Fixation Patterns Research Articles

Fixation patterns in pairs of facial expressions—preferences of self-critical individuals

So far, studies have revealed some differences in how long self-critical individuals fixate on specific facial expressions and difficulties in recognising these expressions. However, the research has also indicated a need to distinguish between the different forms of self-criticism (inadequate or hated self), the key underlying factor in psychopathology. Therefore, the aim of the current research was to explore fixation patterns for all seven primary emotions (happiness, sadness, fear, disgust, contempt, anger, and surprise) and the neutral face expression in relation to level of self-criticism by presenting random facial stimuli in the right or left visual field. Based on the previous studies, two groups were defined, and the pattern of fixations and eye movements were compared (high and low inadequate and hated self). The research sample consisted of 120 adult participants, 60 women and 60 men. We used the Forms of Self-Criticizing and Self-Reassuring Scale to measure self-criticism. As stimuli for the eye-tracking task, we used facial expressions from the Umeå University Database of Facial Expressions database. Eye movements were recorded using the Tobii X2 eye tracker. Results showed that in highly self-critical participants with inadequate self, time to first fixation and duration of first fixation was shorter. Respondents with higher inadequate self also exhibited a sustained pattern in fixations (total fixation duration; total fixation duration ratio and average fixation duration)—fixation time increased as self-criticism increased, indicating heightened attention to facial expressions. On the other hand, individuals with high hated self showed increased total fixation duration and fixation count for emotions presented in the right visual field but did not differ in initial fixation metrics in comparison with high inadequate self group. These results suggest that the two forms of self-criticism - inadequate self and hated self, may function as distinct mechanisms in relation to emotional processing, with implications for their role as potential transdiagnostic markers of psychopathology based on the fixation eye-tracking metrics.

Searching Across Realities: Investigating ERPs and Eye-Tracking Correlates of Visual Search in Mixed Reality.

Mixed Reality allows us to integrate virtual and physical content into users' environments seamlessly. Yet, how this fusion affects perceptual and cognitive resources and our ability to find virtual or physical objects remains uncertain. Displaying virtual and physical information simultaneously might lead to divided attention and increased visual complexity, impacting users' visual processing, performance, and workload. In a visual search task, we asked participants to locate virtual and physical objects in Augmented Reality and Augmented Virtuality to understand the effects on performance. We evaluated search efficiency and attention allocation for virtual and physical objects using event-related potentials, fixation and saccade metrics, and behavioral measures. We found that users were more efficient in identifying objects in Augmented Virtuality, while virtual objects gained saliency in Augmented Virtuality. This suggests that visual fidelity might increase the perceptual load of the scene. Reduced amplitude in distractor positivity ERP, and fixation patterns supported improved distractor suppression and search efficiency in Augmented Virtuality. We discuss design implications for mixed reality adaptive systems based on physiological inputs for interaction.

Applying 3D-Printed Porous Ti6Al4V Prostheses to Repair Osteomyelitis-Induced Partial Bone Defects of Lower Limbs: Finite Element Analysis and Clinical Outcomes.

The clinical management of partial bone defects in lower limbs, particularly those resulting from osteomyelitis, remains a significant challenge. This study aimed to systematically evaluate the effectiveness of 3D-printed porous Ti6Al4V prostheses in addressing osteomyelitis-induced partial bone defects. We established a comprehensive protocol for utilizing 3D-printed prostheses for bone defect repair, encompassing 3D simulation of prosthesis implantation and internal fixation, finite element analysis (FEA), and clinical implementation. Mimics software facilitated simulation of fixation patterns and screw lengths. FEA modeled bone defects in the distal metaphyseal femur and distal diaphyseal tibia to assess changes in stress conduction pre- and post-prosthesis implantation. The clinical study involved eight patients (average age: 56.3 years) with an average defect length of 14.9 cm. Postoperative outcomes were evaluated using X-rays and the Lower Extremity Functional Scale (LEFS). FEA demonstrated that the implanted prostheses effectively shared stress and reduced the load on residual bone in both models, thus lowering the risk of fractures under external forces. The average follow-up period was 24.5 months, with patients initiating weight-bearing activities on average 7.8 days post-surgery. Serial postoperative X-rays demonstrated long-term stability of the prostheses, with progressive bone regeneration around and integration with the prostheses. While two patients experienced infection recurrence requiring prosthesis removal and debridement, the remaining six showed significant improvement in LEFS scores, increasing from 31.5 preoperatively to 61.0 at the last follow-up. 3D-printed porous Ti6Al4V prostheses effectively restore anatomical integrity and optimize stress conduction in lower limbs, resulting in substantial functional recovery. This innovative approach shows promise for wider clinical adoption and warrants further investigation in medical practice.

A spotter's guide to endovascular endograft recognition

Since the first endovascular aneurysm repair of abdominal aortic aneurysms in the 1980s, there has not only been exponential growth of procedures performed per year, but also rapid proliferation of stent grafts. With the resultant growth in revision and explant procedures on these grafts, we developed this guide to aid trainees in surgery and radiology in identifying these grafts. Our goal with this spotter's guide is to allow the identification of key features from commonly implanted devices radiographically, such as points of fixation, radiopaque markers, and stent patterns. The operative approach for the treatment of endograft complications, including endoleak embolization, aortic cuff extension, laser fenestration, limb extension, and endograft explant is often dramatically impacted by the type of endograft and its individual device characteristics. The intent of this guide is to aid practitioners in identifying endovascular aneurysm repair endografts of all ages, even those that have not been implanted in years.

A self-supervised deep Riemannian representation to classify parkinsonian fixational patterns

Parkinson’s disease (PD) is the second most prevalent neurodegenerative disorder, and it remains incurable. Currently there is no definitive biomarker for detecting PD, measuring its severity, or monitoring of treatments. Recently, oculomotor fixation abnormalities have emerged as a sensitive biomarker to discriminate Parkinsonian patterns from a control population, even at early stages. For oculomotor analysis, current experimental setups use invasive and restrictive capture protocols that limit the transfer in clinical routine. Alternatively, computational approaches to support the PD diagnosis are strictly based on supervised strategies, depending of large labeled data, and introducing an inherent expert-bias. This work proposes a self-supervised architecture based on Riemannian deep representation to learn oculomotor fixation patterns from compact descriptors. Firstly, deep convolutional features are recovered from oculomotor fixation video slices, and then encoded in compact symmetric positive matrices (SPD) to summarize second-order relationships. Each SPD input matrix is projected onto a Riemannian encoder until obtain a SPD embedding. Then, a Riemannian decoder reconstructs SPD matrices while preserving the geometrical manifold structure. The proposed architecture successfully recovers geometric patterns in the embeddings without any label diagnosis supervision, and demonstrates the capability to be discriminative regarding PD patterns. In a retrospective study involving 13 healthy adults and 13 patients diagnosed with PD, the proposed Riemannian representation achieved an average accuracy of 95.6% and an AUC of 99% during a binary classification task using a Support Vector Machine.

Investigating the links between sustained attention, gaze fixation patterns, and face identity discrimination performance

Investigating the links between sustained attention, gaze fixation patterns, and face identity discrimination performance

Dark Carbon Fixation Measurements in the East Sea (Sea of Japan)

The vertical distribution patterns of daily primary production and dark carbon fixation were investigated at three stations in the East/Japan Sea (hereafter East Sea), a semi-enclosed marginal sea in the northwest Pacific Ocean. Our results displayed consistent vertical patterns of daily primary production at two of the stations, while the third station exhibited a markedly different distribution pattern, highlighting localized variations in production dynamics. In contrast, dark carbon fixations displaying varying vertical patterns among the stations are not specific enough to have much meaning. Water column-integral values showed differences in the contribution of dark carbon fixation to total primary production, ranging from 4.5% to 27.1%. These variations may reflect environmental parameters such as nutrient concentrations. However, our study is limited by the lack of direct data on the microbial community structure and chemoautotrophic activities, which are crucial for a more comprehensive understanding of these patterns. Understanding the environmental drivers of dark carbon fixation is crucial for elucidating carbon cycling dynamics in the East Sea. Notably, dark carbon fixation could contribute up to one-third of primary production in the region as an additional source of newly produced organic matter, highlighting the need for further investigation into this previously overlooked process.

The medullary cavity morphology of the proximal femur influences the fixation pattern of the rectangular tapered short stem in total hip arthroplasty.

This study aimed to evaluate differences in the pattern of fixation with a rectangular tapered short stem (Fitmore stem) due to proximal femoral medullary cavity morphology based on periprosthetic bone mineral density (BMD) and radiological findings. We analyzed 105 consecutive patients (Dorr type A, 18; Dorr type B, 66; Dorr type C, 21) who underwent total hip arthroplasty using a Fitmore stem. Periprosthetic BMD was measured using dual-energy X-ray absorptiometry from 1 to 24months postoperatively and radiological analysis was performed. Clinical outcomes were evaluated using the Harris hip score (HHS) and the University of California Los Angeles (UCLA) activity score preoperatively and 24months postoperatively. At 24months postoperatively, Dorr type C had significantly decreased BMD changes in Gruen zones 2, 6, and 7 compared to Dorr types A and B, and conversely, significantly increased BMD changes in zone 4 (p < 0.05). Dorr type C had significantly greater subsidence than the other types (p < 0.01) and significantly higher cortical hypertrophy in zone 3 (p < 0.01). Stress shielding was not significantly different between Dorr types. The preoperative and postoperative HHS and UCLA activity scores showed no significant differences between the Dorr types. In Dorr type C, BMD significantly decreased in the proximal femur with a rectangular tapered short stem, suggesting that the stem was fixed at the distal part. Careful observation of this prosthesis over time is needed in patients with Dorr type C.

Designing Novel Physiologic Monitor Displays for Combat Medics.

Combat medics who are responsible for the care of injured warfighters face challenges from their reliance on medical alarms that exceed the noise levels recommended by the WHO. This is because the elevated noise levels in military facilities, particularly from vehicular units and weaponry, compromise the combat medics' effectiveness and attentiveness to medical alarms. We previously designed a graphical ("configural") display to communicate patients' vital signs and found that when the configural display and traditional numerical display were concurrently presented to participants, it produced the fastest identification of patient vital signs and triggered the fewest number of alarms. This study used eye tracking to assess how participants direct visual attention to and engage with concurrently presented numerical and configural vital sign displays. We recruited 30 undergraduate students with normal hearing and vision for this study. Subjects were tasked with monitoring a simulated patient's vital signals using simultaneously presented numerical and configural vital sign displays. Concurrently, they performed an N-back task to simulate the multitasking required in a military environment. We manipulated the eccentricity and display position of the numerical and configural displays through 4 orientations, with each orientation being used in a monitoring block lasting 12 minutes. Continuous eye tracking was utilized to collect physiological data about participant display preference. We used eye tracking to analyze several metrics: Total display viewing time, total viewing time percentage, number of dwells (groups of eye fixations), mean fixations per dwell, and fixation patterns during an emergency event. Participants spent more time looking at the configural display than the numerical display during nominal monitoring and emergency events. During emergencies, the percentage of time individuals spent looking at the configural display increased from 30 to 50%, while there was no corresponding increase in the participants' looking at the numerical display. When there were 2 concurrent emergency events instead of 1, total viewing time did not increase, suggesting that participants did not need to change their viewing strategy when the emergency situation complexity increased. Also, during emergencies, participants directed nearly half of their fixations to the configural display during the first 2 seconds of an emergency, while only directing fewer than 5% of fixations to the numerical display during that same period. The average response time for an emergency event was around 2 seconds, which suggests that participants obtained relevant information from the configural display in this time period. We found that when a patient monitor contains both a configural display and a numerical display, participants look at the configural display. Furthermore, during time-sensitive situations, participants utilize the configural display to provide important information. We suggest this because the configural display integrates the relevant vital signs into one display. These findings provide justification for pursuing integrated vital sign displays to efficiently communicate patient conditions in complex environments. On the battlefield, swift decision-making is essential, as combat medics must minimize the time required to assess and act in critical situations.

Atypical and variable attention patterns reveal reduced contextual priors in children with autism spectrum disorder.

Accumulating evidence suggests that individuals with autism spectrum disorder (ASD) show impairments in using contextual priors to predict others' actions and make intention inference. Yet less is known about whether and how children with ASD acquire contextual priors during action observation and how contextual priors relate to their action prediction and intention inference. To form proper contextual priors, individuals need to observe the social scenes in a reliable manner and focus on socially relevant information. By employing a data-driven scan path method and areas of interest (AOI)-based analysis, the current study investigated how contextual priors would relate to action prediction and intention understanding in 4-to-9-year-old children with ASD (N = 56) and typically developing (TD) children (N = 50) during free viewing of dynamic social scenes with different intentions. Results showed that children with ASD exhibited higher intra-subject variability when scanning social scenes and reduced attention to socially relevant areas. Moreover, children with high-level action prediction and intention understanding showed lower intra-subject variability and increased attention to socially relevant areas. These findings suggest that altered fixation patterns might restrain children with ASD from acquiring proper contextual priors, which has cascading downstream effects on their action prediction and intention understanding.

The effect of screw insertion configuration of Sinus Tarsi plate on biomechanical performance using finite element analysis

Sinus Tarsi plates are used as implants for minimally invasive surgery of calcaneus bone fractures. This study evaluated the screw fixation patterns of Sinus Tarsi plates for optimal biomechanical performance. Six three-dimensional (3D) finite element models with different positional screws were evaluated for calcaneus fracture stabilization using Sinus Tarsi plates with 5, 6, and 7 holes. Walking stance conditions as heel strike, midstance, and push-off phases were used to compare loading. Results indicated that the equivalent (EQV) stress exhibited in the implant was higher than in the surrounding bone, with the highest value during the push-off phase. The maximum EQV stress or risk of failure decreased when an insertion screw was placed in the anterior bone using a 7-hole plate, and the most stable strain result at the fracture bone site was recorded for a Sinus Tarsi plate with 7 holes (TT 7-1). The screw insertion pattern and configuration of the Sinus Tarsi plate impacted the biomechanical performance of the calcaneal fracture.

Performance and eye movement patterns of industrial design students reading sustainable design articles

Sustainable design education plays a crucial role in cultivating sustainability awareness and competencies among students studying industrial design. This research investigates their sustainability levels, reading performance when engaging with articles, and fixation patterns during reading. 60 industrial design students participated in the study. We evaluated their sustainability levels using the Sustainable Consumption Measurement Scale. After reading both theoretical and case article, they completed tests assessing their recall and perspective scores. We collected eye-tracking data to analyze fixation duration and conducted lag sequential analysis on fixation transitions. Students were categorized into higher and lower sustainability groups based on their sustainability scores. Female students demonstrated higher sustainability levels, and students with design experience performed better in the higher sustainability group. While recall scores did not differ significantly, the higher sustainability group exhibited elevated perspective scores in theory article. Perspective scores were generally higher for case article compared to theory article. The higher sustainability group exhibited longer fixation durations in theory article, while the case article had longer fixation durations on images. Fixation transition patterns varied between theoretical and case article, with the former featuring transitions from images to texts, and the latter demonstrating transitions between images. This study provides valuable insights into sustainable design education for students studying industrial design.

Idiosyncratic fixation patterns generalize across dynamic and static facial expression recognition

Facial expression recognition (FER) is crucial for understanding the emotional state of others during human social interactions. It has been assumed that humans share universal visual sampling strategies to achieve this task. However, recent studies in face identification have revealed striking idiosyncratic fixation patterns, questioning the universality of face processing. More importantly, very little is known about whether such idiosyncrasies extend to the biological relevant recognition of static and dynamic facial expressions of emotion (FEEs). To clarify this issue, we tracked observers’ eye movements categorizing static and ecologically valid dynamic faces displaying the six basic FEEs, all normalized for time presentation (1 s), contrast and global luminance across exposure time. We then used robust data-driven analyses combining statistical fixation maps with hidden Markov Models to explore eye-movements across FEEs and stimulus modalities. Our data revealed three spatially and temporally distinct equally occurring face scanning strategies during FER. Crucially, such visual sampling strategies were mostly comparably effective in FER and highly consistent across FEEs and modalities. Our findings show that spatiotemporal idiosyncratic gaze strategies also occur for the biologically relevant recognition of FEEs, further questioning the universality of FER and, more generally, face processing.

Biomechanical evaluation of different medial column fixation patterns for valgus pilon fractures

BackgroundThe purpose of this study was to perform a biomechanical analysis to compare different medial column fixation patterns for valgus pilon fractures in a case-based model.MethodsBased on the fracture mapping, 48 valgus pilon fracture models were produced and assigned into four groups with different medial column fixation patterns: no fixation (NF), K-wires (KW), intramedullary screws (IS), and locking compression plate (LCP). Each group contained wedge-in and wedge-out subgroups. After fixing each specimen on the machine, gradually increased axial compressive loads were applied with a load speed of one millimeter per minute. The maximum peak force was set at 1500 N. Load-displacement curves were generated and the axial stiffness was calculated. Five different loads of 200 N, 400 N, 600 N, 800 N, 1000 N were selected for analysis. The specimen failure was defined as resultant loading displacement over 3 mm.ResultsFor the wedge-out models, Group-IS showed less displacement (p < 0.001), higher axial stiffness (p < 0.01), and higher load to failure (p < 0.001) than Group-NF. Group-KW showed comparable displacement under loads of 200 N, 400 N and 600 N with both Group-IS and Group-LCP. For the wedge-in models, no statistical differences in displacement, axial stiffness, or load to failure were observed among the four groups. Overall, wedge-out models exhibited less axial stiffness than wedge-in models (all p < 0.01).ConclusionsFunctional reduction with stable fixation of the medial column is essential for the biomechanical stability of valgus pilon fractures and medial column fixation provides the enough biomechanical stability for this kind of fracture in the combination of anterolateral fixation. In detail, the K-wires can provide a provisional stability at an early stage. Intramedullary screws are strong enough to provide the medial column stability as a definitive fixation. In future, this technique can be recommended for medial column fixation as a complement for holistic stability in high-energy valgus pilon fractures.

Contact states with femoral cortical bone and periprosthetic bone mineral density changes differ between traditional and newly introduced fully hydroxyapatite-coated stems.

The aim of this study was to compare the pattern of initial fixation and changes in periprosthetic bone mineral density (BMD) between patients who underwent total hip arthroplasty (THA) using a traditional fully hydroxyapatite (HA)-coated stem (T-HA group) and those with a newly introduced fully HA-coated stem (N-HA group). The study included 36 patients with T-HA stems and 30 with N-HA stems. Dual-energy X-ray absorptiometry was used to measure the change in periprosthetic BMD, one and two years postoperatively. The 3D contact between the stem and femoral cortical bone was evaluated using a density-mapping system, and clinical assessment, including patient-reported outcome measurements, was recorded. There were significantly larger contact areas in Gruen zones 3, 5, and 6 in the N-HA group than in the T-HA group. At two years postoperatively, there was a significant decrease in BMD around the proximal-medial femur (zone 6) in the N-HA group and a significant increase in the T-HA group. BMD changes in both groups correlated with BMI or preoperative lumbar BMD rather than with the extent of contact with the femoral cortical bone. The N-HA-coated stem showed a significantly larger contact area, indicating a distal fixation pattern, compared with the traditional fully HA-coated stem. The T-HA-coated stem showed better preservation of periprosthetic BMD, two years postoperatively. Surgeons should consider these patterns of fixation and differences in BMD when selecting fully HA-coated stems for THA, to improve the long-term outcomes.

Visual fixation patterns to AAC displays are significantly correlated with motor selection for individuals with Down syndrome or individuals on the autism spectrum

Eye tracking research technologies are often used to study how individuals attend visually to different types of AAC displays (e.g. visual scene displays, grid displays). The assumption is that efficiency of visual search may relate to efficiency of motor selection necessary for communication via aided AAC; however, this assumption has not received direct empirical study. We examined the relation between speed of visual search and speed of motor selection of symbols. Ten individuals on the autism spectrum (AS; Study 1) and nine with Down syndrome (DS; Study 2) participated in a search task using simulated AAC displays with a main visual scene display (VSD) and a navigation bar of thumbnail VSDs. Participants were given an auditory prompt to find one of four thumbnail VSDs in the navigation bar. Eye tracking technologies measured how long it took participants to fixate visually on the thumbnail VSD, and recorded how long it took participants to select the thumbnail VSD with a finger. A statistically significant relationship emerged between visual fixation and selection latencies, confirming the positive relationship between visual processing and motor selection for both groups of participants. Eye tracking data may serve as a useful proxy measure for evaluating how display design influences selection of AAC symbols, especially when individuals are unwilling or unable to comply with traditional behaviorally-based assessment tasks.

The Temporal and Spatial Evolution Characteristics and Driving Factors of Ecosystem Service Bundles in Anhui Province, China

Identifying ecosystem service bundles and their long-term evolutionary characteristics is essential for the overall enhancement of regional ecosystem services, as well as the division and management of functional areas, providing a basis for decision-making in formulating ecological and environmental protection policies, as well as regional development planning. Based on land use, remote sensing, and meteorological data obtained from Anhui Province, this study assessed six important ecosystem service functions, including food production (FP), water yield (WY), carbon sequestration (CS), soil conservation (SC), habitat quality (HQ), and landscape aesthetics (LA), at the township scale in 2000, 2010, and 2020. On this basis, the k-means clustering method was used to identify ecosystem service bundles, analyze the spatio-temporal evolution trajectory of service bundles, and explore the driving factors of the spatio-temporal evolution of ecosystem service bundles using GeoDetector 2015 The results indicate the following: (1) At the spatial level, diverse ecosystem services demonstrate pronounced spatial differentiation. The distribution pattern of HQ, carbon fixation, and SC services is generally lower in the north and higher in the south, with areas of high value predominantly located in the western Dabie Mountains and the mountains of Southern Anhui. Conversely, FP services exhibit the reverse pattern, and WY services display a gradual increase from north to south, while cultural services are more dispersed, with areas of high value primarily located in the western Dabie Mountains, the Yangtze River Basin, and other locations. On the temporal scale, WY, SC, and FP services mainly exhibit an increasing trend, marked by a significant increase, whereas other services tend to present a decreasing trend. (2) Anhui Province can be categorized into four distinct types of service bundles: the grain production bundle (GPB), mountain ecological conservation bundle (MECB), urban living bundle (ULB), and core protection bundle (CPB). Ecosystem service bundles exhibit clear spatial differentiation, and identical service bundles demonstrate substantial clustering in space. Between 2000 and 2020, ecosystem service bundles displayed a marked spatio-temporal evolution, with the prevalence of GPBs diminishing, whereas the share of ULBs progressively increased, and the number of MECBs and CPBs remained largely stable. (3) In the spatio-temporal evolution process, the average annual precipitation, the proportion of forest land, and slope constitute the principal natural factors influencing the spatio-temporal evolution of ecosystem service bundles, while the proportion of construction land represents the primary socio-economic factor, with natural factors exerting a more significant influence than socio-economic factors.

Contextual cueing—Eye movements in rotated and recombined displays

Contextual cueing leads to improved efficiency in visual search resulting from the extraction of spatial regularities in repeated visual stimuli. Previous research has demonstrated the independent contributions of global configuration and spatial position to contextual cueing. The present study aimed to investigate whether learned spatial configuration or individual locations would elicit fixation patterns resembling those observed in the original displays. We found that search guidance based on either local or global spatial context, by combining distractor locations from two learned displays or rotating displays, kept not only search time facilitation intact, in agreement with previous studies, but also enabled search with less fixations and more direct scan paths to the target. Fixation distribution maps of recombined or rotated displays were more similar to the original displays than random new displays. However, for rotated displays this was only true when the rotation angle was taken into account. Overall, this shows an astonishingly flexible use of the oculomotor system for search in incompletely repeated displays.

Impact of Dynamic Phytoplankton Stoichiometry on Global Scale Patterns of Nutrient Limitation, Nitrogen Fixation, and Carbon Export

AbstractPhytoplankton stoichiometry modulates the interaction between carbon, nitrogen and phosphorus cycles. Environmentally driven variations in phytoplankton C:N:P can alter biogeochemical cycling compared to expectations under fixed ratios. In fact, the assumption of fixed C:N:P has been linked to Earth System Model (ESM) biases and potential misrepresentation of responses to future change. Here we integrate key elements of the Adaptive Trait Optimization Model (ATOM) for phytoplankton stoichiometry with the Carbon, Ocean Biogeochemistry and Lower Trophics (COBALT) ocean biogeochemical model. Within a series of global ocean‐ice‐ecosystem retrospective simulations, ATOM‐COBALT reproduced observations of phytoplankton N:P, and compared to static ratios, exhibited reduced phytoplankton P‐limitation, enhanced N‐fixation, and increased low‐latitude export, improving consistency with observations and highlighting the biogeochemical implications of dynamic N:P. We applied ATOM‐COBALT to explore the impacts of different physiological mechanisms hypothesized to underlie N:P variation, finding that two mechanisms together drove the observed patterns: proportionality of P‐rich ribosomes in phytoplankton cells to growth rates and reductions in P‐storage during scarcity. A third mechanism which linked temperature with phytoplankton biomass allocations to non‐ribosomal proteins, led only to relatively modest impacts because this mechanism decreased the temperature dependence of phytoplankton growth rates, compensating for changes in N:P. We find that there are quantitative response differences that associate distinctive biogeochemical footprints with each mechanism, which are most apparent in highly productive low‐latitude regions. These results suggest that variable phytoplankton N:P makes phytoplankton productivity and export resilient to environmental changes, and support further research on the physiological and environmental drivers of phytoplankton stoichiometry and biogeochemical role.

Population dynamics and games of variable size

This work introduces the concept of Variable Size Game Theory (VSGT), in which the number of players in a game is a strategic decision made by the players themselves. We start by discussing the main examples in game theory: dominance, coexistence, and coordination. We show that the same set of pay-offs can result in coordination-like or coexistence-like games depending on the strategic decision of each player type. We also solve an inverse problem to find a d-player game that reproduces the same fixation pattern of the VSGT. In the sequel, we consider a game involving prosocial and antisocial players, i.e., individuals who tend to play with large groups and small groups, respectively. In this game, a certain task should be performed, that will benefit one of the participants at the expense of the other players. We show that individuals able to gather large groups to perform the task may prevail, even if this task is costly, providing a possible scenario for the evolution of eusociality. The next example shows that different strategies regarding game size may lead to spontaneous separation of different types, a possible scenario for speciation without physical separation (sympatric speciation). In the last example, we generalize to three types of populations from the previous analysis and study compartmental epidemic models: in particular, we recast the SIRS model into the VSGT framework: Susceptibles play 2-player games, while Infectious and Removed play a 1-player game. The SIRS epidemic model is then obtained as the replicator equation of the VSGT. We finish with possible applications of VSGT to be addressed in the future.