# Improved central place foraging modeling: importance of landscape context and modeling strategies in the case of a French sweat bee

Anouk Glad, S. Moulherat, Émilie Andrieu, Matthieu Moulherat, David Sheeren, Annie Ouin

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Anouk Glad, S. Moulherat, Émilie Andrieu, Matthieu Moulherat, David Sheeren, et al.. Improved central place foraging modeling: importance of landscape context and modeling strategies in the case of a French sweat bee. Ecological Modelling, 2025, 508, pp.111208. 10.1016/j.ecolmodel.2025.111208. hal-05127070

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# Improved central place foraging modeling: importance of landscape context and modeling strategies in the case of a French sweat bee

A. Glad<sup>a,b,*</sup>, S. Moulherat<sup>b</sup>, E. Andrieu<sup>d</sup>, M. Moulherat<sup>b</sup>, D. Sheeren<sup>a</sup>, A. Ouin<sup>a,c</sup>

## ARTICLE INFO

### Keywords:

Stochastic movement simulator

Wild bees

Foraging

Individual-based model

SimOïko_CPF

InVEST

## ABSTRACT

Insect pollinators, including wild bees, contribute to the pollination of >90 % of wild flowering plants. A realistic simulation of their movements during foraging behaviour is essential to predict their pollination capability. The aim of this study was to develop a new individual based model called SimOïko_CPF to tackle some of the limitations of current models of wild bees' foraging movement. Its performance was compared with a distance decay model: InVEST crop pollination (InVEST_Poll). For central-based foraging species like wild bees, the SimOïko_CPF model makes it possible to use the SMS algorithm as a support for the movements of individuals during foraging. The SimOïko_CPF model increases the capability to model the interactions between individuals and their landscape components such as physical friction, the attractiveness of floral resources, and collection probability. Sensitivity analysis of the parameterization of the species' life-history traits performed in this study highlights the importance of two parameters in the landscape visitation: the spatial short-term memory size, and the resource collection probability. The two models were used to simulates the foraging pattern of a small species of wild bee (Lasioglossum marginatum). The outputs of the two models showed similar correlations with the capture data. The comparison between SimOïko_CPF and InVEST_Poll revealed discrepancies in the simulated foraging patterns on virtual landscapes varying in patch size, aggregation and composition. It's showing that SimOïko_CPF can be use in various heterogenous landscapes and allows the investigation of a large set of parameters including the effect of physical friction and resource attractiveness.

## 1. Introduction

Insect pollinators provide an essential ecosystem service by contributing to the pollination of 90 % of wild flowering plants and 75 % of food crops worldwide (Cardinale et al., 2012; IPBES, 2016; Klein et al., 2006). Wild bees are known to contribute to the pollination of a wide variety of flowering plants but are declining at alarming rates (Cameron et al., 2011; Potts et al., 2010). This decline is due to multiple factors including habitat fragmentation and destruction, pollution (i.e. pesticide use, heavy metals), floral homogenization, and climate change (Hemberger et al., 2021; Nicholson et al., 2023; Odanaka and Rehan, 2019; Pereira et al., 2021; Senapathi et al., 2015; Wyver et al., 2023). Conservation effort in order to maintain endangered bee species population and to ensure efficient plant pollinations can be achieve by providing high quality nesting and floral resources to pollinators (Brown

and Paxton, 2009).

Wild bees' daily foraging trips starts and ends at their nest site and they are therefore defined as central place foragers (Bell, 1990; Danforth et al., 2019). Like other animals, when making movement decisions, insect pollinators are likely to be influenced by the composition and structure of the landscape (Fahrig, 2007; Nathan et al., 2008). The relevance of functional connectivity in the richness and abundance of wild bees in a heterogeneous landscape was highlighted by Boscolo et al. (2017). Several studies have demonstrated the role of the arrangement and the characteristics of the landscape features on the dispersal capacities and foraging movements of wild bees in both urban and agricultural landscapes (Johansson et al., 2018; Lander et al., 2013). For instance, Griffin and Haddad (2021) showed that ecological corridors influence occupation of nest sites by a solitary-cavity nesting bee, and radio-tracking of bumble bees showed the preferential use of

<footnote><sup>a</sup> INP-ENSAT, UMR 1201 Dynafor, Auzeville-Tolosan, France</footnote>

<footnote><sup>b</sup> OïkoLab, TerrOïko, 2 place Dom Devic, Sorèze, France</footnote>

<footnote><sup>c</sup> LTSEr Zone Atelier “PYRÈNÉES GARONNE”, Auzeville-Tolosane, France</footnote>

<footnote><sup>d</sup> Université de Toulouse, INRAE, UMR 1201 Dynafor, Castanet-Tolosan, France</footnote>

<footnote>* Corresponding author.
E-mail address: gladanouk@gmail.com (A. Glad).</footnote>
ground-level linear features such as trails to navigate, revealing the importance of spatial structure (Brebner et al., 2021). In an urban environment, *Ceratina calcarate* dispersal was facilitated by the presence of vegetation and limited by impervious surfaces (Chau et al., 2023). Specifically concerning foraging movement, a negative effect of roads on foraging trips leading to a decrease in pollination effectiveness between sites on each roadside has been shown (Fitch and Vaidya, 2021). Moreover, Lander et al. (2013) found that pollen movements observed in two different landscapes were better explained by incorporating different friction values between land-use types. The role of patch aggregation in pollinator distribution has been demonstrated as well (Favarin et al., 2022). Fragmentation of floral resources has also been shown to greatly influence the population dynamics, community characteristics (species body size), and foraging strategies of bees (Santos et al., 2021; Warzecha et al., 2016; Wojcik and McBride, 2012). Finally, the composition of the landscape with respect to the amount, quality and location of floral resources has been shown to shape wild bee communities and foraging strategies (Neumüller et al., 2020; Riedinger et al., 2015). Understanding wild bees foraging movements is essential for conservation efforts targeting endangered species and estimates of pollination deficiency that could impact both endangered plants species and crop yields. Realistic modeling is therefore a practical tool to study various scenarios at different spatial and time scales and can give a variety of inputs concerning population dynamics, species interactions and landscape use.

Models designed to estimate bees' foraging movements are based on central place forager (CPF) algorithms. The foraging capacity of the individuals is modeled using various equations or algorithms. The first models summarized these movements as a random walk process (Reynolds et al., 2007; Reynolds, 2009), making the probability of discovering a resource mainly depend on the distance from the nest. Those models are still widely employed today to estimate pollination at large scales. For instance, distance decay models such as the InVEST crop Pollination model (hereafter termed InVEST_Poll) uses an exponential decay curve to weight the effect of distance from the nest in estimating potential pollination (Lonsdorf et al., 2009; Olsson and Bolin, 2014; Pashanejad et al., 2023). More recently, mechanistic models, such as Poll4pop, that include population dynamics and estimates foraging movement based on a variety of simple algorithms (Häussler et al., 2017; Twiston-Davies et al., 2021). These models propose several methods to predict the spatial distribution of wild bees and pollination potential (i. e. distance decay, random walk, correlated random walk, levy flight); (Marchand et al., 2015; Reynolds, 2009). Nevertheless, none of these models account for the effect of landscape composition and the ability of each type of land cover to allow wild bees to move.

Despite the fact the studies do show the role played by landscape structure and arrangement in wild bees' movements, few models are able include explicit foraging movement rules such as interactions between individuals, negative and positive reinforcement, spatial short and long-term memory, flight speed, resource attractiveness, or resource depletion (Mailly et al., 2025). The addition of more complex processes to models is possible using individual-based models (IBMs); (An et al., 2021; Grimm et al., 2017). IBMs simulate the processes and actions of the individuals and are used to examine emergent properties within the system. Most of these models, such as BEESCOUT, have been developed for a particular species, for example, bumble bees or honey bees, and cannot be used for other wild bee species (Dubois et al., 2021; Everaars and Dormann, 2014; Everaars et al., 2018; Morán et al., 2023; Rands, 2014). One of the limits of IBMs is the inability to parametrize such complex models, especially if data and knowledge are lacking about some of the model processes, thereby heightening the challenge of verifying and validating the model outcomes (An et al., 2021).

Animal movements in general have been modeled by a wide range of algorithms to study population dynamics or spatial use patterns (Dutta et al., 2022). Their objectives differ and include habitat selection, home range evaluation, estimating population genetics (breeding movements

and dispersal), and spatial patterns of foraging behavior (Joo et al., 2022). Among them, the Stochastic Movement Simulator (SMS) developed by Palmer et al., (2011) and Coulon et al. (2015) was incorporated in the IBM software SimOïko (the commercial version of MetaConnect developed by Moulherat (2014)). SimOïko_SMS is based on a series of sequential movement decisions incorporating path memory size, a directional parameter, the perceptual range, and the movement cost. Although the SMS outperforms simpler models in estimating dispersal behaviour (Aben et al., 2014; Stevens et al., 2006), it has never been used to explicitly model foraging movement, but has been used to model home range movement (food, shelter, mating, and reproduction); (Pe'er et al., 2011). Yet, incorporating additional rules and interactions with the landscapes to simulate individual movement would have several advantages, as demonstrated by Lourie et al. (2021) in the case of bats' foraging movements.

With this study, we aimed to improve current models of wild bees' foraging movement by developing a new module. For this purpose, we used an existing IBM model, MetaConnect (Moulherat, 2014), and also benefited from a computationally optimized commercial version, SimOïko. This new module was adapted from SimOïko's species population dynamics and dispersal modules. To model the foraging movements of wild bees, we used the SimOïko embedded SMS module in a CPF context (SimOïko_CPF). SimOïko_CPF has the advantage of not only accounting for the presence of resources and their distance from the nests, but also floral resource attractiveness, and physical friction to movement caused by the landscape. Further, it has the advantage of being configurable according to the characteristics of the species studied.

After developing the new IBM module (SimOïko_CPF), we performed a sensitivity analysis of the parameters driving the SMS movement rules and of the landscape components' attributes. The generated outputs were used to evaluate the ability of SimOïko_CPF to fit a wild bee species (*Lasioğlossum marginatum*) that is abundant in southwestern France using a capture dataset. This ability to fit the capture data was compared to a simpler distance decay model, InVEST_Poll. In the second part of the study, the behaviors and outputs of each model were analyzed in landscape contexts with different patch fragmentation, aggregation, and composition. The simulated foraging patterns were compared to investigate similarities and divergences obtained in the different landscape characteristics. We expected that SimOïko_CPF would have an advantage in complex heterogenous landscapes whereas distance decay models might be sufficient in homogenous landscapes.

## 2. Methods

### 2.1. Modeling foraging movement with SimOïko_CPF

#### 2.1.1. SimOïko

SimOïko is an individual-based model (IBM) with a process-based focus, used for population-viability analysis (Moulherat, 2014). SimOïko (version beta-3.1.1) software is the computationally optimized commercial version of MetaConnect (Moulherat and Moulherat, 2012; Moulherat, 2014). The IBM that can be used for both research and decision-making (Gunton et al., 2017; Moulherat et al., 2023). It is designed to be flexible thanks to a modular modeling framework based on two main modules and allows smooth integration of additional modules. One module simulates the population dynamics in suitable habitat patches provided as a raster format i.e. input from the patch map input (Moulherat, 2014). The second simulates the dispersal movements of an individual from its current patch to either a new suitable patch or results in its death (i.e. failure of the dispersal). The movement process can be modeled by using a random walk or the “Stochastic Movement Simulator” (SMS) algorithm (Palmer, Coulon and Travis, 2011). Both algorithms were used as movement algorithms in SimOïko dispersal movement module as random walk option and Stochastic Movement Simulator option.
### 2.1.2. SimOiko_CPF foraging movement module

The ODD protocol (Grimm et al., 2006), which provides a comprehensive description of the SimOiko_CPF is included in supplementary material (section S1). Statistical analysis and data curation were conducted in R 4.3.2 (R Core Team, 2020).

We adapted the general functionality of SimOiko from the population dynamics module and dispersal movement module to model the foraging behavior of wild bees to create the SimOiko_CPF. The population dynamics module was adapted to define suitable patches in the landscape to generate locations of wild bee's nests but not their life cycle. A patch is thus defined as a suitable pixel containing a nest. Multiple individuals can be assigned to each patch. The dispersal movement module simulating movement from patch to patch was modified to simulate the behavior of central place foragers. The CPF algorithm simulates the stages of the general foraging movement of wild bees. An individual starts from the patch (i.e. the nest) and then moves from pixel to pixel. At each step, the probability of collecting a resource is the result of a Bernoulli event driven by the floral resource collection probability map. The friction map is used to calculate the physical cost of the movement for the individual's movement capacity (weighted maximum foraging distance). If the individual collects a resource or reaches the maximal distance, it returns to its nest (Fig. 1). The SimOiko_CPF model does not include an energetic module.

The SMS algorithm that already existed in the dispersal module was used to simulate the movement of an individual foraging in the landscape. SMS uses three parameters to describe the movement: memory size, perceptual range, and directional persistence (Coulon et al., 2015; Palmer et al., 2011). The aim of the overall process is to calculate the probability of moving from the current location in each the eight neighboring pixels and to draw the next pixel to be moved into. This process involves the following parameters and steps. (1) The perceptual range is the number of pixels extending outward from the current location used to calculate the attractiveness of the eight neighboring pixels. Attractiveness is defined as behavioral friction and is provided by the floral resource attractiveness map with the assumption that the cost of crossing is inversely proportional to the attractiveness of the cover. The effective attractiveness of each of the 8 neighboring pixels is calculated using the mean of its own attractiveness and of the attractiveness of its own neighbors surrounding it in an array which extended to the edge of the perceptual range. That is:

$$ \text{Effective attractiveness pixel } X = \frac{1}{n} \sum_{i=1}^{n} A_i $$

where:

* X is one of the 8 neighboring pixels of the current location

* n is the number of pixels in the pixel x own neighbors (himself included).

* Aᵢ is the attractiveness value of the i th pixel x own neighbors (himself included).

* The summation Σᵢ=1 Aᵢ is the sum of all the attractiveness values of the pixels within the specified range. For diagonal cells, the values are weighted by √2.

(2) The memory size is the number of pixels from the individual's starting from the current location on the trajectory counting backwards kept in memory. The individual cannot enter the pixels kept in memory from its current location, but can visits them later as at each step the last pixel in the memory will be available again and the last pixel crossed added in pixel's memory pool. The memory size is thus shaping the trajectory into a straighter movement as the number of pixels in memory increases. It does not interfere with the attractiveness value of the accessible pixels. (3) Directional persistence (DP) defines the tendency of individuals to continue a movement in the same direction as the previous step, thus allowing to simulate curvy to straight trajectories. To do so, the effective attractiveness's are multiplied by a factor, lowest for the neighboring cell located in the same direction as the previous step and highest for the cell in the opposite direction (i.e. a 180° turn). The weight is controlled by the DP with larger values reducing the tendency for the path to be curvy. (Aben et al., 2014). (4) Finally, the probability of moving on to the next cell is calculated as the reciprocal of the weighted effective attractiveness and scaled to sum to 1 to yield selection probabilities for the eight neighboring cells. The probability of entering the next pixel follows a Bernoulli event. When the individual collects a resource or reaches the maximum distance, it returns to its nest following a straight line. Indeed, it has been shown that bees have a tendency to straighten their trajectory over time developing direct route when knowing the location of their goal (Brebner et al., 2021).

### 2.2. Distance decay model: inVEST_Poll

The InVEST® crop pollination model (https://naturalcapitalproject.stanford.edu/software/invest; 'Natural Capital Project, InVEST', 2025) used, is a distance decay model based on the equations of the Lonsdorf model (Lonsdorf et al., 2009) and includes insights from Olsson et al. (2015) that account for the foraging behavior of pollinators. This pollination model is one of the 20 ecosystem service models proposed by the InVest Platform (Integrated Valuation of Ecosystem services and tradeoffs) hosted by Stanford University. This platform aims to provide comprehensive and easy to run models of ecosystem services to "inform decisions about natural resource management". The InVEST_Poll model has been widely used in studies of wild bees and pollination (Davis et al., 2017; Groff et al., 2016; Wentling et al., 2021). By using a distance decay curve based on bees' mean foraging distance, the sum of the abundance of accessible flowers and suitable nesting areas the model estimates the annual pollinator supply. In the second step using the resulting pollinator supply map, the floral resource maps, and the species distance decay curve, it calculates the estimates of the rate of visits to each pixel.

### 2.3. Study site and wild bee dataset

The study area is located in the "Vallées et Coteaux de Gascogne", in southwestern France (Fig. 2). The site is a Long-Term Socio-Ecological Research area named Zone Atelier PYrénée-GARonne (ZA PYGAR) and covers approximately 450 km². This agricultural area is characterized by hilly landscapes with an heterogenous mosaic of annual crops combining woodlots and mixed crop-livestock farming (Ouin et al., 2021).

<figure><img src="image_3.png" /><figcaption>Fig. 1. Conceptual framework of the CPF foraging movement implemented.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 2. The study area in the “Vallées et Coteaux de Gascogne”, Occitanie region, southwestern France, and locations of the capture sites.</figcaption></figure>

We produced the landcover maps using three datasets: the first, the 2016 agricultural Land Parcel Information System (Registre Parcellaire Graphique French acronym RPG; https://geoservices.ign.fr/rpg) defined based on the farmers' annual declaration of the crops they cultivate at the parcel level in the framework of the EU Common Agricultural Policy. The second, the TOPOgraphic DataBase “BD TOPO®” 2010 (http s://geoservices.ign.fr/bdtopo) a nationwide database including anthropogenic infrastructures that is produced by the French Institute of Geography (IGN®). The third datasets is a nationwide database with a large-scale land use map of land other than cultivated land, (OCcupation du Sol à Grande Échelle “OCS-GE”) produced by the IGN® (https://ge oservices.ign.fr/ocsge). We combined these data to produce a vector map of the highest possible spatial accuracy. The resulting map comprised 133 landcover categories for the year 2016 including 116 agricultural land use categories (e.g. wheat, oilseed rape, sunflower) and 15 other land use / land cover categories (e.g. buildings, hedgerows, surface water). We rasterized the vector dataset at a spatial resolution of 3 m and then produced a new map for each of the parameters required for the simulation: nesting resource availability, attractiveness of floral resources, floral resource collection probability, physical friction affecting movement.

Wild bees were collected as part of a previous research project using three colored pan traps (blue, white, yellow) (30 traps in all), filled with soapy water, and left out for four days in April 2016. The bees in the traps were collected and identified to the species level by an expert entomologist (Ollivier et al., 2024). For the present study, we selected in the most common wild bee species in the dataset: *Lasioglossum marginatum*. *L. marginatum*, is a ground-nesting, small, polylectic, social and polyandrous wild bee present in the southwest and center of the Pale-arctic region. The mean distance covered foraging was calculated using an allometric relationship between the interticular distance and the homing distance (Greenleaf et al., 2007). The mean foraging distance of

*L. marginatum* was estimated to be 102 m. For the simulations, we used friction coefficients that reflected the species' ability to cross the 133 natural habitat types cited in the literature and expert knowledge concerning wild bees and vegetation characteristics (Baude et al., 2016; Desaegher et al., 2021, 2022) (supplementary material section S2 Table S2.1).

## 2.4. Sensitivity analysis

### 2.4.1. *SimOiko CPF simulation settings*

To run simulations to account for the impact of trap attractiveness on bees, we modified the landcover maps as follows: at each trapping location, we modified the pixel value to the highest “floral resources attractiveness” value on the map. For all simulations, we randomly generated the nest locations (one nest per pixel with one individual per nest) and their density was weighted by the landcover suitability score for nesting resources. This choice was made to ensure a larger spatial coverage to optimize simulation calculation time. In addition, to obtain reliable results on movement, we did not include any nests in the pixel containing the trapping location. To ensure the results would be comparable, the location of the nests remained the same in all the simulations. We set the number of foraging trips at 100 successive trips per individual. As the objective of the model is to estimate the foraging movement pattern in the landscape, we did not include the straight return trajectory to the nest in the results. We performed 10 repetitions of each type of simulation, to evaluate the stochastic variability of the outputs.

Analyses were performed using the mean foraging distances of the study species *L. marginatum* (mean foraging distance 102 m; see inter- ticular distance in section 2.1.2). Model sensitivity was evaluated for several SMS parameters (memory size, perceptual range, directional persistence; see section 2.1.2) and landscape interaction components
<caption>**Table 1**</caption>

Variations in the sensitivity analysis parameters used in this study (one-at-a-time method) with the two set of fixed values and the variations applied for each of the tested parameter.

<table><thead><tr><th rowspan="2">Fixed values settings</th><th colspan="3">SMS parameters</th><th colspan="2">Landscape interface</th></tr><tr><th>Perceptual range</th><th>Directional Peristence</th><th>Memory size</th><th>Resource collection</th><th>Resource attractiveness</th></tr></thead><tbody><tr><td>Directional Peristence = 1,<br>Memory size = 0,<br>Perceptual range = 1</td><td>Variation from 1 to 6 pixels</td><td>Variation from 1 to 3</td><td>Variation from 1 to 18 pixels (by 2)</td><td>Variation (±) 20 % and 40 %</td><td>Variation (±) 20 % and 40 %</td></tr><tr><td>Directional Peristence = 2,<br>Memory size = 2,<br>Perceptual range = 1</td><td>Variation from 1 to 6 pixels</td><td>Variation from 1 to 3</td><td>Variation from 1 to 18 pixels (by 2)</td><td>Variation (±) 20 % and 40 %</td><td>Variation (±) 20 % and 40 %</td></tr></tbody></table>

(resource collection probability, resource attractiveness). To assess the relative importance of each parameter on output variability, we used the Morris method where one parameter varies while all the others remain fixed (Table 1). The Morris method was used for two sets of SMS fixed parameters to study potential interaction effect between the parameters. In one set, we used the minimum possible value of all the parameters (no memory, a directional persistence of 1, and a perceptual range of 1 pixel). In the second set, we set the following values: memory of 1 pixel, a directional persistence of 2 and a perceptual range of 1. We set the number of individuals at 120 000 and used the original maps of resource collection probability and resource attractiveness (see section 2.1.2).

We defined variations in the SMS parameters as follows. (1) Perceptual range from 1 to 6 pixels; from which we expected a decreasing trajectory length with increasing value due to the higher weight given to resource attractiveness, (2) Directional persistence from 1 to 3, from which we expected a marked increase in trajectory length because more weight is given to the trajectory shape than to resource attractiveness, hence reducing the ability of an individual to find and collect a resource (3) memory size from 0 to 18 with a gap of two pixels between each value, from which we expected an increase in each individual trajectory due to the limited number of available pixels. We set variations in the landscape interaction components at ±20 % and ±40 % of their initial values for the landscape elements in which the overall resource quality and quantity are difficult to estimate (forest, grassland, hedges, non-identified cropland). We expected shorter trajectories with higher resource attractiveness and collection probability as the individuals will be able to locate and collect a resource efficiently.

### 2.4.2. *SimOiko_CPF post treatment*

We corrected all the raw outputs corresponding to pixel visitation by bees at the location of the nests by calculating the mean visitation from the neighboring pixels using a moving window (of 5 m). Indeed, as the individuals return to their nest at the end of each foraging trip are not undertaking a passage resulting from the SMS movement.

We summed the frequency of passage to each pixel within the study area to capture variations in the pattern of movement resulting from the parameter values. We calculated the number of passages separately for two types of landscape compositions, i.e. with and without resources, to analyze possible diverging patterns in the visitation in the presence or absence of resources.

### 2.4.3. *InVEST_Poll simulations*

We performed simulations for *L. marginatum* using the same maps of nesting suitability and floral resource availability as for the *SimOiko_CPF* models and its mean foraging range.

## 2.5. Case study: comparing *SimOiko_CPF* and *InVEST_Poll* estimates with *capture data*

We used the results obtained from the sensitivity analysis to compare the predictions of the two models and how they fit real capture data for the study species *Lasioglossum marginatum*. We performed additional simulations to study the influence of the number of individuals on the fit to the capture data, with population variations ranging from 40 000 to 800 000 individuals (Supplementary material S3 Fig S3.1). We used the mean visitation by pixel (SimOiko_CPF) and mean relative abundance (InVEST_Poll) for different size buffer zones ranging from 5 m to 50 m in diameter around the trap (Desaegher, Sheeren and Ouin, 2021). We compared the simulation results from both SimOiko_CPF and InVEST_Poll with field captures using two methods, a Spearman correlation and a Bland-Altman method. This method is used to analyze the agreement between two sets of observations using a unique scale. It calculates the mean difference for each measurement allowing the detection of disagreements in the two sets.
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Examples of simulated landscapes with the 5 different landscape compositions: (1) green, matrix with no floral or nesting resources, (2) brown patch composed of high-quality nesting resources, (3) white patch composed of high-quality floral resources, (4) blue patch composed of high-quality nesting resources and medium quality floral resources, (5) yellow, patch composed of no nesting resources and medium quality floral resources, (6) orange, patch composed of both high-quality nesting and floral resources.</figcaption></figure>

## 2.6. Effect of patch size, aggregation, and composition

### 2.6.1. Landscape generation experiments

The simulation experiments aimed to compare the SimOïko_CPF and InVEST_Poll prediction along a gradient of landscape complexity: patch size, aggregation and within-patch composition.

A patch generally refers to an area with a homogenous land cover defined as a habitat (hence composed of all the resources needed by a species). Hereafter, patches are defined as areas of similar composition that can host either nesting or floral resources for bees, or both types of resources. We generated virtual landscapes using the package rlflsgen in R (Justeau-Allaire et al., 2022). The different landscapes generated are composed of two types of patches: (1) the first type of patches contain

resources of varying quality for wild bees (nesting and/or floral resources) and are permeable to movement, and (2), the second type contain no resources and are less permeable to movement (i.e. the matrix). The aim is to account for two gradients of configuration (fragmentation and aggregation) and variation in terms of patch composition (presence and quality of resources). We set the size of the selected patches to match realistic dimensions of agricultural parcels in a real landscape. For each type of landscape, we generated ten random repetitions with the same composition and configuration characteristics leading to differences in patch arrangement landscapes but with the same overall characteristics (Fig. 3).
1) Landscape series 1: patch size gradient

We generated five landscapes with different patch sizes and similar percentages of cover, from the landscapes with large patches of 1.9 ha to 2 ha (Landscape 1.A Fig. 3) to the one with small patches 0.1187 to 0.1250 ha (Landscape 1.E Fig. 3). Half the patches contained only high-quality nesting resources (suitability of 0.8) while the other half contained only high-quality floral resources (suitability of 0.8) (i.e. in these landscape series, nesting and floral resources are separate). These simulated landscapes aim to represent an agricultural landscape where crop fields may provide floral resources (i.e. Sunflowers) whereas the bees nest in different types of Landcover (i.e. Grassland, herbaceous areas, forests).

2) Landscape series 2: patch aggregation gradient

We generated four landscapes with different levels of aggregation, from the most segregated landscape 2.A to the most mixed landscape 2.D (Fig. 3). Like in the Landscapes Series 1, half of the patches contain only high-quality nesting resources while the other half contains only high-quality floral resources, with no intra-patch variability (i.e. in these landscape series, nesting and floral resources are separate). The location of the patches is kept constant from landscape 2.A to landscape 2.D, in addition to their size (from 0.475 to 0.5 ha), leading to strictly identical landscapes in terms of patch distribution. Only the values assigned to each patch vary, leading to different nesting and floral resource arrangements. The

number of patches in each resource category was kept constant (62 patches with nesting resources and 63 patches with floral resources).

3) Landscape series 3: intra-patch variations in composition

We generated three landscapes with three different patch compositions (the patch size of 0.475 to 0.5 ha and spatial arrangement remained constant). First, a landscape called 3.A where half of the patches (in terms of number and surface area) were composed of high-quality nesting resources and of medium-quality floral resources and the other half were composed of medium-quality floral resource only (i.e. no nesting resources) (Fig. 3). Second, a landscape called 3.B where half of the patches were composed of nesting resources and of medium quality floral resources, and the other half of high-quality floral resources only. Third, a landscape called 3.C where half of the patches were composed of nesting resources and of medium quality floral resources, and the other half of nesting resources and high-quality floral resources. To compare the results, we used the same landscape maps for the three compositions, while only changing the value of the patch.

2.6.2. Simulation settings

We performed four different SimOiko_CPF parametrizations and compared the results to the results obtained with InVEST_Poll. The first step was to validate the equivalence between a neutral SimOiko_CPF model, and the second step was to evaluate the role of the interaction

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Sensitivity analysis results displaying the variations in visitation of the landscape for the different sets of parameters used for a foraging distance of 102 m. The y-axis displays the overall visitation rate obtained with the SimOiko_CPF model simulation in columns 1 to 5. The x-axis shows variations in parameter values in the three first columns (resources attractiveness, resource collection, directional persistence). The x-axis shows the number of pixel variations in the 4th and 5th columns (memory size and perceptual range). The three rows represent the landscape from which the visitation rate was calculated (whole landscape, with resources and without resources). The two colors represent the two sets of fixed parameters used (see section 2.4).</figcaption></figure>
with the three landscape components for SimOiko_CPF setting (i.e. friction map, attractiveness map, and resource collection) on the resulting foraging pattern. Those three maps are created for each landscape's series regarding their characteristic. The simulation settings are defined as follows: (SMS1) Neutral friction, neutral interface, and no collection of floral resources, used to validate the equivalence between InVEST_Poll and a SimOiko_CPF model. This simulation is equivalent to a random walk as there is no interaction with the landscape; (SMS2) Friction map, neutral interface, and no collection of floral resources; (SMS3) Friction map, attractiveness map, and no collection of floral resources; (SMS4) friction map, attractiveness map, and resource collection map. For each simulation, ten repetitions of 40 000 nests location (1 by pixel) were drawn. The location is weighted by the nesting habitat quality and by the availability of resources by using the pollinator supply output from the InVEST_Poll simulation (example location with

high quality nest resources but no floral resources cannot be drawn). This was done in order to allow the results to be compared with InVEST_Poll. A total of 1 000 successive foraging bouts per individual were simulated. The number of visitations obtained with SimOiko_CPF were rescaled to between 0 and 1 and a moving window of 3 pixels was applied to smooth the results. Those were compared with InVEST_Poll results by using a Spearman correlation between rasters.

## 3. Results

### 3.1. Sensitivity analysis

The parameters that showed the largest variation in visitation across the landscape are the memory parameter and the probability of collecting a resource. The directional persistence and perceptual range had

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Boxplot of the bias obtained between pollination estimates and real captures values of *L. marginatum* by using a Bland-Altman analysis. It represents results for one sets of fixed parameters used for the sensitivity analysis simulations (DIR = 1, MEM = 0 and PER = 1). The different plots represent each parameter tested, with the variation represented by the x-axis and the bias estimation by the y-axis. Each color represents the different size buffer for which the mean visitation rate was calculated.</figcaption></figure>
a lower influence on the overall landscape visitation. Directional persistence led to an increase in visitation with memory, and decrease with no memory. Increased perceptual range led to a decrease in visitation (Fig. 4).

The increase in the number of pixels kept in memory led to an overall increase in visitation across the landscape, but the relation was not linear (Fig. 4). The difference between no pixel kept in memory and a minimum of two pixels caused a marked increase in visitation. Subsequently, the visitation increased with the number of memorized pixels until it reached a plateau. Considering the visitation in areas with resources, a plateau was reached with a minimum value of only 4 memorized pixels revealing the limited influence of memory on the trajectories and on the ability of the individuals to reach resources.

The probability of collecting a resource influence the overall number of visitations in the study area (Fig. 4). When the probability of collecting a resource increase the landscapes overall visitation decreases. Whereas when the probability of collecting a resource decrease the landscapes overall visitation increase.

The increase in the directional persistence parameter values led to an increase in the total visitation across the landscape (Fig. 4). However, the response differed between areas with and without resources. The visitation increased in areas with no resources when the memory fixed parameter was set to 2 pixels. In contrast, a strong decrease was observed with the increase in directional persistence when the memory fixed parameter was set to 0 pixels.

Increasing the perceptual range decreased the total visitation across the landscape, which was expected (Fig. 4). This decrease was more pronounced in areas with resources demonstrating the effect of the weight of this parameter counterbalancing the resources attractiveness values.

## 3.2. Comparison of SimOiko_CPF and InVEST_Poll estimates with capture data

The visitation by *L. marginatum* estimated by the SimOiko_CPF model was positively correlated with the captures at the site with a high number of individuals and for buffer size ranging from 35 m to 40 m (Table 2; Supplementary material S4 Fig. S4.1). The highest correlation was observed when the number of individuals reached 600 000 with the fixed parameters memory set at 0, perceptual distance at 1 and directional persistence at 1 and buffers of 35 m, 40 m, and 45 m with a mean Spearman correlation of 0.65. Focusing on results obtained with buffers of >35 m, the lowest correlations (0.23) were observed for 120 000 individuals, memory set at 0, perceptual distance at 1, and directional persistence at 3.

The Bland-Altman methods used between SimOiko_CPF and the capture data revealed marked differences in the estimated bias. The minimum bias of -1.98 was observed for simulations with 40 000 individuals while the highest bias (-142.16) was observed for simulation with 600 000 individuals. Overall, the number of individuals simulated

<table><caption>**Table 2**
Spearman correlation and Bland-Altman bias between pollination estimates by InVEST_Poll and *L. marginatum* real capture data calculated for mean buffer values ranging from 5 m to 50 m around the traps.</caption><thead><tr><td>Buffer</td><td>Spearman correlation</td><td>Bland-Altman bias</td></tr></thead><tbody><tr><td>5</td><td>0.42</td><td>1.56</td></tr><tr><td>10</td><td>0.63</td><td>1.56</td></tr><tr><td>15</td><td>0.68</td><td>1.56</td></tr><tr><td>20</td><td>0.66</td><td>1.57</td></tr><tr><td>25</td><td>0.63</td><td>1.57</td></tr><tr><td>30</td><td>0.62</td><td>1.57</td></tr><tr><td>35</td><td>0.63</td><td>1.57</td></tr><tr><td>40</td><td>0.61</td><td>1.57</td></tr><tr><td>45</td><td>0.6</td><td>1.57</td></tr><tr><td>50</td><td>0.59</td><td>1.57</td></tr></tbody></table>

is the factor that most influenced bias in all the simulations (Fig. 5). The calculated bias also increased with the increase in the size of the buffer in all cases.

Concerning the correlation between the capture data and the InVEST_Poll estimates, the highest correlation was obtained with a buffer of 15 m (Spearman correlation 0.68) and the lowest correlation was obtained with a buffer of 5 m (Spearman correlation 0.42); (Table 2). The calculated bias did not vary with the different buffer sizes, as we observed a bias of 1.56 (smaller buffers) and 1.57 (larger buffers).

## 3.3. Simulation experiments: responses of SimOiko_CPF and InVEST_Poll models to landscape patch size, aggregation and composition

Regarding the results obtained for landscape with a variation in patch size, the correlations obtained between a InVEST_Poll and SMS1, SMS2 and SMS3 simulations (respectively, neutral; friction added; friction and resource attractiveness) were higher (> 0.92) than SMS4 (friction, resources attractiveness, and collection added) for all landscapes (Fig. 6). The correlation obtained between those three settings (SMS1, SMS2, SMS3) and InVEST_Poll were lower for landscapes with large patches than for landscapes with small patches. With the SMS4 simulation the correlation between with InVEST_Poll was the lowest with a minimum of 0.35 for large patches (Fig. 6 1.A) and a maximum of 0.55 for small patches (Fig. 6 1.E).

When we examined variations in patch aggregation, a different pattern was observed. When a neutral simulation (SMS1) was compared with a InVEST_Poll, all the results were highly correlated (> 0.9) demonstrating the equivalence of the two approaches, the remaining difference (0.1) being due to the stochasticity of the SimOiko_CPF model. A similar result was observed when both friction and resource attractiveness effects were added (SMS3). When only the effect of friction was added (SMS2) the correlations were lower compared to SMS1 and SMS3, the lowest values being observed for the patch aggregated landscape (Fig. 6 2.A). However, when SMS4 (friction, resources attractiveness, and collection added) was used, the correlation with InVEST_Poll was lower compared with SMS1, SMS2, SMS3, with a minimum of 0.32 for aggregated patches and a maximum of 0.37 for mixed patches.

Finally, the correlations obtained between a InVEST_Poll and SMS1 SMS2 and SMS3 simulations (respectively, neutral; added friction; added friction and resource attractiveness) were higher than with SMS4 (> 0.84) for all landscapes despite variations in the composition of the patches. The lowest values were observed for a landscape in which all the patches contain mixed nesting and floral resources (Fig. 6 3.C). When SMS4 (friction, resources attractiveness, and collection added) was used, the correlation between the models was high for both 3.A and 3.B landscapes where half of the patches contain mixed nesting and floral resources and only half of the floral resources are high (respectively 0.82 and 0.78). However, when SMS4 was used on a landscape with in which all the patches contain mixed nesting and floral resources (Fig. 6 3.C), the results were not correlated.

# 4. Discussion

The aim of the present study was to propose a model that simulate wild bees foraging movement pattern in a heterogeneous agricultural landscape based on a central place forager module associated with a stochastic movement simulator. Indeed, the majority of models used to estimate bees' foraging movement and pollination patterns are distance decay models that do not account for the composition and configuration of landscape elements (Lonsdorf et al., 2009; Olsson and Bolin, 2014; Pashanejad et al., 2023). Yet several individual-based models are used to simulate precise foraging movement including interactions between individuals (competition or cooperation), resources' attractiveness and depletion, spatial memory, and flight speed (Rouabah et al., 2024). However, the main limits of these models are (1) the computational time
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Spearman correlation between the SimOiko_CPF and InVEST_Poll models with the different virtual landscapes on the x axis and the correlations values (not similar between plots) on the y axis. (1) Variation in patch size from large (1.A) to small 1.E). (2) Variation in patch aggregation from 2.A (aggregated patch) to 2.D (mixed patch) (3) Variation in patch composition with 3.A, 3.B, 3.C. (SMS1) Neutral friction, neutral interface and no collection of floral resources, used to validate the equivalence between InVEST_Poll and an SimOiko_CPF model. (SMS2) friction map, neutral interface and no collection of floral resources. (SMS3) friction map, attractiveness map and no collection of floral resources. (SMS4) friction map, attractiveness map, and resource collection map.</figcaption></figure>

which does not allow simulations at both fine scale and a large extent and (2) the difficulty involved in parametrizing them due to the lack of knowledge about the traits of each species. Our approach is more generic and accounts for the arrangement of landscape features by using a friction parameter that indicates physical permeability to movement, a resource attractiveness parameter that allows the individual to favor more rewarding resources, and a resource collection parameter that models the probability of collecting a resource. The addition of these parameters allowed us to explore the foraging behavior of wild bees in a complex landscape in more detail by evaluating the effect of the interaction between the landscape components (configuration, composition) on the resulting foraging pattern.

## 4.1. Sensitivity analysis

Two main parameters were found to influence overall landscape visitation: the number of pixels in memory, and the probability of resource collection. The increase in the number of pixels kept in memory results in an increase in landscape visitation. Indeed, increasing the memory size leads to fewer pixels choice at each step of the movement made by the simulated individual. It thus generally reduces the chances of finding a resource located along past pixels. Consequently, a plateau in the number of visitations is rapidly reached in areas with floral resources, showing that increasing the memory does increase the length of foraging bouts toward areas containing resources. In our model, the memory parameter is used as a short-term memory to avoid exploring the same pixels multiple times, but how long or how well bees remember where they have been is not known, making it difficult to parametrize

(Chittka et al., 1997; Pull et al., 2022). The variation in the probability of collecting resources showed that it has a marked influence on landscape visitation, particularly in areas containing floral resources. Indeed, the visitation of those areas decreases with an increase in the probability of collecting resources. This is due to an increase in successful resource collection, leading to shorter foraging bouts overall. In our study, the choice of the probability of collecting a resource was proposed by Desaegher et al., (2021) and, based on the literature and on expert opinion. It has been demonstrated that the description of resources in terms of attractiveness, accessibility, and profitability is key to describing the abundance of wild bees (Alignier et al., 2023). Nevertheless, it is challenging to accurately estimate the availability, quantity, and quality of the resources because they may be species-specific (Rollin et al., 2013).

Some results demonstrated that complex interactions between the parameters from SimOiko_CPF parameters and landscape interface are involved. Future analysis may explore the complex interactions further as proposed by Ten Broeke et al., (2016). This sensitivity analysis also showed that, in our model, variation in different parameters can lead to similar tendencies in the obtained simulation results (i.e. increase visitation) making it challenging to disentangle the effect of each separate variable. This analysis also highlighted differences in the response pattern to landscape composition (with or without resources). It demonstrates that SimOiko_CPF by using a SMS algorithm modeling the movement simulates for variations in visitations linked to the characteristics of the land cover.
## 4.2. Case study: comparing SimOiko_CPF and InVEST_Poll estimates with capture data

By applying our models to a real landscape, we were able to compare the results with a capture dataset of a small wild bee species, *L. marginatum*. We observed a high correlation between several model estimates and the number of individuals captured. The number of individuals (and, by extension, the nest location) had a significant influence on the outcomes, with lower correlations observed in models with an intermediate number of individuals (120 000). In addition, the Bland-Altman analysis showed that the bias between the capture data and the simulated results increased greatly with the number of individuals. This result demonstrates that by increasing the number of individuals, we also increased the difference between the number of captured individual (which are scarce) and the raw outputs obtained with SimOiko_CPF models. Overall, using a Spearman correlation between abundance capture data and simulations results, we managed to obtain similar correlation results for both types of models. The results obtained using a distance decay model (InVEST_Poll) showed slightly better correlation values, thereby giving it an advantage as it requires limited computational time and effort. It also showed smaller bias between capture data and simulation results. Nevertheless, the high correlations obtained between SimOiko_CPF and capture data demonstrated that our model can be used as well, in particular if the modeler wishes to study movement patterns and include the effect of landscape friction.

In their recent review, Creech et al. (2024) found that, despite the increase in the number of connectivity models produced in the period 2006–2021, only an average of 2.5 % included a validation process thereby underlining the difficulties encountered by modelers. The same authors reported that model validation strength depends on the characteristics of (1) the validation data and (2) the validation approach used. Our results echo observations by Creech et al. (2024) and identified two main element limitations: (1) The capture data we used are limited by the small number of traps and only one sampling session, whereas validating an individual-based model requires larger datasets than those usually compiled. Ideally, the data set should be designed to validate the model and should contain *Multiple species* observed in many traps over multiple seasons and years of trapping across a variety of landscapes. This limitation was identified by Rouabah et al. (2024) as one of the main challenges for model validation as such long-term monitoring studies of wild bees are scarce. (2) The methods used in our study might not be sufficient to validate complex models despite being listed among the 11 validation approaches reviewed in (Creech et al., 2024); (i.e. “4. Correlated-based”). In the future, the use of pattern-oriented modeling theory (POM), (Grimm et al., 2017), the opportunities offered by big data (An et al., 2021), the prior identification of the data that will be needed to build and validate the model (Wood et al., 2015) or the use of the virtual ecologist approach (Zurell et al., 2010) should enable better modeling practices.

## 4.3. Effect of landscape patch size, aggregation, and composition

By using multiple landscapes composed of different patch sizes, patch aggregation, and patch compositions, we demonstrated that we can obtain spatially different pollination estimations compared to a distance decay model. The addition of friction to the foraging movement rules revealed its greater influence in the case of aggregated medium-size patches. This is due to the need to move between patches through a larger proportion of the matrix which contains no resources and is physically more difficult to cross. In contrast, incorporating the resource attractiveness effect in the movement process revealed only minor differences compared to estimates obtained using a distance decay model. Nevertheless, the observed correlation between SimOiko_CPF and InVEST_Poll was lower in the case of a landscape composed of patches containing both nesting and floral resources compared to landscapes with containing only one resource. This is because individuals nesting

in a patch with high-quality floral resources are unlikely to forage outside this patch, whereas, in a distance decay model, all reachable resources are assumed to be visited. Finally, the use of a full SimOiko_CPF foraging model (SMS4) showed the lowest correlation between estimated foraging pattern compared to the InVEST_Poll. The disparities largely depend on the landscape context with a higher correlation between models observed for landscapes with smaller patches compared to large patches. Yet, no difference was observed in the variations in the patch aggregation. The observed differences were generally linked to the tendency of distance decay models to overestimate the distance covered by wild bees when foraging by not accounting for behaviors such as avoiding un-attractive landcover (Johansson et al., 2018), the sink and dilution effect of high quality resources (Holzschuh et al., 2016; Nicholson et al., 2019; Riggi et al., 2024) or the mask effect of flower discovery (Morán et al., 2023), which can lead to a variety of effective ways of foraging for individuals (Danner et al., 2016). These results suggest that SimOiko_CPF could be an asset in the case of large patches (ie. presence of large agricultural crops) or mixed resources patches (ie. presence of natural areas, grassland, forests ...). The effect of the matrix on the obtained estimates shows that SimOiko_CPF can also be an asset in estimating pollination in urban landscapes by taking into account the physical friction of impervious surfaces or buildings. SimOiko_CPF can be used to improve conservation effort of wild bees and help to optimized pollination of crops and wild plants.

## 4.4. Future development

Our proposed SimOiko_CPF framework as a foraging movement model for wild bees adds new insights on the importance of landscape context when estimating pollination and can be used and combined with other individual-based models. This model can also benefit from other researches and be ameliorated. The inclusion of a longer-term memory parameter that would allow individuals to return to a previously identified rewarding resource could further improve foraging movement estimates (Klein et al., 2019; Lihoreau et al., 2012). One of the key challenges identified by Rouabah et al. (2024) is accounting for the bees' consumptive competition for pollen and nectar, as competition the intra and inter-species competition may force some individuals to increase their foraging range or to choose a different supply of resources. This effect could be modelled by adding a resource depletion function, as recently done by Walters et al. (2024) to improve a model developed by Olsson and Bolin (2014) and Olsson et al. (2015) for social bees. Furthermore, as the spatio-temporal variations in floral resources are known to influence population dynamics and future nest locations, it should be taken into account in models to better estimate pollination in agricultural landscapes (Blasi et al., 2022; Guezen and Forrest, 2021). Coupling a SimOiko_CPF foraging movement model with models of bee population dynamics, such as SimOiko population dynamics module, Poll4pop or BEEHAVE, could provide valuable insights into the influence of landscape composition and configuration on population viability (Becher et al., 2018; Gardner et al., 2020). Finally, incorporating models of pollinator movements in plant pollination models (pollen dispersal, gene flow) could help to further disentangle the complex interactions between pollinators and flowerings plants (Mailly et al., 2025).

## 5. Conclusion

The development of the SimOiko_CPF to model wild bees' foraging movement makes it possible to include more varied interactions between the simulated individuals and the landscape components (physical friction, floral resources attractiveness and collection probabilities). The sensitivity analysis revealed the importance of two parameters concerning landscape visitation: the spatial short-term memory, and the probability of collecting a resource. Comparing the outputs of InVEST_Poll or the SimOiko_CPF models with capture data revealed minor differences in their ability to fit capture data for *L. marginatum*.
Yet, landscape simulation experiments showed that the correlation between their outputs is stronger in landscapes with small homogeneous patches than in landscapes with large patches or with patches containing mixed resources. The landscape simulation experiments demonstrate that SimOïko_CPF can be use in various heterogenous landscapes and allows the investigation of a large set of parameters, including the effect of physical friction and resource attractiveness on bees foraging movements.

## Funding

The work was financed by the France-Relance plan (n°ANR-21-PRRD-0021-01).

## CRediT authorship contribution statement

**A. Glad:** Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis, Conceptualization. **S. Moulherat:** Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization. **E. Andrieu:** Writing – review & editing, Supervision, Methodology, Conceptualization. **M. Moulherat:** Software. **D. Sheeren:** Writing – review & editing, Supervision, Methodology, Conceptualization. **A. Ouin:** Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization.

## Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Sylvain Moulherat reports a relationship with TerrOïko that includes: equity or stocks. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

We thank the TerrOïko team (Patrice Bridoux, Marine Pasturel and Mélodie Kunegel-Lion) for their help on the project and with simulation management, Fabien Laroche and Melodie Kunegel-Lion for their useful comments on this manuscript, James Daseagher for his previous work and help on the project and all the people at Dynafor who collected the data and created the landcover maps (François Calatayud) used in this study. We thank Daphne Goodfellow for her useful comment on English language. We thank the two anonymous reviewers for their comments which helped us to greatly improve our manuscript.

## Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ecolmodel.2025.111208.

## Data availability

Data will be made available on request.

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