A local risk map using field observations of the Asian longhorned beetle to optimize monitoring activities

A local risk map using field observations of the Asian

longhorned beetle to optimize monitoring activities

Y. Fragnière

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1_{Forest and Fauna Service of the State of} Fribourg, Givisiez, Switzerland

2_{u-m];m;†ˆ;]ub1†Ѵ|†u-Ѵmv|b|†|;o=|_;} State of Fribourg, Posieux, Switzerland 3_{Natural History Museum Fribourg, Fribourg,} Switzerland

4_{"‰bvv ;7;u-Ѵmv|b|†|;=ou ou;v|ķ"mo‰} and Landscape Research WSL, Birmensdorf, Switzerland

5 _{;r-u|l;m|o=boѴo]‹ķ1oѴo]‹şˆoѴ†|bom} Unit, University of Fribourg, Fribourg, Switzerland

Correspondence

Yann Fragnière, Forest and Fauna Service of the State of Fribourg, Givisiez, Switzerland. l-bѴĹ‹-mmĺ=u-]mb;u;Š=uĺ1_

Abstract

$_; vb-m Ѵom]_oum;7 0;;|Ѵ; Anoplophora glabripennis (Motschulsky) (Coleoptera: Cerambycidae) is one of the most dangerous xylophagous pests affecting broadleaf |u;;vbm|_;‰ouѴ7ĺu-7b1-|bomruo]u-ll;v-u;†m7;u|-h;mbmmomŊm-|bˆ;u;]bomvķu;Ŋ t†bubm];Š|;mvbˆ;u;vo†u1;v-m7bmˆoѴˆbm]_b]_1ov|vĺm-7-r|;7v|u-|;]‹l†v|0;v;| up to optimize the ratio cost/probability of success. We developed a method to generŊ ate a risk index of A. glabripennis presence at a local scale, in the surrounding area of an infestation, using field observations (counts of adult insects, exit holes and infested trees). The method, mathematically based on the bivariate symmetric Laplace distribuŊ tion, has thus reasonable input requirements. The output risk map is easy to interpret -m71-m0;7bu;1|Ѵ‹†v;70‹7;1bvbomŊl-h;uvĺ);†v;7o†u-rruo-1_bm|_u;;bm=;v|-Ŋ tions in Switzerland. The risk map represented well the insect pressure (beetle populaŊ tion density). We highlighted the fact that survey boundaries, commonly chosen using constant distances from the infestation, should be selected regarding the spatial distriŊ bution of the insect pressure, to prioritize monitoring activities. The risk map provides a helpful instrument for advanced survey planning after a first overview, for example to decide which area and which host trees should be inspected for infestations.

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$_; vb-m Ѵom]_oum;7 0;;|Ѵ; Őő Anoplophora glabripennis Őo|v1_†Ѵvh‹őķ-0;;|Ѵ;o=|_;;u-l0‹1b7-;=-lbѴ‹ķbvm-|bˆ;|ovb- -m7o11†uvm-|†u-ѴѴ‹bm_bm--m7ou;-Őbm]-=;Ѵ|;uşo;0;h;ķƑƏƏƑőĺ $_bv vr;1b;v ‰-v bm|uo7†1;7 -11b7;m|-ѴѴ‹ bm|o ou|_ l;ub1- -m7 †uor;ˆb-voѴb7‰oo7r-1hbm]l-|;ub-Ѵ-m7|_u;-|;mv†u0-moum-l;mŊ tal broadleaf trees and forests in areas where it has been introduced Ő -11oѴbķ -ˆ-uoķ"lb|_ķş)†ķƑƏƐƔĸ†ķm];Ѵbķ"1_†;|Œķ†oķş-f;hķ ƑƏƏƖĸ -ˆ-Ѵ ;|-Ѵĺķ ƑƏƐƕĸ o‰-hķ -v;hķ ";t†;bu-ķ u-m;ķ ş -v|uoķ ƑƏƏƐĸ );ul;Ѵbm];u ;|-Ѵĺķ ƑƏƐƔőĺ m †uor; -m7 ou|_ l;ub1-ķ |_; -||-1hv_;-Ѵ|_‹|u;;vķrubm1br-ѴѴ‹l-rѴ;vŐAcer spp.), buckeye and horse chestnuts (Aesculus spp.), willows (Salix spp.), elms (Ulmus spp.), birches (Betula spp.), plane trees (Platanus spp.) and poplars (Populus

spp.) (hereafter termed “primary hosts”), although several other genera have been regionally reported as occasional hosts (hereafter termed ľv;1om7-u‹_ov|vĿőŐ--1hķ࣐u-u7ķ"†mķş$†u];omķƑƏƐƏĸ--1h;|-Ѵĺķ ƑƏƏѵĸ ࣐u-u7 ;|-Ѵĺķ ƑƏƏѵĸ ;m]ķ ooˆ;uķ ş ;;m-ķ ƑƏƐƔĸ "-‰‹;uķ 2003). Larvae boring inside tree trunks and branches can cause seŊ vere damage to the tree’s vascular system and the wood’s structural properties. This can lead to the death of the attacked trees (Cavey, o;0;h;ķ-vvo-ķşbm]-=;Ѵ|;uķƐƖƖѶĸ†;|-ѴĺķƑƏƏƖőĺ

ou |_;v; u;-vomvķ |_;  bv 1omvb7;u;7 -v - 7-m];uo†v t†-uŊ -m|bm;r;v|bm†uor;-m7ou|_l;ub1--m7bll;7b-|;;u-7b1-|bom programmes must be undertaken when infestations are discovered Ő ouv|;u ş );ul;Ѵbm];uķ ƑƏƐƑĸ † ;|-Ѵĺķ ƑƏƏƖĸ -1;o7ķ ˆ-mvķ ş -h;uķ ƑƏƏƑĸ Ѵ†;vv ;|-Ѵĺķ ƑƏƐƒĸ &" ķ ƑƏƐѵĸ (-m ;u --] ;|-Ѵĺķ ƑƏƐƏőĺ om|uoѴ v|u-|;]b;v bm †uor; =oѴѴo‰ |_;  v|-m7-u7v om

http://doc.rero.ch

Published in "Journal of Applied Ecology 55 (2): 526–538, 2018"

which should be cited to refer to this work.

r_‹|ov-mb|-u‹ l;-v†u;v Őķ ƑƏƐѵő -m7 1omvbv| bm bm|;]u-|;7 -rŊ ruo-1_;vĺmru-1|b1;ķ|_;7;|-bѴ;7l;-v†u;vl-‹vol;|bl;vˆ-u‹0‹ regions and countries, but generally have to lead to eradication, if =;-vb0Ѵ;ĺ -uѴ‹ 7;|;1|bom bv 1u†1b-Ѵ 0;1-†v; |_; 1_-m1; o= v†11;vv=†Ѵ eradication is higher in small infested areas (Pluess et al., 2012). When -=buv|-7†Ѵ|ou-m-||-1h;7|u;;bv7bv1oˆ;u;7ķ-v†uˆ;‹bvm;1;vv-u‹ to check for symptoms in the surrounding trees. The subsequent eradŊ ication measures involve removal and destruction of all infested trees and capture of adult beetles. Preventive measures must be taken to -ˆob7_†l-mŊl;7b-|;77bvr;uv-ѴŐ;ĺ]ĺķ0‹‰oo7;mr-1h-]bm]l-|;ub-Ѵķ firewood or tree trimming material) and information and education of the residents can help to reinforce the survey. Finally, careful monŊ itoring must be undertaken to evaluate the efficacy of the eradicaŊ tion measures and to detect new infested trees. Usually, 4 years of negative surveys are required to declare successful eradication (Pluess ;|-ѴĺķƑƏƐƒĸ&" ķ&mb|;7"|-|;v ;r-u|l;m|o=]ub1†Ѵ|†u;ķƑƏƐѵőĺ

Surveys are carried out by visual inspection of trees for exit holes, frass or oviposition sites, often requiring tree climbers or bucket |u†1hvĺ=|;m-Ѵvoķ|u-bm;77;|;1|bom7o]v-u;†v;7Őo‹;uŊ$olb1Œ;h ş"-†v;m]ķƑƏƐƒőĺ$_;u;v†Ѵ|bm]1ov|vo=1-u;=†Ѵlomb|oubm]-u;ˆ;u‹ high, and there is never a 100% guarantee of eradication success: the area that can be surveyed is limited, not every broadleaf tree can be systematically controlled and visual surveys are not infallible. The &ĺ"ĺ ;r-u|l;m|o=]ub1†Ѵ|†u;Ľvmbl-Ѵ-m7Ѵ-m|;-Ѵ|_mvr;1|bom ";uˆb1; Ő"ő ;v|bl-|;7 ˆbv†-Ѵ v†uˆ;‹v |o 0; omѴ‹ ƒƏѷŋѵѵѷ ;==bŊ 1b;m|bm|_;&mb|;7"|-|;vŐbѴb†vķƐƖƖƖĸ"lb|_ķ$†u];omķ ;uoo|ķş -vl-mķƑƏƏƖőĺ"†uˆ;‹v_-ˆ;|o0;u;r;-|;7|o=bm7rovvb0Ѵ;vb]mvo= developing larvae in the trees. Consequently, a monitoring strategy should try to minimize the ratio cost/chances of success. Mathematical lo7;Ѵv1-mruoˆb7;-ˆ;u‹ro‰;u=†Ѵ|ooѴ|o_;Ѵrbm7;1bvbomŊl-hbm]ĺ Models have been integrated as a key component in eradication of |_;0‹|_;u;]†Ѵ-|ou‹-];m1b;vbm|_;&mb|;7"|-|;vķ-m-7--m7 †uor;Ő"lb|_;|-ѴĺķƑƏƏƖőĺ

Many researchers have already developed different kinds of lo7;Ѵvķ |o 7;v1ub0;  7bvr;uv-Ѵ u-|;ķ ror†Ѵ-|bom vru;-7ķ bm7bŊ vidual daily movements and infestation risk in different contexts Ő-m1uo=|ş"lb|_ķƑƏƏƐĸ -ˆ-uoķ)b1_l-mmķ!-ˆmķş -11oѴbķƑƏƐƔĸ o†umb;u ş $†u];omķ ƑƏƐƕĸ o†uѴ;‹ ş o†ķ ƑƏƐƓĸ o†uѴ;‹ ş ,o†ķ ƑƏƐƐĸ;|_l-‹;uķƑƏƐƒĸ†ş!†vv;ѴѴķƑƏƏƔĸ-mo†hbvķ-ѴѴķş;b0ķ ƑƏƐƓĸ "_-|Œķ !o]-mķ "-m];ul-moķ ]m;ˆ-Ŋbll;Ѵ0;u];uķ ş _;mķ ƑƏƐƒĸ$uo||;u ş †ѴѴŊ"-m7;uvķ ƑƏƐƔĸ+;lv_-moˆ ;|-Ѵĺķ ƑƏƐƕőĺ "ol; of these models describe the potential spread at a large spatial scale, 0-v;7 rubm1br-ѴѴ‹ om  _-0b|-| -m7 |u;; v†b|-0bѴb|‹ĺ $_;v; lo7;Ѵv are helpful for example for management and prevention strategies at the province or country level (adjustment of communication and prevention campaigns, professional education and control of merŊ chandise accompanied by wood packaging material), but are not really usable to optimize the monitoring activities at a local scale during an bm1†uvbomĺ|_;uvlo7;Ѵv-u;†v;=†Ѵ|o=bŠlomb|oubm]0o†m7-ub;vou to evaluate the infestation risk in the area of an infestation. However, three aspects make many of these models hard to use or unsuitable for a concrete case. (i) They frequently need a large amount of various data to estimate parameters, although the only available and reliable

information in a newly discovered outbreak area is often the position o= |_; 1-†]_| ou o0v;uˆ;7  -7†Ѵ|v -m7 bm=;v|;7 |u;;vĺ Őbbő "ol; models help to delimit the monitored area with a confidence level, in function of the distance to an infested tree, but they do not consider the insect pressure, in other words: the beetle population density at a ]bˆ;mѴo1-|bomĺm7;;7ķ|olbmblbŒ;|_;u-|bo1ov|ņ1_-m1;o=v†11;vvķ the intensity and the spatial extent of a survey should be adapted to |_;ror†Ѵ-|bomķ=ou;Š-lrѴ;‰_;|_;uomѴ‹om;ouƐƏƏ;Šb|_oѴ;v are found on a tree. (iii) Some models are very complex, include many constraints, or their output is difficult to interpret. However, peoŊ ple involved in the management are generally practitioners, and the model output must be easy to read and rapidly and directly usable to v†rrou|7;1bvbomŊl-hbm]ĺ

); ‰;u; 1om=uom|;7 ‰b|_ - m;‰  bm=;v|-|bom bm ƑƏƐƓ bm -uѴ‹Ő-m|om ub0o†u]ķ"‰b|Œ;uѴ-m7ĸƓѵŦƓѵனƔƏபķƕŦƏƖனƑƏபőĺ$_; infestation was severe, divided into two main spots at a distance of 1.5 km (North West spot: about 170 adult insects, between 140 and 200 exit holes, and 31 infested trees located in a radius of about ƑƔƏlĸ "o†|_ -v| vro|Ĺ ;b]_| -7†Ѵ| bmv;1|vķ ѵƔ ;Šb| _oѴ;v -m7 ƑƏ bm=;v|;7|u;;vѴo1-|;7bm-u-7b†vo=-0o†|ƓƏlőĺ||_;|bl;o=7;Ŋ tection, the beetle colony was estimated to have established at least four generations ago. Realizing that the starting points of all surveys -u;|_;=b;Ѵ7o0v;uˆ-|bomvo=-7†Ѵ|v-m7bm=;v|;7|u;;vķ‰;7;Ŋ veloped a simple approach to “use what we know to find what we don’t know.” We propose a model with low input requirements, deŊ veloped from theoretical and empirical studies previously published. The output is a risk map which is easy to interpret. Here, we present the approach and discuss its relevance for the monitoring strategy, regarding three infestations discovered in Switzerland: Marly (disŊ 1oˆ;u;7bmƑƏƐƓőķ)bm|;u|_†uŐ1-m|om,ুub1_ĸƓƕŦƒƏனƕĽĽķѶŦƓƔனƓƑĽĽ ķ7bv1oˆ;u;7bmƑƏƐƑķ-0o†|ƐƕƏ-7†Ѵ|bmv;1|vķƑƏƏ;Šb|_oѴ;v-m7 ƑƑbm=;v|;7|u;;vѴo1-|;7bm-u-7b†vo=-0o†|ƔƏƏlő-m7uুmbvub;7 Ő1-m|om ub0o†u]ĸƓѵŦƓƔனƒƑĽĽķƕŦƐѵனƓƓĽĽķ7bv1oˆ;u;7bmƑƏƐƐķvbŠ adults insects, eight exit holes and 11 infested trees located in a radius of about 150 m).

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lrbub1-Ѵ v|†7b;v †vbm] - l-vvŊl-uh u;Ѵ;-v; -m7 u;1-r|†u; l;|_o7 _-ˆ; v_o‰m |_-| |_; m†l0;u o= u;1-r|†u;7  7;1u;-v;v ;ŠroŊ m;m|b-ѴѴ‹‰b|_bm1u;-vbm]7bv|-m1;=uol|_;u;Ѵ;-v;robm|Ő-m1uo=|ş "lb|_ķ ƑƏƏƔĸ "lb|_ķ -m1uo=|ķ bķ -oķ ş $;-Ѵ;ķ ƑƏƏƐĸ "lb|_ķ $o0bmķ -m1uo=|ķbķş-oķƑƏƏƓőĺmo|_;u‰ou7vķ|_;ruo0-0bѴb|‹o=ru;vŊ ence decreases exponentially as the distance from the point of origin increases. This typical dispersal function was also demonstrated in a real infestation context (Favaro et al., 2015).

m|_;=b;Ѵ7ķ-m;Šb|_oѴ;1ouu;vrom7v|o|_;robm|o=oub]bmo=om; beetle. However, not only finding dispersing beetles but also currently infested trees are important for successful control measures. Thus, we can also assume that, after observing a beetle, the probability to find an infested tree with an exit hole decreases exponentially with disŊ tance. The probability to find newly infested trees also decreases with

distance from trees with exit holes or from observed beetles. Finally, when an infested tree is found (observation of oviposition marks, frass from larvae or presence of larvae or eggs in the wood), the probability to find either the adult female that infested the tree or another inŊ fested tree similarly decreases with distance.

With our approach, we aim to assess not only the probability of ru;v;m1; o= 7bvr;uvbm] 0;;|Ѵ;vķ 0†| -Ѵvo o= bm=;v|;7 |u;;vĺ m o|_;u ‰ou7vķ|_;o0f;1|bˆ;bv|o-vv;vv-ubvhbm7;Šo=|_;ru;v;m1;o=-| any life stage, based on field observations.

ƑĺƐՊ|Պ!;t†bu;7bm=oul-|bom

vbmr†|bmo†ulo7;Ѵķ|_;omѴ‹bm=oul-|bomm;1;vv-u‹bv-Ѵbv|o=‰_-| ‰;‰bѴѴ1-ѴѴŊrobm|vĺmŊrobm|bv-];ou;=;u;m1;7robm|ՊŊ‹" coordinates, at least 5 m precision), created according to the followŊ ing rules:

1. One exit hole leads to one O-pointĹ uol |_bv Ŋrobm|ķ |_; ruo0Ŋ

ability to find the emerged beetle or newly infested trees deŊ 1u;-v;v ;Šrom;m|b-ѴѴ‹ ‰b|_ 7bv|-m1;ĺ  |u;; ‰b|_ ƐƏƏ ;Šb| _oѴ;v ;m];m7;uv ƐƏƏ Ŋrobm|v ‰b|_ |_; v-l; Ѵo1-|bomĺ

2. One adult ALB leads to one O-pointĹ uol|_bvŊrobm|ķ|_;ruo0-0bѴŊ

ity to find the infested tree where the beetle emerged decreases ;Šrom;m|b-ѴѴ‹‰b|_7bv|-m1;ĺ=|_;0;;|Ѵ;bv-=;l-Ѵ;ķ|_;ruo0-0bѴb|‹ to find newly infested trees also decreases similarly with distance.

3. One infested tree (observation of oviposition marks, frass from larŊ

vae or presence of larvae or eggs in the wood) leads to one O-point: uol |_bv Ŋrobm|ķ |_; ruo0-0bѴb|‹ |o =bm7 |_; =;l-Ѵ; 0;;|Ѵ; |_-| infested the tree decreases exponentially with distance. The

probability to find other trees infested by the same female beetle or |_;|u;;‰_;u;b|;l;u];7vblbѴ-uѴ‹7;1u;-v;v‰b|_7bv|-m1;ĺm1omŊ trast to exit holes, infested trees, even when they contain more |_-m om; ;]] 7;rovb|bom ou Ѵ-uˆ-; o= ķ 1o†m| omѴ‹ -v om; Ŋrobm|ĺo‰;ˆ;uķb=b|_-v0;;m-v1;u|-bm;7|_-||‰ooulou;=;Ŋ males infested a tree (for example based on a high number of oviŊ position marks (> 30), genetic analyses of larvae or eggs or if immature stages are of significantly different age), the number of Ŋrobm|v-||_;v-l;Ѵo1-|boml†v||_;m0;bm1u;-v;7-11ou7bm]Ѵ‹ĺ = - 0;;|Ѵ; bv 1-r|†u;7 7bu;1|Ѵ‹ -=|;u ;l;u];m1; -m7 b= |_;u; bv mo u;-vom-0Ѵ;7o†0||_-||_;0;;|Ѵ;‰;m|vol;‰_;u;;Ѵv;ķ|_;Ŋrobm|o= the beetle and of its corresponding exit hole can be deleted, as there is no more risk with this beetle and this exit hole. More generally, double counting will happen. For example, a found beetle might have emerged from one of the exit holes already counted. But as there is no proof that they are linked, both must be counted. Moreover, if the beetle is a feŊ male, other trees could also already have been infested in the meantime. o†0Ѵ;1o†m|bm]‰bѴѴ];m;u-ѴѴ‹bm1u;-v;|_;;v|bl-|;7ubvhbm7;Šo==bm7Ŋ bm]-|-vb|;Őv;;lo7;Ѵ0;Ѵo‰ő-m7|_†v_-v-1omv;uˆ-|bˆ;;==;1|om u;1oll;m7-|bomv‰_;u;|olomb|ou=ouru;v;m1;Őv;;7bv1†vvbomőķbm line with the precautionary principle.

m"‰b|Œ;uѴ-m7ķ|_;=b;Ѵ7o0v;uˆ-|bomvo=ŐŊrobm|vő‰;u;=buv|Ѵ‹ u;1ou7;7 ‰_;m |_; bm=;v|-|bom ‰-v 7bv1oˆ;u;7ĺ 7†Ѵ| 0;;|Ѵ;v ‰;u; captured manually and infested trees were rapidly felled, chipped to small pieces (<3 cm) and burned. However, it is important to collect |_;7-|-0;=ou;-ѴѴ|_;bm=;v|;7l-|;ub-Ѵbv7;v|uo‹;7ĺ;‰Ŋrobm|v were then added during the monitoring, when new beetles or infested trees were found. The monitoring was usually carried out twice a year, that is in spring before the flight period and in autumn after the flight period, by tree climbers and detection dogs. The flight period is mainly 1om1;m|u-|;70;|‰;;m†m;-m7†]†v|bm"‰b|Œ;uѴ-m7Ő);ul;Ѵbm];u et al., 2015). We additionally used potted maple trees as trap trees to attract insects in the infested areas. They were checked every week 7†ubm]|_;=Ѵb]_|r;ubo7ĺ†u;Šr;ub;m1;v†]];v|v|_-||_;|u-r|u;;v 1-m0;_;Ѵr=†Ѵĸ_o‰;ˆ;uķ|_;‹-u;ruo0-0Ѵ‹mo|ˆ;u‹;==b1b;m|ĺmѴ‹- =;‰‰;u;-||u-1|;7ŐomѴ‹|_u;;0;;|Ѵ;vbm|_;=buv|‹;-ubm-uѴ‹ on 15 trap trees, but notice that the majority of beetles was already 1-r|†u;7 0;=ou; |u-r |u;;v ‰;u; bmv|-ѴѴ;7őĺ=|;u |_; v-mb|-u‹ =;ѴѴbm]ķ the density of surviving adults was fortunately low, so it was difficult to evaluate the effectiveness of the trap trees.

$_;Ѵbv|o=Ŋrobm|vbvmo|=bŠ;7ĺ|‰bѴѴ]uo‰‰_;mm;‰=b;Ѵ7o0Ŋ servations are collected and the corresponding risk map will improve b|vu;Ѵ;ˆ-m1;ĺ$_;t†;v|bombv_o‰|o1omvb7;uľoѴ7Ŋrobm|vĿŐ-m1b;m| observations but also new observations of ancient infestations, like oѴ7oˆbrovb|boml-uhvouoˆ;u]uo‰m;Šb|_oѴ;vőĺvĽv=†ѴѴѴb=;1‹1Ѵ; normally lasts 2 years in Switzerland, one could recommend to delete Ŋrobm|v|_-|-u;v†u;|o0;lou;|_-mƑ‹;-uvoѴ7ĺo‰;ˆ;uķb|bvmo| that simple and we think that a generally valid solution does not exist. For example, a newly found ancient exit hole is the evidence that |‰o ];m;u-|bomv‰;u;ru;v;m| -| |_-| Ѵo1-Ѵb|‹ĺѴ|_o†]_ |_bv Ŋ point is ancient, the area should be considered as potentially infested -m7-lomb|oubm]v_o†Ѵ70;1-uub;7o†|ĺ"†1_-mŊrobm|v_o†Ѵ7mo|   & !   Ɛ Պ The probability density function of the univariate

Laplace distribution, ℒ (0, 150) (black line, mean = 0, scale

parameter = 150), is compared with the normal distribution N (0, 150) (grey line, mean = 0, standard deviation σƷƐƔƏőĺmѴ‹|_;rovb|bˆ; range is shown. Heavier tails and the central peak of the Laplace 7bv|ub0†|bom-u;r;u|bm;m||olo7;Ѵvru;-7

be removed before 4 years of negative survey. We recommend the =oѴѴo‰bm] ruo1;7†u;Ĺ -=|;u -m -m-Ѵ‹vbv o= |_; vb|†-|bomķ oѴ7 Ŋrobm|v should only be removed if they obviously do not contribute to the current population dynamics within the concerned infestation spot -m‹lou;ĺ = bm 7o†0|ķ bm1Ѵ†7bm] -m1b;m| Ŋrobm|v bm1u;-v;v |_; ubvh index and thus has a conservative effect on recommendations where |olomb|ou=ouru;v;m1;ĺ

ƑĺƑՊ|Պ-|_;l-|b1-Ѵ-rruo-1_ru;v;m|-|bom

v -Ѵu;-7‹ -77u;vv;7 -0oˆ;ķ |_; ruo0-0bѴb|‹ 7;mvb|‹ o=  ru;vŊ ;m1;ķ-v-=†m1|bomo=|_;7bv|-m1;=uol-mŊrobm|ķ1-m0;lo7;ѴѴ;7 by the exponential distribution. The double exponential distribuŊ tion, better known as the Laplace distribution, seems consequently to be the adequate probability density function choice along one axis (Figure 1). Because of the central limit theorem, the normal distribution is commonly selected to show the spread of independŊ ;m|u-m7olˆ-ub-0Ѵ;vŐbĺ;ĺķbmo†u1-v;ķbm7bˆb7†-Ѵvőķ‰_;m|_;bu numbers are sufficiently high (Lyon, 2014). However, the Laplace 7bv|ub0†|bom 1-r|†u;v  vru;-7 0;||;u |_-m |_; moul-Ѵ 7bv|ub0†Ŋ tion, because the towering peak of the Laplace distribution at the Ŋrobm|rovb|bom-11o†m|v=ou0;;|Ѵ;vmo|7bvr;uvbm]=uol|_;|u;; |_;‹;l;u];7=uolŐ-m1uo=|ş"lb|_ķƑƏƏƔĸ†ѴѴŊ"-m7;uvķ;rr;uķ -ˆbvķ ş $uo||;uķ ƑƏƐƕĸ ;_l;ķ ƑƏƏƖĸ )bѴѴb-lvķ bķ ş -oķ ƑƏƏƓőĺ Commonly, the estimation of the “tail” of the dispersal distribution is a problem in ecology, and the normal distribution may underesŊ |bl-|;7bvr;uv-Ѵb=Ѵom]Ŋ7bv|-m1;7bvr;uv-Ѵo11†uv=u;t†;m|Ѵ‹Ő"lb|_ ;|-ѴĺķƑƏƏƐĸ$†u1_bmķƐƖƖƕőĺ$_;-rѴ-1;7bv|ub0†|bom_-vvoŊ1-ѴѴ;7 _;-ˆ‹ |-bѴvķ †mѴbh; |_; moul-Ѵ 7bv|ub0†|bom Őo|Œķ oŒ†0o‰vhbķ ş o7]ouvhbķƑƏƏƐĸ;Ѵmb1hşˆ;ub||ķƑƏƏѶĸ b]†u;Ɛőĺ$_bvbv-rruoŊ rub-|; =ou lo7;ѴѴbm]  7bvr;uv-Ѵ -v vol; bm7bˆb7†-Ѵv 1-m vru;-7 over long distances, in extreme cases more than one or two kiloŊ metres, or even more according to flight mill experiments (Smith ;|-ѴĺķƑƏƏƐķƑƏƏƓĸ;m|u;=ou]ub1†Ѵ|†u-Ѵbov1b;m1;m|;um-|bom-Ѵķ ƑƏƐѵķ †ѴѴŊ"-m7;uv ;|-Ѵĺķ ƑƏƐƕĸ -ˆ-Ѵķ !o†Šķ !ot†;vķ ş "-†ˆ-u7ķ ƑƏƐƕĸor;Œķo77Ѵ;ķ u-m1;v;ķ-m1;ķş!-‹ķƑƏƐƕőĺou;oˆ;uķ‰;

1olr†|;7-m†l;ub1-Ѵvbl†Ѵ-|bomo=vru;-7|_-|u;bm=ou1;vo†u b7;- |_-| |_; -rѴ-1; 7bv|ub0†|bom ‰-v -rruorub-|; Őv;; rr;m7bŠ "Ɛőĺ m |_bv vbl†Ѵ-|bomķ ‰; u;Ѵ;-v;7 ƐķƏƏƏ ľˆbu|†-Ѵ Ŀ =uol |_; same point. The different parameters (for example: daily flying disŊ tance and lifespan) for every individual were estimated from the literature. The resulting dispersal shows the same pattern as exŊ plained above: most of the individuals are concentrated at the reŊ lease point and their numbers decrease exponentially with distance. Some of them can however reach long dispersal distances (about 400–1,000 m).

v|_;bmr†|v-u;Ѵ-|ŊѴom]1oou7bm-|;vķ‰;_-ˆ;|o1omvb7;u|‰o spread dimensions. We therefore finally use a bivariate symmetric Laplace distribution BSℒ (Oi, σ1, σ2), where Oi is the centre of the distribution (position of the ith_{Ŋrobm|őķ-m7‰_;u;σ}

1 and σ2 are the scale parameters (standard deviations) for the two axes (Kotz, 2002; o|Œ;|-ѴĺķƑƏƏƐőĺv|oo†uhmo‰Ѵ;7];mov|†7‹bm7b1-|;vvb]mb=b1-m| ru;=;u;m1;vbmvru;-7-Ѵom]r-u|b1†Ѵ-u1-u7bm-Ѵ7bu;1|bomvķ|_;u; is no reason to use a Laplace asymmetrical distribution or different scale parameters for the two axes. We consequently assume that σ1 = σ2 = σ.

The probability density function f of the bivariate symmetric Laplace distribution with a unique σ is given by

for each coordinate (x, y), where O_xi and O_yi are the coordinates (x, y) of the ith

Ŋrobm|-m7‰_;u;

The resulting curve has a typical “circus tent” shape and is spatially 1;m|u;7om;-1_Ŋrobm|Ő b]†u;Ƒőĺ

The total volume below the curve is equal to 1 (total probability of presence) and the volume over a given area represents the probability |o =bm7 -m‹ ru;v;m1;ķ 0;1-†v; o= |_; 1ouu;vrom7bm] Ŋrobm|ĺ vblbѴ-u1†uˆ;l†v|0;1-Ѵ1†Ѵ-|;7=ou;-1_Ѵbv|;7Ŋrobm|ĺ

-v|Ѵ‹ķ‰;7;1b7;7|o‰ouh-||_;-u;Ŋ†mb|v1-Ѵ;ŐƐ-u;ƷƐƏƵƐƏl2). ou;-1_vt†-u;o=ƐƏƵƐƏl2ķ|_;ruo0-0bѴb|‹o=ru;v;m1;P_i (due to ith_{Ŋrobm|ő1-m0;7;|;ulbm;7†vbm]|_;-rѴ-1;1†uˆ;1-Ѵ1†Ѵ-|;7}

for the ith

Ŋrobm|ķ0‹bm|;]u-|bm]|_;ˆoѴ†l;†m7;u|_;1†uˆ;=ou|_; ]bˆ;mƐƏƵƐƏl2 square. Finally, our risk index (RI) was calculated as =oѴѴo‰v=ou;-1_ƐƏƵƐƏl2:

where nbv|_;|o|-Ѵm†l0;uo=Ŋrobm|vĺ

RI corresponds in a theoretical way to the probability to find at

Ѵ;-v|om;ru;v;m1;bm-]bˆ;mvt†-u;o=ƐƏƵƐƏl2ĺmru-1|b1;ķ this is not always true because of the model characteristics (double 1o†m|bm] rovvb0Ѵ;ķ Ѵ-1h o= †m7bv1oˆ;u;7 Ŋrobm|vķ ;|1ĺőĺ o‰;ˆ;uķ RI 1-m0;†v;7|oruboub|bŒ;‰_;u;|ov;-u1_1omvb7;ubm]|_;1†uu;m| collected field observations (see discussion). The range of RI goes from

f(x,y) = 1 πσ2K0 ⎛ ⎜ ⎜ ⎝ √ 2(x−Oxi)2+ (y−Oyi)2 σ2 ⎞ ⎟ ⎟ ⎠ K0(u) = 1_{2 ∫} ∞ 0 1 texp ( −t− u2 4t ) dt, u > 0. RI = 1 − (1 − P1)(1 − P2) … (1 − Pn) = 1 − n ∏ i = 1 (1 − Pi)

  & !   Ƒ Պ Bivariate symmetric Laplace distribution, with the unique scale parameter (standard deviation) σ = 150. The curve is 1;m|u;7_;u;om-Ŋrobm|Ѵo1-|;7-|ŐƏķƏő

0 (lower risk) to 1 (higher risk). The calculated RI=ou;-1_ƐƏƵƐƏl2

vt†-u;7o;vmo|1omvb7;u|_;Ѵ-m71oˆ;uĺ=1o†uv;ķ|_;Ѵ-m7v1-r;bv not homogenous and RI is principally relevant for areas containing host trees, especially primary hosts.

The script for calculating RI was coded in R language (R ;ˆ;Ѵorl;m|ou;$;-lķƑƏƐƓő-m7bv-ˆ-bѴ-0Ѵ;bm|_;rr;m7bŠ"Ƒĺ The script automatically produces a table with the central coordinates o=;-1_ƐƏƵƐƏl2 square and the corresponding RIĺv|_;1-Ѵ1†Ѵ-Ŋ |bom1-m0;t†b|;Ѵom]ķ‰;];m;u-ѴѴ‹Ѵblb||_;o†|r†||o-ƒƵƒhlv†uŊ =-1;-u;-ŐƖƏķƏƏƏvt†-u;vo=ƐƏƵƐƏl2). The output can be visualized -vl-r†vbm]"vo=|‰-u;ĺ

ƑĺƒՊ|Պ-u-l;|;u;v|bl-|bom

vbm]Ѵ;r-u-l;|;ul†v|0;-vv†l;7bmo†ulo7;Ѵķ|_-|bv|_;v|-m7Ŋ ard deviation σ of the bivariate symmetric Laplace distribution. This parameter is similar to the mean in the corresponding exponential 7bv|ub0†|bomĺ|bvrovvb0Ѵ;|o=bm7bm|_;Ѵb|;u-|†u;7bˆ;uv;bm=oul-|bom -0o†|l;-mvru;-77†ubm]om;v;-vomĺ|‰-v=o†m7bm7b==;u;m| 1om7b|bomv|o0;ƐƏƒĺѵlŐ);mķ+;ķbķş;ķƐƖƖѶőķ0;|‰;;mƐƖƑ-m7 ƒƐѵlŐ"lb|_;|-ѴĺķƑƏƏƐőķ-|ƐƑƖlŐ-m1uo=|ş"lb|_ķƑƏƏƐő-m7o†u vbl†Ѵ-|bomŐrr;m7bŠ"Ɛő]-ˆ;†v-l;-m7bvr;uv-Ѵ7bv|-m1;o=-0o†|

130 m. The local conditions (e.g., density of hosts, weather, presence o=m-|†u-Ѵou-u|b=b1b-Ѵ0-uub;uv-m7momŊm-|†u-Ѵvru;-70‹|u-mvrou|ő1-m have a great impact on the mean dispersal distance. However, there is no reliable possibility to evaluate dispersal in a new infestation. Thus, in the absence of data and to limit and simplify the input requirements, we propose an average standard mean dispersal distance of 150 m (σ = 150). Thus, after calculation using the Laplace distribution with σƷƐƔƏķ|_;|_;ou;|b1-Ѵl;7b-mvru;-77bv|-m1;bvƐƏƒĺƖƕlŐσ ln(2)) -m7|_;ƖѶѷѴblb|bv-|-0o†|ƔƑƔl=uol-mŊrobm|ĺ$_;bm=Ѵ†;m1;o= the parameter’s value modification is discussed later (see discussion).

ƑĺƓՊ|Պˆ-Ѵ†-|bm]u;Ѵ;ˆ-m1;

m-uѴ‹ķ-];ou;=;u;m1;77-|-v;|o=-ѴѴrubl-u‹_ov||u;;vbm-u-7b†v of about 400 m around the infestation spots was recorded. Between 2014 and 2016, all of these trees were checked six to eight times by tree climbers and detection dogs. We therefore assume that we know with a good accuracy which trees were infested and which were not. We used this dataset (primary hosts with trunks larger than 3 cm,

nƷƐķƑƏƒķrr;m7bŠ"ƒő|o1olr-u;|_;|u†;ruo0-0bѴb|‹o=0;bm]bmŊ

fested and the RIr;uƐƏƵƐƏl2 _{given by our model at the location}

of the tree. To investigate this, a generalized linear model (GLM) with

  & !   ƒ Պ Risk map for the Marly infestation (Switzerland). The colour gradient indicates the risk index (RI), from purple (RI > 0.5) to white (RI < 10ƴѵ_).

The upper map gives an overall view of |_;|‰ol-bmbm=;v|;7vro|vŐ*Ŋ+"‰bvv 1oou7bm-|;v‹v|;lķƐƖƏƒ(Əƒőĺ$_; areas in the black dashed rectangles a) and b) are zoomed below, with positions of all o0v;uˆ;7Ŋrobm|vĺ)_b|;7o|vƷrovb|bom of infested trees (observation of larvae, eggs or oviposition marks); blue |ub-m]Ѵ;vƷrovb|bom-m7m†l0;uo= adults; orange stars = position and number of exit holes

(a) (b)

0bmolb-Ѵ;uuou7bv|ub0†|bom-m7Ѵo]b|Ѵbmh=†m1|bom‰-v†v;7Ő o0vomķ ƐƖƖƏőĺ$_;]oo7m;vvo==b|o=|_;1olr†|;7‰-v-vv;vv;7†vbm] Nagelkerke’s pseudo R2_{ Ő -u-‰-‹ķ ƑƏƏѵĸ -];Ѵh;uh;ķ ƐƖƖƐőķ -m7 -}

Ѵbh;Ѵb_oo7 u-|bo |;v| ‰-v r;u=oul;7 -]-bmv| |_; m†ѴѴ lo7;Ѵ Őo_mvom şlѴ-m7ķƑƏƏƓőĺ

ƒՊ|Պ!"&$"

We present in detail the results and the risk map for the Marly inŊ festation (Figure 3). Results and data for two other infestations in "‰b|Œ;uѴ-m7Ő)bm|;u|_†uķuুmbvub;7ő-u;v_o‰mbmrr;m7bŠ"Ɠĺ

$_; ru;v;m1; o= ‰-v 7bv1oˆ;u;7 bm -uѴ‹ bm v†ll;u ƑƏƐƓĺ For the present publication, we used in the model all field observaŊ tions made since the first discovery up to spring 2016. Most of the observations were made during the year 2014 when the first eradŊ ication activities took place, and only two infested trap trees were 7bv1oˆ;u;77†ubm]|_;lomb|oubm]bmƑƏƐƔĺѴ|o];|_;u‰;_-7-|o|-Ѵ o=ƓƑƓŊrobm|vĺm;_†m7u;7-m7ƕƔo=|_;v;‰;u;-7†Ѵ|vķƑƏƑ were exit holes (fresh and old) observed on 15 different trees and 47 ‰;u;bm=;v|;7|u;;vŐrr;m7bŠ"Ɣőĺ$_;Ŋrobm|v-u;7bˆb7;7bm|o|‰o l-bmbm=;v|-|bomvƐĺƔhl-r-u|ĺ$_;mou|_Ŋ‰;v|;umŐ)ővro|‰-v|_; oѴ7;u-m7lou;;Š|;mvbˆ;om;ĸ_;u;ķ-|o|-Ѵo=-0o†|ƐѵƏ-7†Ѵ|v and heavily infested trees were discovered, for example one with at Ѵ;-v|ƐƏƏ;Šb|v_oѴ;vĺm|_;vo†|_Ŋ;-v|;umŐ"ővro|ķomѴ‹-=;‰-7†Ѵ|v were discovered but some infested trees and a moderate number of exit holes were discovered in a circular area of approximately 100 m 7b-l;|;u Ő b]†u;ƒőĺ | bv mo| hmo‰m _o‰ |_; v;1om7 " bm=;v|-|bom spot in Marly started, but genetic analyses (mitochondrial sequencing) showed that the beetles belong to the same origin as individuals from |_;oѴ7;u)vro|Ő ouv|;uşक़ѴѴbm]ķ†mr†0Ѵbv_;77-|-őĺ);7omo| know whether a female flew that far without laying eggs on trees in between, or whether beetles were passively transported by humans, for example with firewood or tree trimming material, or simply hitchŊ hiking on vehicles.

The modelled output risk map highlights this difference between the two infestation spots (Figure 3). The RI was highest close to heavily infested trees with many exit holes and adults in the vicinŊ b|‹ĺm|_;)vro|ķ|_;|u;;‰b|_ƐƏƏ;Šb|_oѴ;v-m7Ѷƒ-7†Ѵ|v_-7 a great weight in the model and produced the highest risk peak. m|_;v;1om7vro|ķ|_;|‰o1om|b]†o†v|u;;v‰b|_u;vr;1|bˆ;Ѵ‹ƒƏ and 20 exit holes also had a large weight and led to another peak. $_;o|_;uŊrobm|v‰;u;r-u|b-ѴѴ‹l-vh;70‹|_;v;|‰oubvhr;-hvķ but each of them increased RI-||_;buѴo1-|bomĺƒ rѴo|_;Ѵrv|o ˆbv†-ѴbŒ;vl-ѴѴr;-hv7†;|oo|_;uŊrobm|vŐ b]†u;ƓőĺRI was higher than 0.01 on a larger area in the NW spot (RI > 0.01 on about 4480 vt†-u;vo=ƐƏƵƐƏl2ŐƓƓĺѶ_;1|-u;vőbm|_;vro|-m7om-0o†| ƐƐѶƏ vt†-u;v o= ƐƏƵƐƏl2 ŐƐѶĺѶ _;1|-u;vő bm |_; " vro|ő -v |_; bmv;1|ru;vv†u;Őm†l0;uo=Ŋrobm|vő‰-vl†1__b]_;u-m7‰-vˆbvŊ b0Ѵ‹;Š|;m7;7|o|_;vo†|_-m7vo†|_Ŋ;-v|0;1-†v;o=-7bv1oˆ;u;7 group of infested trees. No further infestations have been observed yet between the two spots; however, the map indicates that the area was at a certain risk (Figures 3, 4b).

Figure 5 shows, for the Marly infestation, the logistic GLM fit of the calculated RI r;u ƐƏƵƐƏl2 _{against infested/uninfested host}

|u;;vĺvt†-u;7-m7-1†0b1|;ul‰;u;-77;7|oblruoˆ;|_;=b|ĺ The terms added were significant according to a Wald test or a likeliŊ _oo7u-|bo|;v|Őm]Ѵ;ķƐƖѶƓőĺ$_;h-bh;bm=oul-|bom1ub|;ubomŐh-bh;ķ ƐƖƕƓő‰-v Ѵo‰;u‰_;m |_; vt†-u;7 -m7 |_; 1†0b1 |;ul‰;u; -77;7 bm|_;ĺ11ou7bm]|o-Ѵbh;Ѵb_oo7u-|bo|;v|ķ|_;1olr†|;7 Ő7;]u;;v o= =u;;7olƷƐķƐƖƖķ u;vb7†-Ѵ 7;ˆb-m1;ƷƑѵƓĺѶő ‰-v vb]mb=bŊ cantly different (pŊˆ-Ѵ†; ƺ ƏĺƏƏƏƐő =uol |_; m†ѴѴ lo7;Ѵ Ő7;]u;;v o= freedom = 1,202, residual deviance = 422.2). RI was correlated with the true probability for trees of being infested (Nagelkerke’s pseudo

R2 _{= .41), and the model roughly followed the diagonal.}

The lowest RI in Marly at the location of an infested primary host ‰-vƏĺƏƐƖĺ o†ubm=;v|;7v;1om7-u‹_ov|v‰;u;7bv1oˆ;u;7bm|_;1;mŊ tre of the NW spot, all at locations with very high RI values. The lowest

RI at the location of an infested secondary host was 0.356.

m )bm|;u|_†uķ |_; bm=;v|-|bom ‰-v -Ѵvo v;ˆ;u;ķ Ѵo1-ѴbŒ;7 bm om; ;Š|;m7;7 vro|ĺ0o†| ƐƕƏ -7†Ѵ|v -m7 ƑƏƏ ;Šb| _oѴ;v ‰;u; 7bvŊ 1oˆ;u;7ĺ$‰;m|‹Ŋ|‰o|u;;v‰;u;Ѵbv|;7-vbm=;v|;7ķbm1Ѵ†7bm]om;v;1Ŋ ondary host near the infestation centre. The lowest RI at the location of an infested primary host was 0.008 and 0.281 at the location of |_; bm=;v|;7 v;1om7-u‹ _ov|ĺ bm-ѴѴ‹ķ |_; uুmbvub;7 bm=;v|-|bom ‰-v less severe with only six adults, eight exit holes and 11 primary hosts infested. No secondary hosts were infested; it is however possible that a beetle attempted to lay eggs on a Prunus sp. near the infestation centre. The lowest RI at the location of an infested primary host was ƏĺƏƏѵŐrr;m7bŠ"Ɠőĺ

ƓՊ|Պ "&""

The risk maps show that our mathematical approach captures the 0;;|Ѵ;ru;vv†u;Őm†l0;uo=Ŋrobm|vőķ-vv_o‰m=ou|_;|‰obm=;v|;7 vro|vbm-uѴ‹Ő b]†u;vƒķƓőĺ_b]_ru;vv†u;bm|_;)vro|Ő-0o†| ƑƔƏŊrobm|vbm-1bu1Ѵ;o=-0o†|ƒƏlu-7b†vőѴ;7|o-_b]_RI and on a Ѵ-u];uv†u=-1;1olr-u;7|o|_;"vro|Ő-0o†|ѵƏŊrobm|vbm-ƒƏl u-7b†v1bu1Ѵ;őĺm|_;)vro|ķ|_;7bvr;uv-Ѵo=-7†Ѵ|v-m7bm=;v|;7 trees was wider, probably linked with higher beetle pressure and age o=bm=;v|-|bomĺ|‰-v-Ѵvoru;ˆbo†vѴ‹v_o‰m|_-||_;ubvho=vru;-7 increases with population size (Favaro et al., 2015). We observed in Switzerland that secondary hosts (e.g., Fraxinus sp., Prunus sp. and

Fagus sp.) were infested only where the insect pressure (and conseŊ

quently RIő‰-v_b]_ķ-vbm|_;)vro|bm-uѴ‹ĺvbvo=|;mmo| able to complete its life cycle on secondary hosts, it is difficult to unŊ derstand why some insects sometimes decide to infest such tree speŊ 1b;vĺ=morubl-u‹_ov|vr;1b;v-u;bm|_;ˆb1bmb|‹ķ|_;‹_-ˆ;o=1o†uv; no other choice. But when primary host species are still present, as in Marly, it is possibly a rare random phenomenon linked with dispersal, which will occur more frequently when the beetle population (insect pressure) is higher. Similar phenomena have been observed in other alien species, for example in the horse chestnut leafminer (Cameraria

ohridellaő|_-|-Ѵvooˆbrovb|vommomŊ_ov||u;;vŐAcer sp.) when populaŊ

|bom7;mvb|b;v-u;ˆ;u‹_b]_Ő࣐u࣐ķ†]†v|bmķ$†uѴbm]vķş;mbvķƑƏƐƏőĺ

†u v|†7‹ -m7 |_; ubvh l-r _b]_Ѵb]_| |_-| |_; 7;1bvbomŊl-h;uv 1om=uom|;7‰b|_bm=;v|-|bomvv_o†Ѵ7|-h;bm|o-11o†m||_;bmv;1| pressure to optimize the further monitoring strategy. Commonly, conŊ stant distances from the discovered infestations are used to fix surŊ ˆ;‹0o†m7-ub;vŐķ†uor;-m-m7;7b|;uu-m;-mѴ-m|uo|;1|bom u]-mbŒ-|bomķ ƑƏƐѵĸ Ѵ†;vv ;|-Ѵĺķ ƑƏƐƒĸ &" ķ &mb|;7 "|-|;v ;r-u|l;m|o=]ub1†Ѵ|†u;ķƑƏƐѵőķ‰_b1_bvmo|-Ѵ‰-‹vf†7b1bo†v‰_;m the aim is to invest efforts and money cleverly, in order to maximize the chance of success with given means and resources.

Therefore, our risk map can be a useful tool to visualize priorities =ou lomb|oubm] -1|bˆb|b;v bm -m bm=;v|-|bom vro|ĺ | 1-m _;Ѵr |o 7;vb]m the surveyed zones and to decide which potential host trees should be checked. Considering the RI, we made recommendations about monitoring actions. The proposed approach is compiled in Table 1 and compared with the actual observations in the three analysed Swiss infestations. The thresholds were determined mainly by considering the lowest RI at the location of infested primary and secondary hosts, in the different Swiss infestations. These recommendations and the thresholds stay of course subjective and should be considered as miniŊ mum recommendations. The extent of the monitoring depends mainly om-ˆ-bѴ-0Ѵ;l;-mvĹb==†m7v=ou;u-7b1-|bom-u;u;v|ub1|;7ķ‰;v†]Ŋ gest following as closely as possible the above recommendations for lomb|oubm]ĺ=lou;;Š|;mvbˆ;l;-mv-u;-ˆ-bѴ-0Ѵ;ķ|_;|_u;v_oѴ7v1-m be lowered and thereby the monitoring area and intensity increased   & !   Ɠ Պ ƒ rѴo|o=|_;ubvhbm7;ŠŐRI), for the Marly infestation (Switzerland). X -m7+bm"‰bvv1oou7bm-|;v‹v|;lƐƖƏƒ (ƏƒŐƐ†mb|1ouu;vrom7v|oƐl;|u;őĺ-ő linear scale, b) logarithmic scale

  & !   Ɣ Պ Logistic generalized linear model (GLM) fit of the calculated risk index (RI) against infested/uninfested host trees (n = 1,203), for the Marly infestation (log–log scale). The solid line indicates the GLM fit and the grey areas represent one, two and tree standard errors, respectively. The plot diagonal is shown by the dashed line. The vertical segments indicate for each tree the corresponding RI, for uninfested trees (bottom, n = 1,152) and infested trees (top, n = 51)

for more precaution. However, in any case, we suggest considering the risk map to prioritize the area that should be monitored to keep the 1ov|Ŋ0;m;=b|0-Ѵ-m1;-v]oo7-vrovvb0Ѵ;ĺ

m -uѴ‹ķ |_; RI was correlated with the true probability of priŊ mary host trees of being infested (Figure 5); this result is expected considering how the model is built. However, interestingly, the GLM fit was closely following the diagonal, indicating that the RI could provide an approximation of the probability of primary host trees to 0;bm=;v|;7ķ‰_;mlov|o=|_;Ŋrobm|v-u;-Ѵu;-7‹hmo‰mĺ|‰o†Ѵ7 be interesting to also analyse this in other infestations, if similar dataŊ sets including all infested and uninfested primary hosts in the infesŊ |-|bom-u;-‰;u;-ˆ-bѴ-0Ѵ;ĺ†ul;|_o7‰-v-Ѵvomo|-rrѴb;7|o-ˆ;u‹ large dataset of massive infestations (as occurs for example in some 1-v;v bm |_; &" ou u-m1;őķ vo‰; 1-mmo| v-‹ _o‰ |_; lo7;Ѵ‰bѴѴ perform in large outbreaks. However, there is no reason to think that |_;o†|1ol;l†v|0;bm|;uru;|;77b==;u;m|Ѵ‹‰_;mlou;Ŋrobm|v-u; included in the dataset. The difficulty could come with the dataset b|v;Ѵ=ķ|oh;;romѴ‹u;Ѵ;ˆ-m|Ŋrobm|vo=|_;1†uu;m|ror†Ѵ-|bom outbreak.

=|_;moul-Ѵ7bv|ub0†|bombv†v;7bmv|;-7o=|_;-rѴ-1;7bv|ub0†Ŋ tion (with the same parameter), the risk map is not very different, howŊ ever, the Laplace distribution has two advantages (graphs 2.1–2.6 in rr;m7bŠ"ѵőĺ buv|Ѵ‹ķ|_;moul-Ѵ7bv|ub0†|bom†m7;u;v|bl-|;v|_;ubvh -||_;Ŋrobm|Ѵo1-|bomĺ ou;Š-lrѴ;bm-uѴ‹ķ|_;l-Šbl†lRI in the _b]_Ѵ‹bm=;v|;7-u;-ŐƑƔƏŊrobm|vbm-ƒƏlu-7b†vő‰-vomѴ‹-0o†|ƏĺƑ ‰b|_|_;moul-Ѵ7bv|ub0†|bomĺ|bvѴo‰bmv†1_-m-u;-‰_;u;|_;bmv;1| pressure was very high and where the probability of primary hosts to be infested is very significant. With the Laplace distribution, the maxŊ imum RI increases to about 0.7. The risk of primary host trees to be

infested is better captured by the Laplace distribution in those areas, especially where RI > 0.1. Secondly, the Laplace distribution considŊ ;uv 0;||;u |_; ubvh o= u-u; Ѵom] 7bvr;uv-Ѵĺ m -uѴ‹ķ ‰b|_ |_; -rѴ-1; distribution, RI > 0.001 up to about 600 m of the centre of the highly infested area (500 m with the normal distribution) and RI > 0.0001 up to about 820 m (600 m with the normal distribution).

 lo7;Ѵ bv -Ѵ‰-‹v - vblrѴb=b1-|bom o= u;-Ѵb|‹ķ -m7 - ]oo7 -m-Ѵ‹vbv of the field characteristics is necessary to evaluate the pertinence of the RI. The tree distribution and the possible presence of natural or artificial barriers such as cliffs, large open surfaces or buildings must 0;1omvb7;u;7ĺ$_;7olbm-m|‰bm77bu;1|bomŐ†ѴѴŊ"-m7;uv;|-ѴĺķƑƏƐƕő -m7|_;ru;v;m1;o=ˆ;_b1Ѵ;v-vˆ;1|ouv1o†Ѵ7-Ѵvobm=Ѵ†;m1;|_; vru;-7ĺ ;1bvbomŊl-h;uv l†v| -m‹‰-‹ -Ѵvo 1omvb7;u |_;v; =-1|ouv when the monitoring strategy is set up.

We proposed a fixed parameter in our model (default value, σƷƐƔƏőĺ 11ou7bm] |o |_; Ѵb|;u-|†u; -m7 o†u vbl†Ѵ-|bomķ |_bv ˆ-Ѵ†; seems to be a good compromise and simplifies our approach. Nevertheless, in practice, this value can be adapted, for example conŊ sidering the field characteristics (for example the host trees density). We calculated the risk map with other parameter values (σ = 100, 200, ƒƏƏķ]u-r_vƐĺƐŋƐĺƐƑbmrr;m7bŠ"ѵőĺˆ;u-ѴѴķ-]u;-|;uˆ-Ѵ†;=Ѵ-||;mv the centre of the curve and thickens the tails. But it is not possible to _-ˆ; - vblrѴ; ruo1;7†u; |o 1_oov; |_; or|bl-Ѵ r-u-l;|;u ˆ-Ѵ†;ĺ m general, we suggest to keep the default value.

The host tree density is one important aspect that can influence the spread of the beetle that is not directly covered by our approach. We avoided to include this parameter because it is very complex to link host density and beetle movement directly, and because it can 0;ˆ;u‹|bl;1omv†lbm]|o1oѴѴ;1||_;7-|-|o;ˆ-Ѵ†-|;b|ĺ|ruo0-0Ѵ‹ $      Ɛ Պ Proposed monitor actions after the calculated risk index (RI) and true presence of attacked primary and secondary hosts in three analysed Swiss infestations in the corresponding RI range

! uorov;7lomb|oubm] -uѴ‹ presence of attacked rubl-u‹_ov|v -uѴ‹ru;v;m1; of attacked v;1om7-u‹ hosts uুmbvub;7 presence of attacked rubl-u‹_ov|v uুmbvub;7 presence of attacked v;1om7-u‹_ov|v )bm|;u|_†u presence of attacked rubl-u‹_ov|v )bm|;u|_†u presence of attacked v;1om7-u‹_ov|v

>0.25 All broadleaf host trees Yes Yes Yes Noa _{Yes Yes}

0.25–0.1 ѴѴrubl-u‹_ov|vķ-ѴѴ v;1om7-u‹_ov|vŐbm particular if lack of rubl-u‹om;vő

Yes No Yes No Yes No

0.1–0.01 ѴѴrubl-u‹_ov|vķ v;1om7-u‹_ov|vomѴ‹ b=|_;‹-u;-||-1h;7bm infestation centre

Yes No Yes No Yes No

0.01– 0.005

ѴѴrubl-u‹_ov|v No No Yes No Yes No

0.005 – 0.001 ѴѴrubl-u‹_ov|vŐƑm7 ruboub|‹ķ7;r;m7bm]om l;-mvő No No No No No No <0.001 ubl-u‹_ov|vķѴblb|;7 controls in pertinent zones No No No No No No

Bold indicates the most important data. a

mѴ‹†mv†11;vv=†Ѵ;]]7;rovb|bomvomPrunus.

depends of multiple underlying factors, for example the tree species, |_; |u;; 7b-l;|;uvķ |_; vl-ѴѴŊv1-Ѵ; |u;; 7bv|ub0†|bom Ő1Ѵ†v|;u;7ķ v1-|Ŋ tered), the local beetles’ preferences and other geographical and cliŊ matic factors. We intuitively suggest, as addressed above, to modify the σ parameter if the host tree density is very low (trees very sparse or no trees) or high (for example in a forest containing mostly primary host tree species). We also suggest reading other studies considering this factor (e.g., Favaro et al., 2015).

); 1_ov; |o ]bˆ; |_; v-l;‰;b]_| |o ;-1_ Ŋrobm| |o h;;r |_; input requirements simple. We could have for example weighted male and female adult beetles differently, because females can generate new infestations and seem to disperse over larger distances (Bancroft ş"lb|_ķƑƏƏƔőĺo‰;ˆ;uķ-7†Ѵ|l-Ѵ;vl†v|-m‹‰-‹0;1omvb7;u;7ķ-v they indicate an infested tree in the surrounding, where they emerged. Moreover, the probability that a male fertilized a female is high in the surrounding area and decreases with distance.

v |_; ubvh =ou †m7;|;1|;7 v-|;ѴѴb|; bm=;v|-|bomv bm - ‰b7;u 7bvŊ |-m1;l-‹0;bm1u;-vbm]‰_;m-mror†Ѵ-|bombvru;v;m|=ouv;ˆŊ eral generations, sampling within a buffer zone (Pluess et al., 2013) is an accurate method of monitoring preferably combined with adapted r†0Ѵb1u;Ѵ-|bomvŐ;ĺ]ĺķ7bv|ub0†|bomo==Ѵ‹;uv|o|_;r†0Ѵb1őĺ=|;um;‰Ѵ‹ discovered beetle activities, the model can be rerun to keep the risk map up to date. Thus, during an eradication campaign, it is very imŊ portant to track and record all field observations, which is sometimes m;]Ѵ;1|;7bm|_;_-v|;ĺ†ulo7;ѴomѴ‹m;;7vѴo1-|bom7-|-=uolo0Ŋ v;uˆ;7 vb]mvķ‰_b1_ -u; u;-vom-0Ѵ‹ ;-vbѴ‹ ]-|_;u;7‰b|_ - 7bѴbŊ gent effort.

vb-m Ѵom]_oum;7 0;;|Ѵ; l†v| 0; v†uˆ;‹;7 -m7 ;u-7b1-|;7 0‹ Ѵ-‰bml-m‹1o†m|ub;v|o‰_b1_b|bv-Ѵb;mĺm|_;o11-vbomo=-m;‰ 7bv1oˆ;u‹o=-mbm=;v|-|bomķ-=buv|uo†]_Ŋ-m7Ŋu;-7‹7;v1ubr|bomo=;ŠŊ tent and colonized host trees can be established within a few days. =|;u_-ˆbm]|_bv=buv|oˆ;uѴoohķo†ul;|_o71-m0;†v;7ĸl;-mv-m7 manpower for surveys like arborists or detection dog teams can be more efficiently organized. People will be able to monitor the most v;mvb|bˆ; -u;-v -v - ruboub|‹ bm ou7;u |o h;;r |_; 1ov|Ŋ0;m;=b| u-|bo as good as possible. The risk map is a big help to visualize the area |_-|1o†Ѵ70;1oѴombŒ;70‹ĺ=1o†uv;ķ‰;-Ѵvou;1oll;m71omŊ sulting other studies cited in this manuscript, to get the maximum information and always work on the best strategy. We assume here to work on a simple and accessible method, but it can be enriched with other approaches, if necessary. We for example recommend the “spatial decision support system” of Fournier and Turgeon (2017) that can help in general organization during the surveillance phase with - Ѵoor -m7 u;Ŋ;ˆ-Ѵ†-|bom ruo1;7†u;ĺ $_bv lou;oˆ;u 1o†Ѵ7 0; r;u|bŊ nently coupled with our method. Yemshanov et al. (2017) proposed a mathematical approach where they attempt giving a tool to select the best among different strategies to reduce the risk of high costs 7†ubm]-1-lr-b]mĺ|_;uv|†7b;v1omvb7;ubm]=ou;Š-lrѴ;0boѴŊ ogy and individual movements give valuable information that should be considered.

†u -rruo-1_‰-v mo| omѴ‹ †v;7 bm -uѴ‹ķ 0†| -Ѵvo bm |‰o o|_;u "‰bvvbm=;v|-|bomvro|vo=uুmbvub;7-m7)bm|;u|_†uĺˆ;mb=-ѴѴ|_u;; Ѵo1-Ѵb|b;v -u; t†b|; 7b==;u;m|ķ |_; ubvh l-rv Ő b]†u;ƒķ rr;m7bŠ "Ɠő

u;ruo7†1;‰;ѴѴ |_; ru;vv†u; -m7 -u; bm 1om=oulb|‹‰b|_ |_; u;Ŋ 1;m|=b;Ѵ77;|;1|bomvo=bm7bˆb7†-Ѵvou|_;bu|u-1;vĺ$_;ubvhl-r is a valuable support tool for the design of the monitoring strategy and helps implementing the Swiss guidelines (Pluess et al., 2013) by ruoˆb7bm]or|bl-ѴѴ-‹o†|vo=|_;u;t†bu;7v†uˆ;‹Œom;vĺr|blbŒbm]|_; survey strategy is essential to keep a good balance between costs and efficacy for such long periods of monitoring.

The infestation in Winterthur was considered as eradicated in ƑƏƐѵ-m7|_;om;bmuুmbvub;7v_o†Ѵ7-Ѵvo0;1omvb7;u;7-v;u-7bŊ 1-|;7-||_;;m7o=ƑƏƐƕb=mom;‰7;|;1|bomvo=ru;v;m1;o11†uĺ m-uѴ‹ķmolou;-7†Ѵ|ou;Šb|_oѴ;v‰;u;o0v;uˆ;7bmƑƏƐƔ-m7 ƑƏƐѵķ0†|-11ou7bm]|obm|;um-|bom-Ѵv|-m7-u7vŐķ†uor;-m-m7 ;7b|;uu-m;-mѴ-m|uo|;1|bomu]-mbŒ-|bomķƑƏƐѵőķ|_;lomb|oubm] needs to be continued for two beetle generations (usually 4 years). We started using our approach in the year 2015 as a support for rѴ-mmbm] |_; lomb|oubm] -1|bˆb|b;vĺ m |_; bm=;v|;7 -u;-ķ |_; Ƒ‹;-uv o=bm|;mvbˆ;lomb|oubm]_-ˆ;ruoˆb7;7-|u†v|‰ou|_‹Ѵbv|o=Ŋrobm|vĺ The resulting risk map is highly pertinent to point out the trees that are most at risk, and where monitoring has to be very thoroughly continued.

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YF developed the concept, the mathematical approach and wrote the l-bml-m†v1ubr|ĺ+ ķ -m7 1oѴѴ;1|;7|_;7-|-ĺ+ ķ ķ -m7 "-m-Ѵ‹v;7|_;u;v†Ѵ|vĺ+ ķ ķ ķ)ş"u;ˆb;‰;7|_;l-m†Ŋ v1ubr|ĺ+ ķ ķ ķ)ş"u;-7-m7-rruoˆ;7|_;=bm-Ѵl-m†v1ubr|ĺ

) $"

); -1hmo‰Ѵ;7]; m7u࣐ _-vvo| o= |_; _‹|ov-mb|-u‹ ";uˆb1; o= u-m];m;†ˆ;]ub1†Ѵ|†u-Ѵmv|b|†|;o=|_;"|-|;o= ub0o†u]-m7Ѵ-bm Lambert of the Forest and Fauna Service of the State of Fribourg for their support and Gregor Kozlowski of the University and the Natural History Museum of Fribourg and Heike Lischke of the Swiss ;7;u-Ѵ mv|b|†|; o= ou;v|ķ "mo‰ -m7 -m7v1-r; !;v;-u1_ Ő)"ő bm Birmensdorf for their advices.

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ѴѴ†|_ouv7;1Ѵ-u;|_-||_;‹_-ˆ;mo1om=Ѵb1|o=bm|;u;v|ĺ

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Y. Fragnière _||rĹņņou1b7ĺou]ņƏƏƏƏŊƏƏƏƒŊƓƐѵƕŊƒƕƖ*

B. Wermelinger _||rĹņņou1b7ĺou]ņƏƏƏƏŊƏƏƏƒŊƒƑƒƔŊѵƕƓƐ

S. Bacher _||rĹņņou1b7ĺou]ņƏƏƏƏŊƏƏƏƐŊƔƐƓƕŊƕƐѵƔ

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h-bh;ķ ĺ ŐƐƖƕƓőĺ  m;‰ Ѵooh -| |_; v|-|bv|b1-Ѵ lo7;Ѵ b7;m|b=b1-|bomĺ

IEEE Transactions on Automatic Control, 19(6), 716–723. https://doi.

ou]ņƐƏĺƐƐƏƖņ$ĺƐƖƕƓĺƐƐƏƏƕƏƔ

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