Warm temperatures and host tree abundance explain variation in directional spread by laurel wilt

Abstract

The rate at which invading organisms disperse into novel habitats is fundamental to their distribution and abundance. Forecasts of spread often assume that invasion speed is constant through time and among directions but, depending on the extent to which this assumption is violated, the efficacy of delimitation surveys and eradication programs could suffer. Knowledge of the mechanisms underlying spatiotemporal variation in spread could help refine forecasts and guide management, particularly in the early stages of invasions. We investigated rates of spread by laurel wilt, one of the most damaging non-native forest pests in North America, using three standard approaches (effective range radius, distance regression, and boundary displacement) and evaluated the strength and drivers of variation in directional spread (i.e., anisotropy). Estimates of mean annual spread varied from 24 to 40 km/yr, but spread was highly anisotropic with invasion speeds reaching approximately 100 km/yr south, 80 km/yr west, and 50 km/yr north, a pattern that we attribute to the abundance of host redbay trees and warmer temperatures fostering rapid southern and western spread. This pattern—quicker spread of laurel wilt from the point of introduction into areas forecasted as highly suitable for its persistence—suggests that establishment location might have a major influence on rates of anisotropy. Our findings underscore the utility of habitat suitability modeling—in which host availability and suitable climate are widely used to forecast establishment risk—for identifying areas into which spread will proceed most rapidly following establishment of a new invader and/or a satellite population via a long-distance dispersal event.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10530-023-03069-5.

Introduction

Spread of invading species often results from the coupling of population growth with dispersal (Liebhold and Tobin 2008), and spatial and/or temporal variation in factors that govern either of those processes can lead to changes in invasion speeds. Predictions of spread and pest arrival help natural resource managers with timely implementation of management. However, predictions of spread can be less reliable when spread rates vary directionally (anisotropy) (Morin et al. 2009), temporally (Andow et al. 1990), or both. Spread might accelerate as populations transition through an initial lag phase following establishment into a period of accelerating spread as the population grows and/or more suitable habitat is encountered, followed eventually by a deceleration as suitable habitat becomes exhausted (Shigesada et al. 1995). It is exceedingly difficult to reliably predict long-distance jumps, but quantifying annual rates of spread, drivers of directional variation in spread, and, thus, in which direction(s) spread might be quickest can help guide delimitation surveys and/or the design—or potential feasibility—of slow the spread and/or eradication programs.

Three commonly used statistical methods to quantify spread are effective range radius (Shigesada et al. 1995), distance regression (Liebhold and Tobin 2008), and boundary displacement (Tobin et al. 2007; Elkinton et al. 2014). The effective range radius approach treats the invaded area as a circle and estimates the annual increases in the circle’s radius as a function of time using regression. The distance regression approach involves regressing the distance to each invaded location on time-to-invasion at each location whereas the boundary displacement method involves calculating mean annual changes in the boundary of the invaded area along radii emanating from the initial discovery location or another fixed point in space. The first two approaches typically estimate rates of spread without consideration of direction (i.e., treating spread as isotropic) and can exhibit different sensitivities to anisotropy and/or the frequency and distance of long-distance jumps, leading to variable estimates in both the mean and variance of spread. Conversely, the boundary displacement method enables estimates of anisotropy as part of the analytical steps, as spread rates along radii in different directions are averaged to provide a single estimate of mean annual spread. These methods, even when applied to the same invasion, however, can provide different estimates of spread (Tobin et al. 2007). Early in an invasion—when statistical evaluations of the role of invasibility and/or propagule pressure are challenging due to the paucity of data (e.g., only a small number of locations might be invaded in the first few years)—simple estimates of spread can be critical management tools for forecasting risk and provide a benchmark for assessing efficacy of management interventions (Sharov et al. 2002). However, assessing the potential spatial transferability of estimates requires an understanding of the factors that govern the rate of spread, which might change with the spatial patterning of habitat features (e.g., climate, topography) (Lantschner et al. 2014; Walter et al. 2015) and/or following a discrete jump into a novel habitat.

Variable spread rates in both space and time are commonly observed, with previous analyses implicating temperature (Lantschner et al. 2014; Bayles et al. 2017), host tree availability (Morin et al. 2009; Bayles et al. 2017; Hudgins et al. 2017; Ward et al. 2022), habitat heterogeneity (Rigot et al. 2014), geographic barriers (Walter et al. 2015), and wind (Lander et al. 2014; Hull-Sanders et al. 2017; Trotter et al. 2019) as drivers. A logical extension is that any factors that commonly govern dispersal, such as human activities (Gilbert et al. 2004; Liebhold and Tobin 2008), and that exhibit directional patterns could result in anisotropy (Verdasca et al. 2021). Minor levels of anisotropy—potentially arising from individual-level stochasticity in fecundity, survival, and/or reproduction—are likely inherent to invasions (Melbourne and Hastings 2009), and the magnitude and drivers of anisotropy could substantially alter forecasts that rely on historical invasion patterns. Here, we investigated the rates and drivers of anisotropy for laurel wilt, a vector-pathogen complex native to Asia that has become one of the most damaging non-native forest pests in the United States (US) (Hughes et al. 2017; Riggins et al. 2019; Fei et al. 2019; Olatinwo et al. 2021).

Laurel wilt, caused by the fungus Harringtonia lauricola (T.C. Harr., Fraedrich & Aghayeva) Z.W. de Beer & M. Procter (Ophiostomatales: Ophiostomataceae), is primarily vectored by the redbay ambrosia beetle, Xyleborus glabratus Eichhoff (Coleoptera: Curculionidae) (Kendra et al. 2013; De Beer et al. 2022) but has been laterally transferred to and subsequently isolated from other ambrosia beetle species (Carrillo et al. 2014; Ploetz et al. 2017). Spread first progressed into forests containing redbay (Persea borbonia (L.) Spreng.) and swampbay (Persea palustris (Raf.) Sarg.), with the first reported mortality from laurel wilt occurring on Hilton Head Island (South Carolina, US) in 2004 (Fraedrich et al. 2008). Approximately a decade later, detections increased in more northern/western counties that (1) harbor few to no redbay and (2) contain sassafras (Sassafras albidum (Nutt.) Nees) (Olatinwo et al. 2016, 2021; Loyd et al. 2020), which has a patchy distribution (Peters et al. 2020) and is less preferred by redbay ambrosia beetle compared with redbay (Kendra et al. 2014). Natural infestations have also been documented in other members of the Lauraceae (e.g., northern spicebush (Lindera benzoin L.)), which might have and could continue to influence invasion dynamics, particularly at northern latitudes. In addition to threatening natural forests containing members of the Laureaceae (Fraedrich et al. 2008; Harrington et al. 2008; Olatinwo et al. 2021), laurel wilt can colonize and kill avocado trees (Persea Americana) (Mayfield III et al. 2008; Kendra et al. 2013).

The distribution of laurel wilt in the US is non-contiguous, achieved through stratified dispersal in which diffusive spread and long-distance jumps operate in tandem (Liebhold and Tobin 2008). Investigations during the early stages of the invasion (2004–2006) indicated that spread away from the discovery location near Port Wentworth, GA (Fig. 1a) occurred at approximately 55 km/yr (Koch and Smith 2008) and approximated a semicircle due to the Atlantic coastline. Similar analyses considering an updated time series (2004–2021) indicated that spread slowed around ~ 2009, with rates ranging from 24 to 40 km/yr depending on phase of the invasion being evaluated. More recent efforts have statistically evaluated the habitat features governing spread and the resulting models were used to forecast future risk of invasion (Ward and Riggins 2023). However, these analyses are limited in that, while they elucidate potential drivers of invasion risk, they do not provide insights into the role of habitat features in governing variation in directional spread. Whereas geographical barriers such as the coastline have inhibited spread, it remains unknown if other habitat features have influenced directional spread of laurel wilt. Our study objectives were to (1) assess robustness of spread estimates by using two additional analytical methods and (2) investigate the presence, strength, and drivers of anisotropy.

Fig. 1.

County-level invasion by laurel wilt in the southeastern US (a) with bearing intervals overlaid (b). Bearing intervals depicted are emanating every 5° (gray) and 22.5° (black)

Methods

Spread data

The invaded range of laurel wilt across the southeastern US has been documented annually by many state, federal, and university forest health experts. The occurrence of the disease at the county-level was obtained for 2004–2021 in February 2022 from the Georgia Forestry Commission. For all analyses, a first discovery point was set at 32.1480° N, 81.1629° W near Port Wentworth, GA and spatial data were projected with the Albers equal-area conic projection (NAD 1983). Spatial and statistical analyses were conducted using R (R Core Team 2021). The following packages enabled data processing and analyses: geosphere (Hijmans 2019), ggpubr (Kassambara 2020), sd (Pebesma 2018), sp and spdep (Bivand et al. 2013), terra (Hijmans 2021), tidyverse (Wickham et al. 2019).

Spread rates and anisotropy

Estimates of the mean and variance of spread can be influenced by the strength of anisotropy as well as the frequency and length of long-distance jumps. Previous efforts have used the effective range radius method in which the radius of the invaded area (= summed county area multiplied by two to reflect the semicircular distribution of the laurel wilt invasion) is regressed on year; spread rates estimated with this method varied considerably depending on the time period being evaluated (Ward and Riggins 2023). We built upon these analyses by employing two additional methods commonly used to quantify invasion speed (Table 1). For the distance regression approach, distances between the centroids of each invaded county from the first discovery point were regressed on year of invasion; the resulting slope coefficient provides an estimate of annual spread (km/yr).

Table 1.

Summary of analytical techniques used to estimate spread rate

Short descriptor	Methodical steps	Estimate	Further details and examples
Effective range radiusa	Invaded area is treated as a circle, $A=\pi r^2$, which is rearranged as $r=\sqrt{A/\pi }.$ $r$ of cumulative invaded area through time is then regressed on year, t. The slope coefficient, ${\beta }_1,$ is an estimate of annual spread rate	$r={\beta }_0+{\beta }_{1}t$	Shigesada et al. (1995)
Distance regression	Distance, d, from each invaded location to initial detection location (or a fixed point in space) is regressed on year of invasion, t. The slope coefficient, ${\beta }_1,$ is an estimate of annual spread rate	$d={\beta }_0+{\beta }_{1}t$	Tobin et al. (2007), Liebhold and Tobin (2008)
Annual boundary displacement	Radii emanating from the initial discovery location (or a fixed point in space) are generated that intersect the invaded range boundary in each year. The length of boundary displacement (d) along each radius j from year i to i + 1 is then calculated. Lastly, mean distance spread in year i, si, is calculated by averaging displacement distances ($d_{\mathit{ij}})$.b	$s_i=\frac{{\sum }_j^{n_i}{d}_{\mathit{ij}}}{n_i}$	Tobin et al. (2007), Elkinton et al. (2014)
Boundary displacement	Equivalent to annual boundary displacement, but mean spread is estimated by averaging displacement distances ($d_i$) across all radii and years	$S=\frac{{\sum }_j^n{d}_j}{n}$	Tobin et al. (2007), Elkinton et al. (2014)

^aInvaded area can also be treated as semicircular, in which case A is multiplied by two

^bRadii can be excluded from estimates, for example, due to intersection with geographic barriers

We used the boundary displacement method to estimate mean annual spread rates as well as quantify anisotropy. First, we obtained spread rates within bearing intervals emanating 1500 km every 5° from the initial discovery location (Fig. 1b). Spread rates in each bearing interval were calculated by obtaining the distance from the initial discovery point to the centroid of the farthest invaded county (= range boundary) each year and estimating the mean displacement between range boundaries in successive years. County membership in a bearing interval was determined using county centroids, as several counties occurred in more than one bearing interval, particularly near the discovery location (Fig. 1). We also did not assign counties to bearing intervals using borders (1) because the entirety of each county is rarely if ever invaded and (2) to avoid using the same county multiple times when generating interval-specific estimates. If the furthest county in a bearing interval was invaded in year i—which only occurred when the range reached coastal geographic boundaries—then spread in such bearing intervals was evaluated from 2004 through year i to prevent inclusion of several years of 0 km of spread. Annual displacement distances were averaged across years and bearing intervals to produce a single estimate of mean annual spread; bearing intervals mostly overlapping the ocean (45–157.5°) were removed from this calculation. A summary of each of the three spread methods used to quantify invasion speed by laurel wilt is provided in Table 1.

We then estimated spread using three methods in each of 11 bearing intervals emanating every 22.5°, as five intervals were removed due to substantial overlap with the ocean (Fig. 1). For the effective range radius approach, the invaded area was multiplied by 16 to reflect spread in a circle, which did not affect relative (i.e., among bearing interval) differences in spread rates estimated with the effective range radius method but enabled comparisons with the other two analytical approaches. For all methods, the invasion time series for each bearing interval was truncated on an interval-by-interval basis such that the time period of spread analyzed was 2004 to year i, in which year i was the most recently invaded county per bearing interval. This step prevented inclusion of years in which spread was 0 km strictly owing to geographic constraints.

We also estimated and graphed mean displacement distances per bearing interval to visualize anisotropy (i.e., averaging across years per bearing interval). Lastly, the farthest distances spread along each bearing interval were categorized by year and graphed, enabling visualization of any changes in anisotropy through time. All estimates of spread are provided as mean ± SE unless stated otherwise. We did not account for county area in our analyses. County size did not vary meaningfully by year of invasion, but (1) county size increased with distance from the discovery location (owing to larger, western counties) and (2) bearing intervals emanating north and west had several larger counties (Online Resource 1). However, no counties in the western US were invaded and, irrespective of the analytical method, spread was slowest moving northwest; larger counties can artifactually increase estimates of spread when using the effective range radius method, but the opposite pattern was observed (see Results). Thus, we do not believe county size influenced findings.

Drivers of anisotropy: bivariate regressions

We then quantified drivers of anisotropy by using bivariate regression models. For this analysis, we divided the invaded range into 22.5° bearing intervals (i.e., 16 total intervals; Fig. 1b) following the approach of Morin et al. (2009). We chose this coarser bearing resolution (22.5°) because, even though higher resolution bearing intervals (5°; described above) provide insights into directional spread, such estimates involve fewer counties per bearing interval and thus could potentially provide more statistical leverage to outliers (e.g., exceptionally fast spread in one bearing interval) or long-distance jumps in the analyses described in this section.

We evaluated the explanatory power of the following seven variables that have been associated with invasion risk by laurel wilt (Ward and Riggins 2023) and potentially exhibit directional variation from the point of introduction (e.g., coastal clustering of cities and latitudinal patterns in climate and host tree abundance): (1) human population per county in 2019 (US Census Bureau 2022), (2) biomass (kg) of redbay per county (Bechtold and Patterson 2005; Guo et al. 2019), (3) biomass of sassafras per county, (4) summed host biomass (redbay + sassafras), (5) mean minimum temperature of the coldest month (1 km raster cells were averaged to the county level) (Fick and Hijmans 2017), (6) mean annual precipitation (obtained and processed equivalent to temperature data), and (7) length of long-distance jumps (= detections in counties without invaded neighbors at the time of detection). Host biomass data were obtained from the USDA Forest Inventory and Analysis program (Bechtold and Patterson 2005; Guo et al. 2019), in which redbay and swampbay (P. palustris (Raf.) Sarg.) are considered one species (Shearman et al. 2021).

We calculated the mean of each predictor (population density and host biomass were ln-transformed prior to calculating means) using counties (county membership in a bearing interval was again determined using county centroids) in each interval and then regressed spread (km/yr; described in Spread rates and anisotropy) in each interval on each predictor using individual models (21 models total). That is, each model was built using 11 data points and each method of spread had seven associated models (one for each predictor). We fit each model individually owing to the low power of this approach (11 observations per model) and potential collinearity of variables such as the biomass of hosts and climatic variables. The use of larger bearing intervals (22.5° vs. 5°) also enabled more robust estimates of habitat variables per interval, given that larger bearing intervals contained more counties (or data points). Only counties within 1500 km of the discovery location were used in this analysis because we aimed to quantify effects of habitat owing to space rather than time (i.e., distant counties are assumed not invaded because they are far away). We used a Bonferroni corrected type I error rate of α = 0.0023 (= 0.05/21), given that we developed 21 models in this step (Cabin and Mitchell 2000).

Drivers of anisotropy: Cox proportional hazards model

We extended a time-varying Cox proportional hazards (CPH) model that quantified drivers of time-to-invasion by laurel wilt (Ward and Riggins 2023). A detailed description is available in Ward and Riggins (2023). Briefly, we developed county-level models at three different spatial extents (counties with hosts, invaded area + 500 km buffer, and the entire contiguous US) evaluating the role of the following variables (if not cited, data sources are as cited previously): spatial contagion (= summation of inverse distances to previously invaded counties; the only time-varying predictor) human population size in 2019, number of campgrounds (Hillegass 2021), median county income (US Department of Commerce 2021), a composite metric of redbay + sassafras biomass, non-host biomass (Bechtold and Patterson 2005; Guo et al. 2019), mean minimum temperature, and mean annual precipitation. Findings were highly consistent at the two larger spatial extents: invasion risk increased with human activities, campgrounds, host abundance, temperature, and precipitation (Ward and Riggins 2023).

Here we conducted additional analyses at the largest spatial extent (i.e., all counties in the contiguous US) by (1) splitting the host abundance predictor into redbay biomass and sassafras biomass rather than a single composite estimate because of the different spatial structure of these two hosts (these host trees have overlapping distributions, but the range of sassafras extends farther north) and (2) adding a predictor indicating county membership in one of the 11 bearing intervals described previously. Two invaded counties in one of the five excluded coastal intervals were added to the nearest land-based bearing interval. Equivalent to Ward and Riggins (2023), we fit a full model, identified the model with the lowest AIC, and then averaged coefficients for models within two AIC values of the model with the lowest AIC. Model-averaging was completed using the MuMIn package (Bartoń 2022). Including bearing intervals in the CPH model tested for a bearing-structured spatial pattern that remained after accounting for the variables included in the original CPH model. Variables found to be significant even after accounting for bearing intervals would mean that their spatial signal follows a more complex structure than radial bearings.

Results

Spread rates and anisotropy

In previous analyses of county-level spread rates, estimates from the effective range radius ranged from 55 km/yr when evaluating the first few years (2004–2006) (Koch and Smith 2008) to 28 km/yr when evaluating the entire time series (2004–2021) (Ward and Riggins 2023). In contrast, analyses using the distance regression method and the boundary displacement indicated spread progressed at 40 ± 3 km/yr (Fig. 2a) and 39 ± 7 km/yr (Fig. 2b), respectively.

Fig. 2.

Spread rates of laurel wilt from 2004 to 2021 across the southeastern US using two methods: a distance regression (model statistics: F_1,273 = 137.70, p < 0.0001), and c boundary displacement. In panel a spread is estimated by the slope coefficient of the regression line, whereas panel b provides an estimate of the mean distance spread along all bearing intervals per year. In the latter approach, mean annual spread rate is estimated by averaging across all bearings (some bearings are excluded due to overlap with the Atlantic ocean; see main text) and years. A description of these methods is provided in Table 1

When using the boundary displacement approach, rates of spread varied substantially across bearing intervals (Fig. 3a). Eastern spread was impossible in some intervals, given the introduction occurred along the Atlantic coast. Excluding coastal bearing intervals, the slowest spread was 0 km/yr north, as some bearing intervals (1) did not contain county centroids near the first discovery location and (2) did not have any invaded counties farther away (i.e., some bearing intervals with zero spread still contained portions of invaded counties). The quickest invasion speeds were ~ 100 km/yr and ~ 80 km/yr occurring along bearings of 160° (south into Florida) and 255° (west into Texas), respectively (Fig. 3a).

Fig. 3.

Spread rates (km/yr) for laurel wilt in the southeastern US along bearing intervals emanating every a 5° or b–d 22.5°from the initial discovery location using three methods: a boundary displacement (5° intervals), b effective range radius, c distance regression, and boundary displacement (22.5° intervals) (Table 1 describes each method). Numbers within circles indicate rates of spread. See Fig. 1b for a mapped depiction of bearing intervals and note that spread between 45° and 157.5° is impossible due to the Atlantic coastline

Invasion speed varied markedly among the 22.5° bearing intervals irrespective of the analytical method employed (Fig. 3b–d). Similar to the comparisons of mean annual spread, interval-specific spread varied among the three different approaches such that spread ranged 6–51 km/yr (Fig. 3b), 14–60 km/yr (Fig. 3c), and 12–79 km/yr (Fig. 3d) when using the effective range radius method, distance regression method, and boundary displacement method, respectively. Conclusions arising from the boundary displacement approach were generally consistent between analyses using 5° (Fig. 3a) versus 22.5° bearing intervals (Fig. 3d), although rapid spread along some bearing intervals was only detectable when using the higher resolution (5°). For example, the quickest spread was estimated at 100 km/yr south when using 5° bearing intervals compared with 80 km/yr southwest when using the 22.5° bearing intervals. When using the effective range radius and boundary displacement methods, spread progressed most rapidly southwest whereas the distance regression method indicated that western spread was quickest (Fig. 3).

There also appeared to be changes in rates of anisotropy through time, given that boundary displacement along bearings extending northwest (285° to 330°) appeared to have recently occurred following a jump into sassafras-containing areas of Kentucky; spread along bearings extending south mostly occurred in the first ten years of the invasion before recently slowing (Fig. 4). Indeed, rapid spread to the south and southwest eventually became inhibited by the Gulf Coast. Despite the recent spread northwards, the known invaded range currently extends farthest to the west into areas of Louisiana and Texas (Fig. 4), near the western edge of the natural range of redbay.

Fig. 4.

Absolute distances (km) spread by laurel wilt in bearing intervals emanating every 5° from the first discovery location in the southeastern US. Inset map of the southeastern US provides insight into cardinal directions of bearing intervals

Drivers of anisotropy: bivariate regressions

When analyzing spread in a given bearing interval, the lowest test statistic (largest p-value) for a slope coefficient (i.e., spread rate estimate) in the effective range radius method was t = 5.91 (p = 0.0004) and for the distance regression method was t = 2.99 (p = 0.0060). We caution that models in some bearing intervals could have missed nonlinear changes in spread, however. Adjusted R² values ranged from 0.78–0.98 (median = 0.86) and 0.11–0.92 (median = 0.61) for the effective range radius method and distance regression method, respectively. The effective range radius method was the only approach that indicated that anisotropic patterns were driven by habitat features, unveiling positive and statistically clear correlations of spread with the abundance of redbay (Fig. 5a), temperature (Fig. 5b), and precipitation (Fig. 5c). We caution that when using a Bonferroni corrected type I error rate of α = 0.0023, the association of spread with precipitation (p = 0.0026) was marginally significant. There was a statistically clear and negative association of spread with the abundance of sassafras (slope ± SE: − 2.4 ± 0.8; t₉ = − 2.91, p = 0.0172), but we mostly attribute that finding to cold temperatures limiting northern spread because the abundance of sassafras, a more northern tree species, was strongly, negatively correlated with temperature across our bearing intervals (r = − 0.88). We cannot rule out, however, that that negative relationship was in part strengthened by a potentially lower invasibility of ecosystems continaing sassafras vs. redbay. Nonetheless, the CPH model (see next section) predicting time-to-invasion indicated that invasion risk had a statistically clear, positive association with sassafras abundance (Fig. 6). That is, after adjusting for the effect of other variables such as temperature and spatial contagion, counties with greater values of sassafras biomass became invaded more quickly.

Fig. 5.

Relationship of spread rate with a redbay biomass, b mean minimum temperature, and c mean total precipitation in different bearing intervals (each point corresponds to a 22.5° bearing interval as depicted in Fig. 1). Spread in bearing intervals represented on this figure were estimated using the effective range radius method (Fig. 3b). Statistics for slope coefficients in each model: a t₉ = 2.90, p = 0.0177 b t₉ = 7.18, p < 0.0001 c t₉ = 4.11, p < 0.0026. When using a Bonferroni corrected type I error rate of α = 0.0023 (see main text), the fit in panel c was marginally significant

Fig. 6.

a Slope coefficients for predictors in a time-varying Cox proportional hazards model estimating county-level invasion risk by laurel wilt across the contiguous United States. The model in panel b includes a categorical predictor for bearing interval and slope coefficients associated with bearings indicate comparisons to the baseline hazard for which bearing interval is one (i.e., the first interval). See Fig. 1 for bearing interval locations/directions

Drivers of anisotropy: Cox proportional hazards model

Analyses using CPH models indicated that, regardless of the inclusion of bearing intervals as a predictor or whether interpreting the best fitting model or model averaged coefficients, that proximity to previously invaded counties (Contagion), the number of campgrounds, biomass of redbay, and biomass of sassafras all increased invasion risk (Fig. 6). In the model that did not include bearing intervals as a predictor, three variables did not appear in the best fitting model (income, nonhost biomass, and precipitation) and one variable, human population, was marginally significant in the best fitting model (Fig. 6a). Otherwise, conclusions were consistent between the model with the lowest AIC and model averaged coefficients. When bearing intervals were included as a predictor, minimum temperature dropped from the model, but income entered. Estimates for the slope coefficients are provided as comparisons to the baseline hazard (that of the 0–22.5° bearing interval), and findings in our statistical model—which adjusts for the effects of other predictors in the model—generally reflected graphical patterns (Fig. 3): spread was quickest into counties located south and southwest of the initial discovery location.

Discussion

Arrival in an area with suitable climates or microclimates is a requirement for establishment and spread, and species arriving on the edge of their climatic niche might be more likely to exhibit spatiotemporal variation in spread early in their invasion as their range expands into habitats that maximize dispersal. Climate is a major determinant of the range dynamics of invading species (Renault et al. 2018) and, if an invading species establishes on the edge of their climatic niche, then spread will necessarily proceed into the suitable habitat. Laurel wilt established in the southeastern US such that generally warmer areas with more redbay trees were located to the south and west of the initial discovery location (Koch and Smith 2008; Formby et al. 2018); the ensuing invasion progressed most rapidly into those more suitable regions (Figs. 3 and 4). Indeed, when bearing interval was added as a predictor into a regression model, temperature was no longer associated with invasion risk, indicating potential redundancy in the explanatory power of these two predictors and that, along with being associated with the highest R² values in bivariate models (Fig. 5), temperature was the primary driver of directional spread (Fig. 6). Sassafras is patchily distributed (Peters et al. 2020) and less preferred by redbay ambrosia beetle compared with redbay (Kendra et al. 2014)—factors for which we could not account when analyzing county-level data—could have also inhibited northward spread.

Depending on the analytical approach, mean rates of annual spread ranged from 28 (Ward and Riggins 2023) to 39–40 km/yr (Fig. 2) but rates of directional spread ranged from 0 to 103 km/yr when analyzed along 5° bearing intervals (Fig. 3a). This corresponded to estimates of mean annual spread that were slower by ~ 15–27 km/yr (Fig. 2) compared to the rate (55 km/yr) estimated when evaluating the first three years of county-level invasion data (Koch and Smith 2008). The finding that spread rates are slower when incorporating the more recent data (2006–2021) and regardless of analytical method (Fig. 2; Ward and Riggins (2023)), could indicate that the most susceptible counties have become invaded. That is, counties with lower host biomass values compared to historically invaded countries and/or with cooler temperatures might be less invasible. Slowing spread could also be an artefact driven by a surge in post-detection survey efforts that lead to the discovery of counties that had been invaded for a few years and/or success in outreach and extension efforts that served to reduce long-distance spread of laurel wilt. Disruptions from the COVID-19 pandemic to travel (e.g., reduced rates of firewood movement) and/or surveys could have slowed spread or inhibited the documentation of it, respectively; the latter mechanism could have resulted in inaccurately low estimates of invasion speed. If spread rates are indeed slowing at the county-level and continue to do so, then it might improve the likelihood that management innovations (e.g., resistant hosts) that further reduce spread and associated tree death become available and operationalized (Hughes and Smith 2014; Showalter et al. 2018).

Spread rates for a single species—especially when estimated with different methods –can change with the resolution of the data analyzed (Tobin et al. 2007). Our analyses considered the finest spatial resolution available (i.e., county-level occurrences) for analyzing spread. Subcounty-level occurrence and/or impact data are available (or can be inferred) in some circumstances, but these data are often not resolved at a spatiotemporal scale suitable for analyzing spread (e.g., year of plot-level arrival can be difficult to infer when sites are visited systematically every 5 years, such as in the USDA FIA program). Thus, county-level patterns represent a coarse spatial resolution and different patterns and rates of spread likely exist at smaller spatial scales within counties. Indeed, estimated spread rates had a smaller range of 12–70 km/yr (Fig. 3d) when using artificially higher resolution data (22.5° bearing intervals) owing to long-distance jumps being averaged with the more common, shorter spread distances. Nonetheless, spread rates of laurel wilt in the US have been similar to other invading ambrosia beetles, as spread of Xylosandrus germanus Blandford was estimated at 40–80 km/yr in Europe (Henin and Versteirt 2004; Galko et al. 2019).

Temperature explained the most variation in anisotropic spread of laurel wilt in bivariate regressions (Fig. 5) but, in the best fitting CPH model with bearings included as a predictor, biomass of redbay and sassafras—not temperature—explained variation in invasion risk (Fig. 6). We attribute this apparent contradiction—explanatory power of temperature in one modeling framework that is absent from another—to the stronger directional pattern of temperature compared with host distributions; the strong spatial structure of temperature is more statistically redundant with bearing direction than is host biomass. We also caution that evidence supporting the role of temperature in anisotropy was only found when the data were analyzed using the effective range radius method. It does not appear that mortality from cold temperatures will prevent establishment at higher latitudes beyond the current known rage, however, because the fungus can survive several weeks of storage in a freezer (JJ Riggins, personal observation) and forecasts based on insect cold tolerance indicated that latitudes beyond northern Kentucky are suitable for persistence (Formby et al. 2018). Winter-associated mortality is one component of the multifaceted effects of temperature. Fewer generations of redbay ambrosia beetle are expected at northern latitudes compared with warmer, more southern latitudes (Hanula et al. 2008), which could result in decreased invasion speed in northern areas. For example, univoltine populations would have one period of natural (i.e., adult-driven) dispersal per year compared with multivoltine populations that have opportunities for iterative dispersal achieved by multiple generations in a single growing season (Fahrner and Aukema 2018).

Within our analysis that focused on bivariate regression models, the method used to calculate spread within each bearing interval influenced conclusions on drivers of anisotropy. Each method captures—or ignores—anisotropy differently: for the effective range radius and distance regression methods, we needed to take the additional step of re-estimating spread rates in each bearing interval (compared to generating a single estimate of mean spread that ignores directional patterns) whereas the boundary displacement method necessitates this step—estimating spread in each bearing interval—when calculating the mean spread rate (Table 1). Using the effective range radius method to estimate spread within an interval, however, was the only approach that led to a statistically clear link between invasion speed and habitat features. This does not necessarily indicate that this method outperformed the others when describing the strength of anisotropy, but compared with the other methods, the effective range radius likely provides the most accurate depiction of total area invaded. That is, the distance regression method relies on distances to invaded points and not area invaded, meaning it can be influenced by long-distance jumps that can serve as leverage points in regressions. Additionally, in the boundary displacement method, a single jump to the edge of a bearing interval would effectively render that interval as entirely invaded despite the potential persistence of several uninvaded counties between the initial discovery location and that satellite infestation. The effective range radius method includes every invaded county in its calculation, captures how quickly counties in each bearing interval become invaded, and is less sensitive to long-distance jumps (Shigesada et al. 1995). Our results thus indicate that the total area invaded in each direction, rather than farthest absolute distance moved, was facilitated by the abundance of redbay and warmer temperatures.

In addition to varying by direction, rates of directional spread varied through time. That is, spread accelerated or deaccelerated in different year × direction combinations (Fig. 4), potentially reflecting the exhaustion of the most suitable habitat in certain directions (Shigesada et al. 1995; Shigesada and Kawasaki 1997), changes in propagule pressure and/or Allee affects through time (Walter et al. 2020), and/or limiting influences imposed by geographic barriers or features (Walter et al. 2015, 2016). Whereas host tree abundance and climate explained some of the variation in directional spread, the Atlantic and Gulf Coasts were major contributors: spread east was generally infeasible owing to the initial establishment of laurel wilt in coastal areas of Georgia and spread south and southwest along certain bearings was inhibited by the Gulf Coast. Our analyses of annual spread rates per bearing interval did account for these geographic barriers (i.e., the time series analyzed per interval were truncated based on when the farthest available county became invaded), but such barriers necessarily influenced our estimates of total distance spread by bearing interval (Fig. 4).

Spatial or temporal variation in Allee effects did not seem a likely explanation for anisotropy, to the contrary both redbay ambrosia beetle and the fungal pathogen appear to have low Allee thresholds: a single clonal beetle (or small group of clones) established the US population (Hughes et al. 2017) and as few as 100 conidiospores can kill some host tree species (Hughes et al. 2015). Irrespective of the exact underlying mechanism(s), however, quicker invasion of counties located south and west of the discovery location reported here generally reflected initial forecasts (Koch and Smith 2008), highlighting the utility of habitat suitability modeling for anticipating anisotropy and, thus, spatial variation in invader impacts. Unfortunately, irrespective of spread forecasts and their accuracy, it remains exceedingly difficult to manage laurel wilt with slow the spread or local eradication tactics owing to challenges with movement of the pathogen/beetle inside firewood, difficulties with rapid detection, and the low Allee thresholds and rapid growth of both the fungus and redbay ambrosia beetle populations.

Knowledge of invasion speed is useful for managing invasions, and this work corroborates previous findings that estimates can differ substantially by the analytical framework (Figs. 2 and 3), direction, and/or location. Our work suggests that using environmental niche modeling—frequently pursued to identify areas of potential future occurrence for new invaders—could also help identify areas or regions where spread might be most rapid. Similarly, determining the context in which a method (e.g., statistical vs. mathematical or effective range radius vs. distance regression vs. boundary displacement) provides the most accurate forecasts of spread could also bolster management: ecological information regarding new invaders is often limited and thus sanitation or eradication efforts often necessarily rely on simple estimates of spread or patterns exhibited by ecologically or phylogenetically similar species rather than forecasts from a statistically based model. Indeed, as time since establishment increases, capturing how discrete jumps mediate invasion risk in the modeling framework can improve accuracy, as spread rate estimates alone might ignore important spatial patterning in the invader’s distribution and/or habitat features. Nonetheless, previous forecasts (Koch and Smith 2008; Ward and Riggins 2023) and these current efforts suggest that future risks of invasion and invasion speed by laurel wilt will likely be lower compared with historical patterns. Most of the remaining, uninvaded habitat is located in colder regions with hosts (e.g., sassafras, northern spicebush) that are more patchily distributed than redbay.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

SW conceived study, conducted analyses, and wrote initial draft of the manuscript. JR provided substantial input on analyses and contributed to interpretation, contextualization, and writing and editing subsequent drafts of the manuscript.

Funding

This research was supported by USDA APHIS PPA 7721 APP-16912. This publication is a contribution of the Mississippi Agricultural and Forestry Experiment Station and based upon work supported by the National Institute of Food and Agriculture, U.S. Department of Agriculture, Hatch projects under accession numbers 1025843 and 1018710.

Data availability

All code and data supporting results are provided on Zenodo (10.5281/zenodo.7549369). Code is also available at GitHub (https://github.com/sfward/laurel_wilt_spread).

Declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.