Landscape mosaic induces traveling waves of insect outbreaks

A Time for Every Purpose: Using Time-Dependent Sensitivity Analysis to Help Understand and Manage Dynamic Ecological Systems

AbstractSensitivity analysis is often used to help understand and manage ecological systems by assessing how a constant change in vital rates or other model parameters might affect the management outcome. This allows the manager to identify the most favorable course of action. However, realistic changes are often localized in time-for example, a short period of culling leads to a temporary increase in the mortality rate over the period. Hence, knowing when to act may be just as important as knowing what to act on. In this article, we introduce the method of time-dependent sensitivity analysis (TDSA) that simultaneously addresses both questions. We illustrate TDSA using three case studies: transient dynamics in static disease transmission networks, disease dynamics in a reservoir species with seasonal life history events, and endogenously driven population cycles in herbivorous invertebrate forest pests. We demonstrate how TDSA often provides useful biological insights, which are understandable on hindsight but would not have been easily discovered without the help of TDSA. However, as a caution, we also show how TDSA can produce results that mainly reflect uncertain modeling choices and are therefore potentially misleading. We provide guidelines to help users maximize the utility of TDSA while avoiding pitfalls.

A time for every purpose: using time-dependent sensitivity analysis to help understand and manage dynamic ecological systems

Sensitivity analysis is often used to help understand and manage ecological systems, by assessing how a constant change in vital rates or other model parameters might affect the management outcome. This allows the manager to identify the most favorable course of action. However, realistic changes are often localized in time-for example, a short period of culling leads to a temporary increase in the mortality rate over the period. Hence, knowing when to act may be just as important as knowing what to act upon. In this article, we introduce the method of time-dependent sensitivity analysis (TDSA) that simultaneously addresses both questions. We illustrate TDSA using three case studies: transient dynamics in static disease transmission networks, disease dynamics in a reservoir species with seasonal life-history events, and endogenously-driven population cycles in herbivorous invertebrate forest pests. We demonstrate how TDSA often provides useful biological insights, which are understandable on hindsight but would not have been easily discovered without the help of TDSA. However, as a caution, we also show how TDSA can produce results that mainly reflect uncertain modeling choices and are therefore potentially misleading. We provide guidelines to help users maximize the utility of TDSA while avoiding pitfalls.

From pattern to process? Dual travelling waves, with contrasting propagation speeds, best describe a self-organised spatio-temporal pattern in population growth of a cyclic rodent

The dynamics of cyclic populations distributed in space result from the relative strength of synchronising influences and the limited dispersal of destabilising factors (activators and inhibitors), known to cause multi‐annual population cycles. However, while each of these have been well studied in isolation, there is limited empirical evidence of how the processes of synchronisation and activation–inhibition act together, largely owing to the scarcity of datasets with sufficient spatial and temporal scale and resolution. We assessed a variety of models that could be underlying the spatio‐temporal pattern, designed to capture both theoretical and empirical understandings of travelling waves using large‐scale (>35,000 km²), multi‐year (2011–2017) field monitoring data on abundances of common vole (Microtus arvalis), a cyclic agricultural rodent pest. We found most support for a pattern formed from the summation of two radial travelling waves with contrasting speeds that together describe population growth rates across the region.

Wavelet methods reveal big cat activity patterns and synchrony of activity with preys

Appropriate temporal and spatial scales are important prerequisites for obtaining reliable results in studies of wildlife activity patterns and interspecific interactions. The spread of camera-trap technology has increased interest in and feasibility of studying the activity patterns and interspecific interactions of wildlife. However, such studies are often conducted at arbitrary spatial and temporal scales, and the methods used impose scale on the study rather than determining how activity and species interactions change with spatial scale. In this study, we used a wavelet-based approach to determine the temporal and spatial scales for activity patterns and interspecific interactions on Amur leopard and their ungulate prey species that were recorded using camera traps in the main Amur leopard occurrence region in northeast China. Wavelets identified that Amur leopards were more active in spring and fall than summer, and fluctuated with periodicities of 9 and 17 days, respectively. Synchronous relationships between leopards and their prey commonly occurred in spring and fall, with a periodicity of about 20 days, indicating the appropriate seasons and temporal scales for interspecific interaction research. The influence of human activities on the activity patterns of Amur leopard or prey species often occurred over longer time periods (60-64 days). Two-dimensional wavelet analyses showed that interactions between leopard and prey were more significant at spatial scales of 1 km² . Overall, our study provides a feasible approach to studying the temporal and spatial scales for wildlife activity patterns and interspecific interaction research using camera trap data.

A Theoretical Approach to Analyze the Parametric Influence on Spatial Patterns of Spodoptera frugiperda (J.E. Smith) (Lepidoptera: Noctuidae) Populations

Studies of the influence of biological parameters on the spatial distribution of lepidopteran insects can provide useful information for managing agricultural pests, since the larvae of many species cause serious impacts on crops. Computational models to simulate the spatial dynamics of insect populations are increasingly used, because of their efficiency in representing insect movement. In this study, we used a cellular automata model to explore different patterns of population distribution of Spodoptera frugiperda (J.E. Smith) (Lepidoptera: Noctuidae), when the values of two biological parameters that are able to influence the spatial pattern (larval viability and adult longevity) are varied. We mapped the spatial patterns observed as the parameters varied. Additionally, by using population data for S. frugiperda obtained in different hosts under laboratory conditions, we were able to describe the expected spatial patterns occurring in corn, cotton, millet, and soybean crops based on the parameters varied. The results are discussed from the perspective of insect ecology and pest management. We concluded that computational approaches can be important tools to study the relationship between the biological parameters and spatial distributions of lepidopteran insect pests.

Generation of periodic travelling waves in cyclic populations by hostile boundaries

Many recent datasets on cyclic populations reveal spatial patterns with the form of periodic travelling waves (wavetrains). Mathematical modelling has identified a number of potential causes of this spatial organization, one of which is a hostile habitat boundary. In this paper, the author investigates the member of the periodic travelling wave family selected by such a boundary in models of reaction–diffusion type. Using a predator–prey model as a case study, the author presents numerical evidence that the wave generated by a hostile (zero-Dirichlet) boundary condition is the same as that generated by fixing the population densities at their coexistence steady-state levels. The author then presents analysis showing that the two waves are the same, in general, for oscillatory reaction–diffusion models with scalar diffusion close to Hopf bifurcation. This calculation yields a general formula for the amplitude, speed and wavelength of these waves. By combining this formula with established results on periodic travelling wave stability, the author presents a division of parameter space into regions in which a hostile boundary will generate periodic travelling waves, spatio-temporal disorder or a mixture of the two.

Long-term shifts in the cyclicity of outbreaks of a forest-defoliating insect

Recent collapses of population cycles in several species highlight the mutable nature of population behavior as well as the potential role of human-induced environmental change in causing population dynamics to shift. We investigate changes in the cyclicity of gypsy moth (Lymantria dispar) outbreaks by applying wavelet analysis to an 86-year time series of forest defoliation in the northeastern United States. Gypsy moth population dynamics shifted on at least four occasions during the study period (1924-2009); strongly cyclical outbreaks were observed between ca. 1943-1965 and ca. 1978-1996, with noncyclical dynamics in the intervening years. During intervals of cyclical dynamics, harmonic oscillations at cycle lengths of 4-5 and 8-10 years co-occurred. Cross-correlation analyses indicated that the intensity of suppression efforts (area treated by insecticide application) did not significantly reduce the total area of defoliation across the region in subsequent years, and no relationship was found between insecticide use and the cyclicity of outbreaks. A gypsy moth population model incorporating empirically based trophic interactions produced shifting population dynamics similar to that observed in the defoliation data. Gypsy moth cycles were the result of a high-density limit cycle driven by a specialist pathogen. Though a generalist predator did not produce an alternative stable equilibrium, cyclical fluctuations in predator density did generate extended intervals of noncyclical behavior in the gypsy moth population. These results suggest that changes in gypsy moth population behavior are driven by trophic interactions, rather than by changes in climatic conditions frequently implicated in other systems.

Three centuries of insect outbreaks across the European Alps

Knowledge of the persistence of regular larch budmoth outbreaks is limited in space and time. Although dendrochronological methods have been used to reconstruct insect outbreaks, their presence may be obscured by climatic influences. More than 5000 tree-ring series from 70 larch host and 73 spruce nonhost sites within the European Alps and Tatra Mountains were compiled. Site-specific assessment of growth-climate responses and the application of six larch budmoth detection methods considering host, nonhost and instrumental time-series revealed spatiotemporal patterns of insect defoliation across the Alpine arc. Annual maps of reconstructed defoliation showed historical persistence of cyclic outbreaks at the site level, recurring c. every 8-9 yr. Larch budmoth outbreaks occurred independently of rising temperatures from the Little Ice Age until recent warmth. Although no collapse in outbreak periodicity was recorded at the local scale, synchronized Alpine-wide defoliation has ceased during recent decades. Our study demonstrates the persistence of recurring insect outbreaks during AD 1700-2000 and emphasizes that a widely distributed tree-ring network and novel analysis methods can contribute towards an understanding of the changes in outbreak amplitude, synchrony and climate dependence.

Spatial analysis of harmonic oscillation of gypsy moth outbreak intensity

Outbreaks of many forest-defoliating insects are synchronous over broad geographic areas and occur with a period of approximately 10 years. Within the range of the gypsy moth in North America, however, there is considerable geographic heterogeneity in strength of periodicity and the frequency of outbreaks. Furthermore, gypsy moth outbreaks exhibit two significant periodicities: a dominant period of 8-10 years and a subdominant period of 4-5 years. In this study, we used a simulation model and spatially referenced time series of outbreak intensity data from the Northeastern United States to show that the bimodal periodicity in the intensity of gypsy moth outbreaks is largely a result of harmonic oscillations in gypsy moth abundance at and above a 4 km(2) scale of resolution. We also used geographically weighted regression models to explore the effects of gypsy moth host-tree abundance on the periodicity of gypsy moths. We found that the strength of 5-year cycles increased relative to the strength of 10-year cycles with increasing host tree abundance. We suggest that this pattern emerges because high host-tree availability enhances the growth rates of gypsy moth populations.

Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models

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.

Waves and synchrony in Epirrita autumnata /Operophtera brumata outbreaks. I. Lagged synchrony: regionally, locally and among species

1. In 1990-2003, during a complete 10-year outbreak cycle, the synchrony of the birch defoliating outbreaks of the geometrids Epirrita autumnata and Operophtera brumata was studied quantitatively in the northern part of the Fennoscandian mountain chain (the Scandes). Data were supplemented with similar data from 1964 to 1966 and historical information. A 30-year series of field data from one locality in southern Scandes made possible interregional comparisons. 2. In 1991, outbreaks started in north-eastern Fennoscandia and moved westward like a wave and reached the outer coast of north-western Norway in about 2000. This wave is a new observation. In the same years, a previously documented outbreak wave moved southward along the Scandes. 3. Outbreak periods have usually occurred around the middle of each decade. Seemingly unrelated population peaks at the decadal shift 2000 were reported from islands at the coast of north-western Norway. They are shown here to have been the final ripples of the east-west wave. 4. At some localities, O. brumata peaked 2 years after E. autumnata. A lag of 1 or 2 years also occurred at the locality in southern Scandes. This interspecific time lag is a new observation. In accordance with the north-south wave, a time-lag of 1-2 years occurred between the fluctuations of northern and southern E. autumnata and O. brumata populations. 5. The population peak of E. autumnata occurred 1 year earlier at one locality than at a nearby locality. This pattern and particular altitudinal shifts of the O. brumata population density at these localities repeated in two outbreak periods. This indicates that, for example, local climate may modify outbreak synchrony between nearby localities. 6. At the same localities, O. brumata peaked first at one altitude and 1 or 2 years later at another altitude. This vertical lag is a new observation. 7. E. autumnata shows fluctuation traits similar to some other cyclic animals, e.g. the larch budmoth in the European Alps, some European tetraonid birds and the Canadian snow-shoe hare. These similarities (and dissimilarities) in intra- and interspecific synchronies and causes of E. autumnata and O. brumata synchronies, regionally, locally and among the two species are discussed.