Modelling the population fluctuation of winter moth and mottled umber moth in central and northern Germany
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摘要
Background: Winter moth(Operophtera brumata) and mottled umber moth(Erannis defoliaria) are forest Lepidoptera species characterized by periodic high abundance in a 7–11 year cycle. During outbreak years they cause severe defoliation in many forest stands in Europe. In order to better understand the spatio-temporal dynamics and elucidate possible influences of weather, stand and site conditions, a generalized additive mixed model was developed. The investigated data base was derived from glue band catch monitoring stands of both species in Central and North Germany. From the glue bands only female moth individuals are counted and a hazard code is calculated. The model can be employed to predict the exceedance of a warning threshold of this hazard code which indicates a potential severe defoliation of oak stands by winter moth and mottled umber in the coming spring.Results: The developed model accounts for specific temporal structured effects for three large ecoregions and random effects at stand level. During variable selection the negative model effect of pest control and the positive model effects of mean daily minimum temperature in adult stage and precipitation in early pupal stage were identified.Conclusion: The developed model can be used for short-term predictions of potential defoliation risk in Central and North Germany. These predictions are sensitive to weather conditions and the population dynamics. However, a future extension of the data base comprising further outbreak years would allow for deeper investigation of the temporal and regional patterns of the cyclic dynamics and their causal influences on abundance of winter moth and mottled umber.
Background: Winter moth(Operophtera brumata) and mottled umber moth(Erannis defoliaria) are forest Lepidoptera species characterized by periodic high abundance in a 7–11 year cycle. During outbreak years they cause severe defoliation in many forest stands in Europe. In order to better understand the spatio-temporal dynamics and elucidate possible influences of weather, stand and site conditions, a generalized additive mixed model was developed. The investigated data base was derived from glue band catch monitoring stands of both species in Central and North Germany. From the glue bands only female moth individuals are counted and a hazard code is calculated. The model can be employed to predict the exceedance of a warning threshold of this hazard code which indicates a potential severe defoliation of oak stands by winter moth and mottled umber in the coming spring.Results: The developed model accounts for specific temporal structured effects for three large ecoregions and random effects at stand level. During variable selection the negative model effect of pest control and the positive model effects of mean daily minimum temperature in adult stage and precipitation in early pupal stage were identified.Conclusion: The developed model can be used for short-term predictions of potential defoliation risk in Central and North Germany. These predictions are sensitive to weather conditions and the population dynamics. However, a future extension of the data base comprising further outbreak years would allow for deeper investigation of the temporal and regional patterns of the cyclic dynamics and their causal influences on abundance of winter moth and mottled umber.
Background: Winter moth(Operophtera brumata) and mottled umber moth(Erannis defoliaria) are forest Lepidoptera species characterized by periodic high abundance in a 7–11 year cycle. During outbreak years they cause severe defoliation in many forest stands in Europe. In order to better understand the spatio-temporal dynamics and elucidate possible influences of weather, stand and site conditions, a generalized additive mixed model was developed. The investigated data base was derived from glue band catch monitoring stands of both species in Central and North Germany. From the glue bands only female moth individuals are counted and a hazard code is calculated. The model can be employed to predict the exceedance of a warning threshold of this hazard code which indicates a potential severe defoliation of oak stands by winter moth and mottled umber in the coming spring.Results: The developed model accounts for specific temporal structured effects for three large ecoregions and random effects at stand level. During variable selection the negative model effect of pest control and the positive model effects of mean daily minimum temperature in adult stage and precipitation in early pupal stage were identified.Conclusion: The developed model can be used for short-term predictions of potential defoliation risk in Central and North Germany. These predictions are sensitive to weather conditions and the population dynamics. However, a future extension of the data base comprising further outbreak years would allow for deeper investigation of the temporal and regional patterns of the cyclic dynamics and their causal influences on abundance of winter moth and mottled umber.
引文
Akaike H(1974)A new look at the statistical model identification.IEEE Trans Autom Control 19:716-723
Altenkirch W(1966)Zur Verwendung von Leimringen bei der AbundanzBestimmung von Frostspannern.Zugleich ein kritischer Beitrag zur forstlichen Frostspanner-Prognose.Z Angew Zool 53:34
Altenkirch W(1981)Zur Frostspanner-Situation in Niedersachsen im Herbst 1981.Forst-Holzwirt 20:504-506
Augustin NH,Musio M,von Wilpert K,Kublin E,Wood SN,Schumacher M(2009)Modelling spatiotemporal forest health monitoring data.J Am Stat Assoc104:899-911
Berryman AA(1996)What causes population cycles of forest Lepidoptera?Trends Ecol Evol 11:28-32
B?hner J,Antoni?O(2009)Chapter 8 land-surface parameters specific to topoclimatology.Dev Soil Sci 33:195-226
Bressem U,Steen A(2012)Eichensterben-Erkrankungsschub 2011.AFZ-Wald67:24-27
Connell J(2014)Frostspanner2015-BFW.In:http://bfw.ac.at/rz/bfwcms.web_print?dok=10006.Accessed 9 Jun 2015
Connell J,Steyer G(2007)Raupenfallen-Untersuchung 2006:Artenspektrum von Schmetterlingen an Laubb?umen.Forstsch Aktuell 38:12-17
Conrad O,Bechtel B,Bock M,Dietrich H,Fischer E,Gerlitz L,Wehberg J,Wichmann V,B?hner J(2015)System for automated geoscientific analyses(SAGA)v.2.1.4.Geosci Model Dev 8:1991-2007.https://doi.org/10.5194/gmd-8-1991-2015
Delb H(2012)In:FVA-Einblick(ed)Eichensch?dlinge im Klimawandel in Südwestdeutschland.https://www.waldwissen.net/waldwirtschaft/schaden/krankheiten/fva_eichensterben_klimawandel/index_DE.Accessed 9 Jun 2015
Dempster JP(1983)The natural control of populations of butterflies and moths.Biol Rev 58:461-481.https://doi.org/10.1111/j.1469-185X.1983.tb00396.x
Fischer R(1999)Folgen von Insektenfra?für den Gesundheitszustand der Eichen.AFZ-Wald 7:355-356
Gasparrini A(2011)Distributed lag linear and non-linear models in R:the package dlnm.J Stat Softw 43:1
Habermann M,Hurling R,Krüger F,Bressem U(2007)Waldschutzsituation 2006 in Niedersachsen und Hessen.AFZ-Wald 7:356-361
Hanewinkel M,Zhou W,Schill C(2004)A neural network approach to identify forest stands susceptible to wind damage.For Ecol Manag 196:227-243.https://doi.org/10.1016/j.foreco.2004.02.056
Hartmann G,Blank R(1998)Aktuelles Eichensterben in Niedersachsen-Ursachen und Gegenma?nahmen.Forst Holz 53:733-735
Hosmer DW,Lemeshow S(2000)Applied logistic regression,2nd edn.Wiley,New York
Hunter MD(1998)Interactions between Operophtera brumata and Tortrix viridana on oak:new evidence from time-series analysis.Ecol Entomol 23:168-173.https://doi.org/10.1046/j.1365-2311.1998.00124.x
Ims RA,Steen H(1990)Geographical synchrony in microtine population cycles:a theoretical evaluation of the role of nomadic avian predators.Oikos 57:381-387.https://doi.org/10.2307/3565968
Jepsen JU,Hagen SB,Karlsen S-R,Ims RA(2009)Phase-dependent outbreak dynamics of geometrid moth linked to host plant phenology.Proc R Soc Lond B Biol Sci 276:4119-4128.https://doi.org/10.1098/rspb.2009.1148
K?tzel R,L?ffler S,M?ller K,Heydeck P,Kallweit R(2006)Das Eichensterben als Komplexkrankheit.Eberswalder Forstl Schriftenreihe 25:94-100,https://forst.brandenburg.de/cms/media.php/lbm1.a.4595.de/b25eiche.pdf
King G,Zeng L(2001)Logistic regression in rare events data.Polit Anal 9:137-163
Klemola N,Andersson T,Ruohom?ki K,Klemola T(2010)Experimental test of parasitism hypothesis for population cycles of a forest lepidopteran.Ecology91:2506-2513
Klemola T,Ruohom?ki K,Andersson T,Neuvonen S(2004)Reduction in size and fecundity of the autumnal moth,Epirrita autumnata,in the increase phase of a population cycle.Oecologia 141:47-56
Koenig WD(2002)Global patterns of environmental synchrony and the Moran effect.Ecography 25:283-288.https://doi.org/10.1034/j.1600-0587.2002.250304.x
K?hler M,Ahrends B,Meesenburg H(2015)Wie gut ist einfach?Evaluierung verschiedener Verfahren zur Regionalisierung t?glicher Wetterdaten.Poster zum“Tag der Hydrologie 2015”in Bonn 19.-20.03.2015
Lawrence S,Burns I,Back A,Tsoi AC,Giles CL(1998)Neural network classification and prior class probabilities.In:Orr G,Müller K-R,Caruana R(eds)Tricks of the Trade,Lecture Notes in Computer Sciens State-of-the-Art Surveys.Springer Verlag Berlin-Heidelberg,pp 299-314,https://ro.uow.edu.au/eispapers/271/
Liebhold A,Kamata N(2000)Introduction:are population cycles and spatial synchrony a universal characteristic of forest insect populations?Popul Ecol42:205-209.https://doi.org/10.1007/PL00011999
Liebhold A,Koenig WD,Bj?rnstad ON(2004)Spatial synchrony in population dynamics.Annu Rev Ecol Evol Syst 35:467-490.https://doi.org/10.1146/annurev.ecolsys.34.011802.132516
Manion PD(2003)Evolution of concepts in forest pathology.Phytopathology 93:1052-1055
Menzel A(1997)Ph?nologie von Waldb?umen unter sich?ndernden Klimabedingungen-Auswertung der Beobachtungen in den Internationalen Ph?nologischen G?rten und M?glichkeiten der Modellierung von Ph?nodaten.Forstl Forschungsberichte Münch 164:147
Meshkova V(2000)The impact of insect-defoliators to the oak decline in Ukraine.Instytut Badawczy Le?nictwa(Forest Research Institute),pp 225-229
Moran P(1953)The statistical analysis of the Canadian Lynx cycle.Aust J Zool 1:291-298.https://doi.org/10.1071/ZO9530291
Myers J(1988)Can a general hypothesis explain population cycles of forest Lepidoptera?Adv Ecol Res 18:179-242.https://doi.org/10.1016/S0065-2504(08)60181-6
Nuske R(2015)Determine Vegetation Periods of Forest Trees.In:R-Package Version 021.http://computerfoerster.de/r-pkgs.Accessed 2 Jan 2017
Overbeck M,Schmidt M(2012)Modelling infestation risk of Norway spruce by Ips typographus(L.)in the lower Saxon Harz Mountains(Germany).For Ecol Manag 266:115-125.https://doi.org/10.1016/j.foreco.2011.11.011
Peltonen M,Liebhold AM,Bj?rnstad ON,Williams DW(2002)Spatial synchrony in forest insect outbreaks:roles of regional stochasticity and dispersal.Ecology83:3120-3129
Petercord R(2015)Rolle der Eichenfrassgesellschaft beim Eichensterben.AFZ-Wald 70:17-19
Pinheiro J,Bates D(2006)Mixed-effects models in S and S-PLUS.Springer Science&Business Media
R Core Team(2015)R:A language and environment for statistical computing[Internet].Vienna,Austria:R Foundation for Statistical Computing.Available:http:www.r-proj.org.Accessed 20 January 2015
Robin X,Turck N,Hainard A,Tiberti N,Lisacek F,Sanchez J-C,Müller M(2011)pROC:an open-source package for R and S+to analyze and compare ROCcurves.BMC Bioinformatics 12:77.https://doi.org/10.1186/1471-2105-12-77
Roland J(1994)After the decline:what maintains low winter moth density after successful biological control?J Anim Ecol 63:392-398.https://doi.org/10.2307/5556
Ruohom?ki K,Tanhuanp??M,Ayres MP,Kaitaniemi P,Tammaru T,Haukioja E(2000)Causes of cyclicity of Epirrita autumnata(Lepidoptera,Geometridae):grandiose theory and tedious practice.Popul Ecol 42:211-223.https://doi.org/10.1007/PL00012000
Schmidt W,Stüber V,Ullrich T,Paar U,Evers J,Dammann K,H?velmann T,Schmidt M(2015)Synopse der Hauptmerkmale der forstlichen Standortskartierungsverfahren der Nordwestdeutschen Bundesl?nder.Universit?tsdrucke G?ttingen,G?ttingen
Schwenke W(1978)Die Forstsch?dlinge Europas-Schmetterlinge.Paul Parey
Sel?s V(2000)Is there a higher risk for herbivore outhreaks after cold mast years?An analysis of two plant/herbivore series from southern Norway.Ecography23:651-658.https://doi.org/10.1111/j.1600-0587.2000.tb00308.x
Tenow O,Nilssen A(1990)Egg cold hardiness and topoclimatic limitations to outbreaks of Epirrita autumnata in northern Fennoscandia.J Appl Ecol 27:723-734.https://doi.org/10.2307/2404314
Tenow O,Nilssen AC,Bylund H,Pettersson R,Battisti A,Bohn U,Caroulle F,Ciornei C,Csóka G,Delb H(2013)Geometrid outbreak waves travel across Europe.J Anim Ecol 82:84-95
Thomas FM(2008)Recent advances in cause-effect research on oak decline in Europe.CAB Rev Perspect Agric Vet Sci Nutr Nat Resour.https://doi.org/10.1079/PAVSNNR20083037
Thomas FM,Blank R,Hartmann G(2002)Abiotic and biotic factors and their interactions as causes of oak decline in Central Europe.For Pathol 32:277-307
Topp W,Kirsten K(1991)Synchronisation of pre-imaginal development and reproductive success in the winter moth,Operophtera brumata L.J Appl Entomol 111:137-146.https://doi.org/10.1111/j.1439-0418.1991.tb00304.x
van Asch M,Visser ME(2007)Phenology of forest caterpillars and their host trees:the importance of synchrony.Annu Rev Entomol 52:37-55
Virtanen T,Neuvonen S(1999)Performance of moth larvae on birch in relation to altitude,climate,host quality and parasitoids.Oecologia 120:92-101.https://doi.org/10.1007/s004420050837
Wood SN(2011)Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models.J R Stat Soc B 73:3-36
Ydenberg RC(1987)Nomadic predators and geographical synchrony in microtine population cycles.Oikos 50:270-272.https://doi.org/10.2307/3566014
Zevenbergen LW,Thorne CR(1987a)Quantitative analysis of land surface topography.Earth Surf Process Landf 12:47-56
Zevenbergen LW,Thorne CR(1987b)Quantitative analysis of land surface topography.Earth Surf Process Landf 12:47-56.https://doi.org/10.1002/esp.32901
Zuur AF,Ieno EN,Walker NJ,Saveliev AA,Smith GM(2009)Mixed effects models and extensions in ecology with r,statistics for biology and health.Springer,New York
Altenkirch W(1966)Zur Verwendung von Leimringen bei der AbundanzBestimmung von Frostspannern.Zugleich ein kritischer Beitrag zur forstlichen Frostspanner-Prognose.Z Angew Zool 53:34
Altenkirch W(1981)Zur Frostspanner-Situation in Niedersachsen im Herbst 1981.Forst-Holzwirt 20:504-506
Augustin NH,Musio M,von Wilpert K,Kublin E,Wood SN,Schumacher M(2009)Modelling spatiotemporal forest health monitoring data.J Am Stat Assoc104:899-911
Berryman AA(1996)What causes population cycles of forest Lepidoptera?Trends Ecol Evol 11:28-32
B?hner J,Antoni?O(2009)Chapter 8 land-surface parameters specific to topoclimatology.Dev Soil Sci 33:195-226
Bressem U,Steen A(2012)Eichensterben-Erkrankungsschub 2011.AFZ-Wald67:24-27
Connell J(2014)Frostspanner2015-BFW.In:http://bfw.ac.at/rz/bfwcms.web_print?dok=10006.Accessed 9 Jun 2015
Connell J,Steyer G(2007)Raupenfallen-Untersuchung 2006:Artenspektrum von Schmetterlingen an Laubb?umen.Forstsch Aktuell 38:12-17
Conrad O,Bechtel B,Bock M,Dietrich H,Fischer E,Gerlitz L,Wehberg J,Wichmann V,B?hner J(2015)System for automated geoscientific analyses(SAGA)v.2.1.4.Geosci Model Dev 8:1991-2007.https://doi.org/10.5194/gmd-8-1991-2015
Delb H(2012)In:FVA-Einblick(ed)Eichensch?dlinge im Klimawandel in Südwestdeutschland.https://www.waldwissen.net/waldwirtschaft/schaden/krankheiten/fva_eichensterben_klimawandel/index_DE.Accessed 9 Jun 2015
Dempster JP(1983)The natural control of populations of butterflies and moths.Biol Rev 58:461-481.https://doi.org/10.1111/j.1469-185X.1983.tb00396.x
Fischer R(1999)Folgen von Insektenfra?für den Gesundheitszustand der Eichen.AFZ-Wald 7:355-356
Gasparrini A(2011)Distributed lag linear and non-linear models in R:the package dlnm.J Stat Softw 43:1
Habermann M,Hurling R,Krüger F,Bressem U(2007)Waldschutzsituation 2006 in Niedersachsen und Hessen.AFZ-Wald 7:356-361
Hanewinkel M,Zhou W,Schill C(2004)A neural network approach to identify forest stands susceptible to wind damage.For Ecol Manag 196:227-243.https://doi.org/10.1016/j.foreco.2004.02.056
Hartmann G,Blank R(1998)Aktuelles Eichensterben in Niedersachsen-Ursachen und Gegenma?nahmen.Forst Holz 53:733-735
Hosmer DW,Lemeshow S(2000)Applied logistic regression,2nd edn.Wiley,New York
Hunter MD(1998)Interactions between Operophtera brumata and Tortrix viridana on oak:new evidence from time-series analysis.Ecol Entomol 23:168-173.https://doi.org/10.1046/j.1365-2311.1998.00124.x
Ims RA,Steen H(1990)Geographical synchrony in microtine population cycles:a theoretical evaluation of the role of nomadic avian predators.Oikos 57:381-387.https://doi.org/10.2307/3565968
Jepsen JU,Hagen SB,Karlsen S-R,Ims RA(2009)Phase-dependent outbreak dynamics of geometrid moth linked to host plant phenology.Proc R Soc Lond B Biol Sci 276:4119-4128.https://doi.org/10.1098/rspb.2009.1148
K?tzel R,L?ffler S,M?ller K,Heydeck P,Kallweit R(2006)Das Eichensterben als Komplexkrankheit.Eberswalder Forstl Schriftenreihe 25:94-100,https://forst.brandenburg.de/cms/media.php/lbm1.a.4595.de/b25eiche.pdf
King G,Zeng L(2001)Logistic regression in rare events data.Polit Anal 9:137-163
Klemola N,Andersson T,Ruohom?ki K,Klemola T(2010)Experimental test of parasitism hypothesis for population cycles of a forest lepidopteran.Ecology91:2506-2513
Klemola T,Ruohom?ki K,Andersson T,Neuvonen S(2004)Reduction in size and fecundity of the autumnal moth,Epirrita autumnata,in the increase phase of a population cycle.Oecologia 141:47-56
Koenig WD(2002)Global patterns of environmental synchrony and the Moran effect.Ecography 25:283-288.https://doi.org/10.1034/j.1600-0587.2002.250304.x
K?hler M,Ahrends B,Meesenburg H(2015)Wie gut ist einfach?Evaluierung verschiedener Verfahren zur Regionalisierung t?glicher Wetterdaten.Poster zum“Tag der Hydrologie 2015”in Bonn 19.-20.03.2015
Lawrence S,Burns I,Back A,Tsoi AC,Giles CL(1998)Neural network classification and prior class probabilities.In:Orr G,Müller K-R,Caruana R(eds)Tricks of the Trade,Lecture Notes in Computer Sciens State-of-the-Art Surveys.Springer Verlag Berlin-Heidelberg,pp 299-314,https://ro.uow.edu.au/eispapers/271/
Liebhold A,Kamata N(2000)Introduction:are population cycles and spatial synchrony a universal characteristic of forest insect populations?Popul Ecol42:205-209.https://doi.org/10.1007/PL00011999
Liebhold A,Koenig WD,Bj?rnstad ON(2004)Spatial synchrony in population dynamics.Annu Rev Ecol Evol Syst 35:467-490.https://doi.org/10.1146/annurev.ecolsys.34.011802.132516
Manion PD(2003)Evolution of concepts in forest pathology.Phytopathology 93:1052-1055
Menzel A(1997)Ph?nologie von Waldb?umen unter sich?ndernden Klimabedingungen-Auswertung der Beobachtungen in den Internationalen Ph?nologischen G?rten und M?glichkeiten der Modellierung von Ph?nodaten.Forstl Forschungsberichte Münch 164:147
Meshkova V(2000)The impact of insect-defoliators to the oak decline in Ukraine.Instytut Badawczy Le?nictwa(Forest Research Institute),pp 225-229
Moran P(1953)The statistical analysis of the Canadian Lynx cycle.Aust J Zool 1:291-298.https://doi.org/10.1071/ZO9530291
Myers J(1988)Can a general hypothesis explain population cycles of forest Lepidoptera?Adv Ecol Res 18:179-242.https://doi.org/10.1016/S0065-2504(08)60181-6
Nuske R(2015)Determine Vegetation Periods of Forest Trees.In:R-Package Version 021.http://computerfoerster.de/r-pkgs.Accessed 2 Jan 2017
Overbeck M,Schmidt M(2012)Modelling infestation risk of Norway spruce by Ips typographus(L.)in the lower Saxon Harz Mountains(Germany).For Ecol Manag 266:115-125.https://doi.org/10.1016/j.foreco.2011.11.011
Peltonen M,Liebhold AM,Bj?rnstad ON,Williams DW(2002)Spatial synchrony in forest insect outbreaks:roles of regional stochasticity and dispersal.Ecology83:3120-3129
Petercord R(2015)Rolle der Eichenfrassgesellschaft beim Eichensterben.AFZ-Wald 70:17-19
Pinheiro J,Bates D(2006)Mixed-effects models in S and S-PLUS.Springer Science&Business Media
R Core Team(2015)R:A language and environment for statistical computing[Internet].Vienna,Austria:R Foundation for Statistical Computing.Available:http:www.r-proj.org.Accessed 20 January 2015
Robin X,Turck N,Hainard A,Tiberti N,Lisacek F,Sanchez J-C,Müller M(2011)pROC:an open-source package for R and S+to analyze and compare ROCcurves.BMC Bioinformatics 12:77.https://doi.org/10.1186/1471-2105-12-77
Roland J(1994)After the decline:what maintains low winter moth density after successful biological control?J Anim Ecol 63:392-398.https://doi.org/10.2307/5556
Ruohom?ki K,Tanhuanp??M,Ayres MP,Kaitaniemi P,Tammaru T,Haukioja E(2000)Causes of cyclicity of Epirrita autumnata(Lepidoptera,Geometridae):grandiose theory and tedious practice.Popul Ecol 42:211-223.https://doi.org/10.1007/PL00012000
Schmidt W,Stüber V,Ullrich T,Paar U,Evers J,Dammann K,H?velmann T,Schmidt M(2015)Synopse der Hauptmerkmale der forstlichen Standortskartierungsverfahren der Nordwestdeutschen Bundesl?nder.Universit?tsdrucke G?ttingen,G?ttingen
Schwenke W(1978)Die Forstsch?dlinge Europas-Schmetterlinge.Paul Parey
Sel?s V(2000)Is there a higher risk for herbivore outhreaks after cold mast years?An analysis of two plant/herbivore series from southern Norway.Ecography23:651-658.https://doi.org/10.1111/j.1600-0587.2000.tb00308.x
Tenow O,Nilssen A(1990)Egg cold hardiness and topoclimatic limitations to outbreaks of Epirrita autumnata in northern Fennoscandia.J Appl Ecol 27:723-734.https://doi.org/10.2307/2404314
Tenow O,Nilssen AC,Bylund H,Pettersson R,Battisti A,Bohn U,Caroulle F,Ciornei C,Csóka G,Delb H(2013)Geometrid outbreak waves travel across Europe.J Anim Ecol 82:84-95
Thomas FM(2008)Recent advances in cause-effect research on oak decline in Europe.CAB Rev Perspect Agric Vet Sci Nutr Nat Resour.https://doi.org/10.1079/PAVSNNR20083037
Thomas FM,Blank R,Hartmann G(2002)Abiotic and biotic factors and their interactions as causes of oak decline in Central Europe.For Pathol 32:277-307
Topp W,Kirsten K(1991)Synchronisation of pre-imaginal development and reproductive success in the winter moth,Operophtera brumata L.J Appl Entomol 111:137-146.https://doi.org/10.1111/j.1439-0418.1991.tb00304.x
van Asch M,Visser ME(2007)Phenology of forest caterpillars and their host trees:the importance of synchrony.Annu Rev Entomol 52:37-55
Virtanen T,Neuvonen S(1999)Performance of moth larvae on birch in relation to altitude,climate,host quality and parasitoids.Oecologia 120:92-101.https://doi.org/10.1007/s004420050837
Wood SN(2011)Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models.J R Stat Soc B 73:3-36
Ydenberg RC(1987)Nomadic predators and geographical synchrony in microtine population cycles.Oikos 50:270-272.https://doi.org/10.2307/3566014
Zevenbergen LW,Thorne CR(1987a)Quantitative analysis of land surface topography.Earth Surf Process Landf 12:47-56
Zevenbergen LW,Thorne CR(1987b)Quantitative analysis of land surface topography.Earth Surf Process Landf 12:47-56.https://doi.org/10.1002/esp.32901
Zuur AF,Ieno EN,Walker NJ,Saveliev AA,Smith GM(2009)Mixed effects models and extensions in ecology with r,statistics for biology and health.Springer,New York