The aim of this study was to find a reliable method for measuring lip force and to find the most important factors that influence the measurements in terms of magnitude and variability. The hypothesis tested was that suction is involved and thus the instruction and the design of the oral screen are of importance when measuring lip force. This is a methodological study in a healthy population. This study was conducted in a general community. The designs of the screens were soft and hard prefabricated screens and 2 semi‐individually made with a tube allowing air to pass. The screens and the instructions squeeze or suck were tested on 29 healthy adults, one at a time and on 4 occasions. The test order of the screens was randomized. Data were collected during 4 consecutive days, and the procedure was repeated after 1 month. The participants were 29 healthy adult volunteers. The instruction was an important mean to distinguish between squeezing and sucking. The design of the screen affected the lip force so that it increases in relation to the projected area of the screen. A screen design with a tube allowing air to pass made it possible to avoid suction when squeezing. By measuring with and without allowing air to pass, it was possible to distinguish between suction related and not suction related lip force. The additional screen pressure when sucking was related to the ability to produce a negative intraoral pressure. In conclusion lip force increases in relation to the projected area of the screen, sucking generally increases the measured lip force and the additional screen pressure when sucking is related to the ability to produce a negative intraoral pressure. OSPoral screen pressure1Orofacial dysfunction caused by neurological disorders such as stroke, peripheral palsy, operation of brain tumors, infections, head, and neck cancer results in drooling, accidental biting, food retention, and problems to form and transport a bolus. In rehabilitation, prefabricated and individually oral screens are commonly used. Studies of the outcome of the training are unclear as different soft and hard prefabricated oral screens have been used. Thus, there is a great need for reliable, sensitive, and objective methods evaluating orofacial muscle function  in a pressure unit, for example, kPa  measurements from screens with different areas can be compared , and it was performed in accordance with the Declaration of Helsinki.2.1Twenty‐nine healthy adults, 20 females and 9 males, aged 31–68 years with ordinary morphology of the face, normal oral motor function, and occlusion were recruited on voluntary basis for the study. They mainly comprised dental health personnel at the Public Dental Service clinic in Mölndal, Sweden. All the individuals gave their informed consent to participate and continued through the entire testing period.2.2A soft prefabricated screen Figure a, Ulmer Two sizes of oral screens, medium and large, were made in acrylic from plaster casts measuring 49 and 56 mm between the buccal surfaces of teeth 15 and 25. The oral screens were made with a hole and a small tube around the handle  was calculated in the MS Excel graphs. The individual means data were analyzed in SPSS for normality by the Shapiro–Wilk test. Confidence ellipses for the bivariate Gaussian distribution were calculated from the chi‐square distribution with elliptical axes = k = 1.177 for 50% confidence and k = 2.448 for 95% confidence.The dataset was first analyzed in MS Excel for calculating the OSP by dividing force values with appropriate screen areas. Ninety‐five percent confidence levels of the different means were calculated from 2.8One of the screens (Screen C) was modified to permit measurement of the established vacuum in the oral cavity during lip force measurement. A silicone tube was used to connect the low‐pressure side of a differential pressure transducer  to the central tube of the screen. The high‐pressure side of the sensor was exposed to the room atmosphere. The sensor output voltage was amplified by an instrumentation amplifier (INA126) and recorded in a personal computer by a multifunction USB device . By using a silicone tube filled with water, the sensor could be calibrated by well‐defined hydrostatic water columns. The sensor sensitivity was found to be 0.109 V/kPa. Estimated uncertainty based on sensor data was a maximum error of less than ±0.2 kPa in the range 0–50 kPa. A small control group of six healthy adults were recruited on a voluntary basis for this test. The measurements were carried out as described previously with three measurements for each of the two instructions at the same (one) occasion. The intraoral negative pressure was recorded during the lip force measurement with suction, and the maximum value of the differential pressure was selected for further analysis.32 and reduced to 8.3 cm2 when it was subjected to a load of the same magnitude as the average lip force (18–25 N). The pressure was subsequently calculated with the reduced area. The error in area measurement for all screens is estimated to maximum 5%.The labelling and projected area of the different screens used is presented in Table When evaluated as an OSP, the measurements for the different screens could be compared. In Table In Figure PSu+ is evaluated as the difference between measured OSP at instruction “Suck” PSu and OSP measured at instruction “Squeeze” PSq.In order to check the influence of suction on OSP measurements, the data were further processed. In Figure PSu+ and PSq. The trend line for Screen C is almost horizontal with a coefficient of determination r2 = 0.0024 indicating that the parameters PSu+ and PSq are practically uncorrelated. On the other hand, with Screens A and B, it is not possible to extract the contribution from suction. The trend line for Screen B has a negative slope with a much higher coefficient of determination of r2 = 0.264 indicating that suction may be present with the squeeze instruction.The two clusters can still be identified, but there is now a significant difference between screens with and without a hole preventing suction. For Screens C and D, there is almost no correlation between PSu+ and PSq. These parameters are summarized in Table p values in the Shapiro–Wilk tests were greater than 0.05. In Figure The results from Screens C and D motivate the definition of two independent OSP parameters PSu+ is related to the intraoral pressure that is present during suction. In Figure PVac is plotted against the OSP parameter PSu+. It was found that there seems to be a linear relation between PVac and PSu+, but in absolute values, the PVac is approximately twice the value of the OSP parameter PSu+.It seems natural to investigate in what respect the new parameter 44.1In this study, there is consistency between the values from Screens C and D and the values in a previous study where these screens had the most similar overall mean value (Wertsén & Stenberg, 4.2The projected area for the soft oral screen decreased with 25% under load with the same forces that were measured with the testing subjects. This means that the active area is substantially smaller than the projected and the measured value of screen force might thus be smaller compared to a hard screen of similar size. This aspect has not been taken into account in studies performed with soft prefabricated oral screens (Sjögreen et al., When measuring lip force using prefabricated oral screens without a hole to let air in, it becomes difficult for the patient to execute the instruction “Squeeze.” However, when using a semi‐individual screen with a tube allowing air to pass, it is likely to get clearly separated values for the abilities squeezing and sucking. The screen design is obviously of great importance for the outcome. No studies have been found where oral screens with a similar design have been used.4.3A problem when studying a normal population is that in healthy adults, the force when sucking is so high that the measuring procedure might be interrupted because of pain from the mucosa. This may result in a poorer performance in the first but mainly in the second session, the subjects having the experience of the first measurement in mind. In this study, the measured values for Screen D showed this phenomenon. Moreover, with Screen D, there was a great variation between the pressures performed by different healthy individuals compared to Screen C. This indicates some kind of impact on the measured values but no further analysis of this observation has been done in this study. However, a person with impaired oral motor function will probably never reach these high values.4.4PSq, and one is also related to suction, PSu+. It is essential to have threshold values for both these parameters. A plot of longitudinal data in a two‐dimensional diagram such as Figure To evaluate oral motor function in patients, it is desirable to have a cut off value for lip force that is independent of the equipment used. To make the value useful, it should be comparable to values from other studies. Therefore, a value of OSP expressed in kPa is preferable. In this study, we have proposed two independent parameters of oral screen pressure. One is related to the mechanical strength in the perioral muscles, 4.5The additional OSP as defined in this work is not identical to the vacuum in the oral cavity resulting from suction. One possible explanation could be how much tissue area actually is in contact with the screen during suction. The mechanism of how these parameters are related is not the subject of this work and should be interesting to study in future works.4.6Santander et al.  showed t5To suck generally increases the measured lip force.The instruction is an important mean to get the correct measurements to distinguish between squeezing and sucking.Measurements with the prefabricated screens indicate that the subjects mix squeezing and sucking in spite of the instructions.The instruction:The lip force increases in relation to the projected area of the screen.It is possible to avoid suction when squeezing if the screen is designed with a tube allowing air to pass.The design of the oral screen:The additional screen pressure when sucking is related to the ability to produce a negative intraoral pressure.The authors declare that they have no conflict of interest.


To assess the number of children born with microcephaly in the State of Paraíba, north-east Brazil.We contacted 21 maternity centres belonging to a paediatric cardiology network, with access to information regarding more than 100 000 neonates born between 1 January 2012 and 31 December 2015. For 10% of these neonates, nurses were requested to retrieve head circumference measurements data from delivery-room books. We used three separate criteria to classify whether a neonate had microcephaly: (i) the Brazilian Ministry of Health proposed criterion: term neonates  with a head circumference of less than 32 cm; (ii) Fenton curves: neonates with a head circumference of less than −3 standard deviation for age and gender; or (iii) the proportionality criterion: neonates with a head circumference of less than ((height/2))+10) ± 2.Between 1 and 31 December 2015, nurses obtained data for 16 208 neonates. Depending on which criterion we used, the number of neonates with microcephaly varied from 678 to 1272 (4.2–8.2%). Two per cent (316) of the neonates fulfilled all three criteria. We observed temporal fluctuations of microcephaly prevalence from late 2012.The numbers of microcephaly reported here are much higher than the 6.4 per 10 000 live births reported by the Brazilian live birth information system. The results raise questions about the notification system, the appropriateness of the diagnostic criteria and future implications for the affected children and their families. More studies are needed to understand the epidemiology and the implications for the Brazilian health system. Congenital microcephaly is a neurological condition defined by an occipital-frontal head circumference that is smaller than expected for the gestational age and gender. Head circumference is a validated measurement for intracranial brain volume, since the growth of the cranium depends on the forces of the expanding brain. Microcephaly could, therefore, be used as an indicator of an undersized brain. However, controversy exists concerning the suitable lower limit for this measurement, as well as over the need for ethnically controlled data.Microcephaly is a rare condition. In the United States of America, the prevalence has been estimated to range from 2.0 to 12.0 newborns with microcephaly per 10 000 live birthsCírculo do Coração, a nongovernmental organization. The network has screened and stored cardiovascular data from more than 100 000 neonates from this state. However, the original data set does not include head circumference data. To increase the knowledge about microcephaly prevalence in Paraíba, the network carried out a four-week exercise between 1 and 31 December 2015, to obtain head circumference data from 10% of the neonates in the data set. This article summarizes the results from this research.Since 2012, the government in Paraíba has run a paediatric cardiology network,The network collected data on all neonates born in the 21 participating maternity centres. To retrieve data on head circumference for a subset of these neonates, we exported data – including an identification number, the date of birth and the mother’s name, for all neonates in the network – from the database to an electronic spreadsheet. We added an extra column to the spreadsheet with the heading head circumference. We sent the spreadsheet to each participating centre by email, and in the email asked the nurses to retrieve the head circumference measurements from the delivery-room books. In Brazil, a newborn’s occipital-frontal head circumference is measured in the delivery room by a nurse or a paediatrician, who uses a common measuring tape. The measurement is noted in the delivery room book as part of the routine perinatal practice in Paraíba state.The goal was to retrieve data on approximately 10% of the neonates born between 1 January 2012 and 31 December 2015. To distribute the collection of data evenly over time, we suggested that the nurses should randomly select 10% of each month’s deliveries. The nurses first printed the spreadsheet and wrote down the head circumference of the selected neonates on the list. Then, they logged on to the network’s database, typed in the identification number for each selected neonate and manually entered the measurement in the newly added field for the head circumference data.We obtained additional information about the mother’s name and address, the gestational age, the length and weight, and the gender of the neonate at birth, from the network’s database. Data on ethnicity were not collected. We only included neonates with complete data.We classified neonates as having microcephaly by using one of the following criteria: (i) the criterion proposed by the Brazilian Ministry of Health, for which a term neonate  is diagnosed with microcephaly if the head circumference is less than 32 cm;We made four different analyses: one for each criterion and one where the neonates had to fulfil all three criteria. In addition, within each of the criterion, a neonate was classified as having severe microcephaly when the measurement was −3 standard deviation or more for that criterion.We used the software R, version 3.3.0  for all data analysis. For statistical analysis we used the Friedman test.Nurses retrieved data from 16 208 neonates, of whom 7750 were females and 8458 were males. Most of the babies  were full term neonates, 12 146 (74.9%) weighed more than 3000 g and 15 572 (96.1%) measured more than 45 cm in length, at birth .Depending on which criterion we used, 4.2% (678) to 8.2% (1272) of neonates were classified as having microcephaly and 316 (2.0%) neonates fulfilled all three criteria. Of the neonates that fulfilled all three criteria, three were classified as having severe microcephaly .P = 0.001) from the third quarter of 2015 , if we use the proposed criterion from the health ministry, the estimated number of neonates born with microcephaly in that year is 4652; if we use the Fenton curves, the estimated number is 2442; and if we use the proportionality criterion, the estimated number is 2907. The estimated number of neonates fulfilling all three criteria is 1105.Between 2012 and 2015, the Brazilian live birth information system reported a microcephaly prevalence of 6.4 per 10 000 live births in Paraíba.These observations raise several questions. First, what is the true prevalence of microcephaly in north-east Brazil? The discrepancy in numbers between the Brazilian Ministry of Health and this study may reflect underreporting in recent years associated with an even greater incidence of microcephaly than presumed. It is possible that a high prevalence of the non-severe forms of microcephaly had been occurring before the current outbreak, but health workers had only notified the live birth information system about the cases of neonates with typical severe phenotypes. As a result of the number of neonates with severe microcephaly increasing in the last quarter of 2015, the health workers' awareness might have increased, therefore causing them to notify the live birth information system about the milder forms as well.Second, what is the most appropriate diagnostic criterion for microcephaly in this setting? If we only consider the number of neonates with severe microcephaly in our study, this number is in the expected range of 2–12 neonates with microcephaly per 10 000 live births, reported by the United States Centers for Disease Control and Prevention.Third, what is the cause of the increase in microcephaly prevalence? This question has attracted a lot of attention and the most likely explanation is the Zika virus outbreak that started in mid-2014 in Brazil. It is believed that the Zika virus was introduced to Brazil during the 2014 FIFA World Cup.,The Zika virus was identified in Africa more than 50 years agoAedes aegypti mosquitoes and infections transmitted by this vector demonstrate temporal fluctuations similar to the fluctuations of microcephaly that we present here.Ae. aegypti, such as dengue and chikungunya, might explain the increase in microcephaly seen in Brazil. The hypothesis is that concurrent infections have an additive effect that promotes microcephaly. A study from the island of La Réunion– an overseas department of France – showed an association between chikungunya infections and microcephaly.,The Zika virus is transmitted by Ae. aegypti vector has been a major public health strategy to combat the arboviruses. This strategy is justified both by its potential to reduce the number of babies born with microcephaly – if the association with Zika virus infections proves true – and for the reduction of other Ae. aegypti transmitted diseases, such as dengue and chikungunya infections.In Brazil, controlling the At this stage, we can only conclude that Brazil is facing a new and challenging public health problem. The current epidemiological and clinical data are insufficient to make conclusions concerning the risk factors of microcephaly and the pathogenic mechanisms of the Zika virus. Further retrospective studies and follow-up investigations on children with well-defined or borderline microcephaly will be important to clarify the etiology as well as the neurological consequences of these diagnoses. Children born with microcephaly can also have other birth defects, which could further aggravate the neurological manifestations. For the affected children and the families it is paramount that the government provides management strategies, such as social inclusion programmes and access to specialized health care.


Adverse early life experience and development may have long-term health consequences, but later environmental conditions may perhaps protect against the effects of such early life adversities. The aim was to investigate whether cause-specific and overall mortality rates among adoptees are associated with the age at which they were transferred to the adoptive family and whether the social class of the adoptive family modifies this association.A cohort of 10,592 non-familial adoptions  of Danish-born children formally granted in 1924–47 and with follow-up of total and cause-specific mortality through ages up to 85 years. The rates of death after the age of 16 from all causes combined, all natural causes, all external causes, and suicide were compared according to the age at which adoptees were transferred to their adoptive family by estimating hazard ratios in Cox regression models.Death rates from all causes were significantly higher in adoptees transferred between age 1 month and 4 years compared to those transferred immediately after birth with the hazard ratio peaking at 1.19 (95% confidence limit: 1.08 to 1.32) for adoptees transferred between 6 and 11 months. This result was primarily driven by a similar pattern for natural causes of death. For death from external causes and for suicide the hazard ratios were increasing with increasing age at transfer, and tests for trend were statistically significant. The social class of the adoptive family did not significantly modify these associations.Transfer to an adoptive family later than at the time of birth may have adverse long-term consequences affecting overall and cause-specific mortality. These effects were not modified by the environment provided by the adoptive family as indicated by the social class of these families.The online version of this article (10.1186/s12889-018-5338-4) contains supplementary material, which is available to authorized users. Adverse early life experience and development may have long-term health consequences , but latMiller et al. discussed associations between exposure to major psychological stressors in early life and elevated rates of morbidity and mortality from chronic diseases of aging . They suSocioeconomic circumstances during up-bringing influence cause-specific and overall mortality in adulthood . It is tThe Danish Adoption Register includes information on adoptions of Danish-born children granted in 1924–47 . AdopteeThe study was based on the Danish Adoption Register, which contains records on all 14,425 non-familial adoptions formally granted in Denmark during the period 1924 through 1947 . Among tTo avoid assuming linearity we categorized age at transfer, but due to the fewer adoptees transferred after the age of two years, the categories were broader at later ages than early ages. The available studies of mortality in adoptees do not suggest specific transfer age categories, but the more detailed categorization of the first year of life used in the present study is in line with attachment theory and with a critical factor being whether the child is sufficiently old to become conscious of the transfer and the associated change in social environment.In the present study the social class of the adoptive family was based on occupation of the fathers, and it was available from the adoption records for 96% of the adoptive fathers. In the first half of the previous century most women were housewives and it was common to define family social status by the father’s education and occupation .The occuMortality rate ratios were calculated in a Cox model with age as the underlying time variable using Stata version 12.0 . Calendar time was categorized in 10 year groups and adjusted for as a time-varying covariate, in order to account for changes in rate of death during the calendar period covered. Sex was adjusted for using separate underlying hazard functions in men and women, to reflect that men and women have different mortality rates.In the main analyses, adoptees were divided into six groups according to their age at the time of transfer to the adoptive parents: 0 months, 1–5 months, 6–11 months, 12–23 months, 2–3 years, and 4–7 years. The social class of the adoptive family was considered a factor potentially modifying the effects of age at transfer and was categorized into high and low social class. High social class included advanced professional, academic and sub-academic professions and self-employed, while low social class included subordinate clerk, skilled worker, semi-skilled worker, and unskilled worker. In the analyses including the potential modifying effect of paternal social class, age at transfer was reduced to four categories: 0 months, 1–5 months, 6–23 months, and 2–7 years.Interaction terms were added to test if gender modified the association between age at transfer and the mortality rates. The proportional hazards assumption was tested in the main analyses by Schoenfeld’s residuals and was not rejected. Linearity was tested using cubic splines, and if not rejected, tests for trend were performed assuming linearity of the age at transfer on the log hazard scale. In additional analyses age at transfer was used as a continuous variable, and cubic splines were applied in the Cox regression. As a supplementary analyses we used age at transfer to predict mortality among birth parents.Mortality rates among adoptees were compared according to the age at which the adoptee was transferred to the adoptive family, using those who were transferred immediately after birth as the reference.Death rates from all causes were significantly higher in adoptees transferred between age 1 month and 4 years compared to those transferred immediately after birth with the relative rate peaking at 1.19 (95% confidence limit: 1.08 to 1.32) for adoptees transferred between 6 and 11 months (Table p > 0.16).We tested whether the effect of age at transfer differed in men and women and found that this was not the case for any of the causes of death (p > 0.21). In adoptees who were adopted to low social class families, transfer interval 2–7 years was associated with a significantly higher rate of suicide than among those transferred at birth. This was not the case for those adopted to high social class families, but for those transferred at birth, high social class was associated with a non-significantly higher rate of suicide than among those transferred to low social class families.The number of adoptees and number and percentage of deaths from all causes of death combined, natural causes, external causes, and suicide are presented in Table n = 1365) and biological fathers (n = 1194) [To assess confounding due to increased relative mortality in birth parents, we made a supplementary analysis of the association between age of transfer and mortality in the biological parents based on available subsamples of biological mothers n = 135 and bioAn association of age at transfer with overall and cause-specific mortality rates was observed. For all causes combined the critical period of transfer seemed to be between 1 month and 4 years of age at transfer, while for natural causes it was 1 month to 2 years of age. For death from all external causes and for suicide the mortality rates were increasing with increasing age at transfer. The results gave no indication that the effects of age of transfer differed between those adopted to high and low social class families, although high social class was associated with a non-significantly higher rate of suicide.The pattern found for natural causes suggested a difference between transfer at birth and later transfer. The lack of a clear trend of increasing mortality with increasing age of transfer suggests no cumulative effects of adversities during the first 7 years of life. For the rate of suicide and all external causes the trend is significant, but a pattern of increasing rate with increasing age is most clear for suicide. This may be related to the behavior and emotional problems that have been observed in many studies of adopted children and adolescents. Thus, while some studies of international adoptees have found late age of transfer to predict behavioral and emotional problems , 24, 25,Our study of domestic adoptees born in the first half of the twentieth century represents circumstances that are very different from those of international adoptees at present. In our study, neither the reasons for adoption, nor information on institutional rearing before transfer to the adoptive family were available but a number of different factors may predict behavior problems and the increase in mortality from natural causes associated with transfer at 1 month or later. Familial environment such as parental attachment patterns has been found to affect attachment in adoptees  and coulThe important contrast for age at transfer seems to be between transfer at birth and later in childhood, and thus there is little evidence of cumulative effects of adverse psychosocial circumstances before adoption on the rate of death from natural causes. An alternative interpretation is that attachment is affected differently in different developmental periods. Thus, age at transfer is likely to correlate with adversities and prolonged sojourn in institutions, but with the information available the different explanations for our findings cannot be disentangled. The period of vulnerability to change in family differed between natural and external causes of death, and this suggests that the mechanisms leading from timing of transfer into the adoptive family to increased rate of death may be different for natural and external causes of death, in particular suicide. For natural causes of death it is possible that the difference between adoption at birth and later reflects differences in health related characteristics between the biological parents of children transferred early and late. Thus, late transfer was often associated with prolonged sojourn in institutions related to maternal inability to take care of the child , 32, andWe find that transfer to an adoptive family at a later time than at birth may have long-term consequences affecting mortality. Being transferred later than birth was associated with a higher rate of death from natural causes, whereas the later the age at transfer, the higher the rate of suicide and other externally-caused death. These effects were not modified by the environment provided by the adoptive family as assessed by the social class of these families.Additional file 1:Table S1. Associations between age of transfer and mortality in the biological parents. (DOCX 37 kb)


Our research is based on a technique for time sampling, an innovative method for measuring the working hours of Dutch general practitioners (GPs), which was deployed in an earlier study. In this study, 1051 GPs were questioned about their activities in real time by sending them one SMS text message every 3 h during 1 week. The required sample size for this study is important for health workforce planners to know if they want to apply this method to target groups who are hard to reach or if fewer resources are available. In this time-sampling method, however, standard power analyses is not sufficient for calculating the required sample size as this accounts only for sample fluctuation and not for the fluctuation of measurements taken from every participant. We investigated the impact of the number of participants and frequency of measurements per participant upon the confidence intervals (CIs) for the hours worked per week.Statistical analyses of the time-use data we obtained from GPs were performed. Ninety-five percent CIs were calculated, using equations and simulation techniques, for various different numbers of GPs included in the dataset and for various frequencies of measurements per participant.Our results showed that the one-tailed CI, including sample and measurement fluctuation, decreased from 21 until 3 h between one and 50 GPs. As a result of the formulas to calculate CIs, the increase of the precision continued and was lower with the same additional number of GPs. Likewise, the analyses showed how the number of participants required decreased if more measurements per participant were taken. For example, one measurement per 3-h time slot during the week requires 300 GPs to achieve a CI of 1 h, while one measurement per hour requires 100 GPs to obtain the same result.The sample size needed for time-use research based on a time-sampling technique depends on the design and aim of the study. In this paper, we showed how the precision of the measurement of hours worked each week by GPs strongly varied according to the number of GPs included and the frequency of measurements per GP during the week measured. The best balance between both dimensions will depend upon different circumstances, such as the target group and the budget available. Insight into the working hours of doctors is of great importance for health workforce planning. How many hours doctors actually spend working, with their patients or not, is critical for assessing how many of them are available now and will be needed in the future. This applies, in particular, to general practitioners (GPs) who function as the gatekeepers to care in many health care systems. Thus, the working hours of GPs need to be monitored in order to ensure that primary care remains accessible . Given tMost studies investigating the working time of health care professionals are based on surveys, diaries or observations. In surveys, participants are asked to report their average time spent working per week over a certain period . This isDiaries are considered as a more reliable research technique as they provide a more systematic way of measuring working time and a limited period of recall . DiariesFinally, observations are considered as the most reliable method. Two widely accepted techniques are “time and motion” and “work sampling”. With a time and motion study, an observer measures precisely how much time a participant spends on a specific activity. This is known as an accurate but also time-consuming technique, because the researcher is constantly observing the participant . For thiWork sampling is an alternative observation technique which involves an observer logging the activity of the participant at random moments . This teBased on the principles of time sampling, we conducted an extensive survey of time use among Dutch GPs who were questioned about their activities at random moments during 1 week. A critical asset compared to other methods is reducing the potential of recall bias, because GPs were reporting about their activities in real time. Several instruments for performing this time-sampling technique were possible and considered, but we decided to use SMS text messages to perform the measurements of time use. Although SMS is assessed as relatively outdated, its underlying technology is highly standardized, it is accessible and its use is straightforward for all types of users. Currently, in Western countries, almost all citizens including doctors have a mobile phone at their disposal and are able to send SMS text messages . To the The method provided a real-time measurement of the working hours of GPs and offered positive results regarding its feasibility for the respondents. In an earlier report, these results and the design of the study based upon time sampling and conducted with an SMS tool were discussed in detail . The preAn important consideration in the use of a time-sampling method is the need to achieve a balance between the number of measurements for each participant and the number of participants. A higher number of measurements per participant means that fewer participants are required in order to obtain precise results. On the other hand, this decision will increase the workload for each participant and the probability too that they will drop out during the measurement period. We conducted a pilot study prior to our time-use study, which confirmed that it was feasible for GPs to send one SMS during every period of 3 h over all 7 days of 1 week . In addiThe actual required sample size to attain a level of precision of working hours is an important issue for time-use researchers and health workforce planners who want to apply this method based on time sampling. This is particularly true if it concerns a study among GPs or other health care professionals who are harder to reach. It is also the case if fewer resources are available compared to our time-use study. In studies based on work or time sampling, however, there is hardly any information given about the sample size and the effect on the precision of the results. Even so, the technique is widely accepted and applied . In a feIn the present paper, we address the question of to what extent the CI, the main precision indicator for the estimates of working hours, is related to the number of participants and the frequency of measurements per participant. To answer our research question, we used equations and conducted simulations on the time-use data among Dutch GPs as described above.All GPs who participated during 1 week were questioned about their activities by sending SMS text messages. The message contained the single question: “What are you doing at this moment?” Included too was the time the message was sent in the format 00:00:00. Below this line, four possible categories of responses were listed on the SMS screen: (a) I am not working as a GP; (b) I am doing work directly related to my patients; (c) I am doing work indirectly related to my patients; and (d) I am not doing work related to my patients. Prior to the weeks of receiving SMS text messages, participants received an instruction including the definitions of the response categories.SMS text messages were sent to the participants at random moments during 3-h time slots over a 24-h period. This implied that, per GP, eight messages per day and 56 messages per week, including the weekend days, were scheduled. In addition, so-called planning messages were sent at 7 am and 7 pm, by which GPs could indicate if they definitely would not work during a day part. If they used this option, their activities for these time slots were coded as “not working”.Participants had to reply to every message which was pre-scheduled by entering their response letter and the order number of scheduled messages. The numbering started every day at 7 am. Numbering the SMS text messages was required to identify the specific message sent and to attach them to the activity answer of the participant to which it was related.The data collection was conducted during 57 consecutive weeks over the period from December 2012 to January 2014. This was partly for logistic reasons, but it also enabled the researchers to account for seasonal variability in the data on working times which was collected. In total, 1051 GPs were included in the study of which 44 participated twice. In total, the participants represented about 9% of all the 11 075 GPs employed in the Netherlands in 2013. The composition of the response group regarding gender and position of employment corresponded to a large degree with the composition of the stratified sample that was drawn on the basis of these variables from the national registration of GPs conducted by NIVEL .On average, 19 GPs participated for every week of the study of time use. More female (11) than male GPs (eight) were included, which corresponds with the distribution of gender within the sample. On average, 11 self-employed GPs participated. Furthermore, salaried GPs and GP locums were reasonably well represented in most of the weeks of the study.Working hours were calculated by multiplying the replies to the activity questions with 3 as these were the time slots in which the messages were sent over the course of the week. For instance, the working week of a GP who replied that activity “b”, “c” or “d” was performed 13 times is calculated as 13 times 3 or 39 h. This seems to be a rough or inaccurate estimate of every GP’s working week. This is because the time measurements were taken only at samples of moments. However, as we included a large number of participants, this enables an accurate calculation to be made of the average working hours for the total group of GPs and its subgroups.We used data from 1051 GPs for our extended analyses regarding the precision of the results. The first week of SMS text messages for the 44 GPs who participated twice was excluded from the analysis. We then analysed means, standard deviations and CIs for the working hours per week for all GPs and then the six subgroups. We used the total dataset of all GPs and measurements to explore the question of how the CI as a main indicator of precision varies, both for the number of participants and for the frequency of measurements for every participant.Our data and analyses are based on sampling in two stages. Firstly, we analysed the sample of GPs out of the total population of GPs who were active in the Netherlands in 2013. Secondly, we analysed, for every GP, a random sample of moments of measurement in 3-h time slots during a week. As a result, the CI consists of two types of uncertainty. These are sample fluctuation and, secondly, moments of measurement fluctuation. The total CI was calculated through the following three steps.Sample fluctuation reflects the uncertainty of the sample of GPs drawn from the population. This is the conventional CI of an estimate that is commonly calculated for survey research.We calculated the CIs for different numbers of GPs by adhering to the constant—that is the decision in our SMS study to ensure every participant received one message within 3-h time slots in the course of 1 week. This was done by using the standard deviation of the total measurements gathered from all GPs who participated. This standard deviation was weighted by the position of employment and gender of all GPs employed in the Netherlands in 2013. Then the following equation was applied:N represents the total number of measurements of different numbers of GPs and 1.96 is the z-value for the 95%-CI. The result is the one-sided divergent value, above or below, the average working hours within the total sample.We then calculated the CIs for a varying frequent number of measurements per GP. We achieved this by multiplying the time measurements by 1.5 as if one measurement was taken every 2 h, by 3 as if one measurement was taken per hour and by 6 as if one measurement was taken every 30 min. Again, CIs were calculated for a varying number of GPs.40 h per weekonly on weekdays from 7:30 am until 4:30 pm, with a 1-h break in the afternoonWe simulated 1000 weeks of measurements taken from a fictional GP in order to gain insight into the uncertainty that result from the random points in time chosen for the measurements. We then calculated the one-tailed 95%-CI, the hours above or below the average value. This fictional GP works:We took this type of working week as analyses conducted previously had shown that most of the GPs were active at approximately these moments during the week . ObviousThe simulations were performed taking 3-h time slots in the same manner as our SMS study. Subsequently, time slots of 2 h, 1 h and half an hour were simulated in order to investigate the effect on the precision of the results.Figure and for a varying number of GPs included in the dataset, based on the sample fluctuation (step 1) and measurement fluctuation (step 2). As both variances are independent of each other, we summed both types of uncertainty by applying the following equation:We calculated the total CIs for a number of different measurement frequencies This total one-sided CI is the key dependent variable that is analysed and presented in the next section of this paper. The two-sided CI will not be reported, but can simply be calculated by multiplying the one-sided results by factor 2.The statistical analyses were performed in Stata 14.0.Table Considering the two types of uncertainty we explained in the previous section, it becomes clear that the largest part of the total CIs presented in Table What would be the CI if fewer GPs were included in the sample of our study and if more measurements per participant were taken? Figure The same patterns are revealed if more measurements per GP were taken. Obviously, the CIs for these scenarios are lower compared to the CIs based on our design in which one measurement per 3-h time slot was conducted. For example, if one measurement per 3 h is taken for every participant, 300 GPs are needed to achieve a CI of 1 h. One measurement every hour requires just 100 GPs for the same result and one measurement every half an hour only 50 GPs.We researched how a varied number of participants and measurements per participant have an impact upon the precision of the estimates of mean working hours per week, i.e. the one-tailed 95%-CIs. This was conducted on the basis of time-sampling data obtained by sending SMS text messages to 1051 Dutch GPs. The answer could support researchers and health workforce planners in determining the appropriate design and sample size required to obtain valuable time-sampling data about the working hours of GPs or other health care professionals.Our results showed that the CIs of the mean working hours per week decreased from 21 h until approximately 3 h between the one and 50 GPs we included in the dataset and simulation. This was given a fixed number of time measurements per GP that was applied in our empirical study, i.e. once in every 3 h during the week. As a result of the formulas applied for calculating CIs, the impact of an increasing number of participants was smaller if a relatively high number of participants were already included. This means that proportionally a higher number of additional GPs were required for an increase of the precision.Likewise, the number of participants required decreased if measurements were taken on a more frequent basis, for example once per hour instead of once per 3 h. Hence, the frequency of the measurements for every participant during the week is an important decision that determines the sample size required when this time-sampling technique is used. This is summarized by Table Considering these results, it is important to note that a standard is needed in order to claim what is the best level of precision required—the “optima”. The threshold for the minimal CI will depend on the purpose of a certain study. In our study, the working hours were needed for health workforce planning for which a certain precision is needed. However, like other key parameters in the model, some margin is possible as in most cases this will have no major impact on the advice regarding the number of GPs needed. Generally, we assess the CI cannot be larger than approximately 2 h, which implies that a maximum of 100 GPs are needed if at least one measurement per 3 h is taken from every participant during the week (second row of Table In addition to the purpose of a study, there are several other circumstances that could play a role in deciding upon the appropriate sample size. This is, among others, the availability of the participants and the available time and resources of the researcher , the numSome limitations should be taken into account. Firstly, it was shown that the CI based on sample fluctuation increased with 11% if measurement fluctuation was taken into account. The measurement fluctuation was calculated by simulations of the data for participants during a specific 40-h working week. This should be assessed as an attempt to gain insight into this type of uncertainty as part of the CI, which is difficult to determine precisely. On the other hand, conducting these simulations on other working schedules resulted mostly in small differences with the total calculated CI. Further research is needed if a more detailed insight into the impact of measurement fluctuation is needed. This can be done by asking participants, prior to a week of measurement, to provide their working schedule on which simulations could be conducted separately.Secondly, we relied on the accuracy of the GPs replies to the SMS text messages. Inaccurate reports may have biased the results. We believe this had only a limited impact as when we provided the respondents with an overview of their replies to the SMS text messages, we received only 10 to 20 emails with a few corrections. These were mainly regarding the type of activity which was not an issue in our analyses in this paper. Furthermore, 80% of all messages were replied to within 1 h which indicates a limited recall bias .A third limitation of the analyses is that we focused only on the sample needed for measuring the total working hours as this is an important indicator for health workforce planning. However, in many studies, the work or time-sampling technique is applied in order to gain insight into a share of various different activities, expressed in percentages , 8, 10. Finally, we used time-sampling data about GPs’ working hours obtained with an SMS tool that was assessed as a feasible and reliable technique. As we indicated in the introduction to this paper, different tools have been used in previous studies. These included beepers, PDAs or more recently smartphone apps –16. ThesIn an earlier study, we collected data on time use among Dutch GPs using a technique based on time sampling and an SMS tool. This appeared to be a valid method for measuring the number of hours GPs work each week and is an accessible and feasible research technique which can be applied to other target groups and countries. In the present paper, we have shown how the precision of the measurement of the hours worked by GPs each week varied according to the number of GPs included and the frequency of measurements per GP during the week measured. The best balance between both dimensions will depend upon different circumstances, among others the target group and the budget available.


This study reports the superlubricity between graphite and silica under ambient conditions, induced by the formation of multiple transferred graphene nanoflakes on the asperities of silica surfaces after the initial frictional sliding. The friction coefficient can be reduced to as low as 0.0003 with excellent robustness and is independent of the surface roughness, sliding velocities, and rotation angles. The superlubricity mechanism can be attributed to the extremely weak interaction and easy sliding between the transferred graphene nanoflakes and graphite in their incommensurate contact. This finding has important implications for developing approaches to achieve superlubricity of layered materials at the nanoscale by tribointeractions. Its lamellar structure and very weak van der Waals (vdW) interactions between atomic layers facilitate the sliding between adjacent layers, which is the origin of the superlubricity characteristics.] However, there exists a limitation that the superlubricity of graphite can only be achieved with some specific materials, such as layered materials (graphite or graphene) or inert metal (like gold) nanoparticles under very low load.] The friction force usually increases several times and even more if the sliding occurs between graphite and common materials (nonlayered).] To solve this limitation, a novel method was proposed to achieve the robust superlubricity between graphite and nonlayered material silica (silica was chose here because its probe is easily fabricated and widely used in nanotribology); that is, forming the multiple transferred GNFs on the asperities of the silica surface through the frictional sliding (presliding) on the graphite. This method provides the direct experimental evidence for the superlubricity between graphite and nonlayered materials via the tribointeractions. Therefore, in this study, the superlubricity behavior between graphite and silica achieved by this method was studied and its efficient lubrication mechanism was revealed at the nanoscale.22 probe  of these asperities were in the range of 50–80 nm, with a peak‐to‐peak distance of ≈30 nm. Meanwhile, a highly ordered pyrolytic graphite  substrate was freshly cleaved by using the adhesive tape to give a clean atomically flat surface. The frictional forces as functions of normal loads were measured on AFM, by driving the probe sliding on the freshly cleaved HOPG as the load was increased gradually, as shown in Figure The silica particle with a radius of 11.5 µm was first glued onto a rectangular tipless cantilever end by using epoxy glue, yielding a SiObe Figure1a. The2 at a load of 185 nN and a velocity of 20 µm s−1 continuously. After this initial sliding , the frictional force reduced suddenly to close to zero , there would appear friction peaks caused by the geometric effect,At the initial stage of measurement, the frictional forces maintained high values and exhibited a linear relation with the applied load. The friction coefficient (μ) was approximately μ = 0.012 ± 0.003, obtained from the slope of the linear fitting line to these points. It was observed that there was an offset frictional force when the applied load was zero, indicating that there exists a strong adhesive force between the probe and HOPG. Thereafter, the probe was compelled to slide on the HOPG with a scanning area of 10 × 10 µmFigure−1, confirming that the frictional force in the superlubricity regime is independent of the sliding velocity.Because the superlubricity of graphite can be greatly influenced by the sliding velocity, distance, and rotation angle, the relationship between the superlubricity behavior and these parameters was investigated, as shown in The scanning angle of the probe was varied from 0° to 120° to give different sliding orientations on the HOPG, and the frictional force was measured at an interval of 5°at a constant normal load of 185 nN  of the silica surface by the tribointeractions, which can create a beneficial condition for the significant reduction of frictional force.As there are only two kinds of materials (graphite and silica) in the superlubricity system, the interactions between graphite and silica during the presliding process play the key role in friction reduction. It is impossible to produce new materials by the tribochemical reaction between graphite and silica because this reaction requires very high temperature.Figure2 carbon bonds, sp3 carbon bonds, and O—C=O bonds, respectively, which is in accordance with the C 1s spectra of pristine graphene.ds) of the multiple layers was about ds = 0.38 nm, a little larger than that of pristine graphite (ds = 0.33 nm),To confirm this hypothesis, the topographies of the probe before and after the presliding were investigated by the field emission scanning electron microscope (FESEM), as shown in FigureR is the radius of the probe, A is the Hamaker constant that depends on the dielectric properties of the two surfaces, and D is the separation between two surfaces. By fitting the vdW force with Equation Fa = 70 ± 13 nN) were much lower than that in the high friction regime before presliding (Fa = 281 ± 23 nN), which indicates that the adhesive force between the probe and HOPG was significantly reduced during the presliding process. It is in accordance with the change in the offset frictional force (at zero load) in Figure 2, extracted from 100 normal force curves after the presliding. It was seen that all the adhesive forces maintained low values and varied slightly (<12%) over the entire measured region, indicating that the adhesive force after entering the superlubricity regime is independent of the contact positions of HOPG.The above frictional results and surface analysis of the probe indicate that it is highly likely to form the GNFs on the asperities of the silica surface after the presliding. In order to verify this further, the normal forces versus separation were measured before and after the presliding as the probe first approached HOPG and then detached from the HOPG, as shown in FigureFvdW=−AR6R is the radius of the probe, σ is the roughness of the probe, σ0 is the constant, and WAB is the dispersive work of adhesion per unit area of surface A in contact with surface B , which can be expressed by Equation γAd and γBd are the surface energies of surface A and B, respectively. In the case of silica and graphite, their surface energies have been measured at ambient conditions by many researchers, which gives the surface energy of graphite and silica as γgrad≈54.8 mJ m−2 and γsio2d≈600 mJ m−2.Wgra‐sio2 ≈ 363 mJ m−2. As the radius and roughness of the probe remained constant during the sliding process, the reduction in WAB is the only explanation for the significant reduction in the adhesive force after the presliding. In this case, the dispersive work of adhesion after the appearance of superlubricity (WAB–sup) can be obtained by the following equationFa and Fa–sup are the measured adhesive forces before and after the presliding. Based on Equation WAB–sup was calculated as WAB–sup ≈ 91 mJ m−2. Combined with Equation γsio2−supd≈38 mJ m−2, which becomes about one sixteenth of its original value. The value of γsio2−supd is consistent with the surface energy of graphene at ambient conditions,[[qv: 18a]] confirming that there are GNFs exfoliated from the outermost layer of graphite via the tribointeractions and transferred onto the asperities of the silica surface after the presliding  of asperities contact with HOPG in the entire contact zone can be estimated by the following equationFa is the adhesive force and r is the average radius of the asperities . This result also exhibits that the superlubricity can be achieved on the rough surfaces, which is different from the superlubricity state achieved by the two atomically smooth surfaces, such as graphite or MoS3In summary, our work has demonstrated that the superlubricity of graphite can be achieved by the formation of multiple transferred GNFs on the asperities of silica surfaces via the tribointeractions in the presliding process. The friction coefficient can reduce to as low as 0.0003 and remain very stable at a maximal local contact pressure of up to 700 MPa. The superlubricity state is independent of the sliding velocity, rotation angle, and surface roughness, which can be attributed to the extremely weak interaction and easy sliding between the transferred GNFs and graphite in their incommensurate contact. Our finding provides a possible method to achieve the robust superlubricity state of layered materials at the nanoscale by taking advantage of the tribointeractions that enables the transfer of 2D layered nanoflakes onto the opposite surface.4Frictional Force Microscopy Tests: The friction measurements were performed using the Asylum Research MFP‐3D AFM in contact mode. A rectangular tipless cantilever (TL‐CONT) with a normal spring constant of 0.02–0.77 N m−1 and a lateral spring constant of 0.01–0.1 N m−1 was used, and the silica particles  were glued onto the cantilever ends by using epoxy glue, yielding a SiO2 probe. Meanwhile, a HOPG  substrate was freshly cleaved by using the adhesive tape to give a clean atomically flat surface. The spring constant was determined by the frequency method,2 to 20 × 20 µm2 , and the scanning velocity was set in the range of 0.3–30 µm s−1. The presliding process was performed at an applied load of 185 nN, and a scanning velocity of 10 µm s−1. The scanning area was set to 10 × 10 µm2 on different positions, and the presliding was stopped when the frictional force was observed to have a significant reduction. The distance for the presliding was varied from 102 to 104 µm, which was dependent on the SiO2 probe. The frictional forces before and after the presliding process were determined from the difference in the lateral force detector signal in one complete friction loop (20 friction loops were averaged for every load) and the lateral detector sensitivity.Surface Characterization: The AFM image of the SiO2 probe was captured on the same AFM in tapping mode using a silicon tip array with a period of 3 µm. The topography of the SiO2 probe was measured on FESEM (HITACHI SU8220) under low voltage to protect the surface from damage. The TEM cross‐sectional sample was prepared by focused ion beam, picked out from the top of the probe. Cr film was first sputtered on the probe and Pt film was deposited subsequently as protective layers. The chemical composition on the top region of the probe (contact with HOPG) was measured by using XPS.Normal Force and Adhesive Force Measurement: The normal force curves were obtained as the probe first approached the HOPG substrate and then retracted from the substrate with a velocity of 400 nm s−1. The adhesive forces were obtained by measuring the pull‐off forces as the probe detached from the HOPG substrate. The adhesive force mapping was obtained by measuring the pull‐off forces at 100 sites (1 µm2 per site) in an area of 10 × 10 µm2.The authors declare no conflict of interest.SupplementaryClick here for additional data file.


We used an individual‐based simulation model to examine the role of phenotypic plasticity on persistence and adaptation to two patterns of environmental variation, a single, abrupt step change and continual, linear change. Our model tested the assumptions and predictions of the theory of genetic assimilation, explored the evolutionary dynamics of the Baldwin effect, and provided expectations for the evolutionary response to climate change. We found that genetic assimilation as originally postulated is not likely to occur because the replacement of plasticity by fixed genetic effects takes much longer than the environment is likely to remain stable. On the other hand, trait plasticity as an enhancement to continual evolutionary change may be an important evolutionary mechanism as long as plasticity has little or no costs. Whether or not plasticity helps or hinders evolutionary rescue following a step change in the environment depends on whether plasticity is costly. For linear environmental change, noncostly plasticity always decreases extinction rates, while costly plasticity can create a fitness drag and increase the chance of extinction. Thus, with changing climates plasticity can enhance adaptation and prevent extinction under some conditions, but not others. Environmental change can take many forms, such as variability around a central value without any directional trend, a one‐time, abrupt shift in the environment, or a continual, directional change in the central value that may or may not also include nondirectional change around that central value. In this study, we focus on two simple patterns—a single, abrupt shift and continual, linear change—that for convenience we refer to as “step change” and “continual change.” Although environmental heterogeneity in nature is generally more complex, our exploration through simulation models considers each of these simple types of change alone so as to isolate salient patterns of adaptation. While environmental heterogeneity has always been a factor in evolution, our analyzes take on increased urgency in the face of large, human‐induced environmental shifts, including global warming, which continues to move our world into novel patterns of selection and demographic risk for many species.Changes in the mean traits exhibited by a population in response to a shift in optimal trait values can include two components: changes in genes that have a fixed effect on phenotype and a plastic change in the phenotype. Often these are posited as alternative responses, but they can occur together  formalize the assumptions and test the verbal predictions of the theory of genetic assimilation, (2) explore the evolutionary dynamics of the Baldwin effect, and (3) indicate how those models might inform our expectations for the evolutionary response to climate change, including evolutionary rescue (or not), and what we would need to measure to use that information for management purposes. Considering the first goal, genetic assimilation, and related theories make the following assumptions. A population in a stable environment has some sort of unexpressed plastic capacity in trait expression. That trait plasticity gets expressed following a step change in the environment to a new stable environment. Following that change, the plastic capacity in trait expression is selected to disappear. We tested these predictions with a series of comparisons: a starting population with no initial mean plasticity versus one with initial plasticity, and plasticity being costly or having limitations versus having no cost or limitations, each for a range of magnitudes of the step change. The test consists of examining: the probability of the population surviving the change, the rate of the evolutionary response, whether the evolutionary response is primarily due to changes in plastic or nonplastic loci, and the pattern of change in the genetic variation of those loci.To address the second goal, in addition to exploring the effects of a step change in the environment, we also examined the effects of continual change, the Baldwin effect. The same types of conditions were compared, except that differences in the rate of environmental change were considered instead of differences in the magnitude of the step change. We only explored the effects of a cost of plasticity, not limitations. The latter will be included in a future study. For response variables, we also consider the extent to which the mean phenotype of the population lagged behind the optimal phenotype.Our two scenarios—a stable environment before and after a step change and steady continual change—are meant to bracket real‐world patterns of environmental change. Long‐term, directional environmental change is almost never unidirectional. It always consists of some average trend imposed upon change that varies in rate and direction. The environment is always varying even if there is no directional change. And a step change‐like response could occur during a directional change in the environment if there was a period of relatively slow change followed by a sudden, rapid change and then additional slow change.Thus with regard to our third goal, predicting and managing the effects of climate change, our models do not make specific predictions about any single system. Rather, they indicate when phenotypic plasticity might or might not play an important role in nature's response to coming changes. They tell us when it might behoove us to measure trait plasticity and the costs of that plasticity, given expectations about the rate and pattern of environmental change. Armed with that information, more targeted models can then be developed  that determines its juvenile survival (which is when selection takes place).We used an individual‐based model (implemented in Fortran 90) to simulate the effects of phenotypic plasticity on environmental rescue in response to an environmental change that happens either once (a step change) or continuously (a linear change). The model is based on that of Bürger and Lynch , to whic2.1Tij of the ith individual developing in generation j is given by: Nijk are allelic values at the n nonplastic loci, and zij is a zero‐mean, unit‐variance independent Gaussian random deviate (the random component of phenotype); these are the components of the original model of Bürger and Lynch  with an intercept of a  and a slope (d) equal to the product of parameter b and the sum of plastic allelic values. The plasticity parameter (b) determines the magnitude of the plastic response by the phenotype for a given genetic value, scaling the phenotypic variation due to plasticity relative to the variation due to the nonplastic alleles. In the starting environment (until generation = 0) the value of Ej = 0, so that the phenotypic value is due only to the nonplastic alleles.In our model, an organism's total phenotype is the sum of three components: contributions to the phenotype due to nonplastic loci, contributions due to plastic loci that interact with the environment, and a random component. The phenotype nd Lynch . The mid2.2Wij for the ith individual in generation j) that was a Gaussian function of the difference between the individual's phenotype and an optimum phenotype for its environment : Wij and fecundity. The survival probability was 1 for an individual with trait Tij equal to the optimum Topt,j, and decreased as the difference between Tij and Topt,j increased. The effective selection was stabilizing when the population mean trait value was near the optimum, and directional when the mean was far from the optimum. We scaled the optimum phenotype so that Topt,j = Ej, assuming that the environments at the times of development and selection in any generation were the same .Selection occurred during survival from juvenile to adult, which had a probability  the cost of plasticity. This cost of plasticity was independent of allelic expression; even when plasticity was not expressed , the plasticity loci still had an effect on fitness. An example of such an independent cost would be maintaining additional cellular or organismal machinery needed to translate an environmental signal into a phenotypic change. Alternative forms of cost could be either a fixed cost, given the existence of any nonzero plastic alleles, or a cost that scales with the phenotypic expression of the plastic alleles, not just their genotypic values. We consider the implications of these alternatives in the Discussion.To this basic model we added either a cost of or a limitation to plasticity. To model a cost, we modified the survival function by allowing stabilizing selection on the sum of the plasticity alleles around 0  as in Chevin and Lande . Adding To model a limitation, we introduced developmental noise in the effect of plasticity on the phenotype by adding a second variable that randomly altered the phenotype. The magnitude of this noise was linked to the expression of the plasticity alleles: yij is a zero‐mean, unit‐variance independent Gaussian random deviate and s scales the amount of developmental noise. In other words, plasticity was pleiotropically related to a portion of the developmental noise. This term could include random differences in the microenvironments in which individuals develop or in effects of the environment on expression of the plastic loci, and random variation in the processes initiated or influenced by the plastic loci. Throughout the rest of the paper, we refer to this portion as “developmental noise” recognizing that the zij term is accounting for the other portion . This new term operationalizes Waddington's  to act as females. μ, μ being the per‐locus mutation rate. If a mutation occurred, a random locus was selected, and a zero‐mean Gaussian with variance α2 was added to the previous allelic value; the mutation rate and variance for plastic and nonplastic alleles were the same. After the alleles of each offspring were determined, the random component of its phenotype was chosen. Because the plasticity parameter (b) determines how genetic variation gets translated into phenotypic variation, a greater value means that the same mutational change has a greater phenotypic effect. That is, the plasticity parameter is proportional to the rate of new plastically determined phenotypic variation.During reproduction, there was free recombination. Allelic values could take on any real value. Each offspring haplotype mutated with probability ; we used the stochastic house‐of‐cards variance in Bürger and Lynch ] needed to increase the mean relative plasticity to the desired value. This procedure resulted in all simulations having the same initial genetic variance in plasticity alleles.We investigated two different starting conditions for plasticity, a mean relative plasticity of the population at 0.0 and at 0.2. Because the environment was constant during the equilibration period, there was no benefit to plasticity and the cost of plasticity created stabilizing selection on those loci resulting in a mean plasticity of approximately 0.0. For simulations with a nonzero (0.2) initial mean plasticity, we used a procedure that was equivalent to simply adding to each plastic allele at the end of equilibration the constant amount [0.2/ For a step change, the amount of change varied from 2 to 4 times the width of the fitness function (ω); for continual change, the total amount of change varied from 20 to 500 times the width of the fitness function, depending on the rate of change. For a step change, the simulation was continued for 500 generations; for continual change it continued for 1,000 generations. These periods were chosen because (1) for a step change, in 500 generations all populations either went extinct or adapted, and the long‐term trends were apparent in the response parameters for the surviving populations, or (2) for continual change, it is highly unlikely that a continuous, steady change would persist for longer than that period. For continual change, in our model the phenotypic response of a plastic individual will get larger, even if there are no additional genetic changes, because of the change in the environmental inducer. Thus, we assumed that there were no intrinsic morphological, physiological, or developmental limits to the plastic response.2.7Topt,j, so that a perfectly adapted population has a relative phenotype of 1.0. Its relative plasticity is the mean plastic component of phenotype [the middle term on the right side of Equation Topt,j, which is a measure of the contribution of the plastic alleles to adaption . A population with a relative plasticity of 1.0 can remain at a changing optimal phenotype without any evolution of the nonplastic alleles because the middle term of Equation Topt,j = Ej.Our results are presented in terms of relative phenotype and relative plasticity, which are values of mean phenotype and plasticity normalized to the optimum phenotype. The relative phenotype for a population is therefore its mean phenotype divided by the optimum phenotype b, and the degree of change of the environment. To examine the cost of plasticity, we set c to 0 or 1; for simulations with a cost there was no developmental noise (s = 0). When both b = 0 and c = 0, our model matches previous models without plasticity and serve as a baseline for comparison. For parameter values of b = 0 and c = 1, the plasticity loci incur a fitness cost but never affect trait values and serve as an indicator of just the cost effect. For each parameter set, 1,000 replicates were run, and the probability of persistence was the fraction of such populations that were not extinct after a specified period .We examined the effects of a cost of plasticity for both types of environmental change. For each we varied the initial average relative plasticity (0 or 0.2), the plasticity parameter s), set the plasticity parameter (b) to 0.6, and set the cost of plasticity to 0. As above, we varied the initial average relative plasticity (0 or 0.2), the plasticity parameter b, and the degree of change of the environment, and ran 1,000 replicates for each parameter set.We examined the effects of a limitation on plasticity only for a step change. We varied the developmental noise parameter , and variance of mutation size α2 = 0.05. For each parameter set, at each generation we recorded the relative phenotype, relative plasticity, the variance of the phenotype, the genetic variances and covariance of the plastic and nonplastic components of the phenotype , and the fraction of populations that survived to that generation. These variables (except the last) were averaged over all populations that survived to the end of the simulation. In the results, we show final values of these quantities and, in some cases, their time courses. As a test of the effects of initial population size, for the step change and no initial mean plasticity, we also performed simulations with and without plasticity costs for K = 64 and K = 1,024, and found very similar patterns to those reported here (results not shown).For all simulation, the other parameters were as follows: maximum population size 33.1Following a step change in the environment, the probability of population survival decreased with the size of the step change, unless the change was small enough that all populations survived or large enough that none survived Figure . If a pob = 0). Increasing the average initial plasticity caused a large increase in survival  increased the probability of survival  was large or developmental noise was low  had a simple relationship to the size of the step change and the plasticity parameter, but it had a complex temporal dynamic. After 500 generations, when plasticity was not costly or linked to developmental noise, the amount of genetic variation decreased with the size of the step change and the magnitude of the plasticity parameter Figure a. When pd Figure a. If thed Figure a,b and ad Figure a. The reb. In later generations, however, for small parameters the second increase in variation was much less with plasticity costs than without. For the genetic variation due to the nonplastic loci, the pattern was yet more complex with a similar threefold to fourfold change in magnitude , survival occurred only at low rates of change Figure a,b. Plasb = 0) because the cost of plasticity outweighed the benefit. As the plasticity parameter increased, survival increased, becoming greater than without plasticity at b = 0.6, because now the benefit was greater than the cost.As with a step change, when plasticity was not costly the probability of survival increased as the plasticity parameter increased  and decreased with a greater rate of environmental change. Unlike the step change case, when plasticity was costly the probability of survival was not monotonic with the plasticity parameter Figure b. At theb = 0.1 where survival was lower with initial plasticity again because the costs outweighed the benefits.One general difference from a step change was that with continual change the initial amount of plasticity was less important, as might be expected. In the absence of a cost of plasticity, having plasticity in the initial generation increased the probability of survival Figure a; when pb = 0.1–0.3), those extinctions occurred before substantial plasticity evolved  plasticity variation to increase unconstrained.The requirement for plasticity to be costly or be linked to developmental noise adds another burden to the theory. In those cases, plasticity can be maintained in the initial population only through mutation. For the purposes of our model, we set the mutation rate to a relatively high value. The only estimate of the mutation rate for trait plasticity that we are aware of is that of Latta et al.  for morpFor trait plasticity to be replaced by fixed genetic effects there needs to be strong selection against plasticity. In the model of Lande , plasticCaenorhabditis remanei survival in response to heat shock  of the reaction norm. Instead, evolution might have occurred on the elevation of the reaction norm, in our parlance selection on the nonplastic loci. Only by measuring the reaction norm over multiple environments, including those intermediate to and outside the range of the two selective environments, can the evolution of reaction norm on a threshold response be assessed.We are not aware of any demonstration of the process of genetic assimilation in a natural population. By this, we mean a strict interpretation of Waddington's theory entailing a step change between two stable environments. The closest to a demonstration that we are aware of are the papers of Aubret and Shine , 2010 anThus, despite the wide acceptance of genetic assimilation as a mechanism as evidenced by the hundreds of times that Waddington  has beenAlso worth noting in the results , it always helps evolutionary rescue Figure a,c, espeFor continual environmental change, the evolutionary process is somewhat different than that for evolutionary rescue following an abrupt change. With evolutionary rescue after a step change there is an initial period of maladaptation and a decline in population size until adaptive evolution leads to positive population growth. With continual change, the population may initially be reasonably well adapted to the environment, but as the magnitude of the change becomes greater, maladaptation increases as the population trait value lags behind the moving optimum. Our base model without plasticity resulted in 100% extinction at relatively low rates of environmental change Figure a,b, consThus, for the two types of changes – step and continual – the magnitude of environmental change had opposite effects in combination with plasticity costs. For a step change, a greater one‐time change meant that the benefits of plasticity outweighed its costs. For continual change, a greater rate of change increased the fitness drag due to plasticity costs. How these two cost effects might play out for more complicated patterns of environmental change is unclear.4.4Changes in the global climate, along with other human‐caused environmental alterations, are having profound effects on Earth's biota. One class of effects is changes in patterns of trait selection. Many questions have been raised about what sorts of evolutionary responses will occur (Hoffmann & Sgrò, The environment is changing, but that change varies in both rate and direction. Nor is there a simple, linear relationship between a change in the environment and a change in optimal trait value. We need information on likely patterns of environmental change and how they will affect trait plasticities and fitness, meaning that all components of the process must be carefully measured. Our model did not consider variation in the rate or direction of change. Such variation can increase selection for plasticity, but that result strongly depends on the pattern of variation (Scheiner, A key parameter in our model was whether plasticity was costly. There is little evidence for plasticity costs in multicellular eukaryotes (Murren et al., 4.5We can study the process of adaptation to environmental heterogeneity at two levels that of the entire organism and that of individual traits. In advocating for the importance of phenotypic plasticity in evolution, Bradshaw  distinguOur model considered selection on a single trait. But the environmental tolerance of an organism results from the interactions of all parts of the phenotype, interactions which might themselves depend upon environmental conditions. Such interactions might be important for long‐term patterns of adaption. Plasticities of different traits can be genetically correlated (e.g., Scheiner et al., All authors contributed to the development of the ideas and the writing of the manuscript. The models were coded and run by MB.None declared.


The shallow incidence angles used in GISAXS lead to a very large footprint of the X-ray beam on the sample. Here it is shown that, despite these large footprints, GISAXS measurements of targets with sizes down to 4 µm × 4 µm are possible. e.g. for characterization of metrology fields in the semiconductor industry, where up to now it has been considered impossible to use this method due to the large beam footprint.Grazing-incidence small-angle X-ray scattering (GISAXS) is often used as a versatile tool for the contactless and destruction-free investigation of nanostructured surfaces. However, due to the shallow incidence angles, the footprint of the X-ray beam is significantly elongated, limiting GISAXS to samples with typical target lengths of several millimetres. For many potential applications, the production of large target areas is impractical, and the targets are surrounded by structured areas. Because the beam footprint is larger than the targets, the surrounding structures contribute parasitic scattering, burying the target signal. In this paper, GISAXS measurements of isolated as well as surrounded grating targets in Si substrates with line lengths from 50 µm down to 4 µm are presented. For the isolated grating targets, the changes in the scattering patterns due to the reduced target length are explained. For the surrounded grating targets, the scattering signal of a 15 µm × 15 µm target grating structure is separated from the scattering signal of 100 µm × 100 µm nanostructured surroundings by producing the target with a different orientation with respect to the predominant direction of the surrounding structures. As virtually all lithographically produced nanostructures have a predominant direction, the described technique allows GISAXS to be applied in a range of applications,  We explain the length-dependent changes in the scattering patterns using the theory for slit diffraction. For the measurement of targets surrounded by other nanostructures, we produce the grating targets with a different direction with respect to the predominant direction of their surroundings. This allows us to separate the scattering signal of the targets from the signal of the surroundings by aligning the incident X-ray beam to the target.2.et al., 1989x–y-plane is the sample plane and the x-axis lies in the scattering plane, with the z-axis perpendicular to the sample plane. In this coordinate system, the scattering vector The measurement geometry of GISAXS ] lying parallel to the reciprocal a). The intersection of the GTRs and the Ewald sphere is a series of grating diffraction orders on a semicircle, evenly spaced in p. If the grating is rotated in the sample plane by the angle φ such that the grating lines are no longer parallel to the x-axis, the GTR plane is rotated around the et al., 2001The diffraction of gratings in GISAXS geometry can be described as the intersection of the reciprocal-space representation of the grating and the Ewald sphere of elastic scattering (Mikulík supporting information for the derivation) p.Using the same construction as Yan & Gibaud 2007, but in 3.3.1.6 and C4F8 and resist stripping with an oxygen plasma treatment  is maintained.The experiments were conducted at the four-crystal monochromator (FCM) beamline , we obtain scattering patterns of all targets. Measurements for all targets were taken at For the measurements of the very small targets in GISAXS, we need to consider how much of the incoming X-ray beam can interact with the measured target. Due to the shallow incidence angle, the beam footprint on the sample is enlarged by abcl and is due to the size and divergence of the incoming X-ray beam. Additional scattering peaks visible in Fig. 2(a)et al., 2014bWhile the scattering from the longest grating Fig. 2a shows shx-direction. The finite length enlarges the grating truncation rods in I after diffraction on a single slit is  and 4(c)a)a) and 4(b)l very well. Form and width of the main peak are identical for the theoretical description in comparison with the measured data, and the relative magnitude and position of the side lobes agree satisfactorily up to the high background in the measured data. In contrast, the theoretical description and measured scattering do not match for the shorter lengths; in particular, for bb)et al., 2016et al., 2017h. For the nominal line height of c)We have extracted the FWHM peak width as shown in Figs. 4 of the target with respect to the surroundings, which would lead to a separation in p is not very high, and for surroundings with multiple dominant length scales it might be difficult to find a suitable p for the target. Therefore, it is advantageous to rotate the target in the sample plane with respect to the surroundings, which leads to a separation of the scattering in In most cases, small targets are not isolated on a blank wafer. Therefore, it is essential to separate the parasitic scattering of the surroundings from the scattering of the target structure. Assuming incoherent addition, we can separate the scattering by describing the individual contributions. One way to separate the scattering of the target and the surroundings if both the target and the surroundings are oriented internally would be a variation of the dominant length scale  for both targets and all energies are shown in Fig. 7z-direction. The distance between the peaks is about −1, which roughly corresponds to the nominal line height of z. Comparing the measurements for the two targets with different line widths, et al., 2016et al., 2017We measured target GISAXS patterns (φ = 0°) at photon energies from 6.et al., 2007We have shown that even with millimetre-sized beams, which are available at many synchrotron and laboratory-based X-ray sources, micrometre-sized targets can be measured. The minimum target sizes which were investigated are an order of magnitude smaller than the smallest micro-beam footprints which have been used in GISAXS experiments so far . DOI: