D respectively, with the corresponding reductions in the EDP compared to the baseline shown in Figs 4A, 4B and 4C.

The optimal number of sentinel plants to include in the sample depended strongly on the sample interval and on the relationship between the sample size and the total number of sentinels available (Figs 3B, 3C and 3D). When Δ = 90 days, 120 days or 150 days, the optimal strategy in every case we considered was to sample the maximum possible number of sentinels (i.e. ). Since this result is identical for all three of those cases, they are represented by the single yellow line in Figs 3B, 3C and 3D. However, for the shorter sample intervals of Δ = 30 and 60 days (blue and pink lines respectively), the optimal monitoring strategy involved sampling a combination of sentinel plants and crop plants. In other words, in those scenarios it was preferable to sample fewer than the maximum allowable number of sentinels (i.e. ) for a range of choices of P S and N, particularly when the total number of sentinels in the population was not substantially larger than the sample size.

These results may be explained by noting that, if the total number of sentinels available to sample from (P S ) is not substantially larger than the sample size (N), then sampling the maximum allowable number of sentinels (min(P S , N)) results in many or all of the same plants being repeatedly selected in every sampling round. If the sample interval is short, this leads to the frequent re-inspection of plants whose disease-free status was already established in the recent past, limiting the information gained per sampling round. However, this effect diminishes as the sample interval increases, because the disease status of plants inspected in the previous sample becomes less informative of their state at the next sample time. Thus, when the sample interval is large, sampling the maximum possible number of sentinels is the optimal strategy ( ) regardless of the sample size (N) or the total number of sentinels available (P S ). These results confirm the need to consider the division of the sample between crops and sentinels as a variable quantity that should be chosen carefully based on the precise conditions under which surveillance is taking place. If the number of sentinels included in the sample is suboptimal, smaller reductions in the EDP will be achieved, and sentinel plants may even have a detrimental effect (Fig 3A).

As expected, the resultant EDP following the implementation of the optimal sentinel strategy decreased with greater sampling effort: taking larger samples and/or sampling more frequently always led to a lower EDP (S12 Fig). However, larger percentage reductions in the EDP relative to the baseline level were mostly achieved when the sampling effort was low (i.e. when the sample size was small and/or the sample interval was large) (Figs 4A, 4B and 4C). This is because, when the sampling effort was low, the baseline EDP was much higher to begin with (Fig 2C). In those cases, the potential for the use of sentinel plants to lead to a large relative improvement in the EDP was greater than when the sampling effort was high and the baseline EDP was already low.

As well as affecting the magnitude of the reduction in EDP compared to the baseline, the choice of sample size and sample interval also affected the total number of sentinels for which the greatest reduction was achieved (Fig 4D). For example, when the sample size was N = 25 and the sample interval was Δ = 150 days, choosing P S = 50 led to the greatest reduction in EDP of the three values considered (54%, compared to a 50% reduction when P S = 100 and a 39% reduction when P S = 200). However, for N = 100 and Δ = 30 days, choosing P S = 200 gave the greatest reduction in EDP (11%, compared to 2% and 6% when P S = 50 and 100, respectively). Overall, introducing fewer sentinels was preferable when the sampling effort was either low or very high, with larger numbers preferable for intermediate sampling efforts (Fig 4D).

This variation in the optimal number of sentinels for different values of (N, Δ) reflects the crucial trade-off between the benefits and drawbacks of sentinel plants. Although adding sentinels to the population helps to facilitate early detection, it also leads to an increased rate of pathogen transmission (particularly if sentinels are more infectious than crop plants when Undetectable, as assumed here). Therefore, including more sentinel plants is only beneficial if the advantage gained from sampling them outweighs the impact of increased transmission.

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[1] Url: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1010884

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