A review of process modeling for wood borer pests

Introduction: Wood borer pests represent a growing threat to forestry worldwide, with potential for an increase in climate change induced outbreaks that could significantly impact ecosystem functioning.

Methods: This study reviews the current state-of-the-art in bark beetle modeling as presented in peer-reviewed English language scientific papers and reviews cited in Clarivate Analytics Web of Science (WoS) Core Collection in the period from 2006 to 2023, but earlier influential papers cited in reviews from this period are also in scope. We categorize studies by modeling methodology, by host and by modeled processes.

Results: Ash, pine, and spruce hosts account for 88% of studies, the majority of which focus on the continental USA, British Columbia, Canada and Central Europe. In terms of methodology, statistical methods are the most commonly employed technique, and the majority of articles model just one or two key processes with pest demography and environmental factors being the most studied across different hosts. Commonalities in methods used across pest-host systems include: use of phenology-like models; application of static species distribution models (SDMs) to understand climate impacts; modeling of spread via local and long-range kernels; and use of economic cost-benefit analysis as a tool to guide management.

Discussion: We identify several gaps in current research including quantifying economic consequences of wood borer pests and the need for greater understanding of ecological impacts and resilience. Agent- and individual-based models may also provide useful tools for understanding the complexity of socio-ecological system dynamics. However, such developments should be in tandem with wider use of techniques for parameter estimation and uncertainty quantification, including Bayesian inference in particular of the dynamics of spatial spread. A related challenge is better quantification of pathways - including trade - for entry by invasive pests, coupled with a greater understanding of potential vulnerabilities of forest systems to environmental drivers like climate change, coupled with potentially multiple endemic, emerging and novel pests. Addressing these challenges would enable both better mitigation of risks associated with wood borer beetle infestations and better management of outbreaks when they do occur.

1 Introduction

Biological pest species pose threats to the stability and functioning of ecosystems worldwide. Non-native pests can have complex and significant impacts on invaded ecosystems by affecting a variety of interacting mechanisms, e.g carbon sequestration, nutrient cycling (Ehrenfeld, 2010). Stresses induced by climate change can result in large non-normative outbreaks of native species that devastate ecosystem functioning (Logan et al., 2003). A systematic review found the distribution of evidence for direct (29.9%), indirect (29.8%), and interacting effects (40.8%) of climate change related to forest pests (Seidl et al., 2017). Development in global trade and human activity are increasing rates of arrival and opening new routes for potentially damaging pests (Dalmazzone and Giaccaria, 2014).

Wood borer pests exemplify such issues, representing a growing threat to forestry worldwide (Linnakoski and Forbes, 2019). For example, since 2002, Emerald ash borer (EAB), Agrilus planipennis has emerged as a major invasive pest of Fraxinus species in the USA (Cappaert et al., 2005), where it has caused an estimated US$ 10.7–12.5 billion (bn) of economic damage in the period 2010–2020 (Kovacs et al., 2011). EAB is also present in Western Russia and is steadily spreading west toward continental Europe (Straw et al., 2013). European ash is suffering an ongoing outbreak of fungal pathogen Hymenoscyphus fraxineus—the causal agent of ash dieback. In the UK alone, damages from ash dieback are estimated at GBP£15bn (Hill et al., 2019), which illustrates the potential impact of EAB introduction even without considering the increased impact of introduction into H. fraxinus infested populations (Musolin et al., 2017). EAB shows how invasive species not considered pests within the native range can cause major damage in invaded environments.

In contrast, an endemic forest pest which experiences large outbreaks under favorable climatic conditions is the European spruce beetle (ESB), Ips typographus. Endemic to central Europe, ESB outbreaks are responsible for the mortality of an estimated 150 million m³ of Norway spruce from 1950 to 2000 (Schelhaas et al., 2003; Økland et al., 2016, 2012). Outbreaks occur after disturbance events such as storms or drought (Seidl and Rammer, 2017), and beetle induced mortality can alter forest hydrology (Beudert et al., 2018), carbon dynamics (Seidl et al., 2014), and food webs (Seidl et al., 2017). Climate change is predicted to increase the likelihood of disturbance events, and ESB outbreaks are likely to become increasingly devastating, e.g. through greater voltinism, the number of generations produced in a year (Wermelinger et al., 2012).

Mathematical and statistical modeling can provide critical insights and predictions that will aid the management of such risks. Modeling has provided insights into our understanding of outbreak dynamics and biological invasions (Logan et al., 2003; Sakai et al., 2001; Murray, 2001), been used to predict outbreak cycles (Kunegel-Lion and Lewis, 2020; Wildemeersch et al., 2019), determine spread rates and how to slow them (Wildemeersch et al., 2019; Sharov and Liebhold, 1998), and to detect tipping-point behavior (Vindstad et al., 2019). Such tools are essential for understanding and predicting destructive outbreaks in a climatically changing, increasingly international world (Ramsfield et al., 2016). However, despite the potential for lessons to be learned across pest-host systems, the literature on modeling of wood borer pests is fractured with a widely dispersed literature and a diverse group of disciplines. As far as we know, no attempts have been made to review modeling within wood borer pests and their societal impacts to date.

Therefore, here we conduct a systematic review that synthesizes relevant advances and techniques used to model key processes for wood borer pests. Studies reviewed are categorized attending to the identified themes of: pest spread; pest demography; environmental factors affecting infestation; and the economics and management of infestation. We synthesized studies based on the modeling techniques used to investigate the dynamics of wood borer bettle infestations, which are grouped into four high-level categories: mathematical models; statistical models; simulation studies; and Geographic Information Systems (GIS) studies (including use of imagery). We also examine the commonalities and differences in the use of different techniques between hosts, and the data requirements. Finally, we identify gaps for future research.

2 Methods

We conduct a systematic search of the scientific literature for articles related to the modeling of wood-boring species infestations and invasions. We followed established guidelines (Pullin et al., 2022) to conduct the systematic review, and our methods are outlined below.

2.1 Search terms

In order to construct a “search-string” to be used when searching for the most relevant studies in the bibliographic databases, search terms were developed based on a previous review of modeling approaches within animal health for which there is significant overlap (MacCalman et al., 2016). We developed a search string with multiple parts to capture the fact that we wanted to search for modeling studies of wood-boring species infestation risk and impacts. These search terms are grouped as follows: (1) terms that describe the pest of interest; (2) terms that capture the ecosystem of interest, forests; (3) terms that capture the focus on models; (4) and terms that cover the risk and economic impact of infestations. We also included parts in the search string related to the invasion process: introduction, establishment, and spread. Other terms used cover climatic effects. The full list of search terms and final search strings used is shown in the Supplementary material.

2.2 Search strategy and screening processes

Search terms are applied to the Clarivate Analytics Web of Science (WoS) Core Collection. We exclude other databases such as Scopus, ScienceDirect (which are operated by journal publishing houses) and Google Scholar because of the absence of features required for a rigorous, replicable search (Gusenbauer and Haddaway, 2020). The WoS database uses Boolean logic to group terms during searches, which we used to connect our search themes. As described in detail in the Supplementary material, the final search was given as “TS=(bark beetles AND forest) AND (models ORrisk) AND (introduction OR establishment OR spread) AND (climatic OR economic)”. In this search, we exclude pre-2006 articles and include only primary research articles, conference proceedings and review papers. The latter were only extracted to be able to include in our database relevant articles pre-2006. Therefore, the exclusion of pre-2006 papers was only partial in that pre-2006 references in post-2006 reviews were included in the database for their screening. This process has the effect of focusing on the more influential pre-2006 papers. When the original review was conducted, AI translation tools were less reliable than they have become, and therefore we excluded non-English language papers. The search for literature was conducted in two stages with the first search conducted on 28th March 2019 with papers from 2006 to 2019 which returned 1,655 articles for inspection, and the second search conducted on 19th September 2024 with papers from 2019 to 2023 which returned 1,068 articles for inspection. This second search was conducted to include articles published after 2019, ensuring the systematic review is up to date, after a change of lead analyst partway through the project. Any duplicates were then removed, and the resulting reference list was placed into a prepared spreadsheet for screening.

The literature sources were screened by title/abstract using a set of eligibility criteria (Table 1). Papers were excluded at this stage if the screening showed that: (1) an abstract was unavailable; (2) the focal study subjects was not wood borer beetles; (3) modeling aspects were not related to wood borer beetles; and (4) the study was solely empirical or observational [see Supplementary material]. The literature that met this eligibility criteria were then filtered into a list for inclusion in the full-text screening phase. Papers were selected if including modeling of wood borer processes: pest spread (including dispersal), pest demography, environmental factors, and economic considerations and management. Papers can use one or more of the modeling techniques to investigate these processes, typically categorized as: statistical, simulation and agent-based model (ABM, also known as individual-based model, IBM), mathematical, GIS-type (including imagery). This categorization reveals patterns across techniques, species, and processes (see Section 3).

Table 1

Table 1. Article eligibility criteria.

The total articles accepted for review was 468 (Figure 1). A full list of the article titles and metadata, including abstracts, process categorisations, specific techniques used, article authors and purpose of the studies, can be found in the Supplementary material.

Figure 1

Figure 1. Flow chart of paper screening results.

We conducted a quality assurance exercise to check the robustness of the screening process using a random sample of 160 articles from the post-2006 search. This corroboration exercise tested the screening of Abstracts (at both levels 1 and 2, as explained in Table 1). This allowed calculation of a κ-coefficient of agreement between the screening process (Cohen, 1960) of the full dataset and an independent screening of the sub-sample. The κ-coefficient is commonly used during the study selection process to demonstrate the consistency of decisions between two independent reviewers when screening titles, abstracts, or full texts for relevance, and compares the expected and observed level of agreement. These corroboration efforts produced a κ-coefficient of 0.687 and 0.637 for Abstract levels 1 and 2, respectively. These agreement coefficients lie within the range 0.64–0.69 deemed acceptable in the literature for a systematic review (McHugh, 2012).

3 Modeling of wood borer dynamics from a host perspective

Figures 2–4 show how species, processes, and techniques are represented within the literature. These findings indicate that most of the articles reviewed focus on pine and spruce as host species (39% & 34% of all articles, respectively, see Figure 1. We found that the majority of articles (52%) modeled two key processes, while 26% modeled one key process and 20% modeled 3 processes. Only 3% of all articles modeled four processes (see Figure 3A). The majority of articles used one or two modeling techniques, accounting for 92% of the total; whereas 7% used 3 techniques and <1% used four techniques (see Figure 3B). We found within each of the key processes modeled, demographic and environmental factors were generally the most numerous (see Figure 4A). We also found that statistical methods were generally the most commonly used method, both for modeling alongside other methods, but also as the sole method used, comprising over 35% of analyses (see Figure 4B).

Figure 2

Figure 2. Proportion of total articles used in the review with respect to pest host. Ash hosts are given in red, Pine in blue, Spruce in green, and any host not covered by the former in purple. The total number of articles for each host grouping is given within the respective bars.

Figure 3

Figure 3. Proportion of total articles used in the review with respect to (A) Numbers of Processes Modelled (Pest spread; Pest demography; Environmental factors; and Economic considerations and management) and (B) Number of Methods Used (mathematical models; statistical models; simulation studies; and Geographic Information Systems (GIS) studies (including use of imagery) used within the article.

Figure 4

Figure 4. Proportion of articles within major modeling techniques identified in the review. (A) shows the proportion of articles within major key processes (pest spread, pest demography, environmental factors, and economic considerations and management) in each panel with respect to the number of other modeled processes and by pest host (shown by colors). (B) shows the proportion of articles within major categories of modeling methods (statistical, simulation, mathematical, GIS) used in each panel with respect to the number of articles of other methods used and by pest host. Total number of articles given within each bar, respectively, of categorization.

We present our findings attending to the three main host species: ash (Fraxinus), spruce (Picea), pine (Pinus) given their dominance in the reviewed articles (see Figure 1). For each host, we break down selected highlights from the reviewed literature according to the key processes (Pest spread, Pest demography, Environmental factors, Economic considerations and management). Note that for our data regarding the “Other” host species, no other host was the subject of more than ten articles. For example, our data contained only seven studies of fir (Abies), and oak (Quercus), from which it is not possible to draw general conclusions.

3.1 Ash—Fraxinus

For Ash, our review procedure found only studies for a single pest species, EAB, providing a relatively simple place to start summarizing the literature.

3.1.1 Pest spread

In our review of the literature we found that satellite imagery and GIS tools have been relatively infrequently used to study EAB compared with the use of such methods in other pest-species interactions (see Figure 4B). Spectral analysis of ash tree crowns from different vegetation indices were compared to identify whether there is an EAB infestation (Zhang et al., 2014). The original site of introduction in the USA and initial spread has been reconstructed from data and statistical interpolation using GIS tools and dendrochronological analysis (Siegert et al., 2014). Lyttek et al. (2019) combined a partial differential equations model with GIS data to predict EAB spread. GIS has also been integrated with network automata to produce a novel framework termed Geographic Network Automata to model dispersal patterns (Anderson and Dragićević, 2020). However, most studies have focused on mathematical modeling of dispersal.

A variety of methods are used for such studies in relation to dispersal modeling, but a common approach is to use a negative exponential function. Mercader et al. (2009) incrementally measure distance and larvae within infested trees from a known initially infested location for which a negative exponential is a statistically good fit. This approach is largely adopted within spatial simulation studies accounting for distance between cells (Kovacs et al., 2011, 2014) and cellular automata/lattice models (Mercader et al., 2011, 2016; McCullough and Mercader, 2012) representing geographical US sub-counties (which are irregular cells) (Muirhead et al., 2006). This approach is also combined with attraction dynamics between EAB females and stressed ash trees (Mercader et al., 2012). Non-exponential kernels can also be used to represent such natural dispersal. Local dispersal has been modeled using a Gaussian kernel (analogous to normal distribution/random walk) (Withrow et al., 2015; Epanchin-Niell and Liebhold, 2015), a Laplace (double exponential distribution) (Lutscher and Musgrave, 2017), and an inverse power law distribution (Prasad et al., 2010). Fixed rate dispersal has been used within a wider modeling framework (Anderson and Dragićević, 2016a; Barlow et al., 2014).

Long-distance dispersal events can be incorporated with local spread in a single kernel function using distributions with non-exponentially bounded tails (Muirhead et al., 2006). However, often these events are associated with human activity so modeling is often conducted separately from local dispersal. Simple methods involve the addition of a fixed proportion traveling farther (Mercader et al., 2011; McCullough and Mercader, 2012). Gravity models predict long distance dispersal where EAB is ‘attracted” to focal sites, such as camp sites (Muirhead et al., 2006; Prasad et al., 2010) as a way to represent human mediated transport. Dispersal of EAB within infested wood through camp sites has been identified as a source of long distance dispersal and captured in models in a variety of ways. One study examined infested camp site locations and used bootstrapping methods to estimate an average distance from an initial location (Tobin et al., 2010). Human transport networks have also been investigated through network analysis (pathway analysis) as a means of spreading EAB (Yemshanov et al., 2012). Stochastic models have used random number generators to draw probabilities for long distance dispersal determined by proximity by road (Anderson and Dragićević, 2015). Hope et al. (2021) modeled both the short- and long-distance spread of EAB to evaluate the effectiveness of different levels of regulation. The short-distance spread used a beta distribution to simulate insect flight, typically within 20 km, whilst the long-distance spread was modeled using a Cauchy distribution to simulate human-assisted spread over much longer distances.

3.1.2 Pest demography

The simplest approach to representing demography is presence-absence within a gridded lattice, or municipality (Jones, 2019; Anderson and Dragićević, 2016a; Yemshanov et al., 2015) and is often used when the focus is on pest dispersal, or the effects of EAB presence. The presence-absence approach can be extended to include the probability of establishment in a cell after arrival, measuring local suitability suggestive of potential population size (Kovacs et al., 2011, 2014).

Empirical methods were developed to make use of data obtained by felling trees and counting larvae beneath the bark, thus enabling models that represent numbers of larvae per tree (Fahrner et al., 2017). These observations are conducted within a known core population and repeated over increasing distances toward the invasion front to produce data that can yield maximum likelihood estimation of density-dependent dispersal (Mercader et al., 2012). Another population modeling approach uses a step function to represent growth rates above and below a carrying capacity based on consumption of phloem (Mercader et al., 2011). This EAB growth function was adopted in further simulation approaches (McCullough and Mercader, 2012; Mercader et al., 2012).

Differential equation models—continuous in space and time—were used to study population dynamics, where logistic growth was considered with statistically estimated parameters for growth and carrying capacity (Barlow et al., 2014; McDermott and Finnoff, 2016; Jones et al., 2016). Integro-difference equations—discrete in time, but continuous in space—were also used to model population dynamics in a similar way (Lutscher and Musgrave, 2017), and a purely discrete in time difference equation for growth is used to iterate growth dynamics within a wider simulation (Fahrner et al., 2017). Some studies used EAB as a variable in relation to ash dynamics and management effort (Jones et al., 2016; Jones and McDermott, 2015).

A key theme in modeling EAB-ash interactions is the availability of phloem as a resource. One population modeling approach uses a step function to represent growth rates above and below a carrying capacity based on consumption of phloem (Mercader et al., 2011). This EAB growth function was adopted in further simulation approaches (McCullough and Mercader, 2012; Mercader et al., 2012). Simulation studies used statistically estimated parameters to account for phloem area (Fahrner et al., 2017; Mercader et al., 2011; McCullough and Mercader, 2012; Mercader et al., 2016; Kovacs et al., 2014). Joint EAB-ash dynamics were considered using coupled systems of differential equations (Jones et al., 2016; McDermott and Finnoff, 2016; Jones and McDermott, 2015), and in one case in a disease context as susceptible and infected (Barlow et al., 2014).

A comprehensive ABM constructed using Spatial Modeling Environment (SME, spatially similar to cellular automata) which can account for GIS layers and system dynamics using STELLA^® (Costanza and Gottlieb, 1998). This modeling framework has been used on a small scale within DuPage County, Illinois, USA (BenDor and Metcalf, 2006). The framework accounts for the spread and population dynamics of EAB, as well as the distribution and population dynamics of ash. Information from GIS raster layers (scale 60 m × 60 m) about land use has been used to determine the suitability of ash growth. Parameters can also be adjusted to take into account quarantine zones for EAB management scenarios. Another ABM which examined EAB infestation in Ontario, Canada has been developed (Anderson and Dragićević, 2015). The model uses GIS layers for ash distributions, local features, and to initialize infested trees. Both trees and EAB are modeled as agents with their own dynamic processes. Dispersal is split into local radial dispersal and long-distance events generated probabilistically. Beetle demographics, such as mating, emergence, and death, are determined probabilistically. This model was the basis for other additions to the processes which included climate (Anderson and Dragićević, 2016a), the inclusion of EAB parasitoid predators (Anderson and Dragićević, 2016b), and the use network connections to model spread dynamics, i.e., infestation between trees (Anderson and Dragićević, 2018).

Finally, another key theme in modeling these EAB-ash interactions was the seasonality of activity. Degree-days are used in order to predict the emergence of beetles. MacDonald et al. (2022) used growing degree-day models, including double sine, single sine and standard degree-day models, to predict first adult emergence of the year. The sine wave method was similarly used by Webb et al. (2021) to determine emergence thresholds. Moreover, degree days were also adopted by Barker et al. (2023) as part of a Degree-Days, Risk, and Phenological event mapping (DDRP) platform to model the EAB life cycle. To compare seasonal activity between various ranges, Maxent used growing degree days combined with other climatic parameters to predict the distribution (Meshkova et al., 2023).

3.1.3 Environmental factors

Models were developed to predict cold-induced mortality for EAB using under-bark temperature. These consist of non-linear statistical models and Newtonian cooling models to predict how EAB would respond to the cold (Cuddington et al., 2018), and are used to develop a species distribution model for the North American continent. A variant of examining cold temperatures involved modeling snow cover effects on under bark temperature with thermal conduction models and iterative temperature equations (DeSantis et al., 2013). Species distribution models have been developed to predict EAB invasive potential using incidence data and climatic factors using Maxent and GARP methods (Sobek-Swant et al., 2012; Liang and Fei, 2014). Both studies also looked at future conditions under IPCC representative concentration pathways of future emissions. Species distribution models were similarly developed with Maxent methods by Dang et al. (2021) using future climate variables from the WorldClim dataset.

3.1.4 Economic considerations and management

The effectiveness of EAB management was examined in detail, examples include the SLAM strategy (SLow Ash Mortality) implemented in 2008 (Mercader et al., 2012), or studies that examined the effects of tree removal on beetle production (Fahrner et al., 2017). Other papers used a cost-benefit analysis to assess the efficiency of quarantined locations (Withrow et al., 2015; Vannatta et al., 2012).

Due to the EAB outbreak and subsequent invasion in the USA, economic analysis of management decisions has been at the forefront of modeling research. Bioeconomic models have been used to determine the optimal allocation of a given budget to the prevention and control EAB infestations, i.e. surveillance, treatment and removal (Bushaj et al., 2021), to improve efficiency on the allocation of surveillance efforts using a portfolio framework (Yemshanov et al., 2014, 2015), or to explore the decision of when to act, with the objective of minimized total cost (Kovacs et al., 2014). A more recent paper optimized the selection of daily routes and the number of host trees to inspect in order to minimmise the impact of EAB infestations using linear programming (Yemshanov et al., 2020).

In these bioeconomic studies, societal costs are typically those resulting from the removal or pesticide intervention and the damages associated with ecosystem services impacts (Kovacs et al., 2011; McDermott and Finnoff, 2016; Kovacs et al., 2014; McCullough and Siegert, 2007; Withrow et al., 2015). (Epanchin-Niell and Liebhold 2015) modeled long-term damages using a lag spread model to show how these are critically affected by invasion lags, damage persistence, and spread rates. Monetary estimates of damages have been provided with multiple techniques. McConnell et al. (2019) used an Impact Analysis for PLANning (IMPLAN) model, that takes an input-output approach to estimate the economic effects of an EAB infestation to the hardwood timber industry of Louisiana. This used a PERT-Beta distribution to predict Ash mortality and a double declining balance method for the depreciation of timber value over time. Environmental valuation techniques, based on econometric modeling have also been used. For example, hedonic pricing was used to isolate the effect of dying/dead trees on house prices from other structural or location features (house characteristics) (Li et al., 2019). Jones and McDermott (2018) used a dose-response relationship between EAB outbreaks and ambient air pollution concentrations to estimate the human health impacts. In a similar manner, Jones (2019) estimated EAB outbreak damages using increased healthcare costs from hospital visits due to loss of shade. Arnberger et al. (2020) used a discrete choice experiment, in order to better understand societal preferences toward EAB-impacted forest scenarios in Vienna, Austria, and Minneapolis, USA. A latent-class analysis was used to investigate visitors' preferences heterogeneity toward viewscape, social and biophysical elements of forest landscapes. More generally, the National Tree Benefits Calculator was used to estimate damages based on differences in ecosystem services provided under different management scenarios (Arbab et al., 2022).

3.2 Pine—Pinus

Studies where pine is the host make up the majority of studies (see Figure 2). Major wood borer pests of pine consist of Mountain pine beetle (MPB), Dendroctonus ponderosae; Southern pine beetle (SPB), Dendroctonus frontalis; and various Ips species, e.g. Pine engraver beetle, Ips pini, and Eastern 5-spined engraver Ips grandicollis. Studies of MPB are the most numerous, followed by SPB and a few related to various Ips species. Demographic modeling has been studied in more detail for MPB than for EAB. The reader should assume the study species is MPB unless otherwise stated.

3.2.1 Pest spread

A variety of methods are used to capture the dynamics of spread through pine; however, in general, estimation of spreading speed is not the aim of these studies. Both diffusion, accounting for local dispersal, and chemotaxis, accounting for the effects of attack pheromones, are found in numerous parameterised partial differential equation models, which also include growth terms (Strohm et al., 2016; Haran et al., 2015; White and Powell, 1997; Powell et al., 1996; Logan et al., 1998). Density-dependent dispersal is modeled using the product of diffusion and a host susceptibility function (Powell and Bentz, 2014). In such scenarios, weakened trees release attractive volatiles, and beetles move up the resulting concentration gradient. A similar dynamic for attack pheromones has also been included in some models; however, there is a threshold value at which the pheromones become repulsive. MPB population sizes have been estimated using dispersal models based on redistribution kernels and covariance structure (Koch et al., 2021). Integro-difference models use dispersal kernels to capture beetle movement with Gaussian distributions (Goodsman et al., 2016, 2018a). SPB dispersal has been similarly quantified by analyzing mark recapture data (Turchin and Thoeny, 1993). These normal-type distributions are best used to study local dynamics as they don't allow significant long range dispersal. However, a historical study examining clustering of MPB occupancy at the landscape scale reveals fractal distributions (Gamarra and He, 2008). This suggests MPB outbreaks can be modeled using fractal dispersal kernels in meta-populations. Simulation studies have made direct use of GIS/imagery data to identify and track “red attack” which can be traced in time to discern MPB spread (Wulder et al., 2009), and similarly using composite vegetation indices (Kaiser et al., 2013).

Statistical methods to quantify spread focus on spatial clustering or the extent of outbreaks using GIS/imagery data. Point process regression models are used in conjunction with environmental variables to determine pathways of spread (Giroday et al., 2012). GLMs were used to investigate how landscape and stand-level variables influence damage using a Gaussian distribution and also the spread and development of beetles using Akaike's information criterion (Zhan et al., 2023; Yu et al., 2022a). Cluster analysis can be used to estimate the spatial pattern of outbreak development (Aukema et al., 2006), using K- means clustering and weather data (Chapman et al., 2012), and have been used to analyse SPB and Ips sexdentatus outbreaks (Egan et al., 2016). Spatial autocorrelation is also used to this effect (Weed et al., 2017). Regression models can determine the likelihood of outbreak occurrence, particularly in relation to climatic factors (Sambaraju et al., 2012; Giroday et al., 2012; Horn et al., 2012), in Ips confusus (Santos and Whitham, 2010), and for SPB (Ungerer et al., 1999). ROC curve analysis was used to compare the Ips sexdentatus susceptibility maps produced by frequency ratio, analytical hierarchy process and logistic regression models (Sivrikaya et al., 2022).

3.2.2 Pest demography

Deterministic mathematical models are applied extensively to capture population dynamics. Discrete time Nicholson-Bailey dynamics using stochastic processes for beetle and susceptible host presence allow interactions between hosts and pest, which can be used to investigate attack threshold dynamics for a tree using parameter estimates from sampled data (Goodsman et al., 2016), and different strengths of density-dependence (Goodsman et al., 2017). Since tree mortality is related to host development, models which account for the age-structure of host interacting with beetle populations have been developed using Leslie matrices. These have been parameterised using maximum likelihood (Heavilin and Powell, 2008) and discrete annual phenology to measure outbreak intensity and recovery (Duncan et al., 2015). Differential equations are studied widely to understand pest dynamics, including: investigating aggregation dynamics using systems of reaction-diffusion equations (Strohm et al., 2016); the effectiveness of time-delay in disease control (Dong et al., 2023); SIR infection dynamics of hosts by pests through neighboring stands (Křivan et al., 2016); Allee effects and temperature-dependent emergence using age-structure (Powell and Bentz, 2014); and to develop models of phenotypic phenology using maximum likelihood parameter estimations for beetle development time (Yurk and Powell, 2010). Integral projection models aid in examining age structure and phenology of beetles (Goodsman et al., 2018a). Deterministic methods are employed to model SPB population dynamics using difference equations to determine the effects of temperature on population dynamics (Friedenberg et al., 2008); and to investigate the population dynamics of temperature modulated density-dependence (Turchin et al., 1991). Dynamic state variables can be applied to investigate how beetle fitness was impacted from energetic costs due to host selection (Chubaty et al., 2009). Two studies examining the case of fungi associated with MPB were found in this review. Respectively a deterministic and probabilistic model are applied to study Grosmannia clavigera and Ophiostoma montium within beetle outbreaks (Addison et al., 2015), and how temperature affects the mutualism (Addison et al., 2013). Euclidean distances were used in a path-finding algorithm to analyse dispersal patterns and investigate the role of human-vectored long-distance dispersal (Lee et al., 2022).

More complex models are less tractable to mathematical analysis, and researchers therefore tend to make use of simulation instead. Mathematical models are often simulated to corroborate results or investigate different parameter selections (Powell et al., 1996; White and Powell, 1997; Logan et al., 1998; Logan and Bentz, 1999; Powell et al., 2000; Powell and Logan, 2005; Powell and Bentz, 2014). A simulator called MPB-R has been developed, which simulates temperature-dependent phenology and beetle emergence and attack synchrony to predict subsequent generational growth rates (Bentz et al., 2016, 1991; Hicke et al., 2006). Bone et al. (2006) have developed a detailed cellular automata model that accounts for MPB phenology and dispersal, over-wintering temperature changes, and stand susceptibility to give an output of stand mortality. The model applies fuzzy set theory to account for uncertainty within the definitions of stand susceptibility, and from the uncertainty of GIS data input, e.g. interpretations of pixels. The model is then used to predict the spread of MPB infestation from GIS data. Brush and Lewis (2023) created a new model using survival, full and Hill functions to capture the key elements of MPB population dynamics. They used the model to simulate different scenarios to investigate forest resilience and the Allee threshold required to overcome them.

ABM models have also been developed for MPB dynamics. ForestSimMPB is an ABM which allows the user to input environmental data via GIS and is able to represent MPB populations at two spatial scales. Since it is a bottom-up model, outbreaks begin on the microscale, but evolve into larger infestations at the macroscale (Pérez and Dragicevic, 2011; Perez and Dragicevic, 2010). Lombardo et al. (2018) constructed an ABM of a SPB development rate model to predict larval development using seasonal temperature data, comparing the southern edge of the range with the northernmost range. Furthermore, Weiss et al. (2019) contructed a model to simulate the dynamics of the Monochamus alternatus beetle. Its various components describe the host availability and suitability of surrounding trees; take into account wind speed and direction; and simulate the entire beetle life cycle, including dispersal to nearby trees.

Statistical methods are primarily used to determine the effects of external factors, such as climate, on beetle demographics. Regression studies are most common when investigating pest demography. Studies which examine aspects of beetle life history include using regression to determine: the maximum rate of population growth and strength of density dependence (Trzcinski and Reid, 2009); changes in cyclical patterns (An and Gan, 2022); overwinter beetle survival rates (Bone and Nelson, 2019); sex-ratio skew within adult and larval populations (James et al., 2016); to determine the relationship between flight activity and climatic conditions (Brockerhoff et al., 2017); parameters for beetle infestation of a single tree in order to scale up to the stand level (Björklund et al., 2009); to compare the abundance of beetles between preferred, less preferred and mixed host trees (van Halder et al., 2022); and density of beetles emerging per m² using experimental data (Negrón, 2019). Effects of temperature on beetle development are well studied and include: temperature dependent population growth rates (Weed et al., 2015); effects of cooling temperature on the mortality of eggs and larvae (Bleiker et al., 2017); and temperature dependent phenology and development using autologistic regression (Aukema et al., 2008). Predictions for attack densities have been calculated for Ips sexdentatus using regression models to determine temperature effects on development rate (Pineau et al., 2017b), and how offspring fitness can be affected by beetle density (Pineau et al., 2017a).

3.2.3 Environmental factors

Modeling that accounts for environmental factors focuses on temperature dependence for development, but also extends to temperature-related climatic factors. Effects of temperature dependence on beetle population dynamics can be captured using a variety of methods. Temperature dependent phenology is captured via parameter estimations for stochastic differential equations for individual beetle development (Yurk and Powell, 2010), and through integral projection models with parameterised air temperature models investigating cold mortality (Goodsman et al., 2018a). Statistical methods which determine the effects of temperature on phenology include: using regression models to determine the effects of temperature on outbreaks using GIS information and long term datasets (Weed et al., 2015); assessing how temperature affects non-linear population dynamics using regression models comparable to a Ricker model (Goodsman et al., 2018b); to determine the cooling mortality point in beetle eggs (Bleiker et al., 2017); and, in a spatio-temporal context with GIS temperature data, to determine phenology during an outbreak (Aukema et al., 2008). Bayesian statistics is used to analyse temperature and development times and uncover thresholds from MPB populations in the southern range of the USA (McManis et al., 2018). Seasonality can be studied using parameterised differential equation models where growth rate is dependent on temperature data linked to seasonality (Powell and Bentz, 2014; Powell and Logan, 2005; Hicke et al., 2006). Such studies use development rate curves developed from temperature data (Logan and Bentz, 1999).

Climate implicitly includes temperature, but also accounts for factors such as rainfall and/or humidity. Climatic effects of cooling on the development of SPB can be captured using difference models where growth is a statistical function of climate variables (Friedenberg et al., 2008), where the proportion that survive is determined by the cooling mortality temperature (Trân et al., 2007), and using a parameterised regressed Ricker's equation with temperature and rainfall estimates (Turchin et al., 1991).

Climatic factors can be investigated alongside other environmental factors, often characterized by GIS data. Spatial mortality measures of MPB have been determined using GLM models with binary response variables to predict new areas of MPB mortality (Liang et al., 2014). Logistic regression models are used to explain the spatio-temporal patterns of MPB outbreaks using annual temperature and drought variables (Preisler et al., 2012), to determine how temperature and elevation impact outbreaks (Sambaraju et al., 2012), predict current and future outbreaks from climate-beetle relationships and stand conditions (Buotte et al., 2016). Cooke and Carroll (2017) have used recruitment curves with correlated thermal response functions to make predictions of MPB spread. More recently, machine learning tools in the form of classification regression trees (CART) have been used with aerial imagery, climate, and elevation data to determine the mortality of Whitebark pine as a result of outbreaks (Jewett et al., 2011). This method has also been used to predict the extent of infestation within the Colorado Range Front of ponderosa pine (Negrón and Popp, 2004). Regression models and aerial imagery can determine which environmental variables are associated with outbreaks in MPB (Giroday et al., 2012; Wulder et al., 2006), and in Jeffrey pine beetle Dendroctonus jeffreyi (Egan et al., 2016). Various Ips species have applied regression methods to predict the mortality of Jeffrey pine in drought stricken Arizona (Negrón et al., 2009).

Climatic factors affecting SPB outbreaks can be included using logistic regression models to determine the probability of outbreaks and how severity is impacted by climatic and topographic conditions (Hernandez et al., 2012). Classification And Regression Trees (CART) methods can assess the predictive power of environmental covariates (Duehl et al., 2011). Other methods for determining outbreak success include PCA analysis of stand characteristics (Aoki et al., 2018).

Species distribution models (SDM) are a popular method to model distributions of MPB and Dendroctonus rhizophagus. Regression models can estimate lower temperature thresholds for SPB mortality to spatially determine northern range limits (Ungerer et al., 1999). Canonical discriminant functions have been used to develop maps for both SPB and MPB (Williams and Liebhold, 2002). This method uses discrete state variables as a linear function of covariates, in this case, infestation and climatic conditions. MaxEnt is widely used to develop distribution maps for several species, including D. rhizophagus using WorldClim climate variables (Fick and Hijmans, 2017) to predict distributions under current and future climate warming scenarios (Smith et al., 2013), in Ips mannsfeldi (Sarikaya et al., 2018), the Pine Wood Nematode (Bursaphelenchus xylophilus) (Wang et al., 2023; Tuomola et al., 2021; Lee et al., 2021) and comparing MPB, Dendroctonus breviconnis, and Ips pini (Evangelista et al., 2011). Comparisons between the SDM methods of MaxEnt BIOCLIM and ENFA using D. rhizophagus suggests subtle differences between the methods. In the context of modeling MPB a comparison of Maxent, GLM, and boosted regression trees (BRT) showed Maxent and BRT to have similar performance (Sidder et al., 2016).

Indirect studies of outbreaks which examine the effects on forests are widely studied using GIS and statistical methods. Efforts to predict the mortality of pine stands have been formed using vegetation indices from aerial imagery, regression, and GAM (Meddens and Hicke, 2014), and using vegetation indices from a time series of MODIS aerial imagery to predict host mortality (Meddens et al., 2012; Franklin et al., 2003). This has also been accomplished using GIS data and CART algorithms to predict stand mortality by examining forest stand characteristics (Vorster et al., 2017). Using MODIS imagery data, the spatial association of scalable hexagons (SASH) method (Potter et al., 2016), which identifies non-random temporal patterns in ecological phenomena, has been used to characterize stand mortality related to MPB outbreaks. One study used the statistical method, least absolute shrinkage and selection operator (LASSO), to determine the effects of climatic factors on outbreaks (Reyes et al., 2012). CART and Random Forest methods, alongside GIS techniques, can estimate the effects of MPB infestation and climatic factors which give rise to wildfires (Mietkiewicz and Kulakowski, 2016), quantifying the links between MPB outbreaks and wild fire (Liang et al., 2016). Partial least squares regression, using Landsat imagery, has been used to determine the importance of key climate variables that drive Tomicus spp. outbreaks (Yu et al., 2022b).

Simulation studies which do not examine beetle infestation directly include: Terrestrial Regional Ecosystem Exchange Simulator (TREES) to assess the effects on tree mortality from attack, specifically, blue stain fungal attack by Grosmannia clavigera (Millar et al., 2017); and to predict which stands are susceptible to attack under different fire management regimes using Spatially Explicit Model for LANdscape Dynamics (SEM-LAND) (Li et al., 2005). Integrated Biosphere Simulator (IBIS) is an ecosystem simulator which allows the user to estimate climate modeling and vegetation phenology in a single framework. Landry et al. (2016) use an extension called Marauding Insect Module (MIM), which accounts for MPB outbreaks, to estimate the effects of merchantable timber biomass, ecosystem carbon, surface albedo, and radiative forcing. Several studies used CLIMEX to simulate the impacts of climate on the development and distribution of beetle populations (Zhou et al., 2019; Yoon et al., 2023; Watt et al., 2011).

3.2.4 Economic consideration and management

Studies modeling management practices for forestry are more dominant than economic studies that take a broader societal perspective. Sims et al. (2010) used a deterministic bioeconomic model that accounts for timber and non-timber benefits to evaluate the optimal management choices of a central forest manager under MPB outbreaks driven by climatic events. A sensitivity analyses allowed to evaluate the effects of changes in the relative value of salvage timber and the public's valuation of timber vs. non-timber benefits. Waring et al. (2009) simulated outbreaks of SPB and the Mexican pine beetle Dendroctonus mexicanus using Forest Vegetation Simulator (FVS) with climatic data from weather stations to predict the dynamics of beetle infestation and economic costs in terms of revenues forgone. Partial differential equations have been simulated to model MPB within a managed stand where parameters were adjusted between different levels of effort to determine the effectiveness of different control strategies (Strohm et al., 2016). The effectiveness of thinning vs. non-thinning strategies has also been carry out by comparing three population modeling scenarios with hypothetical expansion factors (Coggins et al., 2011), and determining the change in beetle density through non-linear (exponential) regression models (MacQuarrie and Cooke, 2011). An individual-based model was developed by Xia et al. (2022) to simulate the spread of pine wilt disease and evaluate the effectiveness of infected tree removal among other control practices. Linear regression and aerial imagery were applied to evaluate the determinants of MPB population growth and compare the effectiveness of multiple management strategies (Trzcinski and Reid, 2009). Logarithmic regression can assess beetle attack densities on individual trees using field data, and findings can inform stand prioritization for MPB control (Björklund et al., 2009). McNichol et al. (2019) used Kaplan-Meier survival analysis and regression to examine the effects of prescribed burning as a management strategy.

Models were also used to inform strategies when the risk of wildfire outbreaks may be associated to beetle infestation. The interaction between beetles, climate, and management is complex and many such studies are simulation based. LANDIS-II has the capability of running simulations with extensions for beetle dynamics (MPB, Jeffrey pine beetle, Fir engraver beetle Scolytus ventralis), carbon dynamics, wildfire, and differing management strategies (Scheller et al., 2018); FVS, an MPB extension, and a fire and fuels extension can be used to develop a risk rating for wildfire occurrence under different thinning practices (Ager et al., 2007; Donato et al., 2013). BioSIM is another simulator which is a decision support tool for pest management planning. This simulator simulates weather suitability for MPB outbreaks to determine how inter-annual changes in weather affect stand mortality from outbreaks (Creeden et al., 2014).

Similarly to EAB, monetary estimates of societal damages have been estimated using a hedonic pricing approach that computes the change in house prices as a result of damage from MPB infestation on the surrounding environment (Price et al., 2010; Cohen et al., 2016). Early work used contingent valuation to estimate the willingness to pay of forest owners to participate in a cost sharing thinning programme for SPB control, using regression analysis to evaluate its socioeconomic determinants (Watson et al., 2013).

3.3 Spruce—Picea

Spruce pests found in our review are European spruce beetle (ESB) Ips typographus, Spruce beetle (SB) Dendroctonus rufinpennis, and two studies on Great spruce bark beetle Dendroctonus micans. Many of the studies originate in Central Europe, e.g., the Czech Republic, Slovakia, Germany, and Poland, where there are large coniferous forests. The majority of the studies focus on ESB, therefore, the reader should assume the subject is ESB unless otherwise stated.

3.3.1 Pest spread

Few models explicitly represent spread, but rather examine aspects of spread within a wider context. Diffusion has been used to model radial spread from timber storage as point sources using mark-recapture data to parameterise the diffusion coefficient (Skarpaas and Økland, 2009), and a parameterised diffusion coefficient for flying beetles that land on an infested tree (Byers, 1996). Dispersal kernels have also been calculated from mark-recapture methods (Dolezal et al., 2016). A parameterised gamma distribution can capture dispersal and aggregation within simulations (Økland et al., 2016).

Statistical methods focus on spatial or spatio-temporal aggregation to give an indication of pest spread. Infestation is often examined in the context of the forest and not primarily about pest dynamics. Non-linear regression is used to predict infestation gradients using distances from outbreak points (Potterf et al., 2019). Hierachial clustering was used to identify high risk pests based on their ecological similarities and geographic distributions to predict future establishment areas (Duffy et al., 2021). Spatial correlations of D. micans have been calculated to determine if outbreak patterns are related to stand characteristics, and if the densities of an obligate predator Rhizophagus grandis can estimate D. micans density (Gilbert and Grégoire, 2003). Concentric spread from point locations has been analyzed over consecutive years using the statistical process known as Kriging (Hlásny and Turčáni, 2013). These authors use sanitary felling data to establish a time series of spreading, which can be used to infer a rate of spread.

A few studies incorporate statistical methods and GIS/imagery data to model spread. This spread was captured by identifying the health of the host pine trees. Linear and partial least squares discriminant analysis was used to determine if spectral vegetation indices can distinguish between healthy, infested and susceptible trees (Trubin et al., 2023; Abdullah et al., 2019b). Principal component analysis and a random forest model were also used to assess the capability of spectral vegetation indices to determine the health or attack phase of a tree (Abdullah et al., 2019a; Mandl and Lang, 2023). Ali et al. (2021) investigated if canopy chlorophyll content could be used to estimate the health of a tree using an Invertible Forest Reflectance radiative transfer model.

3.3.2 Pest demography and environmental factors

We treat pest demography and environmental factors together since very few studies solely examined population processes without an environmental or climatic component using GIS data. Population growth rates have been estimated statistically using Generalized Linear Models (GLMs) to assess the impacts of biological factors using temperature and precipitation data, and biotic factors e.g. voltinism within the population (Marini et al., 2013). Other efforts to estimate growth rates include using oviposition data for different temperature regimes with a statistical exponential model (Wermelinger and Seifert, 1999, 1998). Similarly, Generalized Linear Mixed Models (GLMMs) are applied to predict the proportion of univoltine to multivoltine spruce beetles within stands by including stand characteristics e.g. host height, and air temperature (Hansen et al., 2001). Williams et al. (2021) also used GLMMs to investigate how beetle population dynamics are affected by air temperature and elevation (Williams et al., 2021). They've also been applied to investigate the effects of thermal variability between summer and winter on the flight behavior of SB and associated species (Dell and Davis, 2019). A brief review of parameters which are important when modeling life-cycle dynamics of ESB, such as thermal sum days, and voltinism can be found in (Netherer and Pennerstorfer, 2001).

Pest densities have been estimated by counting larvae within individual wind-felled trees and using linear regression to estimate the density across stand levels from survey data (Borkowski and Podlaski, 2011). Some examples of interactions between beetle species have been examined. Økland et al. (2009), 2011) used experimental data to parameterise simulations of beetle populations using iterative equations to determine if ESB could become invasive in the USA with spruce beetle (SB) facilitating through positive interaction. Competitive interactions between ESB and the six toothed spruce bark beetle Pityogenes chalcographus are studied using GLMs to predict tree deaths from infestation during a prescribed burning programme (Eriksson et al., 2006). Predictions for temperature-dependent development time of each larval instar for D. micans and it's obligate predator R. grandis are estimated from experimental data using non-linear regression (Gent et al., 2017). Jakoby et al. (2019) used a time-varying distributed delay model to predict the phenology of beetle populations and potential climatic effects.

Spatio-temporal predictions of infestations using environmental variables were examined using a variety of methods. Regression models used a combination of point pattern occurrence estimates with stand characteristics and storm damage (Stadelmann et al., 2014) and using stand characteristics and weather data (Stadelmann et al., 2013). Stepwise multiple regression can be applied alongside spatial autocorrelation and kriging to predict population densities of D. micans in relation to stand characteristics (Gilbert and Grégoire, 2003). Logistic regressions, using meteorological data, were used to identify forest stands susceptible to infestation (Mezei et al., 2019). GLM methods are used to predict population densities from stand characteristics and storm damage data (Kärvemo et al., 2014a; Eriksson et al., 2005). Predicting the effects of damage from infestation due to drought is studied using GLMMs to examine forest management data, climate and storm data, and water content of the soil (Pasztor et al., 2014; Overbeck and Schmidt, 2012).

Next, a number of studies that assess the impact of abiotic factors, such as storms, on the risk of outbreaks are discussed. Discrete time survival analysis methods can quantify risk from beetle population structure, variation in precipitation, spatial connectivity, and outbreak history (Seidl et al., 2016). CART methods are used to develop hazard models for SB outbreaks within individual stands using their characteristics (Reynolds and Holsten, 1994), and to predict historic outbreaks from climatic conditions (Hebertson and Jenkins, 2008). Probability models have been developed to estimate the chance a stand is infested using cumulative link models (proportional odds models) using stand characteristics and soil sample data as explanatory variables (Blomqvist et al., 2018).

Spatial correlation and GIS techniques are harnessed to identify or predict factors which may drive infestation. Causal relationships between environmental factors and SB outbreaks can be estimated using Random Forest methods, such as between temperature and drought variables, while simultaneously quantifying spatio-temporal synchrony (Hart et al., 2017, 2014), alongside LANDSAT imagery data to classify the extent of infestation over a defined time period (Latifi et al., 2014), and to map host mortality from SB attack (Woodward et al., 2018). A similar method, known as Boosted Regression Trees, can be combined with GLM methods to create risk maps of infestation using similar data (Kärvemo et al., 2014b). Similarly, evaluation of hyperspectral data from HyMAP can be achieved within ArcGIS to identify and map infestation (Lausch et al., 2013b). Methods have been developed using algorithms to analyse aerial imagery and correct the time-lag between forest disturbance and beetle outbreaks, which is verified on a historic data set (Kautz, 2014). LANDSAT data can be used to predict infestation and outbreaks by identifying the healthy (green) vs attacked trees from color gradients using Bayesian GLM and logistic regression (Hais et al., 2016). A number of techniques generate predicted future distributions of beetle infestation. Probability models and GIS data are used to create outbreak maps from stand infestation distance and temperature data (Kautz et al., 2013). Ortiz et al. (2013) illustrate this by comparing three different types of predictive distribution models (Maxent, GLM, Random Forests) from RapidEye and TerraSAR-X remote sensing tools.

Several ABM/IBM models have been developed to investigate various outbreaks. Although such models do not represent individual beetles, they do typically represent the individual characteristics of a location and can be linked to detailed mechanistic models of beetle development and/or behavior. A widely used example is a comprehensive phenological model for ESB called PHENIPS (Baier et al., 2007), which has been independently validated using climate data (Berec et al., 2013) and extensively linked to various ABMs such as iLand (Dobor et al., 2020). The model combines topographical (e.g. slope and elevation), and thermoclimatic (e.g. air temperature and solar radiation) variables with a parameterised beetle developmental model. PHENIPS can be applied using GIS data to create spatio-temporal models and is used within many studies to account for the phenology of ESB during outbreaks. Authors examine the effects of drought stress on tree stands (Matthews et al., 2018), with GAMMs to determine the effects of sanitary felling on outbreaks (Mezei et al., 2017a), using non-linear regression to determine which PHENIPS variables were most important at predicting timber loss from outbreaks (Mezei et al., 2017b), to predict future forest productivity under future IPCC RCP climate scenarios and to determine which modules are important for forest managers (Thiele et al., 2017), to compare population density before and after disturbance events (Fleischer et al., 2016). PHENIPS can also be combined with other models, such as LandClim, to further bolster the beetle dynamics module included within LandClim (Temperli et al., 2013).

An individual-based gap model for individual trees and forests FAREAST has a module for SB dynamics called UVAFME (University of Virginia Forest Model Enhanced) (Xiaodong and Shugart, 2005; Foster et al., 2018). UVAFME incorporates the probability of SB infestation from climatic inputs, stand and individual tree characteristics. Other ABMs include SAMBIA, Infestation Pattern Simulation (IPS), IPS-SPREADS and PICUS. SAMBIA is a bottom-up spatially explicit model at the stand scale that models beetles, trees, natural enemies, and forest management (Fahse and Heurich, 2011). SAMBIA accounts for beetle life cycle dynamics e.g. dispersal, breeding, natural and tree or management induced mortality. The model has been validated against historical outbreaks using spatio-temporal data collected in the Bavarian National Forest in Germany with results suggesting more research is required due to the complexity of interacting factors (Lausch et al., 2013a). PICUS is a spatially explicit forest patch model which accounts for different forest processes, such as ESB outbreaks in the form of additional modules based on PHENIPS (Seidl et al., 2007). PICUS has been used to examined the effects of ESB outbreaks on carbon sequestration and timber production under different climate and management scenarios (Seidl et al., 2008). It can also be used to integrate with another forest model EFISCEN, which operates at a larger scale than PICUS, to assess management strategies and climate change impacts (Seidl et al., 2009). Pietzsch et al. (2023) used IPS-SPREADS to simulate behavior and spread of ESB populations. The IPS-SPREADS model accounts for the interactions between individual spruce trees and beetles. Markov chains then used the simulation results to predict infestations further into the future. IPS is a bottom-up spatially explicit model which was developed to assess dispersal and infestation based on the interaction between tree and beetle (Kautz et al., 2014). Other modules have been developed to include windthrow dynamics, in particular, to investigate how cluster size and the spatial extent of windthrow affect ESB population dynamics (Potterf and Bone, 2017).

3.3.3 Economic considerations and management

Modeling studies focus on the impacts of management strategies on outbreaks. Dobor et al. (2020) and Zimova et al. (2020) used the landscape simulation model iLand to investigate the management strategies of sanitation logging and shortened rotation lengths, respectively. One study produced a bark beetle susceptibility index as input to a decision support system called Heureka so that users can simulate different management strategies to see how forest stands are affected (Nordkvist et al., 2023). More complex ecosystem simulators are used to investigate bark beetle attacks such as LandClim, and LPJ-GUESS. LandClim is a spatially explicit forest simulator used to investigate forest dynamics with fire, beetle, and wind disturbance. The beetle module has been parameterised using experimental data for SB outbreaks and climatic variables to predict outbreak dynamics in Colorado (Temperli et al., 2015). LPJ-GUESS is an assessment model for making management decisions regarding biodiversity, biogeochemistry, and vegetation while taking into account climatic changes. Jönsson et al. (2007), 2012, 2015) have adapted this model for use in beetle-attacked forests by including a phenological model for ESB to assess the importance of climate within outbreaks.

A combination of Generalized Additive Mixed Models (GAMMs) and PHENIPS can model the spatio-temporal effects of outbreaks from different sanitary felling zones, taking account of stand characteristics and climatic factors (Mezei et al., 2017a). Marini et al. (2012) used an iterative statistical model with historical forest health data on timber loss attributed to beetle attacks to inform management on the role of both biotic and abiotic controls on population dynamics. Management has been modeled in the SAMBIA framework where sanitation felling of infested trees occurs before beetle emergence by adjusting the beetle mortality component with a probability of detection and subsequent removal (Fahse and Heurich, 2011). PICUS and EFISCEN have been used to simulate 110 years of forest management by replacing spruce with non-coniferous alternatives to reduce outbreaks and investigate carbon sequestration dynamics (Seidl et al., 2008). Sanitary felling of infested trees is a common method used to curtail ongoing outbreaks. Ogris and Jurc (2010) use a machine learning algorithm called M5' to predict where sanitary felling should be conducted within a forest. The method uses 45 covariates to develop the prediction, including climatic variables, forest characteristics, topography, and soil, which they validated against existing spatial data.

Another important area of research is the study of pathways for pests to enter an ecosystem via global trade routes. (Skarpaas and Økland 2009) used a Gompertz model of bark beetle dynamics and diffusive dispersal to assess the risk of introductions and examine different pre-emptive measures available (e.g. storage enclosure) to mitigate this risk. A hedonic pricing framework has been used to assess the impact on property value from the joint effects of SB and wildfire risk using spatial econometric techniques (Hansen and Naughton, 2013). The effects of bark beetle attacks on timber revenues were simulated by Subramanian et al. (2016) using a Heureka-Standwise model.

4 A synthesis of wood borer pest modeling research

Our review identifies the key modeling techniques used to investigate the dynamics wood borer beetle infestations and the key pest-host systems and system processes considered in the literature. We systematically categorize studies by modeling methodology, by host and by modeled processes (see Figure 4). A growing number of hosts are being studied; before 2019, ash, pine, and spruce accounted for >99% of studies, whereas currently they only account for 88% of studies. The host species in the remaining studies are quite varied; the next most common hosts, oak and fir, only account for seven articles each.

The global distribution of studies was very uneven, with most papers addressing the insect infestations in the Northern Hemisphere, mostly the USA, Canada and Europe. Focal location and pest species were dominated by studies of pine within the continental USA and British Columbia, Canada, where vast pine forests are located, and significant impacts of wood borer beetles are observed. However, it is also likely that this focus also results from disparities in research funding within but especially between countries. Spruce studies focus on forest disturbance and impacts of infestation on such disturbances, with the effects of silvicultural practices and wind throw damage of particular interest. Studies of European spruce beetle (ESB) were located in Central Europe, while spruce beetle (SB) studies were conducted in the continental USA, and Emerald Ash Borer studies both in the USA and Russia. There were also several pest-host species combinations for which no models were found.

Our review focuses on the current state-of-the-art of bark beetle modeling approaches, rather than on historical developments. We carried out the temporal analysis using our classification of models, but we could not find any clear temporal trends, although there are possible shifts toward using more computationally demanding and data-demanding models.

4.1 Commonality of modeling challenges and approaches

The complexity of real-world wood borer pest-host systems requires modelers to make simplifying assumptions and these are typically based on common approaches. Such simplifications are driven by the questions addressed and thus vary between pest-host systems, as discussed. First, reducing the number of interacting variables of host and pest, e.g. investigating forest dynamics with pest presence/absence as a factor e.g. Blomqvist et al. (2018); Vorster et al. (2017); Jones (2019), or investigating beetle dynamics with simplified environmental (including host) characteristics, e.g. assuming the host has spatially uniform presence (Goodsman et al., 2018a; McDermott and Finnoff, 2016). Second, limiting scope according to study scale e.g. detailed population dynamics within a stand (Fahse and Heurich, 2011), but cruder demographics at larger scales e.g. probability of infestation across a national park (Potterf et al., 2019).

However, many modeling techniques are used across all host systems, reflecting that host-parasite systems share common life cycle elements; laying eggs beneath tree bark to feed on phloem until emergence. Much of the life cycle can be modeled using similar methods with minor system specific adjustments. For example, modeling dispersal via kernels which are used within all the pest species described (see Sections 3.1.1, 3.2.1, 3.3.1). This suggests that existing modeling studies can be used as a starting point for modeling emerging wood borer pests problems.

At large scales, static species distribution model (SDM) methods, such as MaxEnt and Genetic Algorithm for Rule Set Production (GARP), are applied to pests for all three main host species. These models used environmental covariates to establish species distributions, and crucially, can be used to estimate the suitability of other regions. For instance, the suitability of North America for EAB has been predicted from the native range using MaxEnt (Liang and Fei, 2014; Dang et al., 2021), or to predict future suitability for a pest (Smith et al., 2013; Ning et al., 2021).

Study of interventions to control infestation is common across systems. From a management perspective, cost-benefit analysis is a useful tool in guiding the application of limited resources (Yemshanov et al., 2015; Arbab et al., 2022). However, goals of management were markedly different across host species, for example, in ash the control of EAB spread is prioritized with plans such as SLow Ash Mortality (SLAM) (McCullough and Mercader, 2012), whereas in pine and spruce, the focus is use of silvicultural practices such as stand thinning to reduce outbreaks and fire hazards (Donato et al., 2013; Mezei et al., 2017a; Subramanian et al., 2016).

4.2 Modeling approaches driven by specific wood borer pest-host system properties

Differences in study scale vary by host with local (e.g. stand level) population dynamics models of ash and spruce pests less well researched as those in MPB. This is likely due to lack of data availability for associated pest species, which in turn, could be due to study focus, e.g. predicting ESB infestation from previous storm occurrences only requires infestation point data (Stadelmann et al., 2014). Use of remote sensing data was less prominent within ash studies, as these perform better in large coniferous forests, such as pine and spruce, that do not seasonally defoliate. In contrast, ash-EAB studies were often conducted on the smaller state-wide, or county-wide scale (Zhang et al., 2014; Siegert et al., 2014; Lyttek et al., 2019) compared to large-scale spruce or pine forests, for instance, in national parks (Potter et al., 2016; Liang et al., 2016; Pietzsch et al., 2023).

We identified a difference in research questions across systems. In the case of ash and EAB, the focus is primarily mortality of infested stands and the desire to control economic impacts (Kovacs et al., 2014; McConnell et al., 2019). This reflects the fact that infested ash is present within urban areas where municipal considerations, such as property valuations, removal and treatment of infestation, are a concern. Studies in pine and spruce focused on environmental impacts rather than economics, reflecting the scales over which environmental effects can be estimated effectively, and the relative absence of humans dwelling within vast forests. For spruce, the key issue is the broader impact of tree mortality on forest ecosystem function and productivity, e.g. carbon cycling (Seidl et al., 2008) and biodiversity (Thrippleton et al., 2023). For pine, the broader context of forest ecosystem science (Buotte et al., 2016; An and Gan, 2022) has been important, as is understanding pest-host dynamics e.g. Logan et al. (1998); Powell et al. (2000); Ozcan et al. (2022).

4.3 Model parameterisation and data gaps

Robust parameterisation of the bark beetle outbreak models is an essential and yet often overlooked part of the research linking to policy recommendations. Many outbreak models are highly nonlinear and sensitive to thresholds in beetle demography, host condition, and climate. Thus, without empirically constrained parameters, they cannot reliably support management decisions. In our review, we found different approaches from purely strategic, non-calibrated or literature-based mechanistic models and heuristically tuned landscape simulators to formally estimated frequentist risk models and fully Bayesian-calibrated mechanistic or hierarchical models, cf. (Table 2). More recently, ML-based predictors trained on large remote-sensing and monitoring datasets are increasingly playing a role. However, we found that many older models did not fit parameters, and most models that did make use of data were based on standard statistical frameworks rather than models of spread and establishment. Most long-term landscape and Earth-system models still depend predominantly on literature values or heuristic calibration. However, fine-scale and regional models now exploit diverse data (tree inventories, aerial surveys, remote sensing, climate, management records).

Table 2

Table 2. Review of parameter estimation techniques with examples of papers deploying a particular approach.

Data used within modeling studies, whether directly to estimate model parameters or indirectly via statistical inference of parameters, comes from four different sources—laboratory experiments, field studies, remote sensing and operational/administrative data. Laboratory gathered data often investigates the effects of temperature on the development of pest species, e.g. Gent et al. (2017); Yurk and Powell (2010), which can be used directly to inform model parameters. Ideally, modeling and experimental methods should be considered in tandem with experimental studies designed explicitly to inform modeling, but it is often possible to make use of data collected for other reasons. Generally, the aim of field studies and remote sensing is more varied, often comparing effects across populations from different sites, and is usually not focused on the needs of models. Remote sensing is widely used within pine and spruce studies, but not for ash, where only five studies were found to use such techniques. Operational/administrative data can be used to inform on the scale and costs of impacts and interventions, including their distribution in time and space. They can also inform on key risk factors, e.g. trade or movement of people, to understand introduction or dispersal risk. When using field, remote sensing or operational data to inform statistical inference, care must be taken to adequately account for variability and bias induced by the data collection process. To aid future modeling, we now describe data and parameterisation in terms of: host and pest distributions; demographic processes including dispersal, environmental drivers, ecological impacts; and economic costs. The sources which estimated parameters were drawn from a small pool of empirical studies and adding to this limited data would also be a valuable goal of future work.

4.3.1 Distribution of host and pest

Understanding the distribution of hosts—and ideally the extent of pest problems—is critical to modeling impacts in the real world and requires ongoing research and surveillance. Remote sensing from satellite data still has important limitations, but can nonetheless be a useful tool to help in determining the spatial distribution of ground cover, e.g. susceptible forests and used to determine the occupancy of wood borer beetles and track spread. Databases such as MODIS/VIIRS, Sentinel-1, Sentinel-2, Landsat and Google satellite imagery can provide recent information about canopy cover. Land-use data (that classify land cover as e.g. agricultural, urban, forest - for example, the Copernicus CORINE program for Europe) can be used as environmental covariates in models to provide information about how pests are affected by land use (Bossard et al., 2000).

4.3.2 Demographic processes including births, deaths and dispersal

Reproduction rates have been estimated from laboratory or field studies, for example, temperature-dependent growth and development time (Powell and Bentz, 2014; Dell and Davis, 2019), and fecundity from egg counts (Lutscher and Musgrave, 2017). Wood borer species have a “rue carrying capacity”, where only a finite number of larvae can live within an occupied tree (Raffa et al., 2015; Anderbrant, 1990; Coulson, 1979) that has been estimated using diameter at breast height (DBH) of trees (Fahrner et al., 2017; Blomqvist et al., 2018; McCullough and Siegert, 2007). Quantifying competition/mutualism parameters remains a fundamental ongoing challenge and methods of estimation are not universally applied. Doing so would allow more effective assessment of the benefits of pest control from a competing species, or the effect of mutualism between MPB and blue stain fungi e.g. Grosmannia clavigera and Ophiostoma montium (Addison et al., 2013, 2015). Dispersal parameters are particularly difficult to obtain for flying insects such as wood borer beetles. Mark-recapture methods have been used widely for insect species, such as ESB (Dolezal et al., 2016), but logistical challenges remain, particularly with long distance dispersal events (Hagler and Jackson, 2001; Nathan et al., 2003). Flight mill experiments have been popular for estimating flight distance, but more of these would provide a greater pool to draw on for dispersal estimates (Taylor et al., 2010; Evenden et al., 2014).

4.3.3 Environmental drivers

Data from weather stations is helpful in determining environmental conditions at particular locations. Information databases can be used, such as WorldClim (Fick and Hijmans, 2017) or IPCC CMIP databases with predictions for future climatic conditions for data on a global scale (Meehl et al., 2000). Using such global datasets allows comparisons between different regions within the same framework of environmental covariates. This type of data was common among studies within this review, but challenges remain related to the scaling in landscape contexts. Often data must be aggregated from a fine scale to a coarse scale, which can lead to statistical bias, e.g. the “middle number problem” of ecology, where modeled relationships or parameter choices may not be valid in other locations or systems (Newman et al., 2019). CLIMEX is a useful software that also makes use of historical data and future climate estimates to simulate future distributions of pests (Zhou et al., 2019).

4.3.4 Economic costs

Economic information is required for cost-benefit analyses and portfolio optimisation. Most studies use the costing of a single tree, which is then scaled to the desired forest patch. These studies are primarily in ash where the cost is direct application of control measures (McCullough and Mercader, 2012; Hope et al., 2021). Information on house prices were used to value depreciation as a result of reducing the aesthetic appeal for potential buyers (Cohen et al., 2016; Kovacs et al., 2011, 2014). This type of information will have considerable uncertainty from effects not covered by the analysis, for example, the strength of demand and availability within the housing market. Fuchs et al. considered historical fluctuating timber prices as market risk along with bark beetle calamity prices in order to assess management options using portfolio optimisation (Fuchs et al., 2022).

5 Discussion

5.1 Research gaps

Despite the many advances in applying modeling to wood borer infestations, there remain significant gaps. Although the dynamics of host-parasite interactions have been well studied via simulation modeling (forward modeling), techniques to parameterise models (reverse engineer model parameters from data, also known as inverse modeling) in specific host-pest systems are required. Furthermore, ecological effects beyond host-parasite interactions e.g. competition and mutualism, were noticeably absent. We only found evidence of modeling the interaction between MPB and blue stain fungi e.g. Grosmannia clavigera and Ophiostoma montium (Addison et al., 2013, 2015). Examples of host parasitoid systems were only found in the context of biological control for ash-EAB systems (Anderson and Dragićević, 2016a).

Current modeling focuses on what happens after pest arrival, not on quantifying pathways for entry, although it is possible that our search criteria excluded such studies. Species distribution models (SDMs) have been used to quantify climatic suitability for wood borer pests such studies do not identify arrival sites and we found only a single study that examined trade as a point of entry for potential pests (Skarpaas and Økland, 2009). Modeling trade in general, and for entry points that could establish an invasive species, has been studied elsewhere (Dalmazzone and Giaccaria, 2014; Levine and D'Antonio, 2003). Applying these tools to international trade in timber products would help toward quantifying establishment risk from potential pests (Koch et al., 2011; Krishnankutty et al., 2020).

Economic models covered implementation of management strategies (McCullough and Mercader, 2012; Seidl et al., 2009; Strohm et al., 2016), healthcare costs (Jones and McDermott, 2018), and house price depreciation (Kovacs et al., 2014; Cohen et al., 2016), but modeling including the impact of pests on the economics of the timber industry were not well represented. Timber loss was included for pine and spruce hosts, with few studies including the impact of beetle outbreaks on salvage logging operations. We believe that inclusion of timber economics in studies modeling wood borer infestations is currently attainable and would be desirable for the timber industry such as from Fuchs et al. (2022).

5.2 Opportunities for further research

Sustained integration between researchers within different systems is needed. For example, spread models within EAB-ash systems is well developed, but to a much lesser extent when the host is spruce. Using techniques applied to EAB-ash systems would therefore contribute to a greater understanding of spruce-pest systems. The same can be said for pine-pest systems, where a deep understanding of many methods and problems gained via years of applications to MPB should be invaluable in the study of other wood borer-host systems. We nevertheless acknowledge that some relevant models may be missed given the search terms used in our search strategy, for example, the RITY models by Ogris et al. (2019).

A greater degree of generality within models would allow methods to be transferred between species. This is not always possible due to the particular nature of each host-pest system. The PHENIPS model for ESB is an example of a detailed framework which could be used within another system (Baier et al., 2007). However, even when such general frameworks are available, the key problem is how to parameterise them for specific systems. For example, Bayesian methods are not widely used in modeling wood borer pest, but could allow a better use of available data to estimate model parameters and quantify uncertainty in these estimates. A key advantage of Bayesian approaches is that they provide a toolkit to combine widely different sources of information e.g. various sources of hard data and expert opinion. Many of the techniques used in disease transmission modeling (see e.g. Swallow et al., 2022) could inform woodborer modeling, allowing the development of hierarchical models that account for variation at different scales, e.g. through fixed and random effects. However, restricted access to data sets hinders model parameterisation and access via repositories, such as the GBIF, would be highly desirable.

Despite some promising results e.g. classification of ash (62% successful detection) among other broadleaf species in typically urban settings (Zhang et al., 2014), use of remote sensing to detect infestation in highly heterogeneous contexts is a challenge. Key aspects of this challenge for remote sensing technologies include: host distribution, where for mixed stands it is also necessary to distinguish between host species; variation in foliage in deciduous host species; and variation in foliage due to pest damage.

Predicting potential invasion sites outside the native range using SDMs is an emerging area of research. However, static SDM methods should be used with caution since (i) they require focal species distributions to be at equilibrium, which is clearly not true for ongoing invasions (Václavík and Meentemeyer, 2012), and (ii) data from native range distributions, likely to be close to equilibrium, can be poor. Application of dynamic species distribution models to data on observed invasions is a promising area of research. Catterall et al. (2012) have developed a spatio-temporal model which uses the same types of data as SDMs, but allows for temporal variation and can provide similar outputs.

Use of complex ABMs allows a large number of factors within systems to be studied and facilitates the creation of more realistic scenarios. One of the criticisms of ABMs has been that an understanding of the effects any individual process are difficult to attain. However, developments in mathematical analysis are emerging, which allow analysis to be conducted (Cornell et al., 2019), opening further opportunities to analyse complex models and gain a deeper understanding of the processes involved. Furthermore, uncertainty quantification techniques, including history matching, can now be applied to assess complex ABMs against data (Vernon et al., 2022).

Data availability statement

The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

VK: Conceptualization, Data curation, Formal analysis, Writing – original draft. MK: Data curation, Formal analysis, Writing – original draft. GM: Conceptualization, Writing – review & editing. JT: Writing – review & editing. AK: Conceptualization, Writing – review & editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. MK, JT, GM, and AK contribution was funded by two UKRI projects, NE/V019988/1, Learning to adapt to an uncertain future: linking genes, trees, people and processes for more resilient treescapes (newLEAF) and NE/V020099/1, Connected Treescapes. GM was also funded as part of UKRI newLEAF project NE/V020005/1. VK was partly funded by the Scottish Plant Health Center project, PHC2018/14. GM and VK were supported by the Scottish Government's Rural and Environment Science and Analytical Services Division (RESAS). GM was also funded by the UKRI project NE/V020005/1 (newLEAF).

Acknowledgments

Yewen Chen and her contribution is the corroboratory analysis.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors JT, AK declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/ffgc.2026.1706950/full#supplementary-material

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