Ecological Modelling

A high proportion of the world's population relies on marine fisheries as a source of food and employment, highlighting the need for sustainable exploitation strategies. However, fisheries management commonly relies on single-species models that overlook ecological interactions and economic trade-offs, which may lead to stocks being exploited above sustainable levels. To address this gap, we developed a novel size-structured, multispecies bioeconomic module integrated within the spatially explicit, individual-based OSMOSE ecosystem model. OSMOSE represents exploited fish communities in which individuals interact through opportunistic, size-dependent predator-prey interactions which are explicitly incorporated into the bioeconomic framework. The bioeconomic model accounts for multiple species and size classes, allowing for size-dependent market prices. Fishing costs and profits are represented using an extension of the Gordon-Schaefer model to multiple interacting species, while consumer demand is modelled using a nested Dixit-Stiglitz utility function with three levels of constant elasticity of substitution for fish commodity, species and size classes. We present a method for estimating parameters for the bioeconomic module when empirical estimates are unavailable, using the North Sea OSMOSE configuration, which comprises 15 species. Our method successfully estimated the six bioeconomic parameters required to operationalise the model. Results indicate that differences in cost parameters were primarily associated with variability in species biomass rather than fishing gear, while fish prices were more strongly influenced by consumer's demand than by availability. This framework provides a basis for assessing the economic consequences of alternative climate change scenarios and supporting sustainable fisheries management.

After introduction, many non-native marine species are dispersed planktonically. Secondary spread within the non-native range has been shown to prevent the establishment of the introduced species if the advection of larvae prevents sufficient return of larvae to maintain the population in the face of competition with native species. However, those studies have largely neglected the effects of spatial variation in alongshore larval transport. We examine the introduction of a novel species with planktonic dispersal into a more realistic coastal environment which includes spatial variation in larval transport estimated from the Mercator Ocean 1/12th degree global circulation model. The introduction may either be from a distant habitat, or through range expansion. We find that there are locations in the global coastal ocean where introduced species are more likely to persist because of spatial variation of coastal currents. These include regions where alongshore larval transport diverges, such as estuaries. The location where a non-native species is introduced may not be where it flourishes - it cannot be assumed that the region where invading species are first noticed to be abundant is the region where it was introduced. We extend closed-population theory to open coastal systems to estimate persistence as a function of local circulation, habitat extent, and the competitive advantage of the introduced species. Software is provided which allows the estimations of regions where introduced species are more likely to persist and flourish as a function of larval depth behavior, planktonic duration and release timing.

Squid abundance has been reported to increase globally between 1970 and 2010. This increase has been hypothesized to result from two primary factors: the loss of top predators due to overfishing and rising ocean temperatures. The decline in apex predators may lead to the expansion of squid populations either through reduced predation pressure or diminished competition with juvenile predators. Concurrently, increased temperatures could enhance the somatic growth rates of squid, thereby accelerating their population growth. However, empirically disentangling the impacts of predator loss and temperature on squid biomass remains challenging, especially in a food-web context. In this study, we used a size- and trait-based model of upper trophic levels that resolves the ecosystem structure -- biomass and trophic interactions of fish and squid -- for varying depth, temperature, and secondary production, to investigate two hypotheses of the historical expansion of squid, i.e., the effects of predator depletion from fishing and rising temperatures on squid biomass. Our model reveals that intensified fishing of squid predators -- specifically large demersal fish in shelf systems and large pelagic fish in open oceans -- leads to a slight increase in squid biomass. Conversely, elevated temperatures are associated with a decline in squid biomass. This temperature-driven reduction in biomass is attributed to an increased metabolism of squids beyond the available food supply. If historic overfishing on large marine predators continues to be curtailed, we expect a corresponding reduction in global squid biomass and fisheries potential, which could be further exacerbated by rising temperatures.

Spatial expansion is a common feature of many ecological processes, including biological invasions, range shifts, population recovery, and the spread of pathogens and human activities. Although such expansion often arises from diffusive processes, there remain few general statistical methods to quantify these dynamics. Here, we present a diffusion-enhanced spatio-temporal model (DESTM) that approximates diffusive process using Gaussian Markov random fields (GMRF). The model works by incorporating the statistical interaction between spatial diffusion and temporal lags into a joint precision structure of the latent field. To demonstrate, we simulate data from a diffusion movement process using a continuous-time Markov chain (CTMC), and then approximate this mechanistic process using the DESTM. We show that separable spatio-temporal models can lead to large bias in estimates of the local density. In contrast, the DESTM did not appear to bias inferences, and reverts to the separable model when diffusion is not apparent. Finally, we apply the model to two large-scale examples of spatial expansion: (1) the historical spread of the Japanese distant-water longline fleet across the Pacific, representing anthropogenic spatial expansion in the ocean, and (2) the recovery and geographic expansion of Bald Eagle populations across North America. Estimates from both case studies, supported by model comparisons and ecological plausibility, suggest that the DESTM provides a better description of the underlying expansion dynamics, although improvements in forecast performance were more apparent for the Japanese longline fleet. We highlight that the model provides a fast and efficient framework for modeling spatial expansion dynamics, with the potential to represent increasingly complex ecological dynamics through future extensions. We propose that future research explore this framework as a quantitative tool to explain how spatial expansion occurs.

Despite the impacts of within-host disease dynamics on disease outcomes in individual hosts and disease spread among-hosts, generic models of within-host population dynamics have received far less attention than their among-host counterparts. While a number of models have been proposed to explore theoretical eco-evolutionary dynamics, they have yet to be evaluated for estimability, raising questions about their ability to provide reliable inference when confronted with data. We evaluated the estimability of two generic within-host population dynamics models by assessing: (1) parameter estimation, our ability to recover correct values of model parameters from data, (2) the consequences of mis-assigning the underlying mechanistic model on parameter estimation, and (3) the reproduction of qualitative dynamics, or, our ability to use parameter estimates to reproduce observed dynamical behaviours. In some cases, fitting a mis-matched mechanistic model to time series data produced reasonable parameter estimates that were able to reproduce system dynamics, and that when provided the data-generating model, parameter uncertainty can produce substantial behavioural uncertainty. Our findings highlight the impacts of structural, parametric, and behavioural uncertainty on inference, and demonstrate the value of improving system-specific knowledge to prevent the use of incorrect functional forms and of measuring consequential parameters to improve estimability.

O_LIUnderstanding the processes underlying successful eradication of invasive species is essential for achieving global island conservation goals. Despite the widespread availability of capture records from eradication programs, modeling frameworks that utilize these datasets to elucidate spatio-temporal population dynamics remain underdeveloped. C_LIO_LIIn this study, we reconstructed the spatio-temporal population dynamics of the small Indian mongoose on Amami-Oshima Island (712 km{superscript 2}), Japan, where the species was introduced in 1979 and officially declared eradicated in 2024 after more than 30 years of systematic removal. We integrated introduction records, capture data, and monitoring data using a hierarchical harvest-based model (HBM). To evaluate the models capacity to support management decisions and assess eradication success, we conducted retrospective analyses and compared estimated eradication probabilities with those obtained from a rapid eradication assessment (REA; Samaniego-Herrera et al., 2013). C_LIO_LIThe estimated population size (before reproduction) peaked at 5,449 individuals (95% CI: 4,703, 6,175) in 2000 and subsequently declined almost monotonically. The maximum invaded area was 547.78 km{superscript 2} (posterior median, 95% CI: 496.47, 566.04) in 2009, indicating that the removal program successfully prevented island-wide expansion. Retrospective analyses showed that population estimates remained within the 95% credible intervals of the full dataset estimates, demonstrating temporal consistency. Eradication probabilities estimated by the HBM were substantially higher than those from the REA, highlighting the sensitivity of estimates to fine-scale heterogeneity in detection processes. C_LIO_LISynthesis and applications: Hierarchical HBMs provide a powerful framework for reconstructing, predicting, and evaluating invasive species eradication dynamics. Being aware of the limitations for application to eradication evaluations, HBMs can support adaptive management in long-term eradication programs and improve our understanding of the mechanisms underlying successful eradication. C_LI

Habitat destruction leads to a severe decline in biodiversity. Ascertaining effects of habitat loss afterwards is regularly done, whereas predicting the effects of different habitat loss scenarios on biodiversity beforehand is much preferred but as of yet rarely possible. Such predictions would help inform management decisions to prevent biodiversity loss in the first place, or at least mitigate effects if necessary, by providing handles to set priorities in making trade-offs. To this end, we developed and applied an adapted version of the information-theoretical framework of Maximum Entropy Theory in Ecology (METE) to predict species-area relationships in tropical forest landscapes undergoing habitat loss and fragmentation. Species-area relationships provide information about biodiversity and can, in undisturbed systems, be predicted using METE, based on state variables such as the total number of individuals, the total number of species, and the total area size. In disturbed systems, however, it is established that METEs predictions are off. Using an individual-based model, we explore how METEs state variables should be adjusted, based on the landscape characteristics habitat cover and degree of habitat fragmentation, to restore its accuracy of species-area relationship predictions in disturbed environments. We validate our adjusted METE predictions with empirical data. Our adjusted METE predictions demonstrate the severity of fragmentations impact on biodiversity, relative to what could be expected in a pristine, continuous environment. With this new method, we can estimate the immediate effects of habitat loss on biodiversity, as well as its long-term effects.

Offshore wind farms are rapidly expanding to meet growing demands for renewable energy, with development expected to extend further offshore into deeper waters. This expansion requires a robust understanding of the long-term ecological consequences of offshore wind farms (OWFs) and how these may interact with ongoing climate change. We used the coupled hydrodynamic-ecosystem-biogeochemical water-column model (GOTM-ERSEM-BFM) to investigate ecosystem-wide responses to environmental changes associated with OWFs and climate warming. Specifically, we examined OWF-related scenarios of reduced benthic suspension-feeding activity, representing potential effects of contaminant emissions from OWFs, and reduced wind forcing, together with increased sea surface temperature. The scenarios were simulated individually and in combination to explore potential interactive effects. These scenarios were simulated at two contrasting locations in the North Sea, representing a well-mixed coastal site and a seasonally stratified offshore site. The coastal site exhibited comparatively modest ecosystem responses across the scenarios, whereas responses were generally stronger at the deeper offshore site. At the offshore site, changes in stratification altered vertical nutrient dynamics and contributed to pronounced differences in ecosystem responses between the surface and bottom layers. Our results demonstrate that ecosystem responses to OWF-related and climate-driven environmental changes are strongly dependent on local environmental conditions, suggesting that ecological consequences may differ substantially as wind farm development expands into deeper offshore environments.

Translating Tilman resource-ratio model (R) to the metacommunity scale bridges local plant competition and landscape dynamics, moving ecological niche theory beyond controlled experiments. By incorporating scale dependence, stochasticity, dispersal limitation, and the stress-disturbance dichotomy, this framework also accounts for the drivers of both alpha and beta diversity. To achieve this integration, this work presents the Metacommunity Resource-Ratio Model (MetcommR) and its graphical tool, the Patchwork Biplot. This approach adapts the traditional continuous plane with a granular patch space, where each patch represents a discrete community with its area and internal variability, tracking net vectors of resource consumption and release relative to species-limiting isoclines. MetcommR articulates two fundamental regimes. In disturbance-governed metacommunities, biomass loss releases resources, interrupting depletion and preventing competitive exclusion, which promotes coexistence via the competition-colonization trade-off and maintains alpha and beta diversity. Conversely, in stress-governed systems, biomass accumulation and severe resource scarcity push communities toward isoclines, favoring the monodominance of tolerant species through competitive exclusion under the tolerance-fecundity trade-off. We demonstrate the model's empirical utility through a Cerrado case study in the Paraopeba Reserve. Analyzing canopy openness (light) and soil nitrogen reveals that long-term fire suppression induces light stress, elevating competitive exclusion risks for shade-intolerant species. Consequently, the Patchwork Biplot serves as a tool for evaluating ecological dynamics and vulnerabilities to guide management and conservation strategies.

Once central challenge in adopting ecosystem-based fisheries management (EBFM) is understanding and predicting the interconnected processes, feedbacks, and temporal dependencies that characterize ecosystem dynamics. Structural equation models and structural causal models (SEM and SCM) quantify interconnected relationships and evaluate causality from observational data but cannot readily accommodate the incomplete and irregularly sampled data typical of complex systems. Dynamic structural equation models (DSEM) estimate SEMs but accommodate lagged effects, missing data, and non-linear and non-stationary effects. However, there is little guidance regarding how DSEM can be used to support EBFM, particularly within governance and decision-making contexts. Here, we present three case studies that highlight distinct inferential goals for understanding ecosystem processes in the context of EBFM. First, we quantify ecosystem-level indicators to support monitoring of climate-driven ecosystem changes. Second, we examine whether hypothesized direct and indirect ecosystem linkages improve predictions of recruitment. Finally, we compare support for hypotheses of causal drivers of fish productivity. To provide practical advice, we synthesize lessons learned into a workflow to for others navigating DSEM. We suggest that the first step is identifying the inferential objective, which establishes the foundation for the remainder of the workflow, guiding the development of graphical models, model specification, and the selection of statistical and scientific validation steps (e.g., testing conditional independencies) needed to evaluate hypothesized causal relationships. By integrating observational data, expert knowledge, and mechanistic hypotheses within a unified framework, DSEM is a powerful tool for advancing EBFM, and more broadly, understanding the processes that govern complex ecosystems.

O_LITrophic rewilding, the practice of restoring animal species to recover lost ecosystem functions, has been proposed as a nature-based climate change solution (NbCS) due to animal biogeochemical influences potentially extending to ecosystem carbon capture. C_LIO_LIWe examined this potential using a case study of puma (Puma concolor) and guanaco (Lama guanicoe) restoration in a grassland ecosystem in Patagonia National Park, Chile. We parameterized a model of animal-driven ecosystem carbon dynamics with published measurements from Patagonian grasslands and compared three scenarios: (1) a no-rewilding baseline; (2) rewilding only guanaco; and (3) rewilding guanaco and puma. We estimated net primary productivity (NPP), net ecosystem carbon balance (NECB), and plant and soil carbon stocks. Using differences among scenarios, we estimated ecosystem carbon gains attributable to rewilding guanacos and pumas, and validated baseline estimates using published carbon capture data for Patagonian grasslands. C_LIO_LIPatagonian grasslands with pumas and guanacos could capture (NPP and NECB) 1.27-2.5 times more carbon, and increase plant carbon by 1.76-3.25 times, above the no-rewilding baseline. Large uncertainties in parameter values make estimating soil carbon challenging, but the rewilded ecosystem could store up to 1.16 times more soil carbon, or up to 0.57 times less. C_LIO_LIThe model estimates that NECB in the rewilded ecosystem could amount to 94.41 t C km-2 y-1 (94.38 t C km-2 y-1-94.44 t C km-2 y-1) of which 23%-43% attributable to animal effects. Plant carbon storage estimates were [~]290 t C km-2 (280-300 t C km-2), of which 43%-67% attributable to animal effects. Finally, the model estimated soil C stock gains up to 178 t C km-2, or losses up to 4300 t C km-2. C_LIO_LIPractical implications. We illustrate how to develop first approximation estimates of carbon capture and storage to help assess the feasibility of trophic rewilding as a NbCS. Our modelling revealed that restoring a puma-guanaco trophic cascade could be a feasible NbCS, and identified looming uncertainties about the fate of carbon that need further empirical exploration. More generally, the modelling identifies key measurements that can inform whether restoring trophic cascades can contribute to NbCS. C_LI

1. Invasive species pose significant ecological, economic, and public health challenges. Their management requires repeated decisions under uncertainty about when, where and how intensively to intervene. Although structured decision-making and adaptive management provide conceptual frameworks for addressing these challenges, their practical implementation remains limited because optimization methods such as stochastic dynamic programming (SDP) are often perceived as mathematically complex, challenting to apply and difficult to interpret. 2. Here, we provide a practical guide to using SDP and its extensions for invasive species management. Using coypu (*Myocastor coypus*) management as a running case study, we introduce the framework through a minimal working example before progressively extending it to spatial dynamics, imperfect detection using partially observable Markov decision processes (POMDPs), adaptive management under model uncertainty, and value-of-information analyses that quantify the benefits of learning before acting. 3. All examples are accompanied by reproducible implementations in R, together with recommendations on model formulation, parameterization and interpretation. We also discuss the strengths and limitations of SDP. 4. By lowering the technical barrier to SDP, this guide aims to help ecologists and wildlife managers integrate decision theory into invasive species management, enabling transparent, reproducible and objective-driven management strategies under uncertainty. More broadly, the methods presented here are applicable to a wide range of ecological decision problems beyond invasive species, wherever management requires balancing immediate actions against uncertain future outcomes.

Ecologists have long investigated how community complexity affects ecological stability, yet how community complexity influences multistability, defined as the presence of alternative stable states, remains poorly understood. We developed a novel framework integrating stochastic community assembly with stability landscape analysis to quantify multistability from species interaction matrices. Using this framework, we systematically explored how species interaction properties shape the relationship between species diversity (species pool size) and the number of alternative stable states. Mean interaction strength was the primary determinant: competitive interactions amplified the positive relationship between species diversity and the number of alternative stable states. In competitive communities, a greater number of alternative stable states was associated with lower community uncertainty, a measure of the long-term unpredictability of community assembly dynamics. These results highlight the importance of characterizing the entire stability landscape. Our framework provides a general approach for understanding and quantifying multistability in complex ecological communities.

Estimating the postmortem submersion interval (PMSI) remains challenging due to complex biological and environmental interactions during aquatic decomposition. This study proposes a reduced mechanistic ordinary differential equation (ODE) model linking tissue degradation, microbial activity, and dissolved oxygen dynamics. Calibrated against the total aquatic decomposition score (TADS) trajectory for Northern Adriatic Sea cases, the model preserves a strictly monotone TADS--time relationship, ensuring unique numerical inversion from observed TADS to PMSI. Synthetic observation experiments evaluated how data selection influences parameter recovery, practical identifiability, and robustness under measurement uncertainty. Microbial measurements improved parameter recovery for microbial dynamics, whereas dissolved oxygen measurements constrained oxygen-consumption and renewal processes. Combining both types of observation optimized the recovery of coupled parameters. Trajectory reconstruction, profile likelihood analysis, boundary-hit frequencies, and Monte Carlo simulations confirmed these findings. Importantly, while all observation strategies reproduced TADS with comparable accuracy, they differed substantially in recovering underlying biological parameters and latent-state dynamics. Thus, accurately reproducing decomposition scores alone is insufficient for reliable parameter inference. This framework provides a transparent and biologically interpretable foundation for the mechanistic estimation of PMSI. Future applications to case-level and multi-site datasets may enable site-specific recalibration and improved predictive evaluation across diverse aquatic environments.

Ecological stoichiometry allows us to investigate how food quality affects food-web population dynamics. We consider periphyton, phytoplankton, and a shared Daphnia consumer in a closed system with separate benthic and pelagic phosphate pools. The producers have variable phosphorus-to-carbon ratios, while the consumer maintains a constant ratio. We construct the model, establish boundedness under stated conditions, characterize its grazer-free equilibrium families and their local spectra, derive conditions for positive consumer growth, and examine its numerical bifurcation structure as light-dependent carrying capacity varies. The bifurcation diagrams contain stable and unstable equilibrium branches together with a stable periodic family, revealing a more complex response to light enrichment than a single sequence of steady states and oscillations. A descending consumer equilibrium branch illustrates that greater light availability need not increase consumer biomass. We then introduce periodically varying carrying capacities and compare weak and strong seasonal forcing. Stronger forcing produces brief consumer rebounds in the high-light example, although the peaks diminish over the displayed interval. Together, the growth conditions and branch diagrams provide a framework for interpreting population dynamics in terms of food quantity and food quality. Independent numerical continuation identifies a Hopf crossing and a fold; the termination mechanism of the periodic branch remains unresolved.

Biological invasions are a major driver of global change, reshaping ecosystems and threatening biodiversity worldwide. Anticipating where invaders will establish and where they will exert the strongest ecological impacts are key challenges for early detection and targeted management. Although Species Distribution Models (SDMs) are widely used to forecast biological invasions, they often provide uncertain estimates of establishment ranges and limited insight into invader performance, making it difficult to anticipate ecological impacts. Here, we address these limitations by integrating physiological information on invader performance with SDMs to identify regions of high invasion risk. Using the brown alga Rugulopteryx okamurae, one of the most prominent marine invaders in Europe, we first test alternative hypotheses of northern establishment limits: (i) a cold-survival constraint driven by winter temperatures and (ii) a growth constraint derived from the species' thermal performance. To identify the more likely scenario, we combine cold-tolerance experiments with seasonal growth comparisons between the invader and a native macroalga Dictyota dichotoma, whose established distribution allows physiological performance to be directly related to realised presence. Finally, we project seasonal growth of the invader across the predicted establishment range as a proxy for biomass accumulation and potential ecological impacts. Our results indicate that northern limit in Europe will be more likely constrained by winter survival rather than growth, extending the potential establishment range of Rugulopteryx to mid-Norway. In contrast, the highest impacts are likely to remain concentrated in southern Europe, where thermal conditions sustain high year-round growth. Overall, our approach illustrates how understanding the physiological response of invaders to their environment can improve the interpretation of SDM outputs and help identify areas at greatest risk of impact within their potential establishment range.

Movement models often assume that animal decisions depend on perceived environmental conditions. However, optimal foraging and cognition theory predict that accumulated experiences should drive changes in animal motivation and decision-making. Here, we propose a mechanistic framework that models state-switching habitat selection as a history-dependent process, where internal states, such as fear or energy, emerge as latent variables accumulating through environmental exposure. Simulations showed that our model accurately recovers memory timescales and cumulative effects of environmental exposure on behavioural switching that would be undetected by existing state-switching habitat selection models. Applied to woodland caribou, it reveals that an individual integrates predation risk experienced over the previous 15 days, but food intake over only 2 days, when deciding to remain or leave an area. Our model advances perspectives on movement ecology by quantifying how accumulated experiences shape changes in motivation driving animal movement decisions.

The ocean tides influence key Earth system processes at a range of spatial and temporal scales. It is known that the geometry of ocean basins is the leading controller of tidal energetics, so well-constrained palaeogeographic reconstructions and tidal properties for Earths past are imperative when investigating other Earth system processes. Here, we present a novel way to constrain both deep-time tidal model results and reconstructions, by combining palaeoecology with sedimentology. We compare new palaeo-tidal model simulations for the Cambrian period, significant for the early origin and radiation of major animal fauna, to tidal proxies. One of the most abundant soft-bodied organisms preserved during this time are cnidarian medusae (jellyfish). A total of 17 cnidarian medusae localities were obtained through the literature, which had an adequate global distribution and occurred at regular intervals throughout the period of study. In some locations there were also estimates of palaeo-tidal range. Our results show a good agreement between the simulations and proxy data. In the few locations where there is disagreement, it is proposed that the palaeogeographic reconstructions are missing details, e.g., island chains, and our results allow for the palaeogeographic reconstructions to be improved. The proxy method presented is promising and can be applied to other time-periods with different marine fossils, particularly at evolutionary and extinction periods where the marginal marine environment is of importance.

1. Species loss can erode food-web functioning not only through secondary extinctions, but also through biomass redistribution, weakened energy pathways, and threshold-like functional collapse. Common topology-, connectivity-, and extinction-based robustness metrics provide valuable summaries of structural disassembly and cascade risk, but they are not designed to quantify continuous biomass retention, collapse-associated species sets, and non-additive group-level effects within a single dynamic framework. 2. We develop a dynamic biomass-based framework for assessing food-web robustness under progressive species removal. The framework introduces Dynamic Area-based Robustness (DAR), which quantifies the weighted area between slow- and fast-collapse reference trajectories of total ecosystem biomass retention. Building on these trajectories, we operationally define the Minimal Vital Species Set (MVSS) as the smallest fast-collapse-prefix species set whose removal first drives biomass below a predefined functional-collapse threshold. We further propose Cluster Influence (CI), which compares the biomass effect of simultaneous group removal with the mean effect of removing the same species individually. 3. We evaluated the framework using 120 niche-model virtual food webs spanning controlled gradients of species richness and connectance, and further demonstrated its applicability on 16 empirical stream food webs. We compared DAR with AUC- and secondary-extinction-based robustness metrics and assessed the sensitivity of DAR, MVSS, and CI to key bioenergetic parameters and parameter uncertainty. 4. DAR captured biomass-based robustness patterns that were only partly aligned with structural and extinction-based metrics, indicating that dynamic functional degradation provides complementary information. In virtual food webs, MVSS subsets were strongly enriched in basal species or basal resource nodes, and smaller MVSS proportions were associated with stronger positive CI under fast-collapse trajectories. Together, DAR, MVSS, and CI provide a reproducible framework for linking food-web structure, biomass dynamics, collapse thresholds, and non-additive species-set effects, offering a practical tool for dynamic robustness assessment in theoretical and empirical food webs.

Muscle regeneration relies on the coordinated activation of muscle stem cells, whose fate decisions are regulated by intracellular gene expression dynamics and intercellular coupling via the Notch-Dll1 signaling pathway. Central components of this regulatory network include the transcriptional repressor Hes1, its target gene Dll1, and the myogenic regulator MyoD. Experimental and theoretical studies have shown that proliferating muscle stem cells exhibit oscillatory dynamics of these molecules, whereas sustained expression is associated with differentiation. Here, we investigate the dynamics of a previously established delay differential equation model of two coupled muscle stem cells. Using linear stability analysis, we systematically characterize how model parameters affect the transition between stable and unstable steady states. In addition, numerical bifurcation analysis is employed to study the influence of intercellular coupling strength and delay on the system dynamics. Our analysis shows that continuous variation of the coupling delay induces repetitive changes in the stability of the steady state. However, this sensitivity towards the coupling delay is confined to a narrow region of parameter space and therefore requires a fine tuning of all other parameters. Beside the identification of parameter sets for in-phase and out-of-phase oscillations, we demonstrate the possibility of coexisting stable in-phase and out-of-phase oscillations, a dynamical feature that has not been reported previously. While oscillation periods are largely determined by intracellular regulatory mechanisms, oscillation amplitudes can be strongly modulated by intercellular coupling. These results provide new insight into how the intracellular network and intercellular communication interact to generate different collective dynamics.