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. 2026 Aug 4;26(6):e70182. doi: 10.1111/1755-0998.70182

Improving Malaria Parasite Gene Flow Inference Under Sparse Spatial Sampling

Yao Li 1,2,3,✉, Bing Guo 4,5, Timothy D O'Connor 5, Shannon Takala‐Harrison 4, Kathleen Stewart 1
PMCID: PMC13436596  PMID: 42550678

ABSTRACT

Estimating malaria parasite migration is crucial for informing elimination strategies, particularly by identifying regions with higher parasite migration that may serve as transmission sources and intervention targets. Methods that infer spatial variations in gene flow from georeferenced genetic data, including Estimated Effective Migration Surfaces (EEMS) and related approaches such as estimating Migration And Population‐size Surfaces (MAPS), have become widely used to visualize barriers and corridors of organism movement. However, when sampling locations are sparse or unevenly distributed, spatial gene‐flow maps can contain artefacts that are difficult to interpret, and methods such as EEMS provide posterior probability summaries that indicate whether inferred migration rates are statistically supported by the genomic data. However, these summaries do not directly capture whether a spatially inferred feature, such as a migration barrier or corridor, lies in a region with sufficient sampling locations to be geographically reliable. A high posterior probability in a sparsely sampled region reflects model confidence given available data, not spatial sampling adequacy. In this study, we developed a sample location–aware (SLA) filtering workflow that applies topological skeletons and kernel density estimation to assess sample density for each contour and filter out areas with lower sample density. This workflow can be applied to any gene‐flow inference approach that produces spatially explicit migration features (e.g., contours, surfaces, or high/low‐migration regions) from genotype data and sample coordinates. Using simulated genomic data and different barrier configurations under systematic site subsampling scenarios, we show that posterior‐only filtering can retain spurious barrier features, whereas SLA filtering consistently increases the precision of inferred low‐migration regions across sample sites. In an empirical case study of Plasmodium falciparum from Cambodia, SLA filtering produced more stable estimates of parasite migration patterns under location subsampling than posterior probability filtering alone. These results demonstrate that incorporating an explicit measure of geographic sampling density around each inferred migration feature improves the reliability and interpretability of spatial gene‐flow migration patterns for malaria parasites and provides a general diagnostic and filtering approach for a broad class of georeferenced population‐genetic migration mapping methods.

Keywords: EEMS, gene flow, landscape genomics, malaria, Plasmodium falciparum, spatial sampling, topological skeleton

1. Introduction

Population genetic analyses offer insights into demographic and adaptive processes, such as migration and natural selection, respectively (Moorjani and Hellenthal 2023; Degroot et al. 2022). Such knowledge is key in fields like conservation biology (Zhao et al. 2023; Librado et al. 2021) and epidemiology (Shetty et al. 2019; Li et al. 2020), especially when these processes are considered in a geographic context. For instance, geospatial modelling of genetic data has shed light on the population genetics of Triodanis perfoliate (Tackett et al. 2022), genetic susceptibility to IgA nephropathy (Kiryluk et al. 2012), and historical dispersal routes of Liriodendron chinense (Shen et al. 2019). Moreover, they have illuminated the spatial transmission patterns and epidemiology of certain diseases, including influenza (Tsunekuni et al. 2018; Pei et al. 2018), typhoid fever (Ren et al. 2023; Gauld et al. 2022), malaria (Nelson et al. 2019; Memarsadeghi et al. 2023; Li et al. 2023) and dengue (Ng and Wen 2019; Phanitchat et al. 2019), and expanded our understanding of the landscape genetics of malaria parasites, which is a subfield that examines how geographic features such as elevation, land cover, and human movement corridors shape the spatial distribution of genetic variation within Plasmodium populations (Shetty et al. 2019; Li et al. 2020). Applied to malaria, this approach has been used to identify how physical and political barriers modulate P. falciparum gene flow across transmission settings, with implications for understanding how novel genotypes spread between transmission foci.

A growing class of methods leverages georeferenced genomic data to infer and visualize spatial variation in gene flow and population structure. For example, Estimated Effective Migration Surfaces (EEMS) (Petkova et al. 2016) models the spatial structure in genomic data to depict spatial patterns of migration and diversity of a species within a geographic area. Predicated on isolation‐by‐distance, the model highlights regions of varying historic effective migration and produces a map showcasing areas of higher or lower relative migration and diversity within a study area (Petkova et al. 2016). A similar method, estimating Migration And Population‐size Surfaces (MAPS) (Al‐Asadi et al. 2019), that utilizes estimates of identity‐by‐descent as a metric of genetic distance, is also available and can capture more recent migration patterns. In this study, parasite migration refers to the movement of Plasmodium falciparum parasites between geographic locations via infected human hosts, which is likely the primary mechanism of gene flow in this organism. The effective migration rates estimated by methods such as EEMS reflect the relative historical exchange of parasite genetic material between locations, the underlying model assumes that migration rates are symmetric between pairs of adjacent demes, and so EEMS cannot infer a direction of migration on a given edge. A high migration rate between two regions indicates that parasites have moved frequently between them, consistent with isolation‐by‐distance expectations, rather than net directional flow. Some directional information can still be partially captured, however, since each deme has edges radiating in six directions with independent migration rates, allowing EEMS to represent anisotropic patterns (e.g., a corridor in one direction coinciding with a barrier in another) even though it cannot assign a direction to migration along any single edge (Petkova et al. 2016). Regions with lower‐than‐average migration rates therefore represent relative barriers to parasite dispersal, where less genetic exchange has occurred historically, regardless of direction.

EEMS has been employed to decipher the population structure of humans worldwide and to visualize barriers and corridors of gene flow tied to human migration (Fortes‐Lima et al. 2022; Harris et al. 2018). It has also been used to trace the evolutionary history and geographical spread of rice (Gutaker et al. 2020) and to elucidate the speciation of lowland Amazonian birds resulting from river network rearrangements (Musher et al. 2022). In our prior work, we used EEMS alongside identity‐by‐descent‐based methods to analyse migration patterns and population structure of Plasmodium falciparum in the Greater Mekong Subregion (Shetty et al. 2019). Additionally, we developed an optimized workflow to minimize spatial uncertainty in EEMS outputs by providing a systematic approach for selection of grid density used in EEMS estimation (Li et al. 2020).

Despite their advantages, spatial gene‐flow maps are susceptible to spatial sampling artefacts: when sampling is sparse or uneven, inferred barriers and corridors may reflect gaps in geographic sampling coverage rather than true biological structure (Petkova et al. 2016). Although genomics‐based migration mapping methods provide a posterior probability map to assist users in identifying uncertain contours, they only indicate whether the estimated migration rates are high or low enough to be considered significant corridors or barriers and do not directly capture whether an inferred migration contour is supported by spatial sampling (see Methods: Step 1 for the specific distance metric used). Similar challenges arise for gene‐flow mapping approaches where model‐based confidence measures may quantify statistical support given the available data but may not diagnose artefacts driven by spatial sampling design. Few studies have systematically evaluated how sampling locations influence inferred migration features, and practical tools for integrating spatial sampling support into confidence assessment remain limited.

To address this gap, we propose a two‐step, sample location–aware filtering workflow that can be used as a general diagnostic and filtering layer for spatial gene‐flow inference methods that rely on georeferenced genetic data. The workflow combines spatial filtering, which identifies contour or region components supported by nearby sampling locations, with genomic‐confidence filtering based on method‐specific uncertainty outputs (e.g., EEMS posterior probabilities). We evaluate this approach using simulated datasets with known barrier patterns and different subsampling scenarios, and we demonstrate its utility as a general diagnostic tool for identifying contours that lack spatial sampling support, whether due to too few sampling sites overall, spatially uneven site distribution, or both, and as a filtering layer applicable to any spatial gene‐flow inference method that produces georeferenced migration features from genetic data and sample coordinates.

2. Methods

2.1. Migration and Population Structure Estimation Methods

In this study we used EEMS as an example for the migration and population structure estimation method using georeferenced genomic data. EEMS couples gene flow analysis with mapping capabilities, modelling the spatial structure within the genomic data. As part of the EEMS approach, a triangular grid (Voronoi network) is overlaid on a geographic study area and each sample location is assigned to the nearest deme (vertex) on the grid. EEMS assumes a stepping‐stone model, where individuals migrate locally between neighbouring demes, and migration rates vary by location (Petkova et al. 2016). EEMS uses Markov chain Monte Carlo (MCMC) simulations to estimate migration by sampling from the posterior distribution given observed genetic dissimilarities. To model migration at each simulation loop, EEMS generates a Voronoi tessellation representing the spatial pattern of migration that is updated with a birth/death process since the number of Voronoi cells is unknown. These estimates are adjusted during the simulation such that simulated genetic dissimilarity rates fit the observed genetic dissimilarity. For each triangle in the grid, migration estimates are assigned to edges of the triangle. Researchers typically employ an average of the results obtained from running multiple MCMC simulations using different numbers of demes. The outcome of these steps is mapped to produce a spatial visualization of an effective migration surface where the migration contours show relatively high (blue) or low (brown) effective migration or gene flow (Figure 1).

FIGURE 1.

FIGURE 1

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Example of estimated effective migration surface contours showing the intensity of gene flow migration rates. Blue regions correspond to migration corridors, and brown regions correspond to migration barriers.

2.2. Impact of Sample Locations in Estimated Migration Surface Analysis

The stepping‐stone model assumes that gene flow occurs more frequently between neighbouring locations than between those that are more distant. As a result, when a sampling location is geographically remote from the region where a contour is inferred, with few or no intervening sample locations, the model has limited genetic information to constrain migration estimates in that area, leading to increased uncertainty in the inferred surface. In extreme cases, contours can be generated in regions that contain no nearby samples at all, as the model extrapolates across the full study area regardless of sampling coverage. This feature of the model makes the inference of gene flow or demographic history less certain in the absence of sufficient data from specific areas, although migration contours are generated by the mapping tool even for areas with sparse samples.

Gaps or long distances between sampling locations can pose significant challenges for generating reliable contours. Such irregular sampling is common in data collection due to logistical constraints, such as accessibility of the study area, limited resources, and uneven distribution of populations, as well as natural barriers like lakes, mountains, and deserts. These factors can lead to spatial sampling bias, which may affect the accuracy of the inferred population structure maps.

2.3. Data Sets Used in Analyses

2.3.1. Synthetically Generated Data

For the simulated data set, we used msprime, a population genetic simulator of ancestry and DNA sequence evolution (Baumdicker et al. 2021; Kelleher et al. 2016), to generate a synthetic structured population following a two‐dimensional stepping‐stone model. We generated 100 synthetic subpopulations/demes each with an effective population size of 100; we positioned the demes on a grid of equilateral triangles, ensuring that the distance between any two adjacent demes is consistent and demes are evenly distributed. For the data generation, we used a mutation rate (1.0 × 10−8 per bp per generation) and recombination rate (6.67 × 10−7 per bp per generation), similar to the rates in P. falciparum to account for the unique evolutionary parameters of this species. We modelled the genome with a single chromosome of 1.5 million base pairs for simplicity and simulation efficiency. We synthetically generated a single chromosome instead of 14 because simulating all 14 chromosomes simultaneously in one pseudo‐chromosome is computationally prohibitive for complex demographic configurations. Conversely, simulating 14 chromosomes independently introduces issues related to the random combinations of unmatched genome pairs across chromosomes, affecting genome‐wide relatedness or dissimilarity calculations. This simplification is valid and has been used previously (Petkova et al. 2016), as the resulting genotype data still captures population structure and migration patterns. We modelled two sets of migration barrier patterns: a three‐region migration barrier pattern (3‐Hex) within the habitat and hexagon‐shaped barrier regions (Figure 2a), and a totally random barrier pattern (Figure 2b). The migration barrier is simulated with a migration rate of 0.001, which is 20 times lower than the rate in non‐barrier regions (0.02).

FIGURE 2.

FIGURE 2

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Simulated Plasmodium falciparum datasets illustrating the two synthetic barrier configurations used for method evaluation. (a) The three‐hexagon (3‐Hex) barrier pattern, in which three hexagonal regions of reduced migration (migration rate = 0.001, 20 times lower than the background rate of 0.02) are distributed across the simulated habitat. (b) The random barrier pattern, in which barrier regions are distributed without geometric regularity. In both panels, filled circles represent the 100 simulated deme locations; barrier regions are shown in grey. These configurations serve as ground truth against which inferred migration contours are evaluated.

2.3.2. Case Study Data

We tested our methods on a previously published P. falciparum genomic data set comprised of 28,496 biallelic SNPs from 1007 parasite isolates (Shetty et al. 2019; Li et al. 2020) sampled from Cambodia and adjacent districts in Thailand and Vietnam from 2008 to 2013. The data set included 35 locations used to collect P. falciparum samples. To systematically evaluate the impact of the number and location of sample locations using our methods, the data set was subdivided into six subsets, with each subset characterized by a different number and set of geographical locations. These subsets were constructed randomly by incrementing the number of geographical locations in a subarea by intervals of 5. As such, the six subsets contained 5, 10, 15, 20, 25, and 30 geographical locations respectively (Figure 3). The six subsets were constructed by incrementally adding sampling locations within a contiguous subarea of Cambodia, meaning that at lower location counts (e.g., 5–10 locations), selected sites were geographically proximate to one another. This was deliberate since it mirrors a common real‐world scenario in which initial surveillance efforts are geographically concentrated before expanding to a wider region, and it creates a controlled test of how the SLA method performs when spatial coverage is both limited and spatially clustered.

FIGURE 3.

FIGURE 3

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Spatial distribution of sample locations for the six sub‐datasets.

2.4. Validation Design and Accuracy Assessment

To evaluate these effects on parasite migration estimates in a controlled setting, we incorporated explicit migration‐barrier patterns into simulated datasets, which served as ground truth for validation. Specifically, we considered two barrier configurations as mentioned above: (i) a structured three‐hexagon barrier pattern and (ii) a random barrier pattern. We then conducted systematic location subsetting to quantify how the number and configuration of sampling locations affected EEMS inferences. From the full set of 100 simulated locations, we constructed subsets with increasing numbers of locations (10, 15, 20, 25, 30, 35, 40, 45, …, up to 60). For each subset size, we generated 30 sampling scenarios by randomly selecting locations (i.e., 30 independent realizations per location count) and repeated this procedure for both the three‐hexagon and random‐pattern datasets. This design reduced dependence on any single subsampling outcome and enabled assessment of variability in performance attributable to sampling configuration.

For the empirical dataset from Cambodia, where ground truth locations are inherently unknown because, unlike our simulated datasets where we explicitly programmed barrier positions, real‐world parasite genomic data do not come with a verified map of true migration barriers. We therefore used migration contours generated using all 35 sample locations as a referential baseline. This allowed us to evaluate the accuracy of our estimations by comparing the alignment of each estimated contour with the reference contours. Consistency was defined as the percentage of congruence between the estimated and reference migration contours. The detailed two‐step process, consisting of spatial filtering and genomic filtering, will be discussed in the following sections.

2.5. Step 1: Spatial Filtering

2.5.1. Determine the Distance Between Sample Locations and Contours

To assess the impact of sampling resolution in our empirical dataset on the reliability of generated migration contours and to match the analysis we carried out using the simulated data, we first determined the distance between the sample locations and all the estimated contours. To calculate these distance measures, we grouped together all contours with effective migration rates greater than 1 into a single group and all contours with effective migration rates less than 1 into another group. We then computed the topological skeletons using a Python script to test for the presence of migration barriers (regions with lower‐than‐average migration rates).

Topological skeletons distill an object's inherent structure into a series of curves, capturing both its vital topological and geometric traits (Li et al. 2020). Rooted in the principles of topology, these skeletons—often visualized as a shape's “backbone”—provide a streamlined yet topologically faithful representation of the original shape (Li et al. 2020). This representation serves as a bridge, transforming spatial data into a coherent structural interpretation. In this context, the topological skeletons allow for a simplified representation of the contour areas, simplifying from an area to a linear representation (Figure 4).

FIGURE 4.

FIGURE 4

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Sample location–aware selection of topological skeletons using the median nearest‐sample distance D med. Pale blue polygons represent estimated migration contour regions, yellow circles indicate sample locations, black lines indicate retained topological skeletons, and orange dashed lines indicate unselected skeletons removed because of insufficient spatial sampling support. The blue line illustrates the nearest‐sample distance used to derive D med, which is used as the threshold for retaining or removing skeletons. This step identifies contour skeletons that are better supported by nearby sample locations before subsequent genomic‐confidence filtering.

For each contour represented by its topological skeleton, we computed the distance from each skeleton to the nearest sampling location, resulting in a distance vector, D near  = {D sk1, D sk2, D sk3, …, D ski}. We then computed the median distance from D near as D med. Skeletons with D ski values greater than D med were removed and the remaining skeletons were selected for subsequent processing (Figure 4).

2.5.2. Generating Sample Location‐Aware Regions

We established Sample Location–Aware (SLA) regions for the migration surface estimates using the topological skeletons from the preceding step. The SLA regions highlight regions with lower spatial uncertainty due to sample locations. The SLA regions are subsets of the estimated migration surface contours, characterized by a higher density of sample locations. Buffer analysis was applied to create a set of SLA regions around the topological skeletons. Given that migration contours typically encompass a larger spatial area than the new SLA representations, we divided the topological skeletons into separate segments based on the vertices and applied buffers to these segments.

We applied different buffers to individual segments based on the density of sample locations. We used D med/2 as the maximum expansion distance for the buffers and we determined the sample location densities using kernel density analysis. We used a 4‐class Natural Breaks classification for the kernel density results. We overlaid the contour skeletons on the sample density results to determine sampling density for each segment of the skeleton. Based on sampling density, the expansion distance E k used for buffering and for generating the SLA regions is determined for each segment of the skeletons as follows:

Ek=Dmed*SIk−13 (1)

where D med is the median distance between samples and skeletons, SI k is the sample density class of a skeleton K. According to the equation, the maximum expansion distance is D med. To achieve the maximum expansion and create the largest SLA regions, a skeleton segment must be in an area with higher sample density. Conversely, if a segment of the skeleton is in a sparsely sampled region, its expansion will be zero, that is, no expansion will be applied to that skeleton segment and consequently no SLA region will be formed.

2.6. Step 2: Genomic Filtering

In this step, we applied genomic filtering to enhance the reliability of the SLA regions by integrating genomic data into the evaluation process. It is important to clarify that genomic filtering here does not refer to the removal of individual genomes from the analysis, but rather to filtering SLA regions based on the confidence of the genomic data supporting them. The EEMS toolkit produces posterior probability results, which indicate the confidence levels of migration contours based on the genomic data. We overlaid the generated SLA regions with these posterior probability maps, filtering out regions with lower genomic confidence and retaining those with higher confidence. This ensured that the final SLA regions used for further analysis were backed by stronger genomic support. By focusing on areas where genomic data provided robust migration estimates, this filtering step enhanced the reliability of the migration contours. A Python script was developed to automate this genomic filtering process (https://github.com/mgzjys/sparse‐sample‐filtering).

3. Results

3.1. Estimated Effective Migration Surfaces and Corresponding Topological Skeletons Using Simulated Data Sets

Classifying the contours into lower‐than‐average migration rates and assuming a constant number of isolates per location, we found that a smaller number of geographically distinct sampling locations, regardless of the number of isolates per location, consistently produced less reliable barrier estimates. At the lower end of the range of sample locations (nlocation = 15, 20), the estimated location of the uppermost barrier showed substantial spatial displacement relative to ground truth (Figure 5), with contours exhibiting severe distortion that would render them unsuitable for applications requiring spatial accuracy. As the number of sample locations increased, barrier location accuracy improved progressively (Figure 5b,c), demonstrating that sample size is a primary driver of contour reliability. However, even at larger sample locations (nlocation = 55), spurious migration barriers persisted in the top‐left corner of the study area (Figure 5c), indicating that sample locations alone are insufficient to guarantee accurate contour estimation. Taken together, these results suggest that while adequate spatial sampling is necessary, other factors, such as the spatial configuration of sample locations or underlying landscape heterogeneity, also play a critical role in reliably estimating migration contours during modelling. It is worth noting that the present study held the number of isolates per location approximately constant across subsampling scenarios; as such, our results speak primarily to the role of geographic coverage (the number and spatial configuration of sampling locations) rather than within‐site sample depth. In practice, both dimensions likely matter: sufficient geographic coverage is needed to support spatial inference of migration patterns, while adequate within‐site sample sizes are needed to reliably characterize local allele frequencies. Disentangling these two sources of sampling adequacy is an important direction for future work and is noted as a limitation in the Discussion.

FIGURE 5.

FIGURE 5

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Posterior probability restricted barrier regions (orange), SLA restricted barrier regions (black line fill), and ground truth (red dashed lines) for different numbers of locations: (a) 15 locations, (b) 35 locations, and (c) 55 locations.

3.2. Confidence of Regions Generated by Two‐Step Selection Using Simulated Datasets

For this analysis, predicted accuracy was quantified using precision, defined as the proportion of inferred barrier areas that overlap the simulated ground‐truth barrier regions. We compared precision obtained using posterior‐probability filtering alone versus the proposed SLA two‐step method across systematic subsamples of the simulated landscapes (N = 10 to 60 sample locations). For each N, we generated 30 different sampling scenarios (randomly selected site sets) and reported the mean precision with 95% confidence intervals (Figure 6).

FIGURE 6.

FIGURE 6

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Precision of inferred barrier regions under systematic site subsampling for (a) three‐hexagon pattern and (b) random pattern.

Across both simulated barrier configurations, the SLA two‐step method consistently achieved higher precision than posterior‐only filtering. In the three‐hexagon pattern, which represented a simple barrier pattern, posterior‐only precision increased from 0.667 (N = 10) to a plateau of ~0.73–0.75, whereas SLA two‐step increased from 0.684 (N = 10) to 0.768 (N = 15) and remained near 0.77–0.79 thereafter (peaking at 0.790 at N = 25), yielding a persistent improvement of ~0.02–0.04 across most N values (Figure 6a). A paired t‐test confirmed that this advantage was highly significant (t(10) = 11.32, p < 0.0001, one‐sided; mean difference = 0.029, 95% CI [0.023, 0.035]; Cohen's d = 3.41), with the Wilcoxon signed‐rank test in full agreement (W = 66, p = 0.0005).

In the random‐barrier pattern, which is a much more complicated pattern, posterior‐only precision remained comparatively lower and more variable, ranging from 0.549 to 0.673 and ending at 0.652 (N = 60); in contrast, SLA two‐step precision increased with additional sample locations and diverged more strongly at moderate‐to‐high N, rising from 0.603 (N = 10) to 0.775 (N = 60), with improvements reaching ~0.06 at N = 35 and ~0.11–0.12 at N = 50–60 (Figure 6b). A paired t‐test confirmed that SLA two‐step precision was significantly higher overall (t(10) = 3.64, p = 0.0023, one‐sided; mean difference = 0.049, 95% CI [0.019, 0.078]; Cohen's d = 1.10), with the Wilcoxon signed‐rank test corroborating this result (W = 66, p = 0.0005). Together, these results indicate that posterior probability filtering alone leaves a residual false‐positive burden in inferred barrier regions, while the SLA two‐step procedure more effectively suppresses spurious barriers, especially under complex/random barrier geometries, and yields more robust performance across different sampling scenarios.

3.3. Applying the Two‐Step Process to P. Falciparum Genomic Data From Cambodia

Using the published empirical P. falciparum genomic data set, we employed the same two‐step process that was used with the simulated data sets, adapting this process to the complexities of real‐world data. The spatial analysis revealed that the sampling locations for this data set were often sparse and failed to cover the entirety of the research region, as illustrated in Figure 2.

Analysis of the P. falciparum genomic data revealed a progressive increase in consistency between the posterior probability method and the two‐step method. This increase became more pronounced as the number of sample locations grew, peaking at 25 sample locations (Table 1). As the number of sample locations was increased beyond 25 to 30, we observed a 5% reduction in consistency. This pattern mirrored our observations from the simulated data sets, underscoring a weakness with fewer sample locations for relying solely on posterior probability for filtering contours.

TABLE 1.

Consistency using posterior probability exceeding 90% and using SLA filtering method for the empirical P. falciparum genomic data set.

Number of sample locations Posterior probability Two‐step SLA filtering
Area of contours consistent with ground truth (pixels) Predicted contour area (pixels) Consistency Area of contours consistent with ground truth (pixels) Predicted contour area (pixels) Consistency
15 31,104 53,460 0.582 25,347 38,018 0.667
20 40,096 66,707 0.601 22,333 31,380 0.712
25 50,154 66,420 0.755 30,714 39,197 0.784
30 33,662 47,502 0.709 23,078 26,122 0.883
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Integrating spatial metrics with the existing geolocation and genomic information used by migration and population structure estimation methods (e.g., EEMS or MAPS) consistently yielded more reliable contour evaluations compared to relying solely on posterior probabilities to assess contour confidence across different numbers of sample locations. This method specifically reduced spatial uncertainty by filtering out unreliable contours, resulting in an average improvement of at least 10% in consistency over the traditional approach that depends primarily on posterior probabilities for identifying reliable contours. This advantage was realized across all tested sample location numbers, highlighting this approach's utility in producing more reliable and accurate spatial estimations of P. falciparum migration in Cambodia. Through this approach, we not only addressed any spatial limitations (i.e., sparse sampling) inherent in the available data but also refined our understanding of the spatial patterns of disease transmission, offering a more nuanced and effective workflow for analysing genomic data for epidemiological research.

4. Discussion

In this study, we analysed migration contours generated using a spatial gene‐flow simulation method under different spatial sampling distributions including when sampling locations are sparse. We introduced a new two‐step approach to enhance the accuracy of gene flow estimation and the identification of possible migration barriers. Inference accuracy, measured by precision in the simulated setting and by consistency with the full‐coverage baseline in the empirical with the number of sampling locations for both posterior‐probability filtering alone and the proposed SLA two‐step method. Importantly, while both approaches benefited from denser sampling, the SLA workflow consistently outperformed posterior‐probability filtering across all tested sampling scenarios, and this advantage became more pronounced as barrier complexity increased. We observed that both the number and the configuration of sample locations influenced the quality of estimated migration contours. Even with relatively high sampling coverage in the simulated setting, relying on posterior probability alone (e.g., > 90%) retained spurious barrier features. In contrast, the two‐step SLA workflow more effectively identified and removed low‐support regions, producing more reliable migration‐barrier delineations. This improvement is particularly relevant for malaria applications, where correctly identifying regions of elevated parasite migration can inform targeted surveillance and intervention planning.

While this study focused on P. falciparum, the SLA filtering workflow is applicable in principle to other Plasmodium species, including P. vivax (Pv) and P. ovale (Po). However, several biological complexities unique to relapsing malaria warrant consideration. In P. vivax and P. ovale , hypnozoite reactivation can produce secondary blood‐stage infections weeks to months after the initial mosquito bite, potentially at a location geographically distant from the original exposure site. This means that the spatial coordinates associated with a sampled isolate may not accurately reflect the true transmission location, introducing a form of spatial misclassification that is distinct from the sampling sparsity problem addressed here. In such cases, the SLA workflow would still correctly identify contours lacking nearby sample support, but the underlying genomic signal itself may carry location uncertainty that no post hoc spatial filter can resolve. Future work should explore how hypnozoite‐driven relapse rates interact with gene‐flow inference accuracy, and whether integrating travel history or epidemiological metadata can help anchor isolate coordinates to likely transmission sites before applying spatial filtering.

Beyond migration and population structure estimation methods such as EEMS or MAPS, the broader implication of this work is that spatial sampling support should be treated as a necessary component of uncertainty assessment for any gene‐flow mapping method that combines genomic information with sampling coordinates to infer spatially explicit migration features (e.g., barriers/corridors, high/low migration regions, or migration surfaces). Spatial gene‐flow inference approaches provide model‐based confidence summaries (e.g., posterior probabilities or other uncertainty scores), but these summaries do not necessarily reflect whether an inferred spatial feature is supported by sufficient and appropriately distributed sampling locations. This is the key distinction between the SLA workflow and posterior‐probability filtering alone: existing methods produce migration contours across the entire study region, including areas with sparse sample locations, and posterior probability scores reflect statistical confidence given the available genetic data rather than geographic data. A contour spanning an unsampled region can therefore appear statistically significant while being an artefact of model extrapolation across a data gap. The SLA workflow addresses this directly by using the spatial distribution of sampling locations, specifically, the distance from each topological skeleton segment to its nearest sample location relative to the median nearest‐sample distance D med, to systematically identify and remove contours that lack geographic grounding. The result is a reduced, spatially conservative set of contours representing areas where both the genetic signal and the sampling evidence jointly support the inference. By providing a general, spatial‐support filtering layer that can be coupled with method‐specific genomic confidence outputs, the SLA workflow offers a practical way to reduce sparse‐sampling artefacts and to improve the robustness of spatial interpretation across a wider class of georeferenced gene‐flow analyses.

For malaria surveillance and intervention planning, this distinction has direct practical importance. Migration barriers identified through spatial gene‐flow analysis, regions where parasite movement is historically restricted, can help delineate transmission foci that may be targeted semi‐independently through interventions such as mass drug administration or indoor residual spraying (Wesolowski et al. 2018). Conversely, corridors of high migration identify routes along which drug‐resistant genotypes, such as those carrying artemisinin partial resistance mutations in kelch13, are likely to spread, informing where cross‐border surveillance should be intensified (Tessema et al. 2019; Balmer et al. 2025). When contours are inflated by spatial sampling artefacts, these intervention decisions risk being misdirected toward regions that reflect data gaps rather than genuine epidemiological boundaries. By producing spatially conservative, sample‐supported contours, the SLA workflow reduces this risk and provides a more reliable geographic foundation for targeted malaria control strategies.

Consequently, the regions with sparse sampling often correlate with contours of increased uncertainty, a characteristic inherent to the stepping‐stone model underlying EEMS; sample locations therefore need to be distributed across the areas of interest for accurate inference. Our findings underscore the critical importance of designing spatial sampling strategies prospectively. The distribution of sampling locations heavily influences inferences about spatial population structure, as uneven or sparse sampling can introduce spatial uncertainty. This aligns with calls from previous research advocating for the careful consideration of sampling workflow in genomic studies to ensure robust insights (Burgess and Garrick 2021; Hill et al. 2021). However, it is also essential to acknowledge that logistical constraints, such as accessibility, resources, and environmental factors, may limit where sampling can occur, even with a well‐planned strategy. Future studies should prioritize strategically planned sampling schemes, to the extent possible, to optimize the accuracy of population structure and gene flow analyses, thus advancing our understanding of pathogen spread and informing more effective public health interventions.

In this research, we did not consider the impact of sample size (i.e., the number of parasite isolates/genomes) sampled from each location on spatial population structure inference, but this is an ongoing area of investigation. Future studies will also aim to further validate the effectiveness of our approach across different geographic regions and species. Additionally, the integration of more comprehensive data sets, including environmental and socio‐economic factors, could offer deeper insights into the complex interplay between human mobility, malaria transmission, and intervention strategies.

Author Contributions

Conceptualization: Yao Li, Kathleen Stewart, Shannon Takala‐Harrison. Data curation: Bing Guo. Formal analysis: Yao Li, Kathleen Stewart, and Bing Guo. Funding acquisition: Kathleen Stewart, Shannon Takala‐Harrison, Timothy D. O'Connor. Investigation: Yao Li and Kathleen Stewart. Methodology: Yao Li and Kathleen Stewart. Project administration: Kathleen Stewart. Software: Yao Li. Supervision: Kathleen Stewart, Timothy D. O'Connor, Shannon Takala‐Harrison. Validation: Yao Li, Kathleen Stewart. Visualization: Yao Li, Bing Guo. Writing – original draft: Yao Li, Kathleen Stewart, and Bing Guo. Writing – review and editing: Yao Li, Kathleen Stewart, Bing Guo, Shannon Takala‐Harrison.

Funding

Research reported in this publication was supported by a National Science Foundation award to KS (BCS2049805) and by a National Institute of Allergy and Infectious Diseases R01 award to ST‐H and TDO (R01AI145852). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Science Foundation or the National Institutes of Health.

Ethics Statement

This study did not involve the collection of new human subjects data. All P. falciparum genomic data analysed here were previously published and are publicly available in de‐identified form. The parasite isolates were originally obtained between 2008 and 2013 through passive surveillance for clinical malaria and clinical trials conducted under the ARC3, ARCE, and TRAC collaborations. Informed consent was obtained from all participating symptomatic individuals who met the inclusion criteria of the respective study protocols, and each contributing study received prior approval from its local ethical review board. The present work comprises secondary analysis of these de‐identified, publicly available data together with simulated data, and did not require additional institutional review board approval.

Conflicts of Interest

The authors declare no conflicts of interest.

Acknowledgements

We would like to thank the participants in the MalariaGEN P. falciparum Community Project, including study participants and investigators who took part in the ARC3, ARCE, and TRAC collaborations.

Data Availability Statement

Simulated genotyping data is publicly available at: https://github.com/mgzjys/sparse‐sample‐filtering/. The processing scripts can be accessed through: https://github.com/mgzjys/sparse‐sample‐filtering/. Genotyping data are publicly available through the MalariaGEN website (https://www.malariagen.net/data/p‐falciparum‐community‐project‐jan‐2016‐data‐release) or through the NIH Gene Expression Omnibus (www.ncbi.nlm.gov/geo/; Accession number: GSE100704) and European Variation Archive (Accession number: PRJEB28530).

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

Simulated genotyping data is publicly available at: https://github.com/mgzjys/sparse‐sample‐filtering/. The processing scripts can be accessed through: https://github.com/mgzjys/sparse‐sample‐filtering/. Genotyping data are publicly available through the MalariaGEN website (https://www.malariagen.net/data/p‐falciparum‐community‐project‐jan‐2016‐data‐release) or through the NIH Gene Expression Omnibus (www.ncbi.nlm.gov/geo/; Accession number: GSE100704) and European Variation Archive (Accession number: PRJEB28530).

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