Comparative performance of viral landscape phylogeography approaches

Significance

Thanks to their rapid evolution, viral genomes can be analyzed and compared to estimate the dispersal history of the virus responsible for an epidemic, a task known as phylogeographic inference. In our study, we develop and evaluate the performance of novel analytical approaches that exploit phylogeographic reconstructions to understand which environmental factors impact the diffusion velocity of a virus. Our analyses identify three complementary approaches with sufficient statistical performance, enabling us to formulate a blueprint for the future application of the open-source methods we developed. These methods can be applied broadly by epidemiologists to better understand the determinants of viral spatial spread.

Abstract

The rapid evolution of RNA viruses implies that their evolutionary and ecological processes occur on the same time scale. Genome sequences of these pathogens therefore can contain information about the processes that govern their transmission and dispersal. Landscape phylogeographic approaches use phylogeographic reconstructions to investigate the impact of environmental factors and variables on the spatial spread of viruses. Here, we extend and improve existing approaches and develop three novel landscape phylogeographic methods that can test the impact of continuous environmental factors on the diffusion velocity of viral lineages. In order to evaluate the different methods, we also implemented two simulation frameworks to test and compare their statistical performance. The results enable us to formulate clear guidelines for the use of three complementary landscape phylogeographic approaches that have sufficient statistical power and low rates of false positives. Our open-source methods are available to the cientific community and can be used to investigate the drivers of viral spread, with potential benefits for understanding virus epidemiology and designing tailored intervention strategies.

Understanding how environmental factors impact the dispersal of individuals is a fundamental biological question with applications in a wide range of fields, including ecology, conservation, and epidemiology. In situations where direct observation and/or movement-tracking of individuals is not feasible, analysis of the genomic variation among sampled individuals can be used to understand how environmental factors affect their dispersal, an approach which we term “landscape genetics”. First coined over 20 y ago (1), landscape genetics is the study of how landscape attributes impact the gene flow and resulting genetic variability (genetic diversity and structure) of a spatially distributed organism (2), without requiring individuals to be assigned to discrete subpopulations. One popular population genetic approach involves analyzing the association between a matrix of interindividual genetic distances and matrices representing one or more covariates, such as environmental distances between the individuals’ sampling locations (3, 4). Environmental distances can be defined as spatial distances that are weighted according to the environmental values along a path connecting two point locations; models used to define this path include the least-cost path model (5) or models based on graph and circuit theories (3). In the context of landscape genetic analyses, these path models allow us to evaluate whether environmental layers — tested as either potential conductance or resistance factors — can explain certain patterns of interindividual genetic differentiation.

Landscape genetic analyses applied to animal and plant organisms are distinct from phylogeographic analyses that aim to study the spatial distribution and dispersal history of intraspecific (or closely related interspecific) lineages (6, 7). Notably, when studying animal and plant species, there can be multiple generations between the occurrence of a perturbation or environmental impact and the time at which it will be detectable in the genetic variability of the studied population (8). This issue, known as the “time lag” problem, has been cited as a limitation in the field of landscape genetics (6, 8). More generally, for such organisms, landscape genetic and phylogeographic analyses differ in both temporal and spatial scales (6). For fast-evolving organisms, however, this limitation does not necessarily apply. This is particularly true for numerous pathogens, such as RNA viruses, that are characterized by rapid evolution (9), implying that evolutionary, ecological, and epidemiological processes occur on similar time scales (10, 11). By statistically analyzing the genetic differences among viruses sampled from a population, we can gain insights into the underlying processes governing their dispersal. In particular, the development of discrete (12) and continuous (13, 14) phylogeographic inference methods, as well as structured coalescent models (15, 16), have enabled the reconstruction of the dispersal history of target epidemics, and can be exploited to investigate the impact of external factors on the dispersal history and dynamics of viral lineages. This is precisely the goal of a recent field of research coined “landscape phylogeography”, which aims to explain the dynamics of phylogenetically informed-movements through external factors (17). Landscape phylogeographic approaches are thus conceptually distinct from landscape genetics approaches, which primarily test associations between pairwise genetic and environmental distances. Furthermore, by directly analyzing the association between lineage dispersal events and environmental factors, landscape phylogeographic approaches can circumvent the time lag issue explained above.

Over the last 10 y, several methods have been developed to conduct landscape phylogeographic analyses. One such method is the implementation of a generalized linear model (GLM) extension (18) of the discrete diffusion model (12) in the BEAST X software package (19). This model jointly performs a discrete phylogeographic reconstruction and an analysis of covariates that might be associated with the inferred transition rates between sampled locations (18). With a subsequent implementation in a structured coalescent model (20), the GLM approach has been applied in a number of studies that aimed to unravel the drivers of important viral epidemics, such as the Ebola virus outbreak of 2013–2016 in West Africa (21) and the international circulation of SARS-CoV-2 in Europe (22). Furthermore, several post hoc analytical procedures have been developed to exploit the outcome of continuous phylogeographic reconstructions in order to investigate the impact of environmental factors on the dispersal location (23, 24), direction (23, 25), frequency (26, 27), and velocity (28, 29) of viral lineages.

As with most landscape genetic approaches, landscape phylogeographic analyses based on continuous phylogeographic inference (13, 14) do not require prior, arbitrary delimitation of discrete locations. This contrasts with discrete phylogeographic approaches that generally assume that all ancestors of the sampled viruses existed only at a prespecified set of locations (17). In order to take advantage of continuous locations, a first analytical framework has been developed to assess the impact of environmental factors on the heterogeneity of the dispersal velocity of viral lineages (28, 30). In summary (see below for further detail), this framework tests the correlation between inferred branch durations and their associated environmental distances (i.e., the environmental distance between branch start and end locations), which are inferred through a continuous phylogeographic analysis. While this post hoc approach can formally investigate the potential impact of environmental factors on the dispersal rate of viral lineages, it comes with potential limitations inherent to the relaxed random walk (RRW) model used to perform continuous phylogeographic inference. First, although the RRW model relaxes the assumption of a constant dispersal velocity in Brownian diffusion, it remains unknown how well this model can capture the impact of environmental factors, i.e., whether it is flexible enough to accommodate any diffusion heterogeneity imposed by environmental variables. Second, the RRW model remains restricted to dispersal processes that correlate with geographic distance, which may not always be the case, e.g., for human viruses such as influenza, whose global-scale dispersal is better predicted by international air travel than geographic distances (18, 31).

The objective of the current study is fourfold. First, we aim to improve the previously introduced post hoc landscape phylogeographic approach by extending it to investigate the impact of environmental factors on lineage diffusion velocity. This is motivated by the fact that lineage diffusion velocity metrics are more robust to sampling intensity than lineage dispersal velocity metrics (32, 33). Second, we aim to develop a complementary post hoc landscape phylogeographic approach based on isolation-by-resistance (IBR) analyses, which can be used to test to what extent an environmental factor is associated with a deviation from an isolation-by-distance (IBD) pattern. Third, we aim to overcome the two potential limitations of the post hoc landscape phylogeographic approach outlined above by implementing alternative prior-informed landscape phylogeographic procedures that integrate environmental heterogeneity before continuous phylogeographic inference is conducted. Finally, we aim to implement and apply phylogeographic simulations to evaluate the statistical performance of landscape phylogeographic approaches testing the impact of environmental factors on the diffusion velocity of viral lineages, as well as the performance of an alternative approach for testing the impact of such factors on deviations from an IBD pattern. Our analyses reveal the strengths and weaknesses of the different landscape phylogeographic methodologies tested, enabling us to provide clear guidelines for researchers aiming to use these approaches to investigate the drivers of viral spread relevant to public health and One Health.

Results

Improvement of a Post Hoc Landscape Phylogeographic Approach.

The first post hoc landscape phylogeographic approach described and evaluated here has been adapted from the previously established analytical framework introduced above (28, 30). This framework is based on the analysis of lineage diffusion velocity and consists of a sequence of four analytical steps (28): i) the extraction of the spatiotemporal information embedded in a series of annotated trees sampled from the posterior distribution of trees inferred through Bayesian continuous phylogeographic inference using a RRW diffusion process to model among-branch heterogeneity in diffusion velocity (13, 14); ii) the computation of environmental distances associated with each phylogenetic branch using either the least-cost (5) or Circuitscape (3, 34) algorithm, the latter being based on circuit theory, which allows integrating over uncertainty in the path taken by dispersing lineages; iii) the estimation of the correlation between the branch durations and the environmental distances computed for each phylogenetic branch; and iv) a randomization procedure to assess the statistical support of the correlation metric. This correlation metric is the statistic Q₁; the subscript “1” distinguishes this value from the as a distinction to the three other Q statistics defined below. Q₁ is defined as the difference between R²_env and R²_null, where R²_env is the coefficient of determination of the linear regression between four times the branch durations t and the squared environmental distances D_env computed on the environmental raster (4t ~ D²_env), and R²_null the coefficient of determination of the linear regression between four times the branch durations and the environmental distances D_null computed on the “null” raster (4t ~ D²_null). The null raster has the same dimensions as the environmental raster, but all accessible cells (i.e., land areas) have a uniform value set to 1. Environmental distances computed from this null raster serve as a proxy for geographic distance, ensuring that the same path model — based on the least-cost or Circuitscape algorithm — is used for both environmental and geographic distances computations. As mentioned above, with these path models, an environmental raster can be tested as a potential conductance or resistance factor, i.e., increasing or decreasing the diffusion velocity of viral lineages.

The correlation statistic Q₁ therefore measures to what extent taking the environmental heterogeneity into account increases the correlation between phylogenetic branch durations and environmental distances, i.e., the degree to which lineage diffusion velocity can be explained by the investigated environmental layer. In the previous version of this analytical framework (28), Q₁ was defined as the difference between R²_env and R²_null where these coefficients of determination were obtained from a linear regression between branch durations and environmental distances (i.e., t ~ D). In the updated version, however, the regression is performed between 4t and D² (4t ~ D²), because the diffusion coefficient has been identified as a metric more robust to the sampling intensity (i.e., the sampling size) than the lineage dispersal velocity (32, 33). While the lineage-dispersal velocity measures the dispersal velocity associated with a phylogenetic branch (i.e., the ratio d_gc/t between the great-circle geographic distance d_gc traveled by a phylogenetic branch and its duration t), the diffusion coefficient can be considered as a measure of its diffusion velocity (d_gc²/4t). An environmental factor is considered to be potentially explanatory only if both the associated posterior distribution of regression coefficients β_env and Q₁ values are positive (29). In that case, the statistical support for the Q₁ statistic can be formalized as a Bayes factor (BF) estimated through a randomization procedure (28). This procedure involves the randomization of phylogenetic branches within the study area while preserving the tree topology, maintaining the inferred position of the most ancestral node, and preventing nodes from falling into nonaccessible (i.e., sea/water) areas (see Materials and Methods for further detail).

Development of a Complementary Post Hoc Landscape Phylogeographic Approach.

The second post hoc landscape phylogeographic approach introduced and investigated here consists of an IBR analysis. Similar to diffusion coefficient metrics, IBD signal metrics have been found to be more robust to sampling sizes and are complementary to diffusion coefficient metrics (32): while a diffusion coefficient measures the dispersal capacity of viral lineages, an IBD signal metric measures to what extent phylogenetic branches are spatially structured, i.e., the tendency of phylogenetically closely related tip nodes to be sampled from geographically close locations (32). The IBD signal can, for instance, be estimated using the Pearson correlation coefficient between the patristic and log-transformed great-circle geographic distances computed for each pair of tip nodes (32). Directly related to the notion of IBD signal, we propose assessing the IBR signal for a given environmental factor, i.e., the association between the phylogenetic (i.e., patristic) and log-transformed environmental distances between each pair of tip nodes. In other words, we assess how the investigated environmental factor could have impacted the IBD signal. The notion of IBR (3) is conceptually different from the notion of isolation-by-environment (IBE), which refers to a pattern where genetic differentiation increases with environmental differences (rather than distances) independently of geographical distance (35).

Similar to the analyses of lineage diffusion velocity, the IBR analyses were based on the estimation and the assessment of the statistical support of a correlation statistic Q. Here, this alternative Q statistic (Q₂) is defined as the difference between i) the coefficient of determination R²_env of the linear regression between the patristic distances and the log-transformed environmental distances computed on the environmental raster for each pair of tip nodes, and ii) the coefficient of determination R²_null of the linear regression between patristic distances and log-transformed environmental distances computed on the corresponding null raster (where environmental distances serve as a proxy for the geographic distance, i.e., an IBD setting). In the context of an IBR analysis, the Q₂ statistic thus measures to what extent a given environmental factor could potentially explain a deviation from the IBD pattern. As with Q₁, the statistical support of the Q₂ statistic is evaluated with the same randomization procedure of phylogenetic branch positions within the study area, which enables the estimation of BF support (see Materials and Methods for further detail).

Since it is not based on the analysis of phylogenetic branch positions inferred through a phylogeographic reconstruction, the IBR analysis is not necessarily a landscape phylogeographic approach. While a landscape phylogeographic approach aims to analyze the impact of environmental factors on lineage dispersal dynamics, the IBR analysis is conceptually closer to a landscape genetic approach that aims to uncover the environmental factors impacting interindividual genetic differentiation. However, because this analysis is based on pairwise patristic distances computed on (time-scaled) phylogenetic trees, we propose to characterize it as a landscape phylogenetic approach, i.e., an analytical approach to investigate the impact of environmental factors on phylogenetic distances or divergence times (in the context of time-scaled phylogenetic inference) between individuals. Further, we use the same randomization procedures as for the analyses on the lineage-diffusion velocity to assess the statistical support of the Q₂ statistic. Given that those procedures are based on the randomization of branch positions inferred on the map by a continuous phylogeographic inference, the IBR analysis implemented here still requires such a phylogeographic reconstruction, even if the outcome of the phylogeographic inference itself is not involved in the computation of the Q₂ statistic.

Development of Alternative Prior-Informed Landscape Phylogeographic Approaches.

We introduce two landscape phylogeographic approaches characterized as “prior-informed” because the analysis of the environmental factor is integrated before the continuous phylogeographic inference. Instead of assessing the association of environmental factors with phylogeographic estimates a posteriori, as in the post hoc landscape phylogeographic approaches described above, environmental distances are computed first between sampling locations and then used to transform the space. The rationale behind this approach is that diffusion over distances that accommodate an environmental factor impacting the diffusion velocity of lineages should be more regular (characterized by less diffusion rate heterogeneity), or more Brownian, than over geographic distances that ignore such a factor. Therefore, continuous phylogeographic analysis can be performed in a “transformed space” defined by these environmental distances and then we can compare branch diffusion velocity heterogeneity as estimated by this analysis and the one based on original sampling coordinates. Concretely, we explore two possibilities (Fig. 1): transforming the space i) according to a multidimensional scaling (MDS) analysis, also known as principal coordinates analysis (36), or ii) according to a cartogram transformation (37). The choice of these two different transformations was motivated by their complementarity; while MDS transformations are based on pairwise environmental distances between sampling locations, cartogram transformations are based on local environmental values informed by all the cells of the environmental grid covering the study area.

Fig. 1.

Illustration of a cartogram and MDS transformations based on an environmental layer tested as a potential resistance factor slowing the diffusion velocity of viral lineages. We first display an original elevation raster (A; here rescaled from 1 to 11) along with the sampling coordinates (black dots) of the raccoon rabies virus (RABV) dataset sampled in northeastern USA (38), followed by a cartogram transformation (B) of this raster. We then also display an MDS transformation of those coordinates based on environmental distances computed with the Circuitscape algorithm among all pairs of sampling points while treating the elevation raster as a resistance factor (C). In this third panel, sampling points are colored according to the altitude of their position prior to the transformation of the space. As shown in panel B, the cartogram transformation of this elevation raster — here also tested as a potential resistance factor — tends to increase the relative distance between sampling points located in higher altitude areas while decreasing the relative distance between sampling points located in lower altitude areas. As shown in panel C, a similar observation can be made when visually inspecting the relative distance among sampling points before and after the MDS transformation: sampling points in relatively low altitude areas tend to be closer to each other after the MDS transformation. The rationale behind these two prior-informed landscape phylogeographic approaches based on a transformation of the study space (with a cartogram transformation or with a MDS analysis) is to assess whether such a transformation would lead to a more Brownian diffusion process than in the untransformed study space, which would then indicate an association between the tested environmental factor and the diffusion velocity of viral lineages.

The MDS transformations are based on pairwise environmental distances computed among sampling coordinates. The sampling coordinates in the new two-dimensional MDS space (Fig. 1) are subsequently used in the continuous phylogeographic analysis. In the present study, we conduct MDS transformation based on environmental distances between sampling locations, computed using either the least-cost (5) or Circuitscape (3, 34) algorithm. As illustrated in Fig. 1, the principle of cartogram transformations is to transform the size of a series of joint polygons according to values assigned to these polygons. Analogous to the MDS transformation, a cartogram transformation increases the new Euclidean distances between sampling locations associated with relatively high environmental distances, and decreases the new Euclidean distances between sampling locations associated with relatively low environmental distances. We can then assess whether the diffusion process in the transformed space, i.e. defined by environmental distances (MDS transformation) or environmental values (cartogram transformation), indeed required less heterogeneity than a diffusion process in a regular geographic space. MDS transformations have previously been applied in the context of discrete (39) or continuous (40) phylogeographic analyses of viruses although, in the latter case, they have not been used to test the impact of continuous environmental layers on the diffusion velocity of viral spread.

For the analyses based on the MDS transformations, the heterogeneity of branch-diffusion velocities was again measured through the estimation of a Q statistic (Q₃) here defined as the difference between i) the coefficient of determination R²_env of the linear regression between four times the branch durations t and the squared Euclidean distances d_Eucl,env traveled by each phylogenetic branch in the space transformed according to environmental distances computed on the environmental raster (4t ~ d²_Eucl,env), and ii) the coefficient of determination R²_null of the linear regression between four times the branch durations t and the squared Euclidean distances d_Eucl,null traveled by each phylogenetic branch in the space transformed according to environmental distances computed on the corresponding null raster (4t ~ d²_Eucl,null). As for the analyses based on a cartogram transformation, the heterogeneity of branch-diffusion velocities was measured by calculating Q₄ defined as the difference between i) the coefficient of determination R²_env of the linear regression between four times the branch durations t and the squared Euclidean distances d_Eucl,env traveled by each phylogenetic branch in the space transformed according to a cartogram transformation, and ii) the coefficient of determination R²_null of the linear regression between four times the branch durations t and the squared great-circle geographic distances d_gc traveled by each phylogeny branch in the nontransformed space (4t ~ d²_gc), i.e., following a standard phylogeographic reconstruction based on the nontransformed sampling coordinates. As for the Q₁ and Q₂ statistics, the statistical support of Q₃ and Q₄ is again formalized as a BF, but this time by assessing the probability of getting a positive Q statistic (see Materials and Methods for further detail).

Simulation-Based Assessment of Statistical Performance.

To evaluate the statistical performance of the four landscape phylogeographic approaches compared in this study, we applied these different methods to datasets generated by continuous phylogeographic simulations involving or not the impact of an environmental factor on the lineage dispersal dynamics. To our knowledge, existing phylogeographic simulators do not directly allow simulation of the impact of an environmental layer on the diffusion velocity of simulated lineages. We therefore developed two complementary simulation procedures that can accommodate such an impact: i) a birth–death approach for simulations based on a RRW diffusion process, where the diffusion velocity is impacted by the environmental layer (hereafter referred to as “RRW simulations”), with simulation examples displayed in Fig. 2 resulting in spatially annotated time-calibrated phylogenies; and ii) genome-sequence simulations along an actual maximum clade credibility (MCC) tree, with branch lengths modified according to various scenarios (hereafter referred to as “MCC simulations” (see Materials and Methods for further detail). The implementation of these two simulation approaches was motivated by their complementarity: While the MCC simulations involved a deterministic impact of the environmental factor, the RRW simulations involved an intrinsic stochastic impact of the environmental layer on the diffusion velocity of evolving lineages. Furthermore, in MCC simulations, genomic sequences were simulated stochastically, allowing us to investigate the impact of the Bayesian phylogenetic inference. Finally, unlike the RRW simulations, the MCC simulations included a scenario with no impact of the environmental factor on the diffusion velocity of viral lineages, which allowed estimation of the type I error rate (false positives) of the four landscape phylogeographic approaches.

Fig. 2.

Example of continuous phylogeographic simulations based on a birth–death process and a RRW diffusion process during which an environmental layer impacts the diffusion velocity of viral lineages. The two first panels display the phylogenetic tree obtained from a first simulation: (A) the time-scaled visualization of the simulated topology and (B) the mapped visualization on the environmental layer impacting the movement velocity of evolving lineages — here an elevation raster rescaled from 1 to 11 (see Materials and Methods for further detail) and acting as a resistance factor (i.e., slowing down movement velocity in relatively higher altitude areas). The third panel (C) displays the mapped visualization of a second example of simulation. In all panels, tree nodes are colored according to time, with internal and tip nodes colored according to their age and collection time, respectively. The RRW simulation process illustrated here is inspired by the phylogeographic analysis of the RABV spread in North America (13, 30, 38) and has been used in the present study to assess the statistical performance of four landscape phylogeographic approaches aiming at testing the impact of environmental factors on the diffusion velocity of viral lineages.

For the RRW simulations, we implemented a diffusion process with simulation parameters (starting time and position, sampling time window) based on the study of rabies virus (RABV) spread in a North American raccoon population (38). The raccoon RABV dataset, published in 2007 by Biek and colleagues (38), consists of 47 sequences of ~2,800 nucleotides (covering the complete rabies nucleoprotein gene and a large portion of the glycoprotein gene). This dataset was used to infer the dispersal history of viral lineages through a continuous phylogeographic analysis (13, 30), which subsequently highlighted the potential impact of elevation on the velocity of this viral spread (28, 30, 38). We therefore used an elevation raster acting as a resistance factor during the RRW diffusion process. The dispersal velocity of evolving lineages was negatively associated with the underlying elevation values, meaning that the lineages tended to disperse slower in areas associated with relatively higher altitudes. We conducted 50 simulations with this first RRW simulation framework, which led to the generation of datasets with an average size of 140 samples (95% credible interval: [98 to 236]). As for the MCC simulations, we again considered the raccoon RABV dataset mentioned above (38) and the actual MCC tree obtained from the continuous phylogeographic inference based on that dataset (30). These MCC simulations consisted of two successive steps: i) modifying the branch lengths of the MCC tree according to three distinct scenarios (strong, moderate, and no impact of an underlying environmental factor on the diffusion velocity of lineages), and ii) simulating RABV genomic sequences along the resulting time-scaled phylogeny.

The evaluation of the statistical performance of the four landscape phylogeographic approaches is summarized in Fig. 3. It consists of four steps: i) continuous phylogeographic simulations following the RRW or MCC simulation framework introduced above, ii) MDS and cartogram transformation of the sampling coordinates for the prior-informed landscape phylogeographic analyses, iii) continuous phylogeographic reconstructions (either based on nontransformed sampling coordinates or those transformed at the previous step), and iv) the four landscape phylogeographic analyses.

Fig. 3.

Simulation and analytical workflow implemented to assess the statistical performance of four landscape phylogeographic approaches to test the impact of environmental factors on the diffusion velocity of viral lineages or on the deviation from an IBD pattern. We here assessed the performance of two post hoc (IBR and lineage diffusion velocity analyses) and two prior-informed landscape phylogeographic approaches (analyses of continuous phylogeographic reconstructions based on sampling coordinates obtained either after a MDS or cartogram transformation). Continuous phylogeographic simulations illustrated for step 1 either consisted in (1.1) birth–death simulations based on a RRW diffusion process with a velocity impacted by an underlying environmental layer (referred to in the text as RRW simulations) or (1.2) tree topologies obtained by modifying the branch lengths of an actual MCC tree according to three distinct scenarios (MCC simulations). In the subsequent analytical steps illustrated in the graphical workflow, the path taken by those RRW and MCC simulations can then be followed by the reddish and bluish arrows, respectively. For the MCC simulations, three distinct scenarios were considered: no impact of the environmental factor (scenario 1; light blue arrows), as well as a moderate (scenario 2; intermediate blue arrows) and strong (scenario 3; dark blue arrows) impact of the environmental layer on lineage diffusion velocity. In step 2, three distinct versions of each simulated dataset were obtained by transforming or not the tip node coordinates: as illustrated by the different arrow paths, tip node coordinates were left untransformed, transformed using an MDS transformation (2.1), and transformed according to a cartogram transformation (2.2). (*) MDS transformations were conducted based on environmental distances among pairs of tip nodes, which were computed using either the least-cost (5) or Circuitscape (3, 32) path model while either considering the environmental raster (here an elevation raster with values rescaled between 1 and 11) or a corresponding null raster with accessible raster cell values uniformly equal to 1 (see the text for further detail). In step 3, a continuous phylogeographic analysis was conducted for each resulting simulated dataset. In the case of the RRW simulations, these analyses were directly based on the tree topologies and associated tip node coordinates obtained after step 2. In the case of the MCC simulations however, the continuous phylogeographic analyses were based on genomic sequences simulated along the tree topologies. Finally, step 4 consisted of the different landscape phylogeographic analyses developed and evaluated in the present study: two post hoc (IBR and lineage diffusion velocity analyses; 4.1) and two prior-informed landscape phylogeographic approaches (analyses of continuous phylogeographic reconstructions based on sampling coordinates obtained either after a MDS or cartogram transformation; 4.2). As detailed in the text, each of those four landscape phylogeographic approaches is based on the estimation of a distinct Q statistic: Q₁ for the lineage diffusion analyses, Q₂ for the IBR analyses, as well as Q₃ and Q₄ for the prior-informed analyses based on an MDS or cartogram transformation, respectively. All four Q statistics are defined as the difference between two coefficients of determination, R²_env and R²_null. For Q₁, R²_env is the coefficient of determination obtained from the linear regression between four times the branch durations t and the squared environmental distances D_env computed on the environmental raster (4t ~ D²_env), and R²_null the coefficient of determination obtained from the linear regression between four times the branch durations and the environmental distances D_null computed on the null raster (4t ~ D²_null). For Q₂, R²_env is obtained from the linear regression between the patristic distances and the log-transformed environmental distances computed on the environmental raster for each pair of tip nodes, and R²_null from the linear regression between patristic distances and log-transformed environmental distances computed on the corresponding null raster. For Q₃, R²_env is obtained from the linear regression between four times the branch durations t and the squared Euclidean distances d_Eucl,env traveled by each phylogenetic branch in the space transformed according to environmental distances computed on the environmental raster (4t ~ d²_Eucl,env), and R²_null from the linear regression between four times the branch durations t and the squared Euclidean distances d_Eucl,null traveled by each phylogenetic branch in the space transformed according to environmental distances computed on the corresponding null raster (4t ~ d²_Eucl,null). Finally, for Q₄, R²_env is obtained from the linear regression between four times the branch durations t and the squared Euclidean distances d_Eucl,env traveled by each phylogenetic branch in the space transformed according to a cartogram transformation, and R²_null from the linear regression between four times the branch durations t and the squared great-circle geographic distances d_gc traveled by each phylogeny branch in the nontransformed space (4t ~ d²_gc), i.e., following a standard phylogeographic reconstruction based on the nontransformed sampling coordinates. In step 4, for Q₁ and Q₂, a BF support was eventually computed by comparing the resulting posterior distribution obtained for the Q statistic (Q_posterior) with the distribution obtained according to a null dispersal model (Q_{randomizations}); and for Q₃ and Q₄, a BF support was computed by assessing the probability of getting a positive distribution of Q_posterior values (see the text for further detail). Continuous phylogeographic simulations (step 1), transformations of sampling coordinates (step 2), and landscape phylogeographic analyses (step 4) were conducted with the R package “seraphim” (41), the sequence simulations with the program πBUSS (42), and the continuous phylogeographic reconstructions (step 3) with the software package BEAST X version 1.10.5 (19).

Importantly, our assessment of the statistical performance of the landscape phylogeographic approaches revealed that none seemed to be associated with detectable type I errors. When the tested environmental factor did not impact the diffusion velocity of lineages (MCC simulations under scenario 1), no type I errors were detected by any of the approaches (Table 1). Regarding the statistical power to detect a true environmental impact on lineage diffusion velocity (RRW simulations, MCC simulations with scenario 3 and, to some extent, scenario 2), our analyses led to three main results. First, the analyses revealed a notably low statistical power for the prior-informed landscape phylogeographic analyses based on a cartogram transformation (Table 1). This prior-informed approach did not show any statistical power when tested on MCC simulations conducted under scenario 2 and, most importantly, under scenario 3. Second, the RRW simulations revealed a relatively low statistical power for the IBR approach, which we will further discuss below in light of the difference between what is actually simulated and tested by this approach. Finally, our RRW and MCC simulations indicated a moderate and good statistical power, respectively, for the two remaining landscape phylogeographic approaches, i.e., the post hoc approach based on the analyses of lineage diffusion velocity and the prior-informed approach based on an MDS transformation of sampling coordinates. However, we observed a difference when considering either the least-cost or Circuitscape algorithm used to compute the environmental distances associated with phylogenetic branches in the post hoc approach and among sampling coordinates to transform the space in the prior-informed approach. Specifically, when the Circuitscape path model is used, the statistical power tends to notably drop for both these two post hoc and prior-informed approaches when considering the RRW simulations (Table 1). However, these approaches do not seem to be impacted by the choice of the path model when assessed with the MCC simulations conducted under scenario 3.

Table 1.

Statistical performance of landscape phylogeographic approaches for testing the impact of environmental factors on the diffusion velocity of viral lineages or on the deviation from an IBD pattern

			Mean Q	P(Q > 0)	BF >3	BF >20
RRW simulations	Post hoc analyses	IBR analyses (LC)	0.017 [−0.031, 0.111]	37/50*	25/37	9/37
		IBR analyses (CS)	0.005 [−0.109, 0.114]	21/50*	18/21	12/21
		Lineage diffusion velocity analyses (LC)	0.077 [0.021, 0.179]	0.98 [0.82, 1.00]	43/45	33/45
		Lineage diffusion velocity analyses (CS)	0.044 [−0.073, 0.153]	0.77 [0.02, 1.00]	26/29	13/29
	Prior-informed analyses	MDS analyses (LC)	0.072 [0.001, 0.157]	0.91 [0.46, 1.00]	45/50	30/50
		MDS analyses (CS)	0.035 [−0.039, 0.129]	0.72 [0.04, 1.00]	32/50	19/50
		Cartogram transformation analyses	0.030 [0.003, 0.080]	0.80 [0.54, 0.97]	35/50	3/50
MCC simulations	Post hoc analyses	IBR analyses (LC)	−0.296 [−0.315, −0.237]	0.00 [0.00, 0.00]	0/0	0/0
(scenario 1 — no impact)		IBR analyses (CS)	−0.361 [−0.414, −0.247]	0.00 [0.00, 0.01]	0/0	0/0
		Lineage diffusion velocity analyses (LC)	−0.216 [−0.257, −0.185]	0.01 [0.00, 0.04]	0/0	0/0
		Lineage diffusion velocity analyses (CS)	−0.539 [−0.613, −0.462]	0.00 [0.00, 0.00]	0/0	0/0
	Prior-informed analyses	MDS analyses (LC)	−0.252 [−0.295, −0.197]	0.01 [0.00, 0.03]	0/10	0/10
		MDS analyses (CS)	−0.490 [−0.524, −0.411]	0.00 [0.00, 0.00]	0/10	0/10
		Cartogram transformation analyses	−0.033 [−0.039, −0.024]	0.34 [0.29, 0.38]	0/10	0/10
MCC simulations	Post hoc analyses	IBR analyses (LC)	−0.017 [−0.068, 0.067]	0.41 [0.11, 0.85]	0/0	0/0
(scenario 2 — moderate impact)		IBR analyses (CS)	0.006 [−0.055, 0.089]	0.47 [0.15, 0.88]	0/0	0/0
		Lineage diffusion velocity analyses (LC)	0.021 [−0.042, 0.056]	0.75 [0.47, 0.96]	2/2	0/2
		Lineage diffusion velocity analyses (CS)	0.009 [−0.042, 0.064]	0.61 [0.31, 0.93]	0/2	0/2
	Prior-informed analyses	MDS analyses (LC)	0.044 [0.004, 0.074]	0.84 [0.65, 0.97]	8/10	1/10
		MDS analyses (CS)	0.018 [−0.005, 0.041]	0.75 [0.59, 0.88]	4/10	0/10
		Cartogram transformation analyses	0.032 [0.013, 0.059]	0.63 [0.53, 0.71]	0/10	0/10
MCC simulations	Post hoc analyses	IBR analyses (LC)	0.184 [0.168, 0.209]	1.00 [1.00, 1.00]	10/10	10/10
(scenario 3 — strong impact)		IBR analyses (CS)	0.309 [0.285, 0.341]	1.00 [1.00, 1.00]	10/10	10/10
		Lineage diffusion velocity analyses (LC)	0.299 [0.262, 0.327]	1.00 [1.00, 1.00]	10/10	10/10
		Lineage diffusion velocity analyses (CS)	0.307 [0.125, 0.464]	1.00 [0.99, 1.00]	10/10	9/10
	Prior-informed analyses	MDS analyses (LC)	0.181 [0.167, 0.199]	0.99 [0.97, 1.00]	10/10	10/10
		MDS analyses (CS)	0.222 [0.189, 0.249]	1.00 [1.00, 1.00]	10/10	10/10
		Cartogram transformation analyses	0.044 [0.037, 0.052]	0.76 [0.73, 0.82]	5/10	0/10

Two continuous phylogeographic simulation frameworks were used to assess the performance of two post hoc (IBR and lineage diffusion velocity analyses) and two prior-informed landscape phylogeographic approaches (analyses of continuous phylogeographic reconstructions based on sampling coordinates obtained either after a MDS or cartogram transformation). The first simulation framework consists of birth–death simulations based on a RRW diffusion process with a velocity impacted by an underlying environmental layer (RRW simulations); and the second simulation framework consists of modifying the branch lengths of an actual MCC tree according to three distinct scenarios (MCC simulations): no impact of the environmental factor (scenario 1), as well as a moderate (scenario 2) and strong (scenario 3) impact of the environmental layer on lineage diffusion velocity. While 50 simulations have been performed with the first RRW simulation framework, 10 simulations have been performed for each of the three scenarios of the MCC simulation framework. In the latter case, however, the simulated phylogenetic trees have been used to further simulate RNA sequences, which were used as inputs for the different landscape phylogeographic approaches to test (see the text and Fig. 3 for further detail). For each simulation framework and landscape phylogeographic approach we here report i) the mean Q value (averaged across 50 or 10 simulations and associated with a 95% credible interval), ii) the posterior probability P(Q > 0) to get positive Q values (averaged across 50 or 10 simulations and associated with a 95% credible interval), as well as the proportions of simulations associated with a BF higher than iii) 3 and iv) 20, which, respectively, correspond to a positive and strong support according to the scale of interpretation of Kass and Raftery (43). We here only report those proportions of BF supports higher than 3 or 20 for the simulations associated with a positive posterior distribution of Q values (29), i.e., at least 90% of positive Q values. (*) Because the continuous phylogeographic analyses of the RRW simulations are each time based on a fixed time-scaled phylogeny (see the text for further detail), there is no variation within a posterior distribution of Q values computed for an IBR analysis. For those analyses (IBR analyses of RRW simulations), we thus directly report the proportion of simulations leading to a fixed Q value higher than 0. “LC” and “CS” refer to the least-cost and Circuitscape path models, respectively.

Discussion

Our assessment demonstrates that both post hoc landscape phylogeographic approaches exhibit reasonable statistical performance, with an absence of type I errors as well as good and moderate-to-low statistical power when assessed with the MCC and RRW simulations, respectively. The statistical power is particularly low for the IBR approach when evaluated with the RRW simulations. However, this result is unsurprising given the nature of these simulations, which aim to induce an impact of the environmental factor on the diffusion velocity of lineages rather than directly on the deviation from an IBD pattern, which is precisely what the IBR analyses measure. As argued earlier, the IBR analyses should be considered more as a landscape phylogenetic approach located between landscape genetic and landscape phylogeographic approaches. Previous studies (32, 33) have highlighted two types of dispersal metrics estimated by continuous phylogeographic inference, which appear to be robust to sampling intensity: the diffusion coefficient (14, 44) and the IBD signal (32, 45) metrics. While the first post hoc landscape phylogeographic approach is based on the former, the second specifically aims to investigate the cause of a deviation from an IBD pattern. Therefore, both types of metric and their related landscape phylogeographic approaches can be used as they address complementary aspects of the dispersal dynamics of viral lineages.

In this study, we introduced two landscape phylogeographic approaches based on a preliminary analysis and integration of the tested environmental factor. These approaches compare two continuous phylogeographic analyses: one based on original coordinates and one based on transformed coordinates. In the case of the MDS transformation approach, original sampling coordinates are replaced by coordinates that are transformed according to environmental distances computed on the null raster, providing a relevant proxy for pairwise geographic distances under the null dispersal model (see above). The aim is to assess whether the phylogeographic reconstruction based on the environmentally transformed coordinates leads to more homogeneous diffusion velocities among phylogenetic branches. While both the cartogram and MDS transformation approaches do not lead to type I errors, only the analyses based on an MDS transformation reveal satisfactory statistical power (i.e., likelihood of detecting that an environmental factor does indeed affect lineage diffusion velocity). As illustrated here (and in Fig. 1) the cartogram transformation is likely not profound enough to induce a notable signature and impact of the environmental layer on the transformed sampling coordinates. Consequently, even if the environmental factor actually impacted the diffusion velocity of viral lineages, the continuous phylogeographic analysis based on those transformed coordinates appears less likely to lead to a difference in terms of homogeneity of the lineage diffusion velocity as compared to the continuous phylogeographic reconstruction based on the original sampling coordinates.

Based on our results, we recommend use of the MDS instead of the cartogram transformation approach. Leaving aside the IBR approach — which tests a distinct aspect of the dispersal dynamic of lineages (see above) — we provide two complementary approaches that have different benefits and weaknesses. The post hoc nature of the approach based on the analysis of lineage diffusion coefficients allows it to be applied to readily available continuous phylogeographic reconstructions that may have been previously conducted, e.g., in the context of previous studies, without any prior assumption about the impact of an environmental factor on the dispersal dynamic of inferred lineages. However, such a continuous phylogeographic analysis does not integrate the environmental heterogeneity and relies on the flexibility of the RRW diffusion model to capture the potential signature of an environmental impact on the heterogeneity of diffusion velocity among phylogenetic branches, which is not guaranteed. In light of this limitation, the prior-informed approach based on an MDS transformation presents a valuable alternative, although it comes with an important computational burden: For each environmental factor to be tested, a distinct continuous phylogeographic reconstruction has to be conducted using the transformed sampling coordinates according to this environmental factor (and see also below regarding the different rescaling parameter k values to test).

The landscape phylogeographic approaches evaluated here have other limitations. First, as currently implemented, they only allow testing of one particular rescaling and/or transformation of the original environmental raster. In previous applications of the post hoc landscape phylogeographic approach, which analyses the lineage diffusion velocity (24, 27, 46), this issue was partially circumvented by testing a series of linear transformations of the original raster cell values with the following formula: v_t = 1 + k(v_o/v_max), where v_o and v_t are the original and transformed cell values, respectively, and v_max is the maximum cell value recorded in the raster. The rescaling parameter k thus allows the definition of different strengths of raster cell conductance/resistance relative to the conductance/resistance of a raster cell with a minimum value set to 1 (24). Note that in the context of the analyses performed here, we chose to consider only a linear transformation of the original raster with a value of k = 10, because this corresponds to the rescaling parameter k value that was used to rescale and generate the environmental raster used in our phylogeographic simulations. However, in the landscape genetic literature, other approaches have been proposed, such as using a genetic algorithm to simultaneously optimize multiple environmental rasters to generate a composite resistance raster (47). Such an approach would, however, be computationally too demanding in the case of the post hoc landscape phylogeography methods considered here, as it would have to be repeated on multiple trees sampled from the posterior distribution to account for the uncertainty in Bayesian phylogeographic inference. As for the prior-informed approach based on MDS transformations, this procedure would not be relevant because it would not have any response variable to consider for its optimization.

Second, the approaches assessed here cannot analyse time-series environmental factors. This limitation is a consequence of the algorithms used to compute environmental distances. As currently implemented, these algorithms work only on a two-dimensional grid. To enable the use of time-series environmental rasters, these algorithms would need to be adapted to work in three dimensions, allowing for the processing of successive environmental rasters over time.

Third, our landscape phylogeographic analyses were based on simulated datasets composed of a limited number of sequences (only 47 in the case of the MCC simulations; but on average 140 and up to 270 in the case of the RRW simulations) compared to the size of many present-day genomic datasets generated from viral epidemics. All phylogeographic simulations were either based on (MCC simulations) or inspired by (RRW simulations) the aforementioned raccoon RABV dataset (38). The selection of this dataset was motivated by its analysis in the study presenting the initial version of the first post hoc landscape phylogeographic approach (30). In this previous study, elevation was identified as a resistance factor slowing down the spread of viral lineages, despite the limited size of the dataset. It therefore served as a useful reference dataset to inspire the simulation scenarios and evaluate the performance of other landscape phylogeographic approaches. While we might expect increased statistical power when these methods are applied to much larger datasets, it would be computationally challenging to conduct all the analyses presented here. If some of the methods presented here already demonstrate sufficient statistical power when applied to relatively small datasets, then the power of such methods should be greater when applied to larger datasets.

Fourth, the application of these landscape phylogeographic approaches is mostly relevant for fast evolving organisms such as (RNA) viruses, for which molecular evolutionary change and spatial dispersal can occur on the same time scale, such that potential impact of environmental factors can be captured by interindividual genetic variability (10, 11). Moreover, these tools will be most useful for genomic datasets for which we have sampling through time covering a reasonable proportion of the evolutionary history of the pathogen, which is frequently the case when working on relatively short-term viral outbreaks. Such (landscape) phylogeographic approaches will be less useful for evolutionary and dispersal histories going back deep into time with sampling mostly available at present.

Finally, as the outcome of any phylogeographic analysis is impacted by the sampling pattern (48, 49), landscape phylogeographic approaches are therefore also impacted by the heterogeneity in the sampling effort. In particular, Kalkaukas and colleagues have shown that several scenarios of sampling bias can lead to an underestimation of the diffusion velocity estimated through continuous phylogeographic inference (48), which can in turn impact the statistical performance of the hypothesis testing approaches evaluated in this study. Furthermore, failing to sample lineages spreading across certain areas will prevent the exploration of the impact of environmental conditions specific to those areas (28). Ultimately, the statistical power of the different landscape phylogeographic approaches assessed here depends on how well the phylogeographic reconstructions represent the true dispersal history of viral lineages.

In conclusion, our study provides guidelines on the landscape phylogeographic approaches that can be used to investigate the impact of environmental factors on the diffusion velocity of viral lineages: i) a post hoc approach relating phylogenetic branch durations and environmental distances, updated for this study, and ii) a prior-informed approach using MDS transformation of sampling coordinates. These two approaches are complementary given their respective conceptual and practical advantages/disadvantages, as outlined above. In addition to these two approaches, we also introduced a third approach based on an IBR analysis to investigate the environmental factors that could explain significant deviations from an IBD pattern. Collectively, all three approaches are available in the updated version of the R package “seraphim”, and can be applied to gain insights into the impact of environmental factors on the dispersal dynamic of fast-evolving pathogens, thereby increasing our understanding of their ecology and epidemiology.

Materials and Methods

Continuous Phylogeographic Simulations.

RRW simulations were implemented in the function “simulatorRRW3”, now included in the R package “seraphim” (41). The functions “simulatorRRW1” and “simulatorRRW2” were implemented for previous studies: “simulatorRRW1” was designed for conducting RRW simulations along time-scaled phylogenies (26), while “simulatorRRW2” allows birth–death simulations based on a Brownian random walk or RRW diffusion process, without any impact of an underlying environmental factor (32). The new simulator introduced here is implemented in the function “simulatorRRW3” and extends the capabilities of “simulatorRRW2” by incorporating the effect of an environmental factor on the RRW diffusion process. It conducts forward-in-time joint simulations of both time-scaled phylogenies and the dispersal history of their branches on an underlying georeferenced grid (raster) whose environmental values impact the dispersal rate of lineages. The environmental raster considered here is an elevation raster where the values had been rescaled between one and eleven using a rescaling parameter k value set to ten in the following formula: v_t = 1 + k(v_o/v_max), where v_o and v_t are the original and transformed cell values, respectively, and v_max is the maximum cell value recorded in the raster. At each time step of those RRW simulations, both the longitudinal and latitudinal displacements of evolving lineages are randomly drawn from a Gaussian distribution whose SD is proportional (in the case of a conductance factor) or inversely proportional (in the case of a resistance factor) to the underlying raster cell value, and this while preventing lineage dispersal in inaccessible raster cells.

MCC simulations were implemented in two steps consisting of i) modifying the branch lengths of an actual MCC tree according to distinct scenarios, then ii) simulating genomic sequences along the resulting time-scaled phylogenies. Branch lengths of this MCC tree were modified according to three distinct scenarios: 1) a no impact scenario, “scenario 1”, in which branch lengths are proportional to environmental distances computed with the Circuitscape path model (3, 34) on a null raster (i.e., a raster within which the accessible cells have a uniform value set to 1); 2) an intermediate scenario, “scenario 2”, in which branch length values are randomly drawn from the branch length values generated for scenarios 1 and 3; and 3) a strong impact scenario, “scenario 3”, in which branch lengths are proportional to environmental distances computed with the Circuitscape path model on an environmental raster (here an elevation raster rescaled between 1 and 11). For the first and third scenarios, branch lengths were set to a value proportional to the squared environmental distance — either computed on the null (scenario 1) or environmental (scenario 3) raster — divided by four, which led to a diffusion velocity dictated by the environmental distance. The program πBUSS (42) was then used to simulate genomic sequences along the resulting time-scaled phylogenies, with ten genomic datasets simulated per scenario. We simulated alignments of 12,000 nucleotides, roughly corresponding to full RABV genomes, using an HKY+Γ substitution model and an uncorrelated relaxed clock with an underlying log-normal distribution.

Continuous Phylogeographic Reconstructions.

All continuous phylogeographic inferences were conducted using the RRW diffusion model (13, 14, 50) implemented in the software package BEAST X (19) version 1.10.5 (version compiled from the BEAST X GitHub repository on December 30, 2024). Specifically, for all the continuous phylogeographic analyses, we used a gamma distribution to model the among-branch heterogeneity in diffusion velocity (14). The continuous phylogeographic analyses based on the datasets obtained through RRW simulations all used fixed tree topologies: for each simulated dataset, we provided as a fixed tree topology the time-scaled phylogeny directly retrieved from the corresponding birth–death simulation. These phylogeographic analyses therefore did not consider uncertainty in phylogenetic inference and the program BEAST was used only to infer the ancestral positions of the tree internal nodes. For the MCC simulations, continuous phylogeographic analyses were based on genomic sequences simulated with the program πBUSS (42) along MCC trees whose branch lengths had been modified according to the three distinct scenarios (see above). For all the continuous phylogeographic analyses based on simulated genomic sequences, we modeled branch-specific evolutionary rates according to a relaxed molecular clock with an underlying log-normal distribution (51) and the nucleotide substitution process according to a GTR+Γ parameterization (52). As for the tree prior, we specified a flexible skygrid model (53).

For each phylogeographic analysis, we used the program Tracer 1.7 (54) to assess the convergence of the Monte Carlo Markov chain (MCMC) and its mixing properties, ensuring that effective sample size (ESS) value greater than 200 for all relevant continuous parameters. We adapted the MCMC length of each analysis accordingly: all the analyses were initially run with a maximum MCMC length set to 5 × 10⁷ iterations for RRW simulations and 10⁸ iterations for MCC simulations. However, some analyses required rerunning with a longer chain length to achieve ESS values above 200 for all relevant continuous parameters. For all the analyses, we sampled posterior trees every 10⁵ iterations and eventually discarded the first 10% of sampled trees as burn-in. We used the “postTreeExtractions” function in the R package “seraphim” (41) to extract the spatiotemporal information embedded within the 100 trees sampled from each post-burn-in posterior distribution of trees.

Post Hoc and Prior-Informed Landscape Phylogeographic Analyses.

The post hoc landscape phylogeographic analyses, based on measures of viral lineage diffusion velocity and IBR, were conducted using the updated “spreadFactors” and new “isolationByResistance” functions implemented in the R package “seraphim” (41). The transformations of sampling coordinates according to an MDS and a cartogram transformation were conducted with the new functions “mdsTransformation” and “cartogramTransformation”, respectively, and also implemented in “seraphim”. The former function calls the “cmdscale” function implemented in the R package “stats” and the latter conducts a cartogram transformation of the environmental raster (here an elevation raster) with the rubber sheet distortion algorithm of Dougenik and colleagues (37), implemented in the R package “cartogram”. All post hoc landscape phylogeographic analyses were conducted by considering either the least-cost (5) or Circuitscape (3, 34) algorithm to compute the environmental distances associated with phylogeny branches (when analyzing the lineage diffusion velocity) or between each pair of tip nodes (for the IBR analyses). Similarly, the MDS transformations were based on environmental distances computed on the null or environmental raster — here an elevation raster treated as a resistance factor — either with the least-cost or Circuitscape algorithm. In this study, all environmental distances were computed either on a null raster, with a value of 1 assigned to all accessible raster cells, or on an elevation raster in which the values had been rescaled between one and eleven. Computing environmental distance on a rescaled environmental raster with a minimum cell value set to 1 ensured direct comparison with the environmental distances computed on the corresponding null raster, i.e., the same raster in the absence of environmental heterogeneity according to the target environmental factor.

Statistical support for the Q statistics estimated for the two post hoc landscape phylogeographic approaches (Q₁ and Q₂) was assessed using a randomization procedure in which phylogenetic branch positions are randomized within the study area. This randomization step is implemented by the different functions of the R package “seraphim” and was used to conduct these two post hoc landscape phylogeographic analyses. Specifically, if all trees sampled from the posterior distribution are randomized once, this randomization procedure enables computation of a BF support approximated by the posterior odds that Q_observed > Q_randomized divided by the equivalent prior odds (the prior probability for Q_observed > Q_randomized is considered to be 0.5): BF = [P_e/(1 − P_e)]/[0.5/(1 − 0.5)] = P_e/(1 − P_e), where P_e is defined as the posterior probability that Q_observed > Q_randomized, i.e., the frequency at which Q_observed > Q_randomized in the samples from the posterior distribution. As previously described (28), this is analogous to computing BF support when two competing hypotheses exist, such as in the Bayesian stochastic search variable selection (BSSVS) procedure for discrete phylogeographic inference (12), where BF supports are used to assess the inclusion of rate parameters or predictors. As for the assessment of the statistical support for the Q statistics estimated for the prior-informed landscape phylogeographic approaches (Q₃ and Q₄), it is not based on a randomization procedure but directly on the probability to obtain positive Q values. Specifically, we compute a BF support equal to P_e/(1-P_e), where P_e is defined as the posterior probability that Q > 0.

Data, Materials, and Software Availability

R scripts related to the analyses based on simulated datasets are all available, along with the associated input and output files at Zenodo (https://doi.org/10.5281/zenodo.15082511) (55) and GitHub (https://github.com/sdellicour/landscape_phylogeography) (56). Continuous phylogeographic simulations and landscape phylogeographic analyses were conducted using new functions implemented in the R package “seraphim” available at https://github.com/sdellicour/seraphim (57), which includes new tutorials dedicated to i) the phylogeographic simulations conducted on environmental rasters and ii) the prior-informed landscape phylogeographic analyses based on an MDS or cartogram transformation, as well as iii) an updated tutorial dedicated to the post hoc landscape phylogeographic analyses on the impact of environmental factors on the diffusion velocity of viral lineages (the latest tutorial also including the IBR analyses).