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Population Cycles of the Larch Budmoth in Switzerland

Authors:
Peter Turchin
Peter Turchin
Peter Turchin
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Cherie Briggs at University of California, Santa Barbara
Cherie Briggs
Stephen P Ellner
Stephen P Ellner
Stephen P Ellner
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Andreas Fischlin at ETH Zurich
Andreas Fischlin
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Abstract and Figures

The population dynamics of the larch budmoth (LBM), Zeiraphera diniana, in the Swiss Alps are perhaps the best example of periodic oscillations in ecology (figure 7.1). These oscillations are characterized by a remarkably regular periodicity, and by an enormous range of densities experienced during a typical cycle (about 100,000-fold difference between peak and trough numbers). Furthermore, nonlinear time series analysis of LBM data (e.g., Turchin 1990, Turchin and Taylor 1992) indicates that LBM oscillations are definitely generated by a second-order dynamical process (in other words, there is a strong delayed density dependence—see also chapter 1). Analysis of time series data on LBM dynamics from five valleys in the Alps suggests that around 90% of variance in Rt is explained by the phenomenological time series model employing lagged LBM densities, R, =f(Ni-1,Ni-2,) (Turchin 2002). As discussed in the influential review by Baltensweiler and Fischlin (1988) about a decade ago, ecological theory suggests a number of candidate mechanisms that can produce the type of dynamics observed in the LBM (see also chapter 1). Baltensweiler and Fischlin concluded that changes in food quality induced by previous budmoth feeding was the most plausible explanation for the population cycles. During the last decade, the issue of larch budmoth oscillations was periodically revisited by various population ecologists looking for general insights about insect population cycles (e.g., Royama 1977, Bowers et al. 1993, Ginzburg and Taneyhill 1994, Den Boer and Reddingius 1996, Hunter and Dwyer 1998, Berryman 1999). These authors generally concurred with the view that budmoth cycles are driven by the interaction with food quality. A recent reanalysis of the rich data set on budmoth population ecology collected by Swiss researchers over a period of several decades, however, suggested that the role of parasitism is underappreciated (Turchin et al. 2002). Before focusing on the roles of food quality and parasitism in LBM dynamics, we briefly review the status of other hypotheses that were discussed in the literature on LBM cycles. First, the natural history of the LBM-larch system is such that food quantity is an unlikely factor to explain LBM oscillations.
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    
  
    
     
      
 
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           
          

  


           
        
           
         
      


          
           
          
        
          
  
        
   
         


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
 
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
 

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
      
 
  

 
           
            
 
 


          
 
    
           

    

            
  
          
           
         
      
   
         



     
   
 
   
 

         
      
        

    
 

          

 




  
        
 
          

          
   

    

         
  
       
       
        
        
     
 
        
         
      
         
        
         
    
           
          
         
    
      
         
          
        
          
           
   
         
      
         
         
        
         
         
         
           
          
     
      
         
       
  
            
     
         
   
          
 
        
 
   
  
         
           
           
            
            
        
     
           
  
     
          
    
  
 




    
   
        
    

         
 

 
         

      
         
         
  

      

  



 




 


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
           
            
         
   
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 


 

      


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 






 
   


 

 


 



 
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
 

  
 
 

 







 

             
 
       

    

 
  

      
  
 


 
   
         
 

         
   




        




 
            
         

          
 
         
  

 

 
 


  
   
 


      
       
      




   
    

   
     
             

   

         


  

         


           

  
 
      

         

          

    
  


  


   



   
 

   
  
          


         

 
         
 


  
          
           
          
           
       

     
         
 
        





   
            
       
   

  


          
         
            
         
  
         
            
         
 
         
           
        
 
     
  

   


    




         
    
           
      
  
         
        
  
 
        
   
         
        
     
     
    
           



  
 

     
 

c
  
   
  
0 

 
 
  
 
   

  
    

          
 
 
   



       

 
 
          

      
          




       
   

   



            

       
 
           
           
          
       
          
    
         
 
   


          
    
         
        
 
      
   
        

           
   
        
 

             
       
    
   
       
     
       
         
         
 
 
  
 

        
    
            
          
 
  
     
          
      
       
         

        
 
            
 
  
     
     
... is used to represent the plant's health. Previous work by Turchin and others [10,[13][14][15][16] has shown the necessity of including three species in their model to capture and sustain the budmoth population cycles: the larch trees represented by their PQI, the budmoths which infest them, and parasitoids which live off the budmoths. Turchin's tritrophic model [13,15] is able to reproduce the 9-year budmoth cycles seen in the Swiss Engadine valley but can reproduce no other feature mentioned above. ...
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... Wasteful feeding by budmoth larvae on larch foliage leading to a scorched appearance of the entire landscape, has prompted several investigations of the population cycles of this insect pest (see for instance ref. 5). Previous studies on larch budmoth (LBM) population cycles have established the presence of a third trophic level -parasitoids which prey upon budmoth larvae [6][7][8][9] . The population densities of the budmoth, the parasitoids preying upon them and needle lengths of the larch 10 are all known to show periodic cycles which are mutually synchronized. ...
Impact of climate change on larch budmoth cyclic outbreaks
Article
Full-text available
  • Jun 2016
Periodic outbreaks of the larch budmoth Zeiraphera diniana population (and the massive forest defoliation they engender) have been recorded in the Alps over the centuries and are known for their remarkable regularity. But these have been conspicuously absent since 1981. On the other hand, budmoth outbreaks have been historically unknown in the larches of the Carpathian Tatra mountains. To resolve this puzzle, we propose here a model which includes the influence of climate and explains both the 8-9 year periodicity in the budmoth cycle and the variations from this, as well as the absence of cycles. We successfully capture the observed trend of relative frequencies of outbreaks, reproducing the dominant periodicities seen. We contend that the apparent collapse of the cycle in 1981 is due to changing climatic conditions following a tipping point and propose the recurrence of the cycle with a changed periodicity of 40 years-the next outbreak could occur in 2021. Our model also predicts longer cycles.
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... The larch budmoth populations in the European Alps are one system for which there is strong evidence of periodic travelling waves. The almost metronomic multi-year dynamics of larch budmoth populations has fascinated ecologists for decades (Turchin et al. 2002, ch. 9). ...
Periodic travelling waves in cyclic populations: Field studies and reaction-diffusion models
Article
Full-text available
Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction-diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur. We also discuss wave stability, including recent computational developments. Although we focus on oscillatory reaction-diffusion equations, a brief discussion of other types of model in which periodic travelling waves have been demonstrated is also included. We end by proposing 10 research challenges in this area, five mathematical and five empirical.
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Complex dynamical behavior and control of a discrete ecological model
Article
Full-text available
Cyclic types of ecological dynamics have been found in several biological species of forest Lepidoptera. There are several possible reasons for this, for example, interactions with consumers, predators, plant quality index, and interactions of density-dependent type. Furthermore, interaction with consumers and plant quality index is regarded as key ingredients to alter the dynamics for the parasitoid population. Consequently, the quality of food resources fluctuates due to the level of herbs. Such changes have been observed in different systems of forest pests. Lepidoptera (larch budmoth) is a destructive worm that affects high-altitude trees around the world and is rapidly declining and becoming extinct in large areas of the forest. Considering the interaction between the budmoth and plant quality index for larch trees in the mountain range in Switzerland (Swiss Alps), we discuss the dynamics of a discrete-time system. Ivlev type functional response regarding plant quality index is used for the formulation of discrete-time model concerning the interaction between the index of plant quality and budmoth. Moreover, the existence of steady-states, their local behaviors, and the boundedness of solutions are carried out for the discrete-time model under consideration. It is investigated that the model undergoes flip bifurcation about coexistence by applying the theory of normal forms and the center manifold theorem. Furthermore, the direction and the existence of Hopf bifurcation are explored for the model around its coexistence. Various methods of controlling chaos have been introduced to avoid system fluctuations and bifurcating attitudes. Validation of the analytical findings is illustrated through numerical simulations. Finally, the analytical results are validated by experimental and actual field data.
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Co-existence of periodic bursts and death of cycles in a population dynamics system
Article
  • Sep 2016
We study the dynamics of a discrete-time tritrophic model which mimics the observed periodicity in the population cycles of the larch budmoth insect which causes widespread defoliation of larch forests at high altitudes periodically. Our model employs q-deformation of numbers to model the system comprising the budmoth, one or more parasitoid species, and larch trees. Incorporating climate parameters, we introduce additional parasitoid species and show that their introduction increases the periodicity of the budmoth cycles as observed experimentally. The presence of these additional species also produces other interesting dynamical effects such as periodic bursting and oscillation quenching via oscillation death, amplitude death, and partial oscillation death which are also seen in nature. We suggest that introducing additional parasitoid species provides an alternative explanation for the collapse of the nine year budmoth outbreak cycles observed in the Swiss Alps after 1981. A detailed exploration of the parameter space of the system is performed with movies of bifurcation diagrams which enable variation of two parameters at a time. Limit cycles emerge through a Neimark-Sacker bifurcation with respect to all parameters in all the five and higher dimensional models we have studied.
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Existence of periodic travelling waves solutions in predator prey model with diffusion,
Article
  • Mar 2013
  • APPL MATH MODEL
This paper deals with the qualitative analysis of the travelling waves solutions of a reaction diffusion model that refers to the competition between the predator and prey with modified Leslie–Gower and Holling type II schemes. The well posedeness of the problem is proved. We establish sufficient conditions for the asymptotic stability of the unique nontrivial positive steady state of the model by analyzing roots of the forth degree exponential polynomial characteristic equation. We also prove the existence of a Hopf bifurcation which leads to periodic oscillating travelling waves by considering the diffusion coefficient as a parameter of bifurcation. Numerical simulations are given to illustrate the analytical study.
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The Larch Budmoth in the Alps
Article
Full-text available
  • Jan 1988
During the late 1940s, immediately after World War II, the lush green forests of the Engadine Valley, high in the Swiss Alps, turned an ugly red-brown in the midst of the tourist season. This was due to a spectacular outbreak of the larch budmoth, Zeiraphera diniana Guenée (Lepidoptera: Tortricidae). Preparing for a revival of the tourist industry, and having the new insecticide DDT at hand, it seemed only appropriate that the tourist office urge the forest service to control the pest. This was the beginning of what was to become a 34-year study of the population dynamics of the larch budmoth (Fig. 1).
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Dynamics of Forest Insect Populations: Patterns, Causes, Implications
Book
  • Jan 1988
Insects multiply. Destruction reigns. There is dismay, followed by outcry, and demands to Authority. Authority remembers its experts or appoints some: they ought to know. The experts advise a Cure. The Cure can be almost anything: holy water from Mecca, a Government Commis­ sion, a culture of bacteria, poison, prayers denunciatory or tactful, a new god, a trap, a Pied Piper. The Cures have only one thing in common: with a little patience they always work. They have never been known entirely to fail. Likewise they have never been known to prevent the next outbreak. For the cycle of abundance and scarcity has a rhythm of its own, and the Cures are applied just when the plague of insects is going to abate through its own loss of momentum. -Abridged, with insects in place of voles, from C. Elton, 1924, Voles, Mice and Lemmings, with permission of Oxford University Press This book is an enquiry into the "natural rhythms" of insect abundance in forested ecosystems and into the forces that give rise to these rhythms. Forests form unique environ­ ments for such studies because one can find them growing under relatively natural (pri­ meval) conditions as well as under the domination of human actions. Also, the slow growth and turnover rates of forested ecosystems enable us to investigate insect popula­ tion dynamics in a plant environment that remains relatively constant or changes only slowly, this in contrast to agricultural systems, where change is often drastic and frequent.
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The Effects of Inducible Plant Defenses on Herbivore Populations. 1. Mobile Herbivores in Continuous Time
Article
  • Jun 1989
Describes a quantitative framework that may be used for understanding the effects of inducible plant defenses on herbivore populations. Procedures were used for modeling continuous, structured populations to examine the dynamics of interactions between inducible defenses and mobile herbivores. Inducible defenses can by themselves regulate herbivore populations under a wide variety of conditions and, in conjunction with other regulatory agents (eg predators, parasitoids), they can significantly depress herbivore populations. However, only under unusual conditions can inducible defenses cause persistent fluctuations in herbivore populations. The model suggests that herbivores cannot maintain heterogeneity in the level of inducible defenses within a plant population. Conclusions may not apply to sedentary or selective herbivores or to herbivores with discrete, nonoverlapping generations. -from Authors
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Population Cycles of Forest Lepidoptera: A Maternal Effect Hypothesis
Article
1. Many species of forest Lepidoptera have cyclic population dynamics. Although there are numerous potential causes, including interactions with predators, parasitoids, pathogens, and food-plant quality, strongly density-dependent interactions are often difficult to demonstrate. Both autocorrelation analysis and attractor-reconstruction methods have recently been applied to a number of species' time series. Results suggest that complex dynamics, i.e. cycles or deterministic choas, may be more prevalent than once thought, and that higher-dimensioned models are necessary. 2. We develop a two-dimensional difference equation model that relates the average quality of individuals to patterns of abundance. The delayed density dependence is caused by transmission of quality through generations via maternal effects. We show that the maternal effect model can produce patterns of population fluctuations similar to those displayed by one class of host-parasitoid models. 3. We review empirical evidence for maternal and quality effects in dynamics of forest Lepidoptera. We fit the maternal effect and delayed logistic models to six species of forest moths for which delayed density dependence and maternal or quality effects have been found. The maternal effect model was a good predictor of the period of the oscillations for the species that we examined. We discuss why models of this type give better fits to moth cycles than do first order models with added delays.
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Negative Rückkoppelung durch Raum- und Nahrungskonkurrenz sowie zyklische Veränderung der Nahrungsgrundlage als Regelprinzip in der Populationsdynamik des Grauen Lärchenwicklers, Zeiraphera diniana (Guenée) (Lep., Tortricidae)1
Article
  • Aug 2009
  • J APPL ENTOMOL
Negative feed-back by competition for food and space, and by cyclic induced changes in the nutritional base as regulatory principles in the population dynamics of the larch budmoth Zeiraphera diniana (Guenée). At high density of the larvae of Z. diniana on larch trees in subalpine forests, intraspecific competition causes an increase in mortality of larvae and pupae, as well as reduction of pupal weight and fecundity of the emerging moths. The negative effects become more pronounced by shortage of food at population levels leading to complete defoliation of the larch trees. Defoliation in turn activates specific mechanisms in the trees, which lead to late and slow sprouting of the needles in spring (weak coincidence), short needles (reduced mass of nutritional base), and reduced quality of the needles (elevated contents of fibres and reduced protein contents). Thus the succeeding bud moth populations are depressed by negative feed-back. The cyclic numeric fluctuations with a periodicity of 8 to 10 years, which are characteristic of populations of Z. diniana in its optimum area, may thus be regarded as the expression of an autoregulating life system in which the species multiplies for 4–5 generations under favorable conditions and thus, transgressing the carrying capacity, changes the nutritional base in such a way that environmental resistance to the species becomes high for another 4 generations. Im Hinblick auf eine Erklärung der zyklischen Massenwechsel des Lärchenwicklers Z. diniana in den subalpinen Arven-Lärchenwäldern wurde der Einfluß der Populationsdichte, besonders aber der Nahrungsgrundlage auf Vitalität und Fekundität des Schädlings untersucht. Die Untersuchungen führten zu folgenden Ergebnissen: Diese Mechanismen steigern die Raupenmortalität im 1. und 2. Nachschadensjahr auf 80–90% und bewirken weiterhin eine stark reduzierte Fekundität.
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A contribution to the explanation of the larch bud moth cycle, the polymorphic fitness hypothesis
Article
  • Mar 1993
Studies of fluctuating insect populations generally discuss the regulating processes at high insect numbers, but very rarely why a cycling population at low densities switches immediately from the declining phase to the increasing phase of the cycle. A long-term study of the larch bud moth (Zeiraphera diniana Gn) has suggested that the key to recovery is assortative mating of specific phenotypes. Z. diniana exhibits distinct host races living either on the deciduous larch or evergreen pines and spruces. As an adaptation to its hosts Z. diniana is necessarily rather polymorphic in its life history parameters, i.e. developmental rate, fertility and survival. Apart from the direct association of the larva with the host tree, the colouration of the mature larva provides the only readily apparent trait by which the host race can be recognised; the larch form is black and the pine or spruce form has a light orange head capsule, anal plate and body colour. Evidence that frequencies of the colour morphs on larch regularly change from an intermediate colour type to black during the increasing phase of the cycle suggests that the combination of traits, such as earliest larval emergence, largest body size and homozygosity, characteristic of the black morph, constitutes the inherent driving force of population increase.
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Parasitoids and hyperparasitoids of Zeiraphera diniana [Lep., Tortricidae] and their pole in population control in outbreak areas
Article
  • Mar 1982
There are 109 species of primary and secondary parasitoids associated withZeiraphera diniana Guénée in the Central European Alps. Ninety species are primary, 6 facultative secondary and 13 obligate secondary parasitoids. At family level, the composition of the complex seems to be the same in every outbreak area of the host, with ichneumonids predominating. In the Upper Engadine Valley (Switzerland), where intensive studies were conducted over a period of 3 consecutive outbreak periods (28 years), 65% of the complex is represented. The nomenclature ofZ. diniana parasitoids has been clarified as far as possible. Many species names cited in the literature are synonyms or misidentifications. The complex of parasitoids, together with the associated predators ofZ. diniana, is unable to slow down the rate of density increase of the host in outbreak areas. This fact has stimulated investigations on the most important parasitoid species, i.e.Phytodietus griseanae Kerr. (Ichneumonidae), Sympiesis punctifrons Thomson,Dicladocerus westwoodii West. andElachertus argissa Walker (Eulophidae) over a period of about 10 years. Recent research has demonstrated that immigration ofZ. diniana moths into the outbreak areas during the phase of host density increase is very important. The rate of increase of the natural enemies — which are univoltine —can never equal or exceed that of their host; consequently, control by these natural enemies alone is not possible.
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Why the larch bud-moth cycle collapsed in the subalpine larch-cembran pine forests in the year 1990 for the first time since 1850
Article
  • Jan 1993
The larch bud-moth cycle has been observed in the sub-alpine larch-cembran pine forests 16 times since 1850. Infestation is easily recognized by the characteristic red-brown discoloration of the larch crowns due to the wasteful feeding of the bud moth larvae. The heaviest defoliation recurs at intervals of 8.470.27 (SE) years, and the larval density per kilogram of larch branches varies more than 10000-fold over four or five generations. The basic regulatory mechanism for this cycle is the induced change in food quality for the two or more subsequent larval generations. Defoliation functions as a negative feedback mechanism acting on larval density. In 1989 local discoloration in the Upper Engadine valley was observed in the usual first focus. In 1990 and 1991, however, instead of the expected widespread defoliation damage, larval densities decreased drastically. Based on extensive field data collected from 1961 to 1991 on the development and the survival of the bud moth (Zeiraphera diniana Gn.) and the phenology of the host, Larix decidua L., this paper shows the effect of weather on survival in the egg stage and on the coincidence of larval hatching with the sprouting of the larch. It is shown that the winter and spring weather conditions in 1989–1991 were conducive to unusually high egg mortality. Since these conditions occurred in three successive generations, population growth was effectively reduced and the cycle collapsed prematurely. Thus the rather persistent cyclicity of the larch-larch bud-moth system was disturbed by weather conditions with a very low probability of occurrence, but due to the inherent high resilience of the system, the next population peak with visible defoliation is expected to occur 1996/1997, provided that the weather conditions return to the climatic standard.
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