Philippe Palanque
email: palanque@irit.fr

Sandra Basnyat
email: basnyat@irit.fr

David Navarre
email: navarre@irit.fr

Improving Interactive Systems Usability Using Formal Description Techniques: Application to HealthCare

Keywords: Human-Computer Interaction, Incident and Accident Investigation, Formal Description Techniques, Medical Informatics, Patient Monitoring

In this paper we argue that the formal analysis of an interactive medical system can improve their usability evaluation such that potential erroneous interactions are identified and improvements can be recommended. Typically usability evaluations are carried out on the interface part of a system by human-computer interaction/ergonomic experts with or without end users.

Here we suggest that formal specification of the behavior of the system supported by mathematical analysis and reasoning techniques can improve usability evaluations by proving usability properties. We present our approach highlighting that formal description techniques can support in a consistent way usability evaluation, contextual help and incident and accident analysis. This approach is presented on a wireless patient monitoring system for which adverse event (including fatalities) reports are publicly available from the US Food and Drug Administration (FDA) Manufacturer and User Facility Device Experience (MAUDE) database.

Introduction

The advances of healthcare technology have brought the field of medicine to a new level of scientific and social sophistication. They have laid the path to exponential growth of the number of successful diagnoses, treatments and the saving of lives. On the hand, technology has transformed the dynamics of the healthcare process in ways which increase the distribution & cooperation of tasks among individuals, locations and automated systems. Thus, technology has become the backbone of the healthcare process. However, it is usually the healthcare professionals who are held responsible for the failures of technology when it comes to adverse events [START_REF] Bernhaupt | Model-Based Evaluation: A New Way to Support Usability Evaluation of Multimodal Interactive Applications[END_REF]. It has been estimated that approximately 850,000 adverse events occur within the UK National Health Service (NHS) each year [START_REF]NHS Expert Group on Learning from Adverse Events in the NHS. An organisation with a memory[END_REF]. A similar study in the United States arrived at an annual estimate of 45,000-100,000 fatalities [START_REF] Kohn | To Err Is Human: Building a Safer Health System[END_REF]. While functionality of medical technology goes beyond imaginable, the safety and reliability aspects have lagged in comparison with the attention they receive in other safety-critical industries. The discussion of human factors in medicine has centered on either compliance with government standards or on analyzing accidents, a posteriori.

In this paper we are interested in medical systems that offer a user interface and require operators interaction while functioning. Due to their safety-critical nature there is a need to assess the reliability of the entire system including the operators. The computer-based part of such systems is quite basic (with respect to other more challenging safety-critical systems such as command and control systems (cockpits, Air Traffic Management, …)) and thus current approaches in the field of systems engineering provide validated and applicable methods to ensure their correct functioning 1 . Things are more complicated as far as the user interface and operators are concerned. Human-computer interaction problems can occur because of numerous poor design decisions relating to the user interface (UA). For example, poor choice of color, a mismatch between the designer's conceptual model and the user's mental model or insufficient system feedback to allow the user to understand the current state of the system which is known as mode confusion. Mode confusion refers to a situation in which a technical system can behave differently from the user's expectation [START_REF] Bredereke | A Rigorous View of Mode Confusion[END_REF]. Operator assessment is even harder to perform due to the autonomous nature, independence and vulnerability to environmental factors like stress, workload.

Lack of usability has been proved to be an important source of errors and mistakes performed by users. Faced with poor user interfaces (designed from a non-user centered point of view) users are prone to create alternative ways of using the applications thus causing hazardous situations. In the worst cases, lack of usability may lead users to refuse to use the applications, potentially resulting in financial loss for companies with respect to the need for redesign and possibly additional training. For detecting and preventing usability problems it is important to focus the design process from the point of view of people who will use the final applications. The technique called User-Centered Design (UCD) [START_REF]User-Centred System Design: New Perspectives on Human-Computer Interaction[END_REF] is indeed the most efficient for covering user requirements and for detecting usability problems of user interfaces.

Usability evaluation, both formative and summative, can improve these kinds of issues by identifying interaction problems. However, after the design iteration, another round of usability evaluation is required in order to verify whether there is any improvement. This can be costly in terms of time and resources. A further way to improve design is to apply interface design criteria and guidelines during the design process. Ergonomic criteria have been proved to increase the evaluation performance of experts [START_REF] Bastien | [END_REF] [START_REF] Adolf | Touchscreen usability in microgravity[END_REF]. Safety critical systems have been for a long time the application domain of choice of formal description techniques (FDT). In such systems, where human life may be at stake, FDTs are a means for achieving the required level of reliability, avoiding redundancy or inconsistency in models and to support testing activities. In this paper, we will illustrate our approach using a FDT based on Petri nets. In this paper, we show that FDTs can be used to support a selection of usability related issues including:

• Formative evaluation • Summative evaluation • Contextual help for end users • Investigation of incidents and accidents by providing formal descriptions of the behavior of the system

The next section presents an overview of usability evaluation, including formative and summative evaluation and presents several ergonomic/usability criteria and guidelines for interface design including some that are targeted at touch screen interfaces. Section 3 provides an informal presentation of formal description techniques and the Interactive Cooperative Objects (ICOs) formalism we will use in this paper, before presenting the case study in section 4. Section 5 illustrates the approach by discussing ways in which formal specification of the behavior of the system using ICOs and its environment (Petshop) can improve formative and summative evaluation, provide contextual help for end users and support the investigation of incidents and accidents. We then conclude and provide suggestions for future work.

Usability Aspects for Interactive Systems

Usability addresses the relationship between systems, system interfaces, and their end users. Interactive systems, or systems requiring humans in the loop of control must be designed from a UCD approach in order for the intended users to accomplish their tasks efficiently, effectively and as expected by the user. A system with poor usability can cost time and effort, and can greatly determine the success or failure of a system (See [START_REF] Holzinger | Usability Engineering for Software Developers[END_REF] for guide on usability engineering and [START_REF] Holzinger | Designing Web-Applications for Mobile Computers: Experiences with Applications to Medicine[END_REF] for interface design for medical applications). In this section, we firstly present a brief overview of usability testing, distinguishing between the two main forms of testing, formative and summative (2.1). We then discuss usability criteria and guidelines as a means of improving usability (2.2). This is extended in the third section (2.3) by describing guidelines for a specific kind of interface, touch screens. The fourth section (2.4) describes the importance of providing contextual helps as a means of improving reliability while the final section (2.5) introduces a slightly different dimension in which we discuss the ways in which formal description techniques (FDTs) can assist in improving the design of safetycritical interactive systems, such as medical applications, by helping to avoid incidents and accidents.

Usability Testing

The usability of a system can be tested and evaluated. Typically, the testing serves as either formative or summative evaluation.

Formative tests are carried out during the development of a product in order to mould or improve the product. Such testing does not necessarily have to be performed within a lab environment. Heuristic Evaluation (HE) [START_REF] Nielsen | Heuristic evaluation of user interfaces[END_REF] is an established formative Usability Inspection Method (UIM) in the field of HCI. The analyst, who must have knowledge in HCI, follows a set of guidelines to analyze the user interface. The technique is inexpensive, easy to learn and can help predict usability problems early in the design phase if prototypes are available. Examples of HEs include [START_REF] Pierotti | Heuristic Evaluation -A System Checklist[END_REF], [START_REF] Nielsen | [END_REF] and [START_REF] Bastien | [END_REF]. While this paper focuses on presenting how formal description techniques (FDTs) can support and improve the usability of interactive safety-critical systems, in [START_REF] Bernhaupt | Model-Based Evaluation: A New Way to Support Usability Evaluation of Multimodal Interactive Applications[END_REF] we have shown how they can support usability testing.

Summative tests in contrast are performed at the end of the development in order to validate the usability of a system. This is typically performed in a lab environment and involves statistical analysis such as time to perform a task.

Usability Criteria and Guidelines

Heuristic evaluation is a common usability inspection method achieved by performing a systematic inspection of a user interface (UI) design for usability. The goal of heuristic evaluation is to find the usability problems in the design so that they can be attended to as part of an iterative design process. Heuristic evaluation involves having a small set of evaluators examine the interface and judge its compliance with recognized usability principles (the "heuristics") [START_REF] Nielsen | [END_REF]. Bastien and Scapin [START_REF] Bastien | [END_REF] evaluate the usefulness of a set of ergonomic criteria for the evaluation of a human-computer interface with results indicating that usability specialists benefit from their use. Since their early publications concerning ergonomic guidelines for interface design to improve usability [START_REF] Scapin | Guide ergonomique de conception des interfaces homme-machine[END_REF], Neilsen and Molich coined the term "heuristic evaluation" [START_REF] Nielsen | Heuristic evaluation of user interfaces[END_REF]. Since the original publication of heuristics, Nielsen refined them to derive a set of heuristics with maximum explanatory power. The following lists present Bastien and Scapin's [START_REF] Bastien | [END_REF] and Nielsen's guidelines [START_REF] Nielsen | Heuristic evaluation[END_REF]. Based on the ergonomic criteria set out by Bastien and Scapin, they further define guidelines relating to each criterion. The following is an example of the "user explicit control" criteria. The guideline is called "user control" (see Table 2 in [START_REF] Bastien | [END_REF])

1
Allow users to pace their data entry, rather than having the pace being controlled by the computer processing or by external events 2

The cursor should not be automatically moved without users' control (Except for stable and well known procedures such as form-filling) 3

Users should have control over screen pages Allow users to interrupt or cancel a current transaction or process 5

Provide a 'cancel' option that will have the effect of erasing any changes just made by the user and restoring the current display to its previous version.

We have already shown how formal description techniques can support systematic assessment of user interface guidelines in [START_REF] Palanque | Embedding Ergonomic Rules as Generic Requirements in a Formal Development Process of Interactive Software[END_REF] by relating using explicit states representations as a link between guidelines and behavioral description of interactive applications.

The usability guidelines and criteria mentioned so far in this section relate to UIs in general. However, as we will see in our case study, the interaction between human and system with medical applications is migrating towards touch-screen interfaces. The following subsection presents guidelines relating specifically to these kinds of devices.

Guidelines for Specific Devices: The Case of Touch Screen

Tactile interfaces have, in addition to the above mentioned usability criteria and guidelines, their own interface design challenges. For example, the use of a touch screen of an outdoor cash machine in winter by a user wearing gloves may not be effective. Though standards for principles and recommendations as well as specifications such as ISO13406, ISO 14915, ISO 18789 exist for interface and interaction, they do not specifically target tactile interfaces for neither typical walkup-and-use interfaces, nor domain specific interfaces such as those for the healthcare domain.

In a recent conference called Guidelines on Tactile and Haptic Interactions (GOTHI), Fourney and Carter [START_REF] Fourney | Proceedings of GOTHI-05 Guidelines On Tactile and Haptic Interactions[END_REF] review existing international standards on tactile/haptic interactions and provides a preliminary collection of draft tactile/haptic interactions guidelines based on available guidance. The guidelines are categorized under the following headings:

• Tactile/haptic inputs, outputs, and/or combinations • Tactile/haptic encoding of information • Content specific Encoding • User Individualization of Tactile / Haptic Interfaces We provide below a selection of the guidelines proposed Fourney and Carter [START_REF] Fourney | Proceedings of GOTHI-05 Guidelines On Tactile and Haptic Interactions[END_REF] that particularly relate to the research and case study presented in this paper, that is the improvement of usability of a safety-critical interactive touch screen system. See [START_REF] Fourney | Proceedings of GOTHI-05 Guidelines On Tactile and Haptic Interactions[END_REF] for the complete list of guidelines. [1] has also studied usability of touch screen interfaces and suggests that menus and buttons that are often selected should be located at the bottom of the interface rather than the top to avoid covering the screen (and in the case of a safety-critical application, vital information) with one's arm while accessing the menus. Additional references to research on guidelines for touch screens can be found [START_REF] Holzinger | Finger Instead of Mouse: Touch Screens as a means of enhancing Universal Access[END_REF] and [START_REF] Holzinger | Mobile Computing in Medicine: Designing Mobile Questionnaires for Elderly and Partially Sighted People[END_REF].

Furthermore, critical interfaces, such as those used in to monitor patients in the healthcare domain provide vital information. This means, if selecting an option within the application forces a new window to cover the initial screen, there is a risk that it will be unintentionally missed during that short period of time (see Fig. 1). A lot of work has been done on the visibility of a workspace, with techniques designed to provide contextual awareness at all times even while the user focuses on one aspect of the interface (see [START_REF] Memmel | Agile Methods and Visual Specification in Software Development: a chance to ensure Universal Access[END_REF]).

Fig. 1. Interaction with a touchscreen

Coutaz et al, [START_REF] Coutaz | Early Experience with the Mediaspace CoMedi[END_REF] describe "CoMedi", a media space prototype that addresses the problem of discontinuity and privacy in an original way. It brings together techniques that improve usability suggested over recent years. The graphical user interface of CoMedi is structured into three functional parts: at the top, a menu bar for non frequent tasks (see Fig. 2 and Fig. 3). In the center, a porthole that supports group awareness. At the bottom, a control panel for frequent tasks. The "The fisheye porthole" supports group awareness. Though the example in the paper is of a collaborative tool in a research laboratory, the way in which the fisheye porthole is designed could be useful in a medical environment. The porthole may have the shape of an amphitheatre where every slot is of equal size. When the fisheye feature is on, selecting a slot, using either the mouse or a spoken command, provokes an animated distortion of the porthole that brings the selected slot into the centre with progressive enlargement [START_REF] Coutaz | Early Experience with the Mediaspace CoMedi[END_REF].

The idea of context loss while zooming or focusing on a particular aspect of the interface has been argued and researched by Bob Spence with his database navigation approach [START_REF] Spence | Data Base Navigation: An Office Environment for the Professional Behaviour and Information Technology[END_REF], Furnas, with his generalized fisheye views [START_REF] Furnas | Generalized Fisheye Views[END_REF]and Mackinlay et al., This area of the interface is blocked from view Fig. 2. The graphical user interface of CoMedi Fig. 3. The UI of CoMedi with Porthole when the fisheye view is activated [START_REF] Mackinlay | Perspective Wall: Detail and Context Smoothly Integrated[END_REF] with their perspective wall his perspective wall approach and by John Lamping with his hyperbolic browser [START_REF] Lamping | Laying out and visualizing large trees using a hyperbolic space[END_REF].

Importance of Contextual Help

Contextual help is an important feature that interactive systems should include. It refers to the available of help at any point in time relative to the given state of the system. For example, if a user expects an option or a button to be available and it is not (i.e. a grayed out button in a menu), the contextual help would indicate why this option is not available at that moment. Formal description techniques (FDTs) provide a way to have a complete and unambiguous representation of all states of the system and state changes as well as a means for reasoning about these states and state changes. However, without formal methods fully describing the behavior of the system, providing this kind of advice is very difficult. By simply analyzing a user interface, it is almost impossible (except with a very basic system) to know exactly what state the system is in. In order for the formal description of the system to be directly usable for the end user (i.e. the operator), it would certainly need additional annotations. It is unlikely that medical personnel would be able to read such a model without training and it is not useful to train them in such a way. The main point is that the formal model supports designers and developers' activities by for instance identifying why users are experiencing a problem and how to overcome it. Furthermore, analyzing lines of code to determine the system state is extremely cumbersome and providing developers with an abstract view of the system can support them. We show in section 5.2 that a formal graphical description of the behavior of the system can provide information on the current state, why the option/button is not available and what must be performed by the user for that option to be available. More information on how such contextual help can be supported by FDT can be found in [START_REF] Palanque | Contextual Help for Free with Formal Dialogue Design[END_REF].

Avoidance of Incidents and Accidents

The heading incident and accident investigation can be misleading in a usabilityrelated article, however we believe and described in the introduction, that poor usability of a system can potentially lead to an adverse event.

In terms of supporting their investigation, we have devised an approach exploiting two complementary techniques for the design of safety-critical interactive systems. More precisely we address the issue of system redesign after the occurrence of an incident or accident. The techniques used are Events and Causal Factors analysis, used in accident investigation to identify the path of events and contributing factors leading to an accident, and secondly, Marking Graphs, an analysis technique available after formally modeling the interactive system, using Petri nets for example. Marking graphs are used to systematically explore all possible scenarios leading to the accident based on a formal system model. The formal description techniques (FDTs) allow us to exploit and represent all system states. The techniques serve two purposes. Firstly, it is intended to ensure that the current system model accurately models the sequence of events that led to the accident according to information provided by Events and Causal Factors Analysis. Secondly, our approach can be used to reveal further scenarios that could eventually lead to similar adverse outcomes. The results can in turn be used to modify the system model such that the same accident is unlikely to recur. This is achieved by identifying system states that are undesirable and may want to be avoided. By identifying the state changes leading to such undesirable states, it is possible to adapt the system model to make these states impossible by making the paths (combination of state changes leading to that state) impossible. This is supported by simulating the identified scenarios on the adapted system model. This will be exemplified in section 5.3, on a simple example using the PatientNet case study. The interested reader can see a complete example in [START_REF] Basnyat | Redesigning an Interactive Safety-Critical System to Prevent an Accident from Reoccurring[END_REF].

Formal Specification of Interactive Systems

The previous sections have described usability evaluation techniques, usability guidelines targeted specifically at touch screen interfaces as well as relating usability to incident and accidents. In this section, we present a formal description technique (FDT) for describing the behavior of interactive systems. Most FDT could provide the kind of support for usability we are describing but we present rapidly here the FDT ICOs (Interactive Cooperative Objects) dedicated to the specification of interactive systems based on Petri nets that we will use for the case study in section 4.

Formal verification of models can only be achieved if the formalism is based on mathematical concepts. This allows reasoning on the system models in addition to empirical testing once the system has been implemented. Verification of models has economical advantages for resolving problems in terms of consumption of resources. Further advantages include the possibility to locate an error (though perhaps not the exact causes for the error).

One of the aims of the formal analysis is to prove that there is no flaw in the models. Using the ICO formalism for describing the models, the analysis is done by using the mathematical tools provided by the Petri net theory. Using those tools, one can prove general properties about the model (such as absence of deadlock) or semantic domain related properties (i.e. the model cannot describe impossible behavior such as the light is on and off at the same time).

Modeling systems in a formal way helps to deal with issues such as complexity, helps to avoid the need for a human observer to check the models and to write code. It allows us to reason about the models via verification and validation and also to meet three basic requirements notably: reliability (generic and specific properties), efficiency (performance of the system, the user and the two systems together (user and system) and finally to address usability issues.

ICOs as an Concrete Example of Formal Description Techniques

The aim of this section is to present the main features of the Interactive Cooperative Objects (ICO) formalism that we have defined and is dedicated to the formal description of interactive systems. We encourage the interested reader to look at [START_REF] Navarre | Contribution à l'ingénierie en Interaction Homme Machine -Une technique de description formelle et un environnement pour une modélisation et une exploitation synergiques des tâches et du système[END_REF] for a complete presentation of this formal description technique as we only present here the part of the notation related to the behavioral description of systems. This behavioral description can be completed with other aspects directly related with the user interface that are not presented here for space reasons.

Interactive Cooperative Objects Formalism (ICO)

ICOs are dedicated to the modeling and the implementation of event-driven interfaces, using several communicating objects to model the system, where both behavior of objects and communication protocol between objects are described by the Petri net dialect called Cooperative Objects (CO). In the ICO formalism, an object is an entity featuring four components: a cooperative object which describes the behavior of the object, a presentation part (i.e. the graphical interface), and two functions (the activation function and the rendering function) which make the link between the cooperative object and the presentation part.

Cooperative Object: Using the Cooperative Object formalism, ICO provides links between user events from the presentation part and event handlers from the Cooperative Objects, links between user event availability and event handler availability and links between state in the Cooperative Objects changes and rendering.

Presentation part: The presentation of an object states its external appearance. This presentation is a structured set of widgets organized in a set of windows. Each widget may be a way to interact with the interactive system (user system interaction) and/or a way to display information from this interactive system (system user interaction). Activation function: The user system interaction (inputs) only takes place through widgets. Each user action on a widget may trigger one of the Cooperative Objects event handlers. The relation between user services and widgets is fully stated by the activation function that associates each event from the presentation part with the event handler to be triggered and the associated rendering method for representing the activation or the deactivation.

Rendering function: the system user interaction (outputs) aims at presenting the state changes that occurs in the system to the user. The rendering function maintains the consistency between the internal state of the system and its external appearance by reflecting system states changes.

ICOs are used to provide a formal description of the dynamic behavior of an interactive application. An ICO specification fully describes the potential interactions that users may have with the application. The specification encompasses both the "input" aspects of the interaction (i.e. how user actions impact on the inner state of the application, and which actions are enabled at any given time) and its "output" aspects (i.e. when and how the application displays information relevant to the user).

An ICO specification is fully executable, which gives the possibility to prototype and test an application before it is fully implemented [START_REF] Navarre | Structuring Interactive Systems Specifications for Executability and Prototypability[END_REF]. The specification can also be validated using analysis and proof tools developed within the Petri net community and extended in order to take into account the specificities of the Petri net dialect used in the ICO formal description technique. This formal specification technique has already been applied in the field of Air Traffic Control interactive applications [START_REF] Navarre | Reconciling Safety and Usability Concerns through Formal Specification-based Development Process[END_REF], space command and control ground systems [START_REF] Palanque | Supporting Usability Evaluation of Multimodal Man-Machine Interfaces for Space Ground Segment Applications Using Petri net Based Formal Specification[END_REF], or interactive military [START_REF] Bastide | Petri Net Based Behavioural Specification of CORBA Systems[END_REF] or civil cockpits [START_REF] Barboni | Exploitation of Formal Specification Techniques for ARINC 661 Interactive Cockpit Applications[END_REF]. The example of civil aircraft is used in the next section to illustrate the specification of embedded systems.

To summarize, we provide here the symbols used for the ICO formalism and a screenshot of the tool.

Related Work on Formal Description Techniques and Usability

The use of formal specification techniques for improving usability evaluation has been explored by several authors.

Loer and Harrison [START_REF] Loer | Formal interactive systems analysis and usability inspection methods: Two incompatible worlds?[END_REF] provide their view on how Formal Description Techniques (FDTs) can be used to support Usability Inspection Methods (UIM) such as the formative techniques discussed in the introduction of this paper. In accordance with our views, the authors argue that the costs of using FDTs are justified by the benefits gained. In their paper, the authors exploit the "OFAN" modeling technique [START_REF] Coutaz | Early Experience with the Mediaspace CoMedi[END_REF], based on statecharts with the statemate toolkit for representing the system behavior. Each of the usability heuristics is formalized and tested however, the authors are limited to functional aspects of the system only.

In closer relation to the approach we present in this paper, Bernonville et al [START_REF] Bernonville | Explicit combination between Petri Nets and ergonomic criteria: basic principles of the ErgoPNets method[END_REF] combine the use of Petri nets with ergonomic criteria. In contrast to Loer & Harrison's approach of assisting non-formal methods experts to benefit from FDTs, Beronville et al argue for the necessity of better communicating to computer scientists of ergonomic data.

Bernonville et al [START_REF] Bernonville | Explicit combination between Petri Nets and ergonomic criteria: basic principles of the ErgoPNets method[END_REF] use Petri nets to describe tasks that operators wish/should perform on a system as well as the procedure provided/supported by the software application. By using ergonomic criteria proposed by Bastien & Scapin [START_REF] Bastien | [END_REF], the method supports the analysis of detected problems. While Petri nets can be used to describe human tasks, dedicated notations and tool support such as ConcurTaskTrees (CTT) and ConcurTaskTree Environment (CTTe) [START_REF] Mori | CTTE: Support for Developing and Analyzing Task Models for Interactive System Design[END_REF] exist for the description of operator tasks, this would probably be more practical considering that "ErgoPNets" proposed in their paper currently has no tool support and is modeled using MS Visio.

Palanque & Bastide [START_REF] Palanque | Formal specification of HCI for increasing software's ergonomics[END_REF] have studied the impact of formal specification on the ergonomics of software interfaces. It is shown that the use of an object oriented approach with Petri nets ensures software and ergonomic quality. For example, by ensuring predictability of commands, absence of deadlocks and by offering contextual help and context-based guidance.

Harold Thimbley provides a worked example of a new evaluation method, called Interaction Walkthrough (IW), designed for evaluating safety critical and high quality user interfaces, on an interactive Graseby 3400 syringe pump and its user manual [START_REF] Thimbleby | Interaction walkthrough -a method for evaluating interactive systems[END_REF]. IW can be applied to a working system, whether a prototype or target system. A parallel system is developed from the interaction behavior of the system being evaluated.

Case Study

Before providing details of our approach, an outline of the case study on which we present our approach is provided here. The medical domain differs from the aviation domain (with which we are more familiar) in that it appears that there is more time to analyze a situation, for example, via contextual help. In a cockpit environment, it is unlikely that the pilot or co-pilot will have time to access a contextual help service. The case study we have chosen is a telemetry patient monitoring system.

The PatientNet system, operating in a WMTS band, provides wireless communications of patient data from Passport monitors and/or telepak monitor sworn by patients, to central monitoring stations over the same network. Fig. 4 provides a simplified diagram of the layout of the PatientNet system. Our interest in this system resulted from research on the US Food and Drug Administration (FDA) Manufacturer and User Facility Device Experience (MAUDE) database which has numerous adverse events reported (including fatalities) relating to this device/system. In our search, between the 20/03/2002 and the 08/02/2007, 22 reports were received relating to the PatientNet system including the central station and the passport. Of these 22, 10 resulted in patient death. Table 2 summarizes our findings in terms of patient outcome.

Fig. 5. PatientNet Central Station 16-patient display

The paper does not directly address incident and accident investigation, thus we will not continue our discussion on the adverse events that occurred during humancomputer interaction with this system. We simply highlight the importance of such interactions and potential for abnormal human and technical behavior and the impact they may have on human life. Furthermore, we will not describe the full system in detail; rather focus on the PatientNet central station for which we have screenshots of the application. The central station is a server and workstation where patient information from a variety of different vital sign monitors and ambulatory EGG (Electroglottograph) transceivers is integrated, analyzed and distributed to care providers. Real-time patient data is presented in a common user interface so caregivers have the information they need to respond to critical patient events immediately [39]. In addition to the patient's current status, the Central Station allows for retrospective viewing of patient information, which equips caregivers to make critical decisions and provide consistent, highquality care to their patients across the enterprise (see Fig. 5 and Fig. 6 for Central Station screenshot).

Features of the central station include: Demographics, alarm limits, bedside view, event storage, ST analysis, full disclosure, trend storage, reports, care group assignments, physiological alarm volumes, print setup, choice of single or duel display.

Fig. 6. PatientNet Central Station Full Disclosure

Typical selling points from the product brochure include statements such as "a simple touch of the screen brings up the information you need", "easy-to-read screen focuses attention on vital details" and "find answers to common questions with online Help menus".

The Approach

We demonstrate the applicability of this approach and how it could potentially predict and prevent some of the adverse events associated with a telemetry patient monitoring system made by a major medical technology manufacturer and currently used in a number of hospitals in North America.

Using the case study, we provide a simple example showing how formal description techniques and particularly the ICO notation and its Petshop tool, support the three points discussed in section 2 : usability evaluation, contextual help and incident and accident investigation. Each issue is a research domain within its own right and we are therefore limited to what we want to and will show on each point. The aim here is to give an overview of the types of support formal description techniques methods can provide to usability related methodologies/issues.

Supporting Usability Evaluation

As previously discussed, usability evaluation can be considered as formative or summative depending on the analysis technique used. Here we have decided to describe how the ICO FDT can be used to support a formative evaluation. The formative approach we use to illustrate this part of our approach is the application of ergonomic criteria and guidelines defined in [START_REF] Bastien | [END_REF], a type of usability inspection method. The selected criterion is "user explicit control" which has 5 guidelines. The selected guideline (number 4) is defined as "Allow users to interrupt or cancel a current transaction or process".

The PatientNet Central Station interface (see Fig. 5a, Fig. 5b) does not have a cancel or undo/redo option2 . According to Bastien and Scapin's guideline, the user should be able to interrupt or cancel their current transaction. When the Central Station is in "full disclosure mode" (see Fig. 5b), an "exit" button is available to close the window and return to the 16-patient or 8-patient view mode. However, this "exit" button is not a cancel or an undo/redo function, it simply closes the window to change viewing mode.

Typically, if this problem was identified during a usability evaluation, the system would be redesigned, and a second round of user testing would be performed, to verify if all actions now have an interrupt option. Due to the highly interactive nature of such an application, it is impossible to fully verify if all available actions on the system can be interrupted, cancelled, or undone and redone.

The ICO formalism and its dedicated tool Petshop, can support the usability evaluation of such a guideline by providing a means to exhaustively analyze the system. Once the application's user interface has been modified (to provide a cancel or undo/redo button applicable to all transactions), the Petri net, using the ICO formalism is also modified to represent the same behavior. A link can then be made between the two components using the Activation (and/or rendering) function(s). Following this design modification stage, the benefits of FDTs can be exploited.

In addition to a second round of user testing, FDTs, such as ICOs provide a number of benefits for designers who wish to reason about the effects of proposed changes to a system. For example, a marking tree (an analysis technique based on mathematical foundations) can be used to identify the set of reachable states provided that some information is given about the initial status or 'marking' of the system. This technique helps to produce what can be thought of as a form of state transition diagram. Several tools are currently available to support this analysis (i.e. JARP Petri Net Analyzer version 1.1 developed by Sangoi Padilha (http://jarp.sourceforge.net/ us/index.html) which has been developed as an auxiliary tool for the Petri net analyzing tool ARP developed by Alberto Maziero (http://www.ppgia.pucpr.br/~maziero/ diversos/petri/arp.html).

Thus in our example, marking graph can be used to trace all possible interactions with the system and prove that each action has a cancel or undo/redo option available.

The model provided in Fig. 7 represents the behavior of a small subsection of the PN central station system. The Petri net models the selection of modes (16-view, 8view or full disclosure) and the availability of the cancel button. Assuming the initial state and default state is the 16-view mode, the cancel buttons are therefore available in 8-view mode and full disclosure mode. Furthermore, the user can switch between 8-view and full disclosure modes. We have modeled the system such that a "cancel" operation will take the system back into 16-view mode.

The places have been labeled p1 -p3 while the transitions have been labeled t1 -t6. Transitions that are fireable are shaded in dark grey. This from the initial state, 1 token in place p1, transitions t1 and t2 are the only two transitions that are fireable.

Fig. 7. ICO model proving a cancel option is always available

Since the model is simplistic, it is possible to analyze the model graphically. However, when modeling a complete system the use of systems' generated marking graphs is necessary to prove system properties. Here we provide the marking tree from the current marking of the model provided in Fig. 7. There are 3 possible states: M2: (t3:M1), (t6:M0) -From state M2, transition t3 changes the current state to state M1, while transition t6 changes the current state to M0

The analysis techniques described here provide exhaustive proofs of the availability of the cancel option in different system modes.

Supporting Contextual Help

The use of FDTs can provide accurate contextual help at any moment of system interaction. Since the model describes the concise behavior of the system, it is possible to analyze the exact state the system is in. As an example, we refer back to section 2.4, and discuss the case of an operator wishing to press a button to perform an action, though this button has no effect because it is currently "grayed out", inactive. This kind of interaction problem is encountered often with applications such as MS Word. Though after encountering the same problem numerous times, we begin to learn why the button is inactive and correct our actions accordingly. In the medical domain however, the first time this problem is encountered may result in life threatening scenarios. The operator should therefore be provided with contextual help that specifically states why the problem has occurred and how to resolve it. The FDT would provide a possible (or even an exhaustive list of all the possible) sequence of actions that would activate the required button, and a way of how to do it on the user interface but not whether it is wise to try to do it considering the current state of interaction between the user and the system and the current status of task execution.

Fig. 8. ICO model with laser button inactive

Using ICOs, it is possible to analyze the Petri net and identify the current state (i.e. the distribution of tokens throughout the set of places) and understand why the button is inactive (i.e. which transition(s) must be fired in order for the place representing the button activation to contain its necessary token). Fig. 8 and Fig. 9 illustrate a simple Petri net, using the ICO notation, in order to demonstrate this part of the approach. We take the same model illustrated in the previous section, this time adding the options available when in full disclosure mode. These include options, mode, laser, quality, wave and exit. The exit transition takes the system back into the 16-mode view. Fig. 9 indicates that the "laser" button is currently not available, because its associated transition is not fireable.

The only way that the "select laser" transition can become fireable is for place "full disclosure mode" to contain a token. If the user was searching for the laser button while operating the PN Central station and referred to a help file, the Petri net model could provide detailed help on why the button is not available and how to make it available. Fig. 9 therefore shows the same model, this time in the state allowing the "select laser" transition to be fireable.

Supporting Incident and Accident Investigation

In order to support the investigation of an incident or accident, such as the reports on the US Food and Drug Administration (FDA) Manufacturer and User Facility Device Experience (MAUDE) database , we advocate the use of system modelling to prove that a given incident or accident cannot be triggered in the new system design. We are not claiming that the mishap will not recur in the real system, but in the model describing the behavior of the system. This model is an abstraction of the real system assuming that system engineers will use that model for designing the improved system.

To be more concrete, we have devised an approach that allows a system to be formally modeled and then formally analyzed to prove that the sequence of events described in the accident report is not able to be triggered again in that model.

The aim is to use formal description techniques to model the complete behavior of the system and identify hazardous states that we would wish to avoid. These states can be avoided by eliminating the sequence of state changes leading to that state.

One of our aims for including data from incident and accident investigations in safety-critical interactive systems design is to ensure that the same incident or accident analyzed will not occur again in the re-modeled system. That is, that an accident place within the network will be blocked from containing a token. Due to space constraints we do not illustrate this part of the approach in this paper, though the interested reader can refer to [START_REF] Basnyat | Multidisciplinary perspective on accident investigation[END_REF] and [START_REF] Basnyat | Redesigning an Interactive Safety-Critical System to Prevent an Accident from Reoccurring[END_REF].

Conclusion

This paper has addressed issues of usability for modern medical applications. We have argued that empirical usability evaluations, such as formative and summative evaluations are not sufficient when dealing with complex safety-critical interactive systems that have an extremely large number of system states. We advocate the use of formal methods, particularly those based on Petri nets, such as the Interactive Cooperative Objects (ICOs) formalism, a formal notation dedicated to the specification of interactive systems that can be exploited to provide mathematically grounded analyses, such as marking graphs, to argue and prove usability properties. By producing high-fidelity formally specified prototypes, it is possible to verify whether the new design satisfactorily prevents such ergonomic defects. The paper has given three examples of ways in which Formal Description Techniques (FDTs) can support usability. However, each of these examples (formative evaluation, contextual help and supporting incident and accident investigation) is its own research area, and here we give a taster of each.

•

  States are represented by the distribution of tokens into places • Actions triggered in an autonomous way by the system are represented as and called transitions • Actions triggered by users are represented by half bordered transition ICOs are supported by the Petshop environment that makes it possible to edit the ICO models, execute them and thus present the user interface to the user and support analysis techniques such as invariants calculation.

Fig. 4 .

 4 Fig. 4. Simplified layout of the PatientNet system

  State M0: {p1}, State M1: {p2}, State M2: {p3}The marking tree (represented in text format) is as follows: M0: (t1:M1), (t2:M2) -From state M0, transition t1 changes the current state to state M1, while transition t2 changes the current state to M2 M1: (t4:M2), (t5:M0) -From state M1, transition t4 changes the current state to state M2, while transition t5 changes the current state to

Fig. 9 .

 9 Fig. 9. ICO model with active laser button

Table 1 .

 1 Criteria for interface design to improve usability

	Ergonomic criteria -from Table		Nielsen's Heuristics guidelines [28].
	1 in Bastien and Scapin [6]
	1	Guidance	1	Visibility of system status
	2	User workload	2	Match between system and the real world
	3	User explicit control	3	User control and freedom
	4	Adaptability	4	Consistency and standards
	5	Error management	5	Error prevention
	6	Consistency	6	Recognition rather than recall
	7	Significance of codes	7	Flexibility and efficiency of use
	8	Compatibility	8	Aesthetic and minimalist design
			9	Help users recognize, diagnose, and
				recover from errors
			10 Help and documentation

Table 2 .

 2 Summary of MAUDE adverse report search relating to PatientNet system

	Patient Outcome Description	Number
	Death	10
	Unknown (was not specified in report)	8
	Other	2
	Required intervention	1
	Life threatening	1
	Total	22

Access to the PatientNet system was not available for this study. We base our approach and examples on documented data. The point here is to illustrate the approach on a medical application.

Acknowledgments. This work was supported by the EU funded Network of Excellence ResIST http://www.resist-noe.eu.


Vincent A Viblanc
email: vincent.viblanc@iphc.cnrs.fr

Claire Saraux

Anouch Tamian

François Criscuolo

David W Coltman

Shirley Raveh

Jan O Murie

F Stephen Dobson

Stephen Dobson

Measuring fitness and inferring natural selection from long-term field studies: different measures lead to nuanced conclusions

Keywords: fitness, life history, lifetime reproductive success, mating, natural selection, survival SIGNIFICANCE

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Understanding natural selection and the selective processes that shape the evolution of phenotypic traits in living organisms hinges upon our ability to measure and aptly capture the adaptive influence of traits with respect to specific environments [START_REF] Endler | Natural selection in the wild[END_REF]. Studies of natural selection can be broadly separated into those that model the evolutionary process and those that attempt to measure the action of natural selection in populations in nature. Models of natural selection seek to reveal how the process works through mathematical expressions of change from one generation to the next (Wright 1931;Crow and Kimura 1970;Orr 2009). These models often assume that changes in trait frequencies are the result of natural selection, without the occurrence of other processes such as migration, mutation, drift, or epigenetic modifications of gene expression.

In contrast, evolutionary change in real populations may actually reflect a combination of these different processes. In addition, empirical studies of natural selection, in action in real populations, generally measure change in trait frequencies from short-term measures of survival or reproduction. This is problematic for inferences on natural selection, since fitness advantages of particular trait values are often measured over a shorter time period than a complete generation [START_REF] Lande | The measurement of selection on correlated characters[END_REF]Kruuk et al. 2002;[START_REF] Dobson | Plasticity results in delayed breeding in a long-distant migrant seabird[END_REF]. Such studies measure fitness as success at surviving a storm or at producing juvenile offspring, and then compare the fitness metric to trait values, rather than using success at producing reproducing offspring that themselves reproduce in the next generation (but see [START_REF] Boyce | Optimizing great tit clutch size in a fluctuating environment[END_REF].

Fitness is the complex metric by which one typically measures the adaptive value of organismal traits in evolutionary ecology. Studies that refine the definition of fitness or seek alternative measures of fitness are legion [START_REF] Fisher | The genetical theory of natural selection[END_REF][START_REF] Hamilton | The genetical evolution of social behaviour, I & II[END_REF][START_REF] Grafen | How not to measure inclusive fitness[END_REF][START_REF] Grafen | Biological fitness and the Price Equation in class-structured populations[END_REF][START_REF] Endler | Natural selection in the wild[END_REF][START_REF] Lucas | How to measure inclusive fitness, revisited[END_REF][START_REF] Queller | The measurement and meaning of inclusive fitness[END_REF][START_REF] Oli | Hamilton goes empirical: estimation of inclusive fitness from life-history data[END_REF][START_REF] Qvarnström | Testing the genetics underlying the coevolution of mate choice and ornament in the wild[END_REF][START_REF] Van De Pol | A silver spoon for a golden future: long-term effects of natal origin on fitness prospects of oystercatchers (Haematopus ostralegus)[END_REF][START_REF] Hunt | What is fitness, and how do we measure it?[END_REF]Dobson et al. 2012;[START_REF] Zhang | Fitness prospects: effects of age, sex and recruitment age on reproductive value in a long-lived seabird[END_REF][START_REF] Scranton | The importance of the timescale of the fitness metric for estimates of selection on phenotypic traits during a period of demographic change[END_REF][START_REF] Harris | An evaluation of feather corticosterone as a biomarker of fitness and an ecologically relevant stressor during breeding in the wild[END_REF][START_REF] Rubach | Comparing fitness measures and the influence of age of first reproduction in Columbian ground squirrels[END_REF][START_REF] Levin | Extending the range of additivity in using inclusive fitness[END_REF]. These studies usually propose some practical means of measuring the propensity of a given gene, group of genes, trait, or group of traits, to spread through populations over generations [START_REF] Saether | The concept of fitness in fluctuating environments[END_REF]. In the present paper, we use a trait-based definition of fitness: the change in frequencies of alternative forms of an organismal trait over time in a population [START_REF] Dobson | Fitness[END_REF]. This definition presents the advantage that trait variation integrates sources of both genetic and non-genetic (e.g., early environmental or maternal effects affecting trait expression) variation. It further has the advantage of practicality since it is the phenotypic traits (e.g., individual mass, size, age) that are measured in field studies, with no assumption made about their underlying genetic or non-genetic architecture (e.g., the genetic variance-covariance matrix ;[START_REF] Lande | Quantitative genetic analysis of multivariate evolution, applied to brain: body size allometry[END_REF][START_REF] Arnold | Understanding the evolution and stability of the G-Matrix[END_REF].

Regardless of the metric used, measuring fitness requires understanding how traits are transmitted through the population over time. In terms of evolution, it is the fitness of a trait form relative to others that counts [START_REF] Ayala | Frequency-dependent selection[END_REF]. For sexual organisms, such as many animals and plants, transmission of traits is achieved through reproduction. Thus, most studies evaluate fitness by measuring the propensity of organisms to transmit traits through the number of offspring they produce. For iteroparous organisms, this includes successive reproductions, so that adult survival and longevity, as well as age at first reproduction and reproductive senescence, are also important components of fitness [START_REF] Brommer | Reproductive timing and individual fitness[END_REF][START_REF] Oli | Fitness consequences of delayed maturity in female wood ducks[END_REF][START_REF] Bouwhuis | The forms and fitness cost of senescence: age-specific recapture, survival, reproduction, and reproductive value in a wild bird population[END_REF].

However, when measuring fitness, the most important issues are what ultimately influences changes in trait frequencies, and how our conclusions about trait evolution are shaped by the nature of our fitness measures.

If adaptive traits are those that spread in the population relative to other trait forms, then surely offspring that die before reproducing themselves do not contribute to the fitness of a given trait. Yet, for studies in nature, our ability to monitor individuals over time is often limited: many animal species disperse at a young age [START_REF] Greenwood | Mating systems, philopatry and dispersal in birds and mammals[END_REF][START_REF] Dobson | Competition for mates and predominant juvenile male dispersal in mammals[END_REF], and for many species age at maturity may be delayed [START_REF] Cole | The population consequences of life history phenomena[END_REF][START_REF] Oli | The relative importance of life-history variables to population growth rate in mammals: Cole's prediction revisited[END_REF], so that the contribution of offspring to trait fitness through their own future reproduction is difficult to measure. Thus, as second-best proxies, studies of animals often rely on metrics such as clutch size, brood size, and litter size at birth or at offspring independence, to quantify the number of offspring produced that potentially can contribute to the next generation. Yet, because numerous offspring die at a young age, it is unclear how trait fitness is influenced by further selection or changed by environmental stochasticity as time goes by [START_REF] Hadfield | Estimating evolutionary parameters when viability selection is operating[END_REF]). On one hand, trait fitness may be influenced by genetic correlations and selection on other traits than the one of interest. On the other hand, the further fitness is measured from the production of reproductive offspring, the more environmental variation may change the association between a phenotypic trait and realized fitness (the fitness of alternative traits when offspring begin reproduction).

The purpose of our study was to assess how the evaluation of fitness changed depending on the timing of measurement using a 29-year long-term data set of male and female Columbian ground squirrels (Urocitellus columbianus). Specifically, we were interested in understanding (1) how individual fitness varied depending on whether we considered the offspring born, weaned, at yearling age, and at age at first reproduction; and (2) whether the association of a phenotypic trait and fitness changed depending on the timing of the fitness measurement. To do this, we measured individual survival and reproduction, and estimated the number of gene copies that a breeding parent passes on to the next year, by adding the parent's survival from the current year to the next (1 for surviving, 0 for not) to half the number of offspring it produced. We then compared this measure to other individuals in the population to obtain an estimate of annual fitness [START_REF] Qvarnström | Testing the genetics underlying the coevolution of mate choice and ornament in the wild[END_REF]. We also estimated fitness from adult annual survival and reproduction separately, and here the number of offspring was not halved (both annual fitness and these latter measures were used, for example, by [START_REF] Dobson | Plasticity results in delayed breeding in a long-distant migrant seabird[END_REF]. Offspring production may be measured at different time points, such as birth, weaning, or survival to a later period. We evaluated how important the choice of when to measure offspring production was with an examination of repeatablility (the intraclass correlation coefficient "ICC," used as a measure of consistency) of annual and reproductive fitness measures when using number of offspring measured at birth, weaning, and yearling age and investigated paired correlations between these.

We also evaluated how measuring fitness at different time periods, and using different metrics, affects inferences about natural selection. For illustrative purposes, we focused on a single trait, and examined the strength of selection on emergence date from hibernation, i.e., the date of spring emergence above ground from hibernation. For ground squirrels, this occurs close to the termination of torpor (Williams et al. 2014). We did not know the genetic variance-covariance matrix for traits associated with emergence from hibernation, and thus could not differentiate selection among genetically correlated traits [START_REF] Lande | The measurement of selection on correlated characters[END_REF]. However, adult female Columbian ground squirrels go through a single day of estrus and mating each year, about 3-5 days after emergence from hibernation [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF]. The genetic correlation between emergence and estrus dates was 0.98 ± 0.01 SE [START_REF] Lane | A quantitative genetic analysis of hibernation emergence date in a wild population of Columbian ground squirrels[END_REF], indicating selection on one of these traits would undoubtedly influence selection on the other. Since our sample sizes were greatest for emergence date from hibernation, we chose this trait for analyses. Columbian ground squirrels are hibernating rodents, with a short and intense reproductive season lasting only a few months [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF][START_REF] Dobson | Seasonal activity and body mass of Columbian ground squirrels[END_REF]. The timing of emergence from hibernation is highly variable [START_REF] Tamian | Integrating microclimatic variation in phenological responses to climate change: a 28-year study in a hibernating mammal[END_REF], and previous studies have shown it to be both significantly heritable (h 2 = 0.22-0.34; [START_REF] Lane | A quantitative genetic analysis of hibernation emergence date in a wild population of Columbian ground squirrels[END_REF], and negatively associated with annual fitness when measured using offspring at emergence from their first hibernation, at about one year old (for adult females; [START_REF] Lane | Delayed phenology and reduced fitness associated with climate change in a wild hibernator[END_REF], prerequisite conditions for responding to selection. However, nothing is known about whether the strength or direction of selection gradients differs when the fitness for this trait is measured at different time periods, nor whether selection gradients exist for males.

Thus, emergence date appeared to be a good candidate trait to investigate its association with different estimates of fitness measured from different life stages.

Materials and Methods

Study species and long-term population monitoring

Columbian ground squirrels were studied from 1992 to 2020 in the Sheep River Provincial Park, Alberta, Canada (50° 38′ 10.73″ N; 114° 39′ 56.52″ W; 1524 m; 2.3 ha). Individuals were fitted with permanent numbered ear tags (#1-Monel metal tag; National Band and Tag Company, Newport, KY) when weaned (or at first capture for immigrants). Thus, it was not possible to record data blind because our study involved focal animals in the field. In each year of the study, the entire population was trapped at spring emergence using 13 × 13 × 40 cm 3 live-traps (Tomahawk Live Trap, Hazelhurst, WI, USA) baited with a small amount of peanut butter. Each individual was then dyed with a temporary unique dorsal mark (Clairol® Hydrience black hair dye N°52 Black Pearl, Clairol Inc., New York, USA) for identification during field observations. We followed ground squirrels daily throughout the breeding season to assess breeding phenology and success. Females copulated with multiple males within 3-5 days following emergence from hibernation, typically during a single day of estrus [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF][START_REF] Raveh | Mating order and reproductive success in male Columbian ground squirrels (Urocitellus columbianus)[END_REF].

We determined female mating date through behavioral observations and by inspecting female genitalia (presence of a copulatory plug or plug material in abdominal fur, or sperm in vaginal smears; [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF]. Following mating events, we identified female single-entrance nest burrows during gestation by visual observations of females stocking them with dry grass [START_REF] Murie | Survival of captive-born cross-fostered juvenile Columbian ground squirrels in the field[END_REF], and marked them with colored and flagged metal pins (1 m in length).

Females in the wild gave birth to an average of three (one to seven) blind and hairless offspring in a specially constructed nest burrow, after some 24-days of gestation [START_REF] Dobson | Interpretation of intraspecific life history patterns: evidence from Columbian ground squirrels[END_REF][START_REF] Murie | Mating behavior of Columbian ground squirrels. I. Multiple mating by females and multiple paternity[END_REF]. From 2000 to 2016, we caught pregnant females within 2-3 days of expected parturition, about 21-22 days after mating, and brought them to an on-site field laboratory [START_REF] Hare | Manipulation of litter size reveals no cost of reproduction in Columbian ground squirrels[END_REF]. Females were housed indoor in polycarbonate microvent rat cages (483 x 267 x 200 mm; Allentown Caging Equipment Company, Allentown, NJ), supplied with wood shavings and newspaper as nesting material. Females were provided with apple, lettuce, and horse feed (EQuisine sweet show horse ration; Unifeed, Okotoks, Alberta, Canada) ad libitum. After parturition, offspring were sexed and a small tissue biopsy was acquired for paternity analyses (see below) by clipping a toenail bud as previously described by [START_REF] Hare | Manipulation of litter size reveals no cost of reproduction in Columbian ground squirrels[END_REF]. We returned mothers and their offspring to flagged nest burrows, usually within a day of birth.

After a lactation period of approximately 27-28 days, offspring first emerged above ground around the time of weaning [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF]. We trapped females and their entire litters the day the young first emerged. Mothers were determined by observation of the single lactating female that associated with the natal burrow from which young emerged. Juvenile ground squirrels hibernate within their colony of origin for the winter, and those juvenile males that immigrate typically do so towards the end of the subsequent spring. Thus, in each year, we were able to recapture all yearling males and females that survived their first hibernation.

Paternity analyses

From 2001 to 2017, paternity was estimated following the methods of [START_REF] Raveh | Mating order and reproductive success in male Columbian ground squirrels (Urocitellus columbianus)[END_REF]. Briefly, DNA was extracted from offspring tissue biopsies using DNeasy Tissue extraction kits (Qiagen, Venlo, The Netherlands). We amplified 13 microsatellites with polymerase chain reaction (PCR), using primer pairs previously developed for U. columbianus GS12, GS14, GS17, GS20, GS22, GS25, and GS26 [START_REF] Stevens | Microsatellite loci in Columbian ground squirrels Spermophilus columbianus[END_REF]; Marmota marmota BIBL18 (Goossens et al. 1998); MS41 and MS53; [START_REF] Hanslik | Microsatellite loci for two European sciurid species (Marmota marmota, Spermophilus citellus)[END_REF]; and Marmota caligata 2g4, 2h6 [START_REF] Kyle | Isolation and characterization of microsatellite markers in hoary marmots (Marmota caligata)[END_REF] and 2h4 (GenBank accession no. GQ294553) amplified polymorphic microsatellite loci. We used similar PCR conditions and cycling parameters as [START_REF] Kyle | Isolation and characterization of microsatellite markers in hoary marmots (Marmota caligata)[END_REF], but with an annealing temperature of 54 °C. We tested for deviation from Hardy-Weinberg equilibrium (HWE) at each locus within cohorts, and for linkage disequilibrium between pairs of loci within cohorts using exact tests.

Paternity assignment was done using CERVUS 3.0 [START_REF] Marshall | Statistical confidence for likelihoodbased paternity inference in natural populations[END_REF][START_REF] Kalinowski | Revising how the computer program cervus accommodates genotyping error increases success in paternity assignment[END_REF]. Paternity was assigned with 95-99% trio confidence (assumed dam-sire-offspring relationship). Analyses were conducted for each year separately. The input parameters for the simulation step of CERVUS were 10 000 cycles, 70 candidate fathers, 90% of the population sampled and 1% genotyping error. Parental assignments were accepted when the offspring had no more than 2 mismatches with both parents.

Annual survival, reproduction and fitness

We calculated annual survival (Surv), as adult survival from the spring mating period to the time of emergence in the next spring (1 for surviving, 0 for not surviving), separately for males and females. Second, we quantified annual reproduction (R), as the number of offspring measured at birth, weaning, and yearling age, separately for males and females. All immature individuals (i.e., females not observed mating or males with testes in abdominal position) were excluded from these calculations. However, individuals considered mature (females observed mating and males with testes in scrotal position) were all kept, even when their reproductive success was zero.

We calculated annual contributions to lifetime fitness, viz. annual fitness (𝜆 !" ), following the method of [START_REF] Qvarnström | Testing the genetics underlying the coevolution of mate choice and ornament in the wild[END_REF], as applied to ground squirrels by [START_REF] Lane | A quantitative genetic analysis of hibernation emergence date in a wild population of Columbian ground squirrels[END_REF][START_REF] Lane | Delayed phenology and reduced fitness associated with climate change in a wild hibernator[END_REF] and [START_REF] Dobson | Fitness implications of seasonal climate variation in Columbian ground squirrels[END_REF][START_REF] Dobson | Fitness estimation for ecological studies: an evaluation in Columbian ground squirrels[END_REF]:

𝜆 !" = 𝑆𝑢𝑟𝑣 + 1 2 𝑅
For any given individual, R is halved since only half of an individual's genetic contribution is passed-on to offspring.

The objective of our study was to determine whether fitness metrics were comparable when reproduction was measured at different time points. Thus, annual fitness was calculated based on R being measured as the number of offspring either produced at birth (𝜆 !" # ), or weaning (𝜆 !" $ ),

or surviving up to yearling age (𝜆 !" % ).

Selection analyses

We tested for directional, stabilizing or disruptive selection on emergence date using linear and quadratic regression on annual fitness 𝜆 !" [START_REF] Lande | The measurement of selection on correlated characters[END_REF]. We further ran selection analyses decomposing 𝜆 !" into its constitutive elements including annual reproduction (fecundity selection) and annual survival (viability selection). Those three fitness metrics were calculated relative to the population in a given year by dividing them by the annual population mean for annual fitness, reproduction and survival, respectively, and for males and females separately [START_REF] Lande | The measurement of selection on correlated characters[END_REF]. As selection operates among individuals, we first centered emergence dates per year by subtracting from individual emergence dates the mean emergence date of the population in a given year, hence translating how early or late (number of days) an individual was compared to others in that same year.

We ran three sets of analyses where we estimated (1) directional selection gradients (𝛽) using univariate linear models, followed by (2) quadratic selection gradients (𝛾) from models that included both a linear and quadratic term [START_REF] Lande | The measurement of selection on correlated characters[END_REF]Arnold and Wade 1984a). The general form for these models is:

𝜔 = 𝛼 + 𝛽𝑧 + 𝜀 (1)
𝜔 = 𝛼 + 𝛽′𝑧 + & ' 𝛾𝑧 ' + 𝜀 (2)
where 𝜔 is the considered measure of fitness (i.e., either 𝜆 !" , R or Surv), 𝛼 is the intercept, z the phenotypic trait (here centered emergence date), and 𝜀 an error term. Note that 𝛾 coefficients are reported as [START_REF] Lande | The measurement of selection on correlated characters[END_REF]'s original formulation and do not require doubling to be interpreted as stabilizing or disruptive selection gradients [START_REF] Stinchcombe | Estimating nonlinear selection gradients using quadratic regression coefficients: double or nothing?[END_REF]. We used linear mixed models to account for individual ID as a repeated random term, and individual age as a random factor because of known fitness differences that occur with age [START_REF] Broussard | Senescence and age-related reproduction of female Columbian ground squirrels[END_REF][START_REF] Raveh | Mating order and reproductive success in male Columbian ground squirrels (Urocitellus columbianus)[END_REF]. Statistical significance of the selection gradients for viability was estimated with generalized linear-mixed models (GLMMs) with a binomial error structure [START_REF] Garant | The effects of environmental heterogeneity on multivariate selection on reproductive traits in female great tits[END_REF][START_REF] Dobson | Plasticity results in delayed breeding in a long-distant migrant seabird[END_REF]). Directional selection is indicated by significant linear coefficients (β), the sign of the coefficients indicating the direction of selection. Stabilizing or disruptive selection occurs when g is significantly <0 or >0, respectively [START_REF] Lande | The measurement of selection on correlated characters[END_REF][START_REF] Mcgraw | Estimation of individual fitness from life-history data[END_REF]. We ran the analyses separately in males and females because the variance of fitness metrics was far greater in males than females [START_REF] Jones | Variation in reproductive success of male and female Columbian ground squirrels (Urocitellus columbianus)[END_REF].

Partitioning selection into additive episodes

Statistics

All analyses were done in R v. 4.0.2 (R Core Team 2020). The 95% confidence intervals for male and female survival were obtained by parametric bootstrapping (10,000 simulations, 50% of the individuals resampled each time). The consistency of fitness metrics (repeatability, or intraclass correlation coefficient (ICC)) was calculated at different stages using the 'rptR' package in R [START_REF] Stoffel | rptR: repeatability estimation and variance decomposition by generalized linear mixed-effects models[END_REF]), ICC =

( ! ( " = ( ! ( ! ) ( #
, where 𝑉 + is the among-individual variance, 𝑉 , is the within-individual (or residual) variance and 𝑉 -is the total variance in fitness. The ICC for annual fecundity (number of offspring) was estimated using a Generalized Linear Model with a Poisson distribution [START_REF] Stoffel | rptR: repeatability estimation and variance decomposition by generalized linear mixed-effects models[END_REF], as appropriate when working with count data (we added +1 to offspring numbers to avoid zero values). Correlation between fitness metrics measured at different time points are Spearman rank correlation tests, as not all distributions were Gaussian. Because information at birth and paternity analyses were not available in all years, sample sizes vary and are indicated as n the number of reproductive events, N1 the number of individuals and N2 the number of years in the results.

RESULTS

Male and female annual survival

Sexually mature (scrotal) male survival from one breeding season to the next was on average 65% (CI95 = [59% -71%], n = 209 reproductive events, N1 = 78, N2 = 21). In contrast, sexually mature females (i.e., those that estrus cycled and mated) had survival rates of 73% (CI95 = [70% -76%], n = 732 reproductive events, N1 = 223, N2 = 28), on average.

Male and female annual fecundity

Adult male annual reproductive success varied from 0 to 29 offspring born (mean ± SD = 6.2 ± 5.7, n = 154 reproductive events, N1 = 61 fathers, N2 = 16 years), 0 to 26 offspring weaned

Male and female annual fitness

When calculated using all of the offspring born (𝜆 !" 𝑏 ), weaned (𝜆 !" $ ) or surviving to yearling age (𝜆 !" y ), annual fitness was strongly consistent in males (ICC = 0.67, CI95 = [0.60 -0.73]), but less so in females (ICC = 0.49, CI95 = [0.45 -0.54]). The correlation between annual fitness metrics generally weakened as the period between life stages increased, from 0.95 between birth and weaning to 0.73 between birth and yearling age in males (Fig. 1A) and from 0.74 to 0.65 in females (Fig. 1B).

Selection on emergence date

Annual fitness (𝜆 !" ) selection

In males, we found directional selection for earlier relative emergence date when annual fitness was calculated based on offspring born (b = -0.024; Fig. 2A), and on offspring surviving to weaning (b = -0.018; Fig. 2C), but not when calculated based on offspring that survived to yearling age (b = -0.007; Fig. 2E) (Table 1). The strength of selection appeared to decrease from 6b𝜆 !" 𝑏 6 > 6b𝜆 !" 𝑤 6 >7b𝜆 !" 𝑦 7. In females, we also found directional selection for earlier relative emergence date when annual fitness was calculated based on offspring born (b = -0.007; Fig. 2B), and on offspring surviving to yearling age (b = -0.013; Fig. 2F), but not when calculated based on offspring that survived to weaning (b = -0.004; Fig. 2D). Note, that the directional selection coefficient for relative emergence date almost doubled for females between annual fitness calculated based on offspring born compared to when fitness was based on offspring surviving to yearling age (-0.013/-0.007 = 1.86), but decreased in males (-0.007/-0.024 = 0.29).

Both in adult males and adult females, we found no evidence of substantial disruptive or stabilizing selection on relative emergence date, regardless of whether annual fitness was measured based on offspring born, or on offspring surviving to weaning, or yearling age (Table 1).

Viability selection

In males, we found directional viability selection for later emergence date (b = +0.022), but no evidence of non-linear viability selection on emergence date (Table 1). In females, there was no evidence of significant directional viability selection, but suggestion of weak stabilizing viability selection on emergence date that approached significance (Table 1).

Fecundity selection

In males, we found directional selection for earlier relative emergence date when fecundity was calculated from the number of offspring born (b = -0.032, Fig. 3A), weaned (b = -0.033, Fig. 3C), and surviving to yearling age (b = -0.033, Fig. 3E) (Table 1). Selection gradients were of similar magnitude regardless of the period considered. We found no evidence of disruptive or stabilizing selection regardless of whether fecundity was calculated from the number of offspring born, weaned, or surviving to yearling age (Table 1).

In females, there was mild directional selection for earlier relative emergence date when fecundity was calculated from the number of offspring born (b = -0.007, Fig. 2B), but not when calculated from offspring weaned (b = +0.002, Fig. 3C), or surviving to yearling age (b = -0.012) (Table 1). However, we found weak stabilizing selection for emergence date based on offspring surviving to yearling age that approached significance (𝛾 = -0.005; Table 1, Fig. 3E).

Partitioning selection into additive episodes

In both males and females, selection on the number of offspring born provided a major selective advantage favoring earlier emergence date (Table 2). For males, selection on the number of offspring born accounted for 93% of the total selection differential and shifted the mean emergence date by 2.5 days, while selection acting between birth and weaning or between weaning and yearling age were minor, accounting for only 5 and 2% of the total selection differentials. For females, selection differentials were much lower than in males (0.4 days vs. 2.6 days shift due to total selection). While selection on the number of offspring born, as well as from weaning to yearling, also shifted emergence dates earlier (by 0.6 and 0.3 days respectively), selection from birth to weaning counteracted this by shifting emergence dates later by 0.5 days.

DISCUSSION

Our results in the Columbian ground squirrels show that, overall, measures of fitness are relatively well correlated when fitness is measured from offspring counted at birth, at weaning, and at yearling age. In general, annual measures appeared quite strongly inter-correlated at different stages. Not surprisingly, the correlation between fitness measures changed, generally waning over the progression of life stages of the offspring. Overall, the strongest correlations were for fitness measured from birth and weaning offspring numbers, and associations became weaker, as time went by (from birth to yearling surviving offspring). These results might have been expected, since offspring mortality was low between birth and weaning, and much higher between weaning and yearling age.

Columbian ground squirrel offspring are raised over a short lactation period of 27 days [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF], during which they are secluded in specialized burrow systems and protected by their mothers [START_REF] Murie | Social interactions and dominance relationships between female and male Columbian ground squirrels[END_REF]. As expected, mortality is relatively low during this period. After weaning, they only have a few weeks of foraging to grow and gain sufficient body mass to survive their first hibernation [START_REF] Dobson | Body mass, structural size, and life-history patterns of the columbian ground squirrel[END_REF][START_REF] Dobson | Seasonal activity and body mass of Columbian ground squirrels[END_REF]. Offspring with insufficient body condition are unlikely to survive to the next spring [START_REF] Murie | The relationship of body weight to overwinter survival in Columbian ground squirrels[END_REF][START_REF] Dobson | A comparison of methods for studying life history in Columbian ground squirrels[END_REF]). Thus, not surprisingly, overwinter mortality of juveniles is high [START_REF] Dobson | Interpretation of intraspecific life history patterns: evidence from Columbian ground squirrels[END_REF][START_REF] Zammuto | Life histories of mammals: analyses among and within Spermophilus columbianus life tables[END_REF][START_REF] Neuhaus | Mortality in relation to season, age, sex, and reproduction in Columbian ground squirrels (Spermophilus columbianus)[END_REF], and the correlation between fitness metrics wanes rapidly as the period between life stages of the offspring increases. Nonetheless, it is noteworthy that for annual fitness measures these correlations remain relatively high (> 0.60), so that measuring fitness from the number of offspring weaned in a given year already appears as a reasonable first approximation for estimating fitness. For instance, the correlation between annual fitness measured at weaning and when offspring were yearlings was 0.81 for adult males and 0.75 for adult females.

Sources of variation concerning the changes in correlation between measures between birth and yearling age of offspring remain to be determined. Such variations could include stochastic events that occur on an annual scale and accumulate over time, or other sources of biological variation known to affect early offspring survival such as changes in the social environments (e.g., kin numbers; [START_REF] Viblanc | Kin selection in Columbian ground squirrels (Urocitellus columbianus): littermate kin provide individual fitness benefits[END_REF][START_REF] Barra | Parental investment in the Columbian ground squirrel: empirical tests of sex allocation models[END_REF]. It is possible that selection on the offspring before they begin to reproduce at a later time could operate in a way that could weaken or strengthen associations of fitness estimates (whether or not an evolutionary response to selection occurs). Nonetheless, it is noteworthy that, overall, the correlations between fitness measured from offspring counted at birth, weaning, or yearling age were all high (> 0.65) for annual fitness measures, suggesting that measuring fitness from offspring surviving to the first year is a good proxy to measuring actual fitness from offspring susceptible themselves to passing on traits (as for adult females in [START_REF] Lane | Delayed phenology and reduced fitness associated with climate change in a wild hibernator[END_REF][START_REF] Dobson | Fitness implications of seasonal climate variation in Columbian ground squirrels[END_REF].

How did measuring fitness from an annual perspective at different time points affect our inferences on natural selection? To answer this question, we focused on the entire data set, calculating fitness from both male and female offspring, and regressed individual annual fitness on date of emergence from hibernation, a phenotypic trait known to be heritable [START_REF] Lane | A quantitative genetic analysis of hibernation emergence date in a wild population of Columbian ground squirrels[END_REF], responsive to environmental fluctuation [START_REF] Dobson | The limits of phenotypic plasticity in life histories of Columbian ground squirrels[END_REF], and negatively associated with fitness [START_REF] Lane | Delayed phenology and reduced fitness associated with climate change in a wild hibernator[END_REF]. There appeared to be little or no stabilizing or disruptive selection (no quadratic effects), but only directional selection, acting on emergence date. In general, individuals emerging earlier from hibernation had higher estimated fitness, and this was especially true for males.

In males, selection coefficients decreased when based on measurements from offspring counted at birth, weaning to yearling age. This likely occurred because of relatively strong mortality during the juvenile period, and supports the hypothesis that environmental stochasticity may dilute the association between a phenotypic trait and fitness due to passage of time since the environmental event (viz., emergence from hibernation) increases. This is important, since although the directional selection coefficients measured at different time points are consistent in sign (i.e., negative), the conclusions made would differ substantially. For instance, in males, based on fitness calculated from the number of offspring counted at weaning, significant linear (b) coefficients would give rise to a conclusion of directional selection [START_REF] Lande | The measurement of selection on correlated characters[END_REF] acting on emergence date, whereas non-significant coefficients based on fitness calculated from the number of offspring counted at yearling age would not (if relying on significance thresholds, but see below). Similarly, in females and based on statistical significance, one might conclude on directional selection on emergence when using offspring counted at birth, but not when using offspring counted at weaning or at a yearling age, despite the selection gradients being strongest when using number of offspring that reach a yearling age (Table 1).

Decomposing annual fitness into its annual survival and reproductive components generally revealed consistent patterns. Interestingly, we found mild positive directional viability selection on emergence date for males, but no viability selection for females: males that emerged later had better annual survival. Positive selection on viability in males might occur because males emerge from hibernation early to establish mating territories [START_REF] Manno | Why are male Columbian ground squirrels territorial?[END_REF]), but early emergence has a survival cost [START_REF] Turbill | Hibernation is associated with increased survival and the evolution of slow life histories among mammals[END_REF][START_REF] Constant | Integrating mortality risk and the adaptiveness of hibernation[END_REF]. For females, a weaker pattern of selective advantage was revealed for earlier emergence from hibernation, but the pattern was only significant when the combined index of annual fitness was used. In general, for both sexes, fecundity selection on emergence date revealed overall similar patterns as annual fitness, except perhaps for females where mild stabilizing selection was found using offspring that survive to yearling age as the fecundity fitness estimate.

When fecundity selection was separated into distinct episodes of selection (Arnold and Wade 1984a, b), we found that selection at birth accounted for the vast majority of the selection differentials on emergence date both in males and females. For males dates of emergence from hibernation, selection based on numbers of young at birth was the strongest (by nearly 2.5 days, Taken together, our results over a 29-year long-term study of Columbian ground squirrels, showed that annual fitness measures, whereas generally closely related, may lead to nuanced conclusions on the strength (but not direction) of selection acting on heritable phenotypic traits.

We documented an overall dilution of fitness associations, and in most cases a waning association between fitness and emergence date, as time passed likely due to added stochastic processes affecting offspring survival. Importantly, focusing on the significance of associations between phenotypic traits and fitness led to contrasting conclusions depending on when fitness is measured.

The values of the selection coefficients, however, were fairly consistent using different fitness estimates. Taking a step back from a traditional hypothesis-testing approach and focusing on the magnitude of effect sizes, as more and more frequently is recognized in evolutionary ecology [START_REF] Yoccoz | Use, overuse, and misuse of significance tests in evolutionary biology and ecology[END_REF][START_REF] De Valpine | The common sense of P values[END_REF], likely provides more meaningful information on the strength and patterns of selection acting on phenotypic traits in living organisms.

FIGURE CAPTIONS

Following

  Arnold and Wade (1984a, b), we partitioned selection on emergence date into additive episodes of selection by looking at how selection changed from reproduction measured at birth, weaning and when offspring reached yearling age. To do so, we separated reproduction in three distinct biological episodes: production of offspring at birth, offspring survival from birth to weaning, and offspring survival from weaning to yearling age. To better understand how each of these episodes contributed to total selection, we estimated selection differentials for each of them.Selection differentials represent the change in the mean value of a phenotypic character (here emergence date) produced by selection. Because reproductive success at yearling age can be decomposed in the product of the number of offspring born and the number surviving in the two following episodes, selection differentials corresponding to each of the episode should sum to the total selection differential. Selection differentials are thus presented for each episode in absolute values (shift of the emergence date in number of days), but also as a % of contribution to total selection.

  (4.2 ± 4.8, n = 190, N1 = 73, N2 = 19), and 0 to 16 offspring surviving to yearling age (1.7 ± 2.6, n = 190, N1 = 73, N2 = 19). Adult female annual reproductive success was lower, and varied from 0 to 7 offspring born (3.0 ± 1.2, n = 454 reproductive events, N1 = 167 mothers, N2 = 21 years), 0 to 7 offspring weaned (2.1 ± 1.5, n = 759, N1 = 228, N2 = 29), and 0 to 5 offspring surviving to yearling age (0.9 ± 1.1, n = 732, N1 = 223, N2 = 28). Overall, offspring survival from birth to weaning was 75% (CI95 = [72% -78%], N = 684) for male offspring and 77% (CI95 = [72% -78%], N = 655) for female offspring; and from weaning to yearling age 43% (CI95 = [40% -47%], N = 775) for male offspring and 42% (CI95 = [39% -46%], N = 742) for female offspring. Annual fecundity was strongly consistent in males (ICC = 0.71, CI95 = [0.60 -0.78]), but less so in females (ICC = 0.08, CI95 = [0.03 -0.13]).

Fig. 1 Fig. 2 Fig. 3

 123 Fig. 1 Pairwise correlation plots for (A) male and (B) female annual fitness metrics calculated

FIGURES

  FIGURES

  Fig. 2

Table 2 )

 2 , and might have reflected sexual selection (primarily number of mates) and maternal effects during gestation. Selection during lactation, based on numbers of offspring at weaning, however, was weak. This is consistent with the males contributing virtually nothing to parental care in this species, and reproductive success being determined foremost by the number of mated females early on in the season(CS et al., unpublished data). Finally, ecological influences on male date of emergence from hibernation may have been best reflected by numbers of offspring that survived their first hibernation, but this influence was trivial. For females, selection on emergence from hibernation was relatively weak and only approached significance. Partitioning this pattern into episodes of selection did not appear to produce important insights, other than a slight fitness advantage of emerging earlier from hibernation (by less than half a day).

Table 2

 2 Fecundity was calculated from offspring counted at birth (A-D), weaning (C-F), or surviving to yearling age (E-H). Significant regressions are indicated by black lines, and gray ribbons representing 95% confidence intervals 706 Episodes of fecundity selection(Arnold and Wade 1984a, b). The trait under selection was date of emergence from hibernation, an important phenological trait that is strongly associated with successful reproduction and fitness[START_REF] Lane | Delayed phenology and reduced fitness associated with climate change in a wild hibernator[END_REF]. Selection differentials are given in days

		b	-0.000±0.010	-0.048	0.962	-0.014±0.004	-3.188	0.001*
	Non-linear	g	0.002±0.001	1.161	0.247	-0.002±0.001	-1.719	0.086

ACKNOWLEDGMENTS

We are grateful to J. Mann and M. Festa-Bianchet for inviting us to contribute to this topical collection on "Measuring individual reproductive success in the wild." We sincerely thank M. Morrissey and an anonymous reviewer for thoughtful and helpful comments on a previous version of the paper. We are grateful to Alberta Parks, and Alberta Environment, Fish & Wildlife for granting us access to the study sites and support with the long-term research. The University of Calgary Biogeoscience Institute provided housing at the R. B. Miller field station during data collection in Sheep River Provincial Park (AB, Canada). We are grateful to E.A. Johnson and S. Vamosi (Directors), J. Mappan-Buchanan and A. Cunnings (Station Managers) and K. Ruckstuhl (Faculty Responsible) for providing us with field camp and laboratory facilities over the years, and to P. Neuhaus and K. Rucktuhl for their continued support, help and discussions in the field. We are especially grateful to E.A. Johnson for his continued support on the ground squirrel long-term research throughout the years.

DATA AVAILABILITY

All data generated or analyzed during this study are included in this published article and its supplementary information files.

Conflict of interest:

The authors declare that they have no conflict of interest.

Ethical approval: All applicable international, national, and/or institutional guidelines for the care and use of animals were followed. All procedures carried out in the field and laboratory