For more than a century, many concepts and several theories and principles pertaining to the goals, organization, methodology and evaluation of the effects of resistance training (RT) have been developed and discussed between coaches and scientists. This cumulative body of knowledge and practices has contributed substantially to the evolution of RT methodology. However, a detailed and rigorous examination of the existing literature reveals many inconsistencies that, unless resolved, could seriously hinder further progress in our field. The purpose of this review is to constructively expose, analyze and discuss a set of anomalies present in the current RT methodology, including: (a) the often inappropriate and misleading terminology used, (b) the need to clarify the aims of RT, (c) the very concept of maximal strength, (d) the control and monitoring of the resistance exercise dose, (e) the existing programming models and (f) the evaluation of training effects. A thorough and unbiased examination of these deficiencies could well lead to the adoption of a revised paradigm for RT. This new paradigm must guarantee a precise knowledge of the loads being applied, the effort they involve and their effects. To the best of our knowledge, currently this can only be achieved by monitoring repetition velocity during training. The main contribution of a velocity-based RT approach is that it provides the necessary information to know the actual training loads that induce a specific effect in each athlete. The correct adoption of this revised paradigm will provide coaches and strength and conditioning professionals with accurate and objective information concerning the applied load . This knowledge is essential to make rational and informed decisions and to improve the training methodology itself. The main limitation of current resistance training practice and methodology fundamentally lies in the necessity to ascertain the degree of effort actually performed by the athlete or practitioner in each training session. The monitoring of repetition velocity contributes decisively to overcoming this limitation.A particularly worrying and underlying problem in our field is that of current terminology, which is often inappropriate, misleading and unnecessarily complex, fostering confusion and misconceptions, and hindering the development of a sound and scientific-based training methodology.A new paradigm is proposed for resistance training based on the monitoring of movement velocity. This paradigm, supported by rigorous research performed in the last two decades, guarantees precise knowledge of the loads being applied, the effort they involve and their training effects.The Structure of Scientific Revolutions. According to this author, the paradigm constitutes the practices and knowledge that define a scientific discipline during a specific period, providing models of problems and solutions to the scientific community. In this context, a paradigm shift involves a major change in the way of understanding and addressing the problems of a discipline that leads to overcoming and ultimately replacing the models and framework prevailing until that time. Thus, a new paradigm arises from detecting an “anomaly” or something that “does not work” or something that does not explain reality or does not explain it sufficiently [As a general concept, a paradigm could be defined as a theoretical framework within which a set of theories are formulated to explain how a certain problem or topic is understood at a particular time. The definition of paradigm that best relates to the so-called sports sciences or exercise sciences is perhaps the one proposed by Kuhn  in The Siciently . Specifiiciently –5, it apiciently –11. UntiRT, also known as “weight training” or “strength training,” typically refers to a form of physical activity that is used to improve neuromuscular fitness and performance by exercising a muscle or muscle group against an external resistance. The health and performance benefits of a properly designed and conducted RT program are large, widely known and well documented , 12–15. From a performance standpoint, there is little doubt that the main aim of RT is to increase the movement velocity developed against any absolute load, and especially against the specific load encountered in competition. This objective is evident when an athlete lifts a particular external load (kg) during a test to assess his or her strength level, but the aim would be the same when the performance in competition depends on moving or displacing the body  at maximal intended velocity, which typically occurs in actions such as running, cycling, swimming, paddling, jumping, lifting, throwing, hitting, pushing or pulling opponents, and many other specific actions performed in individual or team sports. Thus, the objective here proposed (to be able to move the same absolute loads at increasingly faster velocities) is applicable to any sport except, partially, to weightlifting. In this particular sport, the main goal during competition is to be able to lift increasingly heavier loads at a certain velocity (velocity of the 1RM). However, to achieve this objective , it is necessary to be able to lift each of the preceding submaximal loads at increasing velocities. Consequently, it seems reasonable to admit that the only possible objective of performance-oriented RT is to increase movement velocity against any absolute load. This, moreover, is a specific measurable outcome to be achieved, which corresponds perfectly with the meaning of the term “objective.” Thereby, if this objective is met, it means that any other secondary mechanical objective of those previously mentioned would have also been accomplished. Indeed, an increase in the velocity developed against a given absolute load for a certain distance means an increment in power output against that load , and it also implies that a greater RFD or “explosive strength” is attained .m) times velocity (v) equals force (F) multiplied by time (t) (m·v = F·t). If we solve for velocity in this equation, it follows that:As indicated, just as the main goal of RT is to increase movement velocity against a given absolute load, it could be considered that the only possible type of RT is training for improving maximal strength. This statement is supported by the fact that the only way to increase the movement velocity developed against an absolute load is to apply more force to that load. Thus, in order to achieve the maximum possible velocity against a certain absolute load, the applied force must be the maximum that the subject can exert against that particular load. This statement can be verified by Newton’s second law of physics which is commonly stated in terms of an object’s linear momentum (mass times velocity) following the equation: mass (d) divided by time (t), Eq. [Taking into account that velocity equals displacement ((t), Eq.  can be om) , and the distance over which the force is applied are stable. Therefore, to increase velocity, it will be necessary to increase the numerator of this equation (F·t). However, this increase cannot be at the expense of an increase in time, since an increase in velocity for the same distance necessarily implies that the movement takes a shorter time. Similarly, in equation [maximal strength training , regardless of whether the training effect is assessed by measuring 1RM, maximum isometric strength or by the change in movement velocity against a given submaximal load or set of loads, which are all measures capable of showing the change in the applied force.In equation , the masequation , assuminOther types of RT commonly used in the literature  could be thought of as different types of training than maximal strength training. However, this is not the case because it is not possible to enhance power output, movement velocity or local muscle endurance without increasing the maximum force applied against the load(s) being used to assess power, velocity, or endurance. Even if the goal were to improve movement velocity or power output against very low loads , this would only be possible if the maximal force applied against these loads increased. Figure F·v), to improve power output, training should be directed toward increasing force application against the load(s) selected. There is no other possible solution to this problem; power cannot be increased unless force increases. Therefore, it could be considered that in reality there is not a specific type of RT that can be termed “power training,” but rather all types of training are, in essence, power training because what is intended and that which precisely allows us to improve power is an increase in the maximal or peak force applied in the corresponding action.This concept could be easily explained using the so-called power training as an example. Since power is not an entity on its own but a compound mechanical variable . However, in all cases, this will remain maximal strength training.Based on the above reasoning, the existing terminology related to both the aims or objectives and types of RT could be considered misleading as it often leads to severe misunderstandings. Even though they are widely used and deeply ingrained terms in our field, a close scrutiny of many of these terms reveals that there is an underlying ignorance of the fundamental laws of Newtonian physics. This is a serious problem that hinders the advancement of knowledge in the exercise sciences and, more specifically, in the field of RT. One of the most common mistakes or misconceptions is to believe that power, ballistic, or velocity training are different types of training than maximal strength training, or to consider that the effects of these alleged types of RT occur without improving the maximal (peak) force applied to the loads used to assess performance. Therefore, it seems reasonable to suggest that the concept and denomination of these alleged types of RT should be redefined, if not eliminated altogether. We consider this to be a critical issue that needs to be addressed to improve knowledge about RT and bring terminology in line with science.nRM) against a given absolute load to know the approximate relative load (%1RM) corresponding to the load lifted and then estimate the 1RM using a table or formula [As with the different aims and types of RT, it is also necessary to clarify the concept of maximal strength. Traditionally, maximal strength has been defined as the maximal force that a subject can apply against a load that can only be lifted once over a given distance, or the maximal force applied in an isometric action , 28, 29. formula , 29. How formula  defines  formula  indicateProper knowledge of the concept of maximal strength allows us to clarify how RT should be performed. It also helps to avoid falling into a set of conceptual and methodological mistakes and misconceptions. Some examples of common inappropriate proposals and assertions could be the following: (1) “we are going to train velocity, but not maximal strength”; (2) “we are going to perform power training, strength–power training, strength-velocity training, velocity–strength training, or strength-explosive training”; 3) “it is necessary to train first strength and then power”; (4) “in many cases, the most important variable is power output rather than strength.” All these assertions are inappropriate because the only possible type of RT is maximal strength training. Therefore, there are no “strength,” “speed,” “power,” or “transfer” exercises, but only exercises performed at different velocities that could improve maximal force application against any absolute load. The absolute velocities used and, particularly, the degree of fatigue incurred during each training set will induce different effects on the force–velocity relationship , 32, 33. “it is nIn conclusion, most of the current terminology is unnecessarily and artificially complex which often fosters confusion and misconceptions, hindering the development of a sound scientific-based RT methodology. Practice and research in RT must stem from a rigorous knowledge of the concept of maximal strength, otherwise it is not possible to know why and how strength must be trained.One of the fundamental problems in RT is to ascertain the actual degree or level of effort that each training session entails. In addition to the type, order and number of exercises performed , 34, 35,nRM [V1RM) [V1RM ≤ 0.20 m s−1 for bench press [V1RM ≤ 0.35 m s−1 for squat [V1RM ≤ 0.50 m s−1 for prone bench pull [V1RM ≤ 0.90 m s−1 for the power clean [−1 would no longer be comparable, since a velocity difference of 0.07–0.09 m s−1 represents ~ 5% of 1RM (depending on the exercise) [Traditionally, the most common indicators used as a reference for dosing the loading intensity during RT have been the 1RM and nRM , 40, 41.nRM –45. FirsnRM –50, the nRM . AnothernRM , 52, 53.M [V1RM) , which ich press , 54, V1Ror squat , V1RM ≤ nch pull , V1RM ≤ er clean , etc. Thxercise) . Thus, inRM method for expressing the relative load is based on the common belief that if several subjects complete the same number of maximum repetitions in a set (each subject using a different absolute load) they are training with the same relative load (% 1RM). However, different studies have shown that not all subjects can perform the same number of repetitions against a certain relative load [nRM as a reference to gauge the relative load in RT would lead to the same problems already outlined for the 1RM: coaches will never be certain of the relative loads used by athletes in training and hence of the actual exercise intensity that resulted in a given effect.On the other hand, the use of the ive load , 59, 60.ive load  most of In addition to relative load, volume is the other key variable that makes up the exercise dose in RT , 8. AlthnRM tests) that could interfere with the scheduled training. To the best of our knowledge, the best way that currently exists to solve these problems resides in the use and monitoring of movement velocity during RT for determining both the relative load used and the degree of effort undertaken [In brief, the improvement in RT methodology requires a different approach capable of overcoming the aforementioned shortcomings and deficiencies that characterize current methods and practices. This renewed approach must allow for precise knowledge of both the actual load applied and the degree of effort made that results in a given effect, be it either positive or negative. Additionally, coaches should have tools to identify the athletes’ current performance capacity and training possibilities on a daily basis, and this should be achievable without using any invasive or exhausting procedures  actually used in each training session.The average mean velocity and degree of effort of each set, session and training cycle.nRM test.The individual training effect experienced on the entire load–velocity curve after one or several exercise sessions, without the need to perform any 1RM or Moreover, several studies have shown that the percent velocity loss reached in an exercise set or group of sets is related to the degree of fatigue incurred during RT , 65, 81.In summary, until very recently, there was no objective method to accurately ascertain the relative load used and degree of fatigue experienced during RT to determine the actual training stimulus that had resulted in a certain effect. Consequently, it seems reasonable to suggest that the conclusions drawn from most studies may be incorrect or flawed, since these are based on false or imprecise indicators of both the load applied and the real effort undertaken . It thusAlthough widely used, “periodization” is a highly controversial term in the sports science literature. In a strict sense, to periodize means “to establish periods for a historical, cultural or scientific process.” However, this term is commonly used to refer to the temporal organization of the training process, primarily the evolution of relative load and volume during the training cycle –85. The The very concept of periodization has been challenged by several authors , 91–93 wMoreover, it is particularly striking to observe that the term “periodization” is, in and of itself, often used as a solution to the problems of training, since many authors assert that periodization during RT, per se, allows for the “correct use of loads and recovery times to avoid excessive fatigue and achieve maximum performance at the right, predetermined time” , 94, 95.Contrary to what appears to be suggested, structuring the training process into several periods does not guarantee, per se, that the prescribed training is adequate or that the intended objectives of that training are going to be accomplished. Furthermore, although periodization includes variations in relative load and volume , 88, 96,Progression Models in Resistance Training for Healthy Adults, "periodization" is identified with the training principle of “variation,” as follows: “variation, or periodization, entails the systematic process of altering one or more program variable(s) over time to allow for the training stimulus to remain challenging and effective.” Other authors have also indicated that periodization introduces “variation” through cyclical phases and time periods [training is numbers, not names! Using the term "periodization" has no meaning or effect on physical performance unless it is accompanied by a detailed numerical expression of the variables that constitute the training load. Unfortunately, this, which should be evident, is often forgotten within a field that considers itself science-based.Several studies have suggested that a more appropriate term to define the manipulation of the different training variables and to organize the training sessions should be “programming” , 97, 98. periods , 88. HowThe common misuse of the term “periodization” often leads to the self-perpetuating assumption that it guarantees the achievement of the following goals: (a) the appropriate balance between training loads and preparation for competition during the season; (b) fatigue management and reduction in overtraining potential; and (c) adequately staging and timing of performance peaks , 88, 99.Basically, there are two main periodization models: (1) traditional or parallel models that supposedly consist of the simultaneous development of multiple physical abilities throughout the training process, and (2) block periodization (BP) or sequential models, based on the concept of concentrating the training load into successive “blocks” in order to develop specific physiological systems and motor abilities , 90, 101In the "strength-endurance" or "muscular endurance" phase, there is also necessarily an effect on muscle hypertrophy, strength and power. In this phase, training usually consists of several sets in which loads of 15-20RM are used in single or multi-joint exercises with 30–60-s rest between sets and exercises , 99, 100In connection with the above, muscular endurance, strength and power should all be improved in the hypertrophy phase. Thus, the hypertrophy phase could also be considered a strength, muscle endurance or power phase. Some questions that could be asked would be: 1) could muscle hypertrophy be increased without an accompanying improvement in muscle strength? and, 2) if the applied force against a given absolute load is increased, is it possible not to improve the power output developed against that load? According to the arguments mentioned above, the answer to both questions is negative.In the third block or phase, the goal is to improve maximum strength. However, it is obvious that if strength has increased, power will also be necessarily improved, and it is likely that hypertrophy and muscle endurance have increased too. As expected, several studies have shown simultaneous changes in these variables following different RT interventions , 48, 67 Finally, as indicated above, it is not possible to increase power output without improving maximal strength, especially when maximal strength is understood in a broad sense and not only as the force developed against maximal or near maximal loads, as previously explained.With regards to RT, BP usually distinguishes between four main phases or objectives: "strength-endurance" or "muscular endurance" phase, "hypertrophy" phase, "maximum strength" phase, and "power" phase , 99, 100One of the arguments usually put forth to support this periodization model is that, in each block or training phase, one single characteristic of physiological development  is being emphasized , 103. HoThe sequence of phases, goals and types of training loads is based on the false belief that the effect produced in each phase is required to obtain better results or adaptations in the next block or training phase , 103. AcSimilarly, another study compared the effect of RT programs that employed the same maximum and relative load (%1RM) in each session, but with different training volumes (low vs. high volume) in a group of experienced weightlifters . AlthougIn other regards, it seems unreasonable to indicate that muscle strength should be increased before improving power , 99. As In addition to the problems raised in relation to periodized training, the question becomes more complicated when the term “non-periodized” training (NPT) is introduced. According to the definition of “periodization,” an NPT would be a “training program that does not have any changes  that would justify differentiating one training period from another.” Therefore, it would be a single period without introducing any type of “variation,” i.e., a training period where the same load, the same stimulus, and the same type of training are applied in every session. However, this situation is unrealistic for at least two reasons: (1) it is unlikely that the same training load can always be applied during successive training sessions for an athlete; and (2) an NPT would not meet one of the basic or core principles of training adaptation, progressive overload , 13, whi. This situation would indicate that the NPT program has induced a positive effect. Therefore, a true or “pure” NPT is not possible in practice and, in some cases, maintaining the relative loading intensity throughout a training cycle, or even tending to reduce it, may be the best indicator of a positive training effect [Since in the NPT model variability apparently disappears, it seems that all the advantages of periodized training are lost. Indeed, NPT has traditionally been considered a considerably "less effective" model compared to periodized training , 118, prg effect .nRM method.Finally, since NPT consists of maintaining a fixed and predetermined maximum number of repetitions during the training period, this type of training presents an additional problem. If all subjects train with an individually determined absolute load (kg) that allows them to perform the same number of repetitions , it is highly unlikely that they are training with the same relative load (%1RM). This results from the fact that the number of maximum repetitions that can be completed against a certain relative load (%1RM) presents a high inter-subject variability , 59, 61.Different authors have established a "hierarchical periodized system" with different levels (time periods and fitness phases) for the organization of training , 128. AlAnother prevalent block periodization is known as the “multi-targeted BP training system” , 128. ThIn addition, and in relation to the above, another aspect worth considering is the terminology used in this alternative BP approach. A careful and thorough examination of the terms used reveals serious inconsistencies. Firstly, the term “accumulation” refers to “gathering a large number of things or collecting a remarkable amount of something.” The main issue here lies in the very meaning of the term “accumulation.” In this regard, several interesting questions could be asked: what is accumulated? how does it accumulate? and, when the accumulation block ends, does this mean that nothing else is “accumulated” from that point on? Moreover, if the “accumulation” block consists of physiological, biochemical, physical and technical skill changes for inducing adaptations in general aerobic endurance, muscle strength and basic technique , 102, whThe following block is called “transmutation” or “transformation,” which means to change or turn something into something else. Based on this concept, it is proposed that the motor and technical capacities, previously accumulated in the “accumulation” block, are transformed so that they are now transferred to specific performance capacities , 128. ToFinally, the last block is called "realization" and lasts about 8–15 days , 128. AcIn brief, a training program including the succession of the so-called accumulation, transformation and realization mesocycles is not a guarantee of success. Any coach or strength and conditioning specialist could design an effective or inappropriate training program, regardless of whether or not they use this convoluted terminology. This is so because the terminology does not determine the program's quality. It would be a serious mistake to think that if coaches use these terms to define and design RT programs, the prescribed training is going to be adequate or optimal for inducing the desired neuromuscular adaptations. Even when considering that the terminology is not the most important aspect of RT methodology, it is necessary to understand and highlight that the use of inadequate terms does not contribute anything positive to the development of the science of sports training. On the contrary, this unfortunate terminology constitutes a grievous impediment to advancement in our field, often leading to confusion and making it very difficult to ascertain the actual training that has been carried out. In our opinion, this artificially sophisticated and unnecessarily complex terminology is empty of content. Use of the “accumulation,” “transmutation,” and “realization” terms seems to suggest or guarantee that training is well designed which prevents an adequate reflection on relevant aspects  of the RT design, thus reducing the possibilities of improving the training methodology. The real problem lies in converting these names into numbers, magnitudes of training loads adjusted to the needs of each sport, capacity to be developed, and particular athlete. If the application of the successive training loads is correct, and it is carried out during a period adjusted to the adaptation time of such training loads, a positive effect on performance is very likely, regardless of the names (or absence thereof) given to the training process or its phases.As already mentioned, the traditional periodization model proposes a sequencing of different and numerous targets to be simultaneously developed  during the preparatory and competitive periods , 102. InWe think it is important to point out that the incompatibility  of RT with the development of other components of physical fitness does not lie in the fact that several objectives are attempted simultaneously, but rather in the type and magnitude of the loads applied during the training program. Based on much of the existing literature , 8, 13, The relative load (%1RM) associated with the absolute loads used in each training session. This should be accomplished in real time and without using invasive procedures that may interfere with the training process.The actual level of effort or fatigue experienced during each exercise set and session.The effects that are taking place, on a daily basis, throughout the training cycle. This information should be obtained without using any specific test or procedure different from the actions being performed during the training process.All the models previously discussed are based on the need to comply with an order or sequence in the application of training loads. This procedure supposedly allows athletes to: (1) obtain more relevant performance improvements, and (2) achieve different objectives. However, the main problems pertaining to RT do not seem to be the training models or the sequencing of loads because, as previously discussed, the goals established for each phase are necessarily achieved in other phases as well, and, moreover, it seems that it is not necessary to achieve a given objective in a certain phase to attain another objective in the following phase(s). To our knowledge, the fundamental problem that needs to be addressed in RT is to improve our knowledge of the following key variables:Obtaining accurate and objective information pertaining to these three variables would be of great value to make rational and informed decisions for an adequate configuration of the resistance exercise protocols and the organization and design of RT. These decisions will be rational and informed because they will be based on a more precise knowledge of the training loads being applied (relative loads and level of fatigue) and the effect that these loads are producing. Obviously, knowledge of this information does not prevent coaches and strength and conditioning professionals from making mistakes in the appropriate choice of the training loads applied in each session. However, unlike what has happened to date, coaches will have accurate information about what athletes are actually doing, what load has been applied (something not satisfactorily known to date), and, consequently, how to make decisions to improve RT. Based on the information provided by these variables, the prescription of training could be improved and regulation of the training loads will depend on: (1) the daily physical condition of the athlete, and (2) the effect that the applied loads are producing.In connection with the above, it should be highlighted that no specific model or sequence of training loads  could be proposed as the best model or the optimal succession of loads to achieve a particular goal. The mechano-chemical transduction response to a given training load is different for each individual. This response fundamentally depends on genetic endowment, although several other factors including training background, age or sex also seem to play a role , 140. ThKnowledge of these three variables has allowed us to verify experimentally that, in some cases, a stable or even regressive sequencing of relative loads during the training cycle (with a level of effort far from failure) is enough to improve maximal strength , 97, 141In summary, in this section it has been shown that there is not an optimal or best RT model or progression of loads for improving maximal strength. In any case, what could and should exist is a rational application of the principles of overload, progression, and individualization based on each athlete's response to the loads being applied and the observed training effects. Furthermore, experience and experimentation seem to confirm that, in many cases, a load progression in absolute terms, with a slight or no increase (sometimes even a decrease!) in the progression of the relative load during the training cycle could be enough for inducing significant strength improvements , 141. AsThe finding that mean velocity could be used as a very good estimate of the relative load being lifted was first published in English in 2010 , but itsMonitoring movement velocity allows us to determine the relative load (%1RM) that is being used as soon as the first (fastest) repetition against a given absolute load (kg) is performed at maximal intended velocity , 76–78. In addition to the first repetition’s mean velocity (which indicates the %1RM being used in a given exercise), the loss of repetition velocity in each exercise set turns out to be a very precise indicator of the actual degree of effort or fatigue experienced as successive repetitions within a set are performed against a given relative load , 59, 65.−1 pre-exercise velocity , and the loss of CMJ height pre-post exercise  [r = 0.90 and r = 0.98 for the full squat and bench press exercises, respectively; p < 0.001) [The information provided by these two key variables (first repetition’s velocity and velocity loss in each set) is complementary, and it allows us to estimate the overall effort experienced by each athlete in the exercise sets that make up each session and training cycle. The product of both variables provides a single indicator of effort or fatigue that we have termed the “effort index” (EI) , 10. ThenRM tests [−1 mean propulsive velocity in the full squat exercise, which represents approximately 60% 1RM [−1), we could be almost certain that the maximum strength of the athlete would have improved, and that increment can be quantified. In this example, the load would now represent ~ 55% 1RM since the velocity difference between each 5% 1RM in this exercise (full squat) corresponds to ~ 0.07 to 0.08 m s−1 [By monitoring repetition velocity, it is possible to quantify the training effect occurring in each training session. For this purpose, it is enough to compare the velocity attained against the same absolute loads during successive training sessions. Thus, if a certain absolute load is lifted at a faster mean velocity than in the previous sessions, it means that this load has come to represent a lower %1RM and, therefore, that the maximal force applied to that load and, very likely, the corresponding 1RM value would have improved. In contrast, if the velocity attained against the same absolute load decreases in successive training sessions, the training effect would be negative. This procedure allows us to assess the training effect in each session with high precision and without the need to perform any 1RM or RM tests , 52, 54.nRM tests to know the strength level of the athletes. Therefore, it appears that there is not a specific and necessary model  that must be followed or applied to improve strength performance. On the contrary, through the proper use of these three variables, it is possible to obtain the most accurate information about the load applied and the training effect. Precise knowledge of the load actually applied and its resulting effect is of paramount importance to establish the cause–effect relationships that should be at the basis of rational decision-making and the improvement in RT methodology. In addition, the monitoring and management of the relative loads used and the level of effort experienced in each training session are critical for a better understanding of the physiological factors underlying performance changes [In brief, with the appropriate monitoring of the above-mentioned three variables , it is possible to rationally and systematically apply the principles of overload, progression, and individualization of the training load, without the need to perform any demanding, time-consuming and interfering 1RM or  changes , 64, 65.nRM tests [nRM tests [−1 against a certain absolute load is equivalent to a ~ 5% change in 1RM. However, this calculation is not even necessary, as the change in movement velocity against a certain submaximal absolute load is what determines athletic or sporting performance in most cases. Indeed, the main performance goal in many sports competitions is to move the same absolute load  at a faster velocity. This increase in movement velocity is critical for many individual sports and many specific actions performed in team sports. This fact reinforces the usefulness of assessing the effect of training through the change in velocity against a certain absolute load or set of loads.Part of this topic has been addressed in previous sections, although we consider it necessary to highlight some relevant issues. Traditionally, muscle strength has been assessed by performing 1RM or RM tests , 13, 29.RM tests , 155. AsRM tests , 52, theRM tests , 51, 133RM tests , 54, a cAnother important application of this procedure is that it allows us to analyze the training effect on the entire force–velocity curve, and not only against the maximum load . We again stress that, in order to obtain the most correct and valid information, only the same absolute loads common to both pre- and post-training tests should be compared. Moreover, the maximum load measured in the initial test does not need to be equivalent to 1RM. Figure As previously discussed, another relevant application of this procedure would be to know the evolution of the training effect throughout the training cycle , 50. If,As can be observed, the applications derived from the analysis of the relationship between the training loads applied and the resulting neuromuscular effects are numerous and of great importance to improve our understanding of RT as well as to find out what are the most useful types of training protocols for the enhancement of athletic performance. Very valuable information can be derived from this type of analyses which had never been possible to date. Furthermore, it is important to consider that all this information is individually obtained for each athlete.This manuscript has exposed many errors and inconsistencies, both conceptual and terminological, that continue to exist in the field of RT. A particularly worrying and underlying problem is that of current terminology, which is often inappropriate, misleading and/or unnecessarily complex which fosters confusion and misconceptions, hindering the development of a sound and scientific-based training methodology. Unless these deficiencies are corrected, progress in our field will remain severely limited. Together with terminology, it seems necessary to modify (which in many cases involves clarifying and simplifying) many crucial aspects of the current approach, such as the very concept of maximal strength, the control and monitoring of the resistance exercise dose, the existing programming models, the training goals or objectives, and the evaluation of training effects. It thus seems evident that a paradigm shift is advisable to effectively address this situation. This new paradigm must guarantee a precise knowledge of the loads being applied, the effort they involve and their effects. To the best of our knowledge, currently this can only be achieved by monitoring movement velocity during training. However, a velocity-based resistance training approach does not guarantee that an RT program is effective for improving physical or athletic performance, since it does not prevent mistakes from being made when programming or prescribing training loads. The key contribution of this approach is that the monitoring of repetition velocity provides the necessary information to know the actual training loads that induce a specific effect on each athlete. This precise and individualized information has never been available before. The correct adoption of this revised paradigm will provide coaches and strength and conditioning professionals with accurate and objective information concerning the applied load . This knowledge is essential to make rational and informed decisions and to improve the training methodology itself. In addition, the valuable information obtained by means of monitoring movement velocity may contribute to opening up new lines of research.


Migrant women with young children, including asylum seekers and refugees, have multiple vulnerability factors that put them at increased risk of social isolation and loneliness, which are associated with negative health outcomes. This study explored the experiences of social isolation and loneliness among migrant mothers with children aged 0–5 years as well as their perceptions on possible health impacts.A qualitative descriptive study was conducted at La Maison Bleue, a non-profit organization providing perinatal health and social services to vulnerable women in Montreal, Canada. Recruitment and data collection occurred concurrently during the COVID-19 pandemic, between November and December 2020. Eleven women participated in individual semi-structured interviews and provided socio-demographic information. Interview data were thematically analyzed.Migrant women in this study described social isolation as the loss of family support and of their familiar social/cultural networks, and loneliness as the feelings of aloneness that stemmed from being a mother in a new country with limited support. Multiple factors contributed to women's and children's social isolation and loneliness, including migration status, socioeconomic circumstances, language barriers, and being a single mother. Women expressed that the COVID-19 pandemic exacerbated pre-existing experiences of social isolation and loneliness. Mothers' experiences affected their emotional and mental health, while for children, it reduced their social opportunities outside the home, especially if not attending childcare. However, the extent to which mothers' experiences of social isolation and loneliness influenced the health and development of their children, was less clear.Migrant mothers' experiences of social isolation and loneliness are intricately linked to their status as migrants and mothers. Going forward, it is critical to better document pandemic and post-pandemic consequences of social isolation and loneliness on young children of migrant families. Supportive interventions for migrant mothers and their young children should not only target social isolation but should also consider mothers' feelings of loneliness and foster social connectedness and belongingness. To address social isolation and loneliness, interventions at the individual, community and policy levels are needed. The province of Quebec (Canada) admitted 255,966 migrants between 2014 and 2018, with 50.6% being women, most of whom were of childbearing age (15–45 years old), and settling in Montreal , 4. StudMigrant mothers experience social isolation and loneliness for various reasons. Key factors that may contribute to, or exacerbate social isolation and loneliness, include family separation, language barriers, past traumas, having a precarious immigration status, and unfamiliarity with the host country's culture –11. CompSocial isolation may also affect the mental and physical health of children, either directly or indirectly, via its impact on maternal mental health. Children aged five and younger are particularly vulnerable since they are highly dependent on the immediate family for care and early stimulations –20. EarlDuring the COVID-19 pandemic, efforts to contain the pandemic have forced people to stay at home and limit their social contacts, and thus intensified social isolation and loneliness and their effects, especially for more vulnerable communities. Isolation through confinement and quarantine in the context of COVID-19 have been associated with negative psychological outcomes including stress, depression and post-traumatic stress disorders , 22. MorDocumenting the experiences of loneliness and social isolation in migrant mothers with young children, as well as the perceived impacts on health, is critical for the development of appropriate interventions for this population. Therefore, this study aimed to answer the following questions:What are the experiences of social isolation and loneliness among migrant mothers of children aged five and younger?What are the perceptions of migrant mothers regarding how experiences of social isolation and loneliness may influence their health and the health of their children?This study took place at La Maison Bleue (LMB), a Montreal-based non-profit organization that provides perinatal health and social services to vulnerable mothers during pregnancy up to age five . FamilieSince the COVID-19 pandemic was declared a public health emergency in March 2020, the Quebec provincial government imposed varying restrictions according to the evolution of the pandemic. These have included the closure of schools, childcare  and non-essential services and activities, the banning of indoor gatherings, and limitations on travel . MoreoveThis study was developed in partnership between McGill University, the University of Montreal and LMB. ML conducted the project as part of her master's degree in nursing and was responsible for developing the protocol, recruiting participants, and collecting and analyzing the data. AVH and LM were the supervisors and SP was the on-site LMB resource person; all three provided guidance throughout the development and execution of the research. The research was conducted at two LMB sites, which are located in ethno-culturally diverse neighborhoods with a high proportion of low-income families; one neighborhood is known for having the largest number of migrants  and visible minorities in the city of Montreal , while tPrior to recruitment, ML spent 2 months doing clinical training at LMB, which provided opportunities to become familiarized with LMB's care approach and their clientele. The LMB staff facilitated recruitment by referring and introducing ML to potential participants. Women with any immigration status , and aged 18 years and older were invited to participate if they had arrived in Canada within the last 10 years and were able to communicate in English or French . ML was responsible for explaining the study, confirming eligibility and obtaining consent. LMB staff referred 25 women, of which 11 accepted to participate; 10 women refused and four did not respond. Women reported a lack of time and privacy concerns  as reasons for refusal of participation.n = 6) and English (n = 5). Four mothers had in-person interviews, which were conducted in a private office at or the other of the LMB sites; five mothers were interviewed by phone, and two were interviewed using Zoom Pro. Data were collected using a socio-demographic questionnaire (used in previous research by the senior author) and an interview guide . These differences also seemed to make it more difficult to create meaningful and close relationships, thus adding to participants' feelings of sadness and aloneness. As described by one participant, P5 said, “When I feel really lonely, it bothers me; it makes me sad... I didn't have chances to make friends in Canada... Now, if I need someone to talk to or need help, I can't find anyone on the phone”.Language barriers further complicated making social connections and accessing support. For example, P11 described how her first 6 months in Canada were difficult because she was not able to connect with neighbors and ask for help: “all neighbor here, people… not too much understand and not help… here all neighbors also speak French. No speak English so too much difficult”.One way that women dealt with the lack of close relationships and their feelings of loneliness in their new social and cultural environment, was by maintaining contact with their families abroad. Eight women reported communicating regularly (at least once a week) with their family members, while two spoke with their families daily . Migrant mothers described this contact as a source of moral and psychological support. P6 said, “when I talk to my family it's less lonely… I feel happy and not alone… And change my mind”. For three mothers, they also received advice on childcare. Transnational communication was also a means for women and their children to maintain closeness when separated from their partner/father and siblings. One mother said (P3), “this allowed them [siblings] to bond with each other, so we don't feel a separation between the two”.All participants also stated that they had some level of assistance or help locally, either through religious or non-profit organizations, friends, neighbors or social services. LMB, particularly, was regarded as an important source of support: “LMB became my family. If I need someone to talk with, I often talk with the LMB staff.” (P1).All eleven participants stated that caring for their children was a priority and that most of their daily activities revolved around caring for their children and doing household work. Tending to the needs of their young children, combined with the lack of access to childcare or more informal support (due to family separation), made it difficult for mothers to create and build a social network, learn English or French, and find paid work. P1 explained, “I wanted to do my courses [in accounting] quickly, but it's difficult with three children… I want to find childcare for the children and to start working” (P1). Similarly, another woman, an asylum seeker, described how not having childcare meant she could not work, and this left her confined to her home and contributed to her sense of stress and boredom. She also explained that cost was the reason she was not able to access childcare:If we stay at home all day taking care of children, we can't go to work. Staying at home is too stressful. We don't do anything; we only take care of the children. We stay at home all day, 24 h a day. I would like to send my children to childcare, but childcare for asylum seekers is too expensive (P10).Two other asylum-seeking mothers also expressed that cost prevented them from using childcare, which in turn meant they could not work or partake in other activities which could help them improve their situation. In contrast, four mothers, who had access to childcare, described it as an invaluable resource. P4 explained, “If we didn't have childcare… It's impossible to work… to study. Childcares are really great support.”Although motherhood and the associated responsibilities contributed to women's isolation, their children also offered them a sense of purpose. Four participants stated not feeling lonely because their children kept them busy. For example, P9 described how she felt before becoming a mother vs. after: “before I was feeling lonely because I was alone. Now I have a family and I am very busy, my schedule, so I don't have time to be lonely”. Ten mothers described how their children were a source of happiness and companionship and thus helped them cope with their situation. For example, P5 said, “Loneliness makes me sad, but then… I have my child. He is 4 years old, but I can talk with him like he is 10 years old. He makes me laugh so much. He is like a friend.”could have negative impacts on their children, which is why they made a point to put on a “façade” and hide their feelings to protect their children. P3 described, “I always try to hide [that I'm tired or stressed]… I'm my children's hope here. All their support. And if they feel their support is getting weak, it's easy for them to also get weak”.All participants thought that their children were generally happy and healthy, which they associated with good physical health , expressions of happiness , having their needs satisfied  and being loved and cared for. When asked about the health of their children, P9 answered, “she plays, she like, enjoy in the playing and she took feed at the time I feed her… she always gives a smiley face whenever I look at her… they are doing regular check-up and she is fine”. Generally, mothers did not seem to think that their challenges and experiences of social isolation and loneliness were affecting their children because they felt that their children were either too young to understand the situation or because the mothers hid their negative feelings. One woman, however, did say that her child had responded negatively to her stress: “in some situations when I feel stressed, she [her daughter] also gets irritated” (P5). And another mother also described how her child being separated from his father was affecting him: “he feels sad… when he sees his friend go with the father… he keeps asking why my father he is not with us” (P8). Six other participants suggested that experiences of social isolation and loneliness Based on the discussions with the mothers, and observations made during the interviews, it seems that young children may have few opportunities to socialize. Mothers' descriptions of their daily and weekly routines with their children indicated that their children tended to have little contact with people outside of home, especially if they were not attending childcare or participating in activities. Eight participants also mentioned that the weather affected their decisions to go outside, which further contributed to keeping their children at home and limiting their activities. For example, P10 stated, “now [in November] I can't [do activities outside]… It's very cold. I can't go out with my children”. P8 explicitly described how delays in accessing childcare and keeping her child at home have had a consequence on her child's language development: “I think my son if since he come, he found a daycare, he should be at this age speaking very well. Because keeping him at home, I'm not free all the time to teach him”. In contrast, mothers whose children had interactions with other children, observed positive outcomes on their children, as described by P5: “He has friends. When he comes back from childcare, he talks about the activities [he did]… he's really starting to express himself, to talk”.Although participants experienced social isolation and loneliness before the COVID-19 pandemic, these experiences were exacerbated by measures put in place to prevent the spread of the virus. Ten participants mentioned that the pandemic has been a challenging period for themselves and/or for their children. It has had an impact on their mood, increased their anxiety and fear, and worsened their situation regarding access to social support and opportunities for self-development and employment.Four participants reported that physical distancing measures affected their mood or the mood of their children. For example, P6 explained how she could no longer participate in group activities organized by community organizations, and this has left her feeling down and disconnected: “after COVID is very lonely. Not happy. No go out, and always home, it's very boring”. Similarly, P8 shared, in a frustrated tone, “now it's not easy to meet friends… COVID is destroying everything. Yeah, I think my life is not easy because of the COVID… isolation of the 3 months [of lockdown] was tough”.Four participants expressed fear of contracting the virus and the consequences this might have on their health and the health of their families, and their ability to care for their children:I have a baby and it's very tough for me to go outside… Because if there's any problem related to COVID, it would also affect my baby and my family… Now we are having fear in mind whenever we are going outside with the baby or alone. (P9)For the single mothers, the circumstances of the pandemic amplified their challenges and fears. One mother shared:When COVID started, I was very scared to take my kids with me to have the groceries. And I was like what to do… I don't want to be sick and I'm the only one who is taking care of the kids. (P8)With the COVID-19 pandemic, participants reported that they limited social interactions and refrained participating in recreational and other activities that could help them secure employment and expand their social network. For example, two participants were no longer attending French classes either because they were canceled or because they feared contracting COVID-19. While some women were able to somewhat break their isolation through online activities, and some even found this option quite advantageous due to its flexibility, it was not an acceptable alternative for all. P8 explained, “because they do the activities online, so I feel not comfortable to join this group… I like to meet people in person”. Four participants also talked about how the restrictions have delayed the initiation of activities for their children. For example, P5 said:I wanted to register him so that he can do sports… but everything is closed… it's better when [children] start at a young age. I want him to be open; that he's not limited to just childcare and home… that he creates a network of friends… that he strives”.Lastly, four participants mentioned that the pandemic has had an impact on the support they usually receive through LMB. Before the pandemic, LMB had an open-door policy where women were welcome to drop by at any time. For many women, this approach aligns with what they are used to in their home country. All eleven participants described LMB as an important resource and space where they could socialize, acquire new skills, and discuss their children and childcare: “There were activities at LMB... It felt good to go out and talk with other mothers, to exchange. We can learn things.” (P3). However, due to the pandemic, LMB had to adapt their services and the open-door policy was no longer possible. Some of the women reported feeling that LMB had become less accessible: “With the pandemic, people need to keep a distance. For example, we could go to LMB when we wanted, but it's not the case now. We speak on the phone... the support is different” (P3).Migrant women in this study described social isolation as the loss of family support and of their familiar social/cultural networks, and loneliness as the feelings of aloneness that stemmed from being a mother in a new country with limited support. Migration status, socioeconomic circumstances, language barriers, and being a single mother, were key factors that shaped these experiences. While women described child-rearing as demanding, their children were also a source of happiness and provided a sense of purpose. Women's experiences of social isolation and loneliness affected their emotional and mental wellbeing, while for children, it reduced their social opportunities outside the home, especially if not attending childcare. While the impacts of social isolation on children could not be elucidated, there were some suggestions that children may be adversely affected. The COVID-19 pandemic also exacerbated the families' situations and experiences.Previous research on the experiences of migrant women during pregnancy and motherhood, shows that women feel isolated, lonely and depressed due to the lack of practical assistance from their extended family, especially during the first year when they are still recovering from childbirth and adjusting to their role as mothers –35. MigrMotherhood was a key element underpinning the women's experiences of social isolation and loneliness. Postpartum and early childhood are known to be periods when mothers may feel isolated and lonely –40. ContThe factors and experiences contributing to migrant women's isolation and feelings of loneliness, including a lack of social support, language barriers, economic difficulties, life and childcare stresses, and having an ethnic minority and/or refugee/asylum seeking status, are also known to be associated with maternal mental health disorders in this population . In our Women in this study generally did not feel that their experiences of social isolation and loneliness affected their children because they thought their children were too young. However, through the mothers' descriptions of their daily routine, we observed that the children had few opportunities for socialization outside the home due to their mothers' limited social contacts. Asylum-seeking women also did not have access to childcare because it was not affordable, so this also contributed to children staying home. In another study, asylum seekers also reported challenges in accessing childcare due to affordability (Quebec has a subsidized childcare program but asylum seekers are not eligible) and reduced social networks , 48. ResTransnational connections  were described as sources of emotional support and advice for childcare, thereby reducing women's stress levels and loneliness. It also allowed couples, as well as children and fathers who were separated, to maintain closeness. Other studies have also shown that maintaining transnational relationships can help migrants cope with isolation and provide a space of belonging, which involves connecting culturally and in their own language –55. HoweThe findings of our study suggest that healthcare providers should not only assess for social isolation, but should also inquire about feelings of loneliness and the circumstances  that may be contributing to these emotions in order to identify an appropriate response , 58. IntOne approach that the women in this study valued and enjoyed was the “open-door policy” offered at LMB, where women could simply drop-in and spend time; this aligned with the collective, community-oriented support that many had in their home country. A pre-pandemic study also showed that LMB played an important role in helping migrant women expand their social networks by connecting them with other mothers, many of whom shared the same ethnic background or country of origin, and/or who shared similar migration trajectories, which provided a foundation upon which women could bond and create a sense of camaraderie .Community and religious organizations were also identified as helpful. Research has shown previously that these organizations can help reduce loneliness by connecting migrants to resources or by directly offering assistance and by creating a sense of belonging . In QuebBreaking social isolation among migrant women and their children also requires addressing the underlying contributing socio-economic factors; in the province of Quebec, this could include improving access to subsidized childcare for asylum seekers and other government services/programs  . ImproviThe results also highlight the importance of families having access to affordable internet and communication technologies considering the role of these in maintaining social connections. Not all migrant families may have access to internet and communication devices or are eligible for support programs that help gain access to these , 70–73. Lastly, the findings underscore the need for the Canadian and Quebec governments to do more to reunite families (in a timely manner) . NumerouAdditional research on the long-term impacts of the COVID-19 pandemic on migrant families with young children is warranted. Studies examining the effects of social isolation and loneliness on young children of migrants via more direct methods, could be beneficial to enhance our understanding of their experiences and risks, and to inform interventions targeting this population. It would also be worthwhile to further develop interventions to address loneliness among migrant families, especially during and post-pandemic.Although it is known that language barriers are associated with social isolation and loneliness , 8, for Migrant mothers' experiences of social isolation and loneliness are intricately linked to their status as migrants and mothers. Mothers' experiences affect their emotional and mental health while for their children, it can impact opportunities for interactions outside the home. The COVID-19 pandemic further exacerbated experiences of social isolation and loneliness and its impacts on migrant women and their families. Supportive interventions for migrant mothers and their young children should not only target social isolation but should also address mothers' feelings of loneliness. To prevent social isolation and loneliness, and to promote a sense of belonging and connectedness, interventions at the individual, community and policy levels are needed.lisa.merry@umontreal.ca.The datasets presented in this article are not readily available because they contain information that could compromise the participants' privacy. Excerpts of data are available upon request. Requests to access the datasets should be directed to The study was reviewed and approved by the Research Review Office of the CIUSSS West-Central Montreal (reference number 2021-2265). The participants provided written or verbal informed consent to participate in this study.ML recruited, obtained consent and interviewed the participants, and took the lead in analyzing the data. AVH and LM supervised recruitment and collection and analysis of the data. ML, AVH, and LM contributed to the interpretation of the results and wrote the manuscript. SP facilitated recruitment and data collection, provided expert knowledge on the target population, and reviewed and provided critical feedback on the manuscript. All authors read and approved the final manuscript.tablissement de jeunes chercheurs grant, FRQ-S.This work was supported by the McGill Global Non-Communicable Diseases Program, the McGill Nursing Collaborative for Education and Innovation in Patient and Family-Centered Care, the SHERPA University Institute, and CERDA . AVH and LM were supported by the Fonds de la recherche du Québec – Santé (FRQ-S), Junior 1 Research awards. Publication fees were paid by LM's ÉThe authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


We discuss implications of our findings for policy and interventions aimed at reducing violence.There is massive variation in rates of violence across time and space. These rates are positively associated with economic deprivation and inequality. They also tend to display a degree of local persistence, or ‘enduring neighbourhood effects’. Here, we identify a single mechanism that can produce all three observations. We formalize it in a mathematical model, which specifies how individual-level processes generate the population-level patterns. Our model assumes that agents try to keep their level of resources above a ‘desperation threshold’, to reflect the intuitive notion that one of people's priorities is to always meet their basic needs. As shown in previous work, being below the threshold makes risky actions, such as property crime, beneficial. We simulate populations with heterogeneous levels of resources. When deprivation or inequality is high, there are more desperate individuals, hence a higher risk of exploitation. It then becomes advantageous to use violence, to send a ‘toughness signal’ to exploiters. For intermediate levels of poverty, the system is bistable and we observe  That is effects –12.Different bodies of research have offered explanations of these observations at different scales. At the population level, several criminological theories view poverty as interfering with the normal functioning of a community, creating ‘strain’ ,14. OtheAt the individual and psychological levels, several authors have pointed to the role of time preferences ,18. Povegenerative sufficiency [candidate explanation [In this article, we show that a single mechanism is able to generate all three key observations: violence is higher in deprived or unequal populations, varies considerably between populations, and can persist in a community despite economic improvement. Whereas the theories mentioned above are stated verbally, we articulate our explanation in a formal model. This serves two purposes. The first is to prove that the mechanism we propose is indeed able to reproduce the empirical observations at a qualitative level (i.e. the model's ficiency ). If it lanation ,28. Secolanation  and complanation ,31. In planation ,33. Thislanation )—yet witThat violence is a social problem  does notAnalysing violence as a contextually appropriate response requires first the specification of its possible costs and benefits for an individual. Violence is commonly assumed—for instance, in the classic Hawk–Dove model —to allowTo formalize this intuition, we make two main assumptions. To represent the ‘signal effect’ of violence, we assume that being violent makes one less likely to be selected as a target of property crime. To represent financial desperation, we assume that agents are defined by a dynamic level of resources and have a ‘desperation threshold’, below which it is harmful to fall. In other words, agents are trying to always meet their basic needs and keep their head above water. The assumption of a threshold is a theoretically innovative idea in the social sciences  that we . 2https://github.com/regicid/model.The model is more thoroughly described in the electronic supplementary materials. The Python code can be found at  (a)r. The model assumes a ‘desperation threshold’, a value below which agents are heavily penalized. They have access to several strategies, defined by probabilistic consequences on their level of resources, conditional on other agents’ strategies. Agents choose the strategy associated with the highest ‘fitness’, a maximand criterion that represents the agents’ goal. We allow the chosen strategy to depend on (i) the agent's level of resources and (ii) the frequencies of strategies in the population. In other words, agents pick the strategy which is optimal for their current level of resources and social environment.Our model combines an individual-level optimal decision model and a population structure. The individual-level component is a state-dependent optimization algorithm, implemented by stochastic dynamic programming ,49. Agenhysteresis, the dependence of the outcome on the initial conditions of the system.The individual-level model identifies the optimal action an individual should choose for any given distribution of strategies in the surrounding population. It is not sufficient for revealing how that distribution will evolve. To address this population-level question, we simulate large populations of interacting agents with different levels of resources. By varying the initial distribution of those resource levels—in particular their mean and variance, representing economic affluence and inequality, respectively—we can test how the economic context affects the level of violence. We run the simulations until the system reaches a stable equilibrium. We also vary the initial distributions of strategies to examine the possibility of  (b)β resources from another agent. This strategy entails two potential costs. First, the exploiter might be caught and sanctioned with a probability γ, costing π units of resources  such that the expected payoff of stealing is always negative, ensuring exploitation stays on average a bad decision. Second, the target agent may react violently: agents either fight (‘violence’ strategy) or not do so (submission). ‘Exploiters’ are also assumed to react violently to exploitation, but henceforth we use ‘violent’ to describe an agent who plays the violent strategy but does not exploit. The fight's winner, selected by a coin toss, obtains or keeps the disputed β resources. The loser pays a proportionate fitness cost λ, described in the next subsection. We also assume that violent agents sometimes enter unnecessary fights: with probability m , they attack a non-exploiter agent by mistake. This triggers a fight if the other individual is also violent.At each time step, agents can choose between three strategies: ‘exploitation’, ‘violence’ and ‘submission’. Exploitation represents property crime. When exploiting, an agent tries to take n randomly drawn agents, among which they prefer submissive targets over violent ones. Agents playing ‘violent’ at this round, therefore, have (if n > 1) a non-zero but lower probability of being victimized than agents playing ‘submissive’ . The parameter n controls how much lower, and thus represents the toughness signal's efficiency: it has no effect if n = 1, whereas if n → ∞, then violent agents are never victimized as long as there is at least one submissive agent in the population. The ‘violent’ strategy is designed to represent forms of violence involving either a material or a reputational stake, our model thus focuses on these forms.The violent strategy also sends a ‘toughness signal’: it is observable and confers a ‘toughness reputation’, which reduces the probability of being the target of exploitation at this round. We assume that choosing the violent strategy suffices to confer this reputation, even for an agent who has never fought. This is a simplifying assumption, that also guarantees the coherence of the model . Exploiters choose their target out of a set of ω for every period spent below the desperation threshold and (ii) a fraction λ for every lost fight, representing the risk of an injury when fighting. In other words, agents try to maintain their head above water financially while fighting as rarely as possible. Since we use a Stochastic Dynamic Programming algorithm, the decision takes into account not only the possibility of being below the desperation threshold immediately but also at any later point in the future.Agents choose the strategy that yields the highest expected ‘fitness’, defined as the resource level attained after T periods reduced by (i) a fraction  (c)n = 105 agents whose level of resources are drawn from a Gaussian distribution. At every time step, we let 10% of the population, randomly chosen, update their strategies. This way, the distribution of strategies in the population can evolve smoothly to an equilibrium rather than oscillating. When updating their strategies, agents take into account their level of resource and the current frequency of ‘exploitation’ and ‘violence’ in the population. For simplicity, we assume agents have perfect knowledge of others’ strategies. We iterate this process enough times for the distribution of strategies to stabilize.We simulate populations of µ and the variance σ of the distribution of resources in the population, representing economic affluence and inequality, respectively. To investigate the possibility of hysteresis, we test if the outcome depends on the initial proportion of violent agents. In the electronic supplementary materials, we explore how the model is affected by varying the other parameters.We then compare the outcomes of the model for different values of the mean . 3 (a)y-axis). A lone violent agent will never be exploited  and never fight, as it never meets other violent agents. Therefore, being violent in a fully non-violent environment has benefits but no costs, and is favoured.Above the threshold, agents should be violent in several cases. First, when exploitation is frequent (in y-axis). The more violence there is, the more exploitation is concentrated on the rare submissive agents. This incentivizes them to be violent, and thus violence begets violence. Finally, agents are prone to violence when close to the threshold. This is due to risk preferences: being violent reduces the risk of being exploited. Just as agents are risk-prone below the threshold because they have ‘nothing to lose’, they are risk-averse just above the threshold as they have ‘too much to lose’, like a person on the edge of a cliff. Intuitively, close-to-the-edge individuals choose to risk their health in an attempt to hang on to their resources.Agents should also choose violence when violence is very frequent (in  (b)µ) and inequality (high variance σ) increase the desperation rate: the lower or the broader the distribution, the larger the left tail consisting of desperate agents  and inequality (σ) increase violence. However, the relationship of the desperation rate to the equilibrium frequency of violence depends on how we initialize the strategies. If we begin with no violent agents in the population, we reach the equilibrium frequencies shown with the crosses on The higher the proportion of desperate agents, the higher the prevalence of violence at equilibrium . In our µ, which, by construction, precludes the role of relative deprivation. We explore this limitation in the Discussion.Here, it must be noted that inequality only plays a role by increasing the amount of desperate agents. In other words, inequality increases violence through absolute poverty, not relative poverty. Concretely, enriching the rich without impoverishing the poor would not increase violence. It must however be noted that we assumed the desperation threshold to be fixed and independent on the average level of resource  (c)hysteresis loop: if the desperation rate (here exogenous) increases from 0 to 0.03, the system follows the lower branch, but if it decreases from 0.03 to 0, it follows the upper branch and remains in a fully violent configuration for a long time. Thus, two equally deprived or unequal communities can have vastly different levels of violence for historical reasons, with high desperation in the past producing a persisting high violence. We can visualize this bistability using a vector field (a). The upper equilibria have small basins of attraction, and will therefore not be reached unless a very large share of the population is violent. However, figure 4b shows that the incentive to be violent soars as the prevalence of violence goes to 1, as rare non-violent agents concentrate exploitation costs. Thus, even though a few non-violent agents would suffice to reach the basin of attraction of the lower equilibrium, the model predicts these equilibria to be stable and robust to small changes in the parameters. In the electronic supplementary materials, we show that the hysteresis effect holds if the parameters r and n are high enough, that is, if toughness signals are efficient enough and the experience of desperation sufficiently persistent.If we initialize the simulation with only violent agents, the population moves to a completely violent configuration in a large range of the desperation rate range , circlesor field a. The up. 4candidate explanation, proving that some conditions are sufficient to generate a particular phenomenon. The innovation in this work resides in demonstrating the consequences that flow from making two original assumptions, namely (i) that agents have a desperation threshold and (ii) that violence sends a ‘toughness signal’ that reduces the risk of being exploited. Assumption (i) has been explored in a previous model to explain property crime, but not in relation with violence. Assumption (ii) has been explored earlier in game theoretical models of conflict [Violence rates vary considerably throughout time and space, in association with economic deprivation and inequality, and scan have a persistent character. We have shown that a single mechanism can account for these three empirical observations. We therefore offer a conflict –52, but  (a)The assumption that agents have a desperation threshold has important consequences. First, it triggers risk-proneness below the threshold . IntuitiTherefore, a larger proportion of desperate agents—as a consequence of either poverty or inequality —leads toThis ‘deflector’ property of violence fundamentally influences the results of the model. In conventional rational choice models , violenc (b)Despite the common intuition that ‘violence begets violence’, standard game theory models actually predict the reverse. For instance, the hawk–dove model  finds viIn some regions of the parameter space, high- and low-violence configurations can simultaneously be stable equilibria in our model. Depending on the starting point, the population can end up in either of the two equilibria: if violence is low, then it stays low due to the negative frequency dependence; if violence is high, it stays high due to the positive feedback. If violence is rare, it is not worth sending a violent signal as the risk of victimization is diluted in the population, whereas if the vast majority of individuals are violent, a rare non-violent agent will bear the brunt of victimization and suffer untenable costs. To understand this result more intuitively, one can think of bike locks, which play a protective role analogous to violence in our model. When leaving your bike among dozens of unlocked bikes, it may not be necessary to lock it, as the risk of it being stolen is diluted among all the bikes. However, if all the bikes around are locked, a stealer passing by would likely steal the only unlocked bike. Similarly, the risk of being exploited might be low enough in the low-violence equilibrium for the cost of violence to be too high to incur. In the high-violence equilibrium, however, any submissive deviant will inevitably concentrate the risks of exploitation.This situation is analogous to coordination games, where positive frequency dependence generates multiple equilibria—for instance left- and right-hand driving. But whereas collective wellbeing is roughly equal whether cars drive left- or right-wing, in our case, settling in a high- or low-violence equilibrium is very consequential. An earlier evolutionary game theory model of toughness signals also reports the possible coexistence of two equilibria with very different levels of aggression . The authysteresis effect: violence rates do not only depend on the current economic conditions, but also on their history. Concretely, a neighbourhood can be more violent than an equally rich neighbourhood because it was poorer and more violent in the past. Thus, violence can persist despite some economic improvement. This result aligns with the ‘enduring neighbourhood effect’ [This bistability generates a  effect’  of viole effect’ . (c)µ would affect equally both agents’ level of resources and the threshold, without consequence. In this setting, the level of violence would only depend on inequality (σ). One could also imagine that an exploited agent loses a proportion of his wealth instead of a fixed amount of resources. In this setting, the presence of very well-off individuals could act as an incentive for exploitation, which could in turn create a stronger need for protection among these individuals.In our model, poverty and inequality only increase violence through the proportion of desperate agents. Thus, the effect is driven only by absolute poverty, and not by relative poverty. Concretely, our model predicts that making the richest individuals richer with no impact on the poorest does not increase violence. This might seem at odds with several empirical findings ,5,8,58 a (d)hysteresis effect holds in this case, and to observe if the insensitivity to deterrence induced by the desperation threshold triggers arms race dynamics through an ‘inflation of toughness’.Our model analyses violence as a binary decision, where choosing ‘violence’ essentially means being ready to fight when exploited, which yields a ‘toughness reputation’, known by all of the other agents. This assumption is restrictive in two respects that we could explore in the future. First, we could allow agents to fine-tune their level of violence. This would require specifying how the fitness costs of violence relate to the level of violence and how exploiters choose their targets in this new context. It would be interesting to test, for instance, whether the Second, our assumptions implicitly entail that an agent simply needs to be ready to fight so that every other agent treats him as tough, even if she has never fought. In our simulations, the majority of violent agents reap the benefits of violence without actually paying the costs, as fights rarely occur. We chose here to directly specify how the signal changes the receiver's behaviour, in order to focus on the population dynamics. An alternative assumption would be to only attribute a toughness reputation to an agent after she actually fought. This would make the model more complex, but would enable it to study another question: under what conditions should an agent be violent without material necessity, for pure reputational reasons? This could shed light on Anderson's observation that, in the deprived communities he studies, ‘there are always people around looking for a fight’, a situation he attributes to ‘campaigning for respect’ .Finally, our model also generates novel testable predictions and can guide empirical data collection. For instance, we predict individuals to be violent when they live in a deprived neighbourhood, whether they are themselves materially deprived or not . This su (e)We discuss implications of our model for public policy and intervention. First, our model predicts that helping the poorest individuals to get back above the threshold of economic deprivation can have a ripple effect. Not only would such help reduce the probability that desperate individuals choose to steal, violence would also diminish among the rest of the population, for whom there has been no change in resource levels. In our model, the dire poverty of some has an emergent effect on the population: in a world where some individuals are ready to do anything to get their head above water, everyone must take protective steps like violence. By eliminating desperation, one might then improve the welfare of all members of the group, even those who do not benefit from the policy.hysteresis effect our model produces. For a community trapped in a high violence equilibrium (figure 4b, it would be necessary to pass the unstable equilibrium to reach the basin of attraction of the low-violence equilibrium, otherwise violence goes back to maximum when the intervention ends. Therefore, our model suggests a nonlinear relationship between intervention magnitude and resulting change. It also calls into question the use of linear models to test the efficiency of these interventions. An empirical researcher might for instance find a null effect of economic support on violence if she only looks at a limited intervention, whereas more of this same intervention could have a tremendous positive impact.The second implication is related to the To conclude, we presented a simple model combining individual optimal decisions and population simulations. We make two original assumptions: agents have a desperation threshold, and violence serves as a ‘toughness signal’. We show that their combination is able to explain three cornerstone empirical findings: the large variation of violence rates between neighbourhoods or communities; the effect of poverty and inequality on violence; and the persistence of violence across time.