Reducing the smoking population is still high on the policy agenda, as smoking leads to many preventable diseases, such as lung cancer, heart disease, diabetes, and more. In Austria, data on smoking prevalence only exists at the federal state level. This provides an interesting overview about the current health situation, but for regional planning authorities these data are often insufficient as they can hide pockets of high and low smoking prevalence in certain municipalities.This paper presents a spatial–temporal change of estimated smokers for municipalities from 2001 and 2011. A synthetic dataset of smokers is built by combining individual large-scale survey data and small area census data using a deterministic spatial microsimulation approach. Statistical analysis, including chi-square test and binary logistic regression, are applied to find the best variables for the simulation model and to validate its results.As no easy-to-use spatial microsimulation software for non-programmers is available yet, a flexible web-based spatial microsimulation application for health decision support  has been developed and used for these analyses. The results of the simulation show in general a decrease of smoking prevalence within municipalities between 2001 and 2011 and differences within areas are identified. These results are especially valuable to policy decision makers for future planning strategies.smokeSALUD to model the spatial–temporal changes in the smoking population in Austria between 2001 and 2011. This is important as no data on smoking exists at this geographical scale . However, spatial microsimulation models are useful tools to estimate small area health data and to overcome these problems. The simulations and analysis should support health decision makers to identify hot spots of smokers and this should help to show where to spend health resources best in order to reduce health inequalities.This case study shows the application of  Smoking is directly responsible for many diseases, sometimes leading to death (worldwide this figure is estimated to be around 10 %). In addition, passive smokers are at high risk of also developing smoking-related diseases –4, but iThis paper focuses on the topic of smoking because smoking is a major risk factor for poor health and premature mortality. As it is based on a poor lifestyle choice, it is in theory preventable. For effective preventive actions at the regional level, it is important to know where high numbers of smokers live and whether significant variations exist in such rates between municipalities. Recent Organisation for Economic Co-operation and Development (OECD) statistics show that 23.2 % of the adult population smoke regularly in Austria, which is 2.2 % above the average across all 41 OECD countries .The demographic and socio-economic changes between 2001 and 2011 are shown by the census and registered-based census, respectively. According to Statistics Austria, the population count in 2015 was 8,584,926, which is an increase of 209,762 persons (2.4 %) when compared to the population count in 2011. Taking a closer look at population change between 2001 and 2011, there was an increase of 4.2 %  which was mainly driven by immigration and less by an increase of births over deaths. Out of the nine provinces in Austria, only one province (Carinthia) saw a population decline (2853 persons or 0.5 %). In contrast, population increase was seen across all other Austrian regions. Vienna had the highest increase with 8.7 % , followed by Vorarlberg with 5.2 %  and Tyrol with 5.1 % . An increase in people aged 25–65 with a tertiary qualification was apparent, especially in the age group 27–36 (7.0 %). There was an increase of 2.4 % for the age group 0–19 years; an increase of only 0.1 % for the age group 20–64 years; but an increase of 2.2 % for the age group 65 and older [smokeSALUD package is constructed using a deterministic reweighting spatial microsimulation methodology and implemented in a web-based software application called simSALUD,smokeSALUD the aim is to explore the spatial variations in smoking at the municipality level at two different points in time, i.e. 2001 and 2011. This information is highly valuable for health policy decision makers to help to understand whether government smoking prevention strategies appear to be working or not. Austria is one of the last countries that will implement a full smoking ban for cigarettes and e-cigarettes in public places from May 2018. So far, there has only been a partial implementation: dividing smoking and non-smoking rooms in bars and restaurants which has caused severe reconstruction costs for many owners in the food and drink industry. Austria also scores lowest on a tobacco control scale in 2007, 2010 and 2013, as was shown by [The aim of this paper is to estimate changes in smoking prevalence at the municipality level between 2001 and 2011 based on population change in Austria. For this purpose, the smokeSALUD is a static model designed to match large scale survey and small area census data based on common key constraints that are most likely to predict the variable of interest; in this case the smoking population. The process can be seen as a form of cloning exercise, where persons from the survey are matched to each small area, in our study the municipality, based on the selected key constraints. A reweighting algorithm thus calculates how well a person with certain characteristics fits the characteristics of persons known to live in a certain small area [Spatial microsimulation models have been built since the 1980s and there are different methods for building such models, including deterministic and probabilistic approaches . There aall area , 13. GivThe structure of the model process is shown in Fig. Three datasets are relevant for this case study. The first dataset is the Austrian Health Interview Survey (AHIS) for 2006/07 which holds variables for demographic, socio-economic and health related information of 15,474 individuals aged 15 or above at the federal state level. The dataset also includes the variable “number of daily smokers”, which is the health variable of interest and (for each person) a weight to compensate for the bias of the survey that corresponds to the total population. The second dataset is the 2001 census for municipalities and the third dataset is the registered-based 2011 census for municipalities. Both census datasets (2001 and 2011) have demographic and socio-economic information concerning the Austrian population but no health related data is included. There are 2379 municipalities in Austria and the 2001 census showed a population of 6,679,444 (people 15 years and over) and the 2011 registered-based census recorded a population of 7,174,250 persons (people 15 years and over). In this first step all datasets are tested for completeness and data cleaning is conducted if required.Statistical analyses prior to building a spatial simulation model are important in order to identify the best predictors (i.e. characteristics of a person) of the variable being estimated—in this case the number of smokers. For this study, the chi-square test, regression analysis and t-test are applied within the statistics software IBM SPSS Statistics 21.0. In addition, an extensive literature review on the influences and characteristics of smokers was undertaken. This is necessary because creating synthetic microdata requires linking datasets based on common variables, but those variables must also be important for estimating the key ‘missing data’. For a detailed discussion of the role of the constraint variables and the choice of constraints in microsimulation see , 15, 16.The chi-square method is chosen because it can be measured at an ordinal or nominal level . Calculating a statistical correlation method is not possible because this would require measuring both variables at the interval or ratio level  which is not the case for this study. However, chi-square is used to find a possible relationship between two categorical variables. The measurement parameters for Phi and Cramer’s V, which vary between 0 and 1, show the same value for all variables. The closer the value is to 1, the stronger is the relationship between the dependent and independent variable. The binary logistic regression is used to predict the probability that an observation falls into one of two categories of a dependent variable, based on one or more independent variables that can be either continuous or categorical. The output also calculates the Cox & Snell R-square and Nagelkerke R-square values, which are both methods of calculating the explained variation. Another statistical test applied is the independent samples t-test that compares the means between two unrelated groups on the same continuous, dependent variable. For example, it can be used to understand whether education level differs between smokers and non-smokers.Tables The explained variation through the binary logistic regression test ranges from 7.7 to 11.8 %. The results for each sub-constraint shown in Table Further, the t-test results verify the importance of the constraint “education” (i.e. the highest level of education) and “age” seen in the binary logistic regression. All other constraints are not applicable for the t-test because the dependent variable needs to be measured on a continuous scale . In this study, the level of education ranges from “university degree” to “no A-level degree”, whereas the independent variable “daily smokers”, consist of two groups: “daily smokers” and “never or never smoked daily”. Results from the t-test show that daily smokers are statistically significant for lower educated (2.80 ± 0.476) compared to “never or never smoked daily people” (2.71 ± 0.585). Further the study found that daily smokers are statistically significant for younger persons (5.62 ± 2.88) compared to people who “never” or “never smoked daily” (7.20 ± 3.36).The census dataset from 2001 and the register-based census dataset from 2011 include demographic and socio-economic variables for people aged 15 and above at the municipality level, but no health related data. As mentioned above, these constraints must be available in both datasets at the municipality level, as well as comparable with the survey dataset so that the deterministic reweighting methodology can be applied and the output gained from the model will be as accurate as possible . Table 3For our final model smokeSALUD five constraint variables consisting of 23 sub-constraints . After finishing the validation run the user can also either save the results as a zip file for further analyses or visualize the results immediately in the application (or transfer to a common GIS package). Additionally the user can start a new simulation and validation by changing the number of constraints to see the influence that each constraint can have on the simulated results.The simulation and validation outputs can be visualized in the form of a map Fig.  and/or bThe spatial–temporal analysis estimates the change of smokers in Austria from 2001 and 2011. The following two subsections describe the model validation results, as well as the estimated smoking prevalence illustrated as a map.Model 1 (matching the 2001 census data with the AHIS 2006/07) and model 2 (matching the 2011 registered-based census data with the AHIS 2006/07) are validated using internal statistical tests. Table  The linear regression analyses for all constraint variables show a good fit, as an ideal fit between the simulated and census data would show a coefficient of determination very close to 1. This analysis indicates a very high coefficient of determination for all variables (0.96–0.99) for 2001 and 2011. The lowest value (with 0.96) is seen for the sub-constraints “widowed” and “age 65 above”. The variable “married” has a high coefficient for 2001  also fits well and the results are robust.After running the simulation model for 2001, smoking rates between 19.0 and 31.6 % were estimated and for 2011, between 14.0 and 31.2 %   and therefore restrictions have to be accepted. The reasons for the mismatch might include the change in the survey method (from paper survey to electronic registered-based survey). However, Statistics Austria plans that in future the registered-based census for certain variables will be published annually, which will be an advantage for future models. Also the forthcoming AHIS will provide further interesting results in terms of changes in the size of the smoking population.A limitation of the smokeSALUD were conducted. Also experiments with the sub-constraints were undertaken and it was found that different age groups did not have a great impact and therefore all eleven age groups were modelled. It is important to use variables that are very strong predictors and significantly correlated with the variable being estimated. Unfortunately the number of census constraints is limited in Austria: for instance, income could be an important predictor variable, but this data is available in the health survey data only and not in the census data, and is therefore not suitable to include in the model.This study also found that the choice and number of constraint variables strongly impact the simulation results for the currently implemented static deterministic reweighting approaches. The advantage of such approach is that the impact of changes relating to input variables can be immediately measured, as it is a deterministic approach. For example, does the constraint variable “nationality” have a positive or negative influence on the model output? Therefore, several tests to find the optimal model of The model results could also benefit from additional external model validation, in addition to internal validation. Nationwide, there is no data on smoking prevalence for municipalities available, but alternatives could include carrying out a survey for some municipalities and potentially adjusting the model based on the results. Also, there might exist such data within an independent governmental survey for a particular region in Austria. However, the availability of such surveys is not known to the authors.In spatial modelling, the modified area unit problem (MAUP) is a commonly discussed issue, as it can affect the outcome depending on the spatial unit chosen. The advantage of spatial microsimulation modelling is to work with individual data that will be matched to the chosen small area level unit based on common constraints. This means that individuals that have the same constraints are allocated to the small areas. The MAUP therefore have very little effect in this case .In an international context, the application simSALUD is freely available to anyone and this means people from all over the world can access or install it on their machines. Further, simSALUD is not limited to health studies only, as the underlying algorithms can be applied in other disciplines, such as economics or environmental science. A main advantage of simSALUD for smoking is that it offers a framework for testing the impact of smoking policies in different parts of the world. Using simSALUD policy makers could estimate smoking rates prior to the implementation of any policy and then again some years after its introduction. Although policy makers will know national responses to the policy  they can use simSALUD to estimate small-area changes and hence allow them to rethink strategies in areas which seemed to have resisted change the most. For these regions other policies may be more appropriate, such as increasing the price of tobacco or adding more stop-smoking clinics. Thus, it is hoped that simSALUD can be implemented worldwide in the future and not just used for Austrian data. For example, simSALUD is currently being tested in New Zealand using New Zealand census and health survey data.Regarding policy, spatial microsimulation is very powerful as it allows to spatially model ‘what-if’ scenarios to identify the impact that certain interventions could have on certain population groups. Also important is the identification of areas most likely to expect highest and lowest impact of a specific intervention. An interesting future research project would be to take successfully proven interventions in other countries and apply these changes in a host country using simSALUD. For example what is the impact on the number of smokers when raising the legal age of purchasing cigarettes from 16 to 18 years and which areas would benefit most and least from this intervention (based on a region’s age profile)? Further steps could then be to link this analysis to economic factors to identify the impact of the costs that this intervention involves in relation to the number of smokers quitting . The latter is especially interesting in identifying most beneficial interventions given available public health budgets. simSALUD not only allows us to specify particular population groups that can be modelled, for example less educated women in the age of 16–24 who are regular smokers, but also to target specific regions that are of high concern of the government, especially in terms of reducing health inequalities.smokeSALUD for modelling the spatial–temporal changes in the smoking population in Austria between 2001 and 2011. This is important as Austria has one of the highest smoking rates in Europe and no data on smoking exists at the municipality level. Policy makers can benefit from such data and spatial analysis in the future to help target specific areas of high need and hence try and reduce smoking prevalence. To build the model a deterministic reweighting algorithm was used that was implemented within the application simSALUD. This spatial simulation model matched data from the AHIS 2006/07 and the census and registered-based census data for the years 2001 and 2011 respectively. Results showed that there was a slight decrease in smoking rates of 0.6 % between the decades. This decline is thought to have been driven by the high increase (40 %) of those in tertiary education who are less likely to smoke and by the aging population, as older people are less likely to smoke. In particular, the province of Salzburg shows the highest decrease (1.6 %) of the smoking population whereas some municipalities in Tyrol show the highest increase. Not much change was seen in the existing west-east divide of the smoking prevalence. Regarding absolute numbers of smokers, all major cities have highest numbers in comparison to rural areas. This can be explained because of the high population size and contributes less to other factors. The findings of the study identified areas with slight and moderate increase of smoking prevalence and more research is needed to explore possible reasons for the increase, other than an increase in higher educated and elderly people. The model was validated using the statistical tests, the PSAE, logistic regression and the t-test, where the input constraints (census data) were compared with the simulated constraints. All three tests showed (for each model) acceptable and very good values (e.g.: high coefficients of determination) so that we can be confident that our model is robust.This case study shows the application of The results presented in this paper are also being presented and discussed with various governmental health departments in Austria to highlight the importance of health data at the municipality level and the advantage of integrating this modelling algorithm into simSALUD. This package can help to support health care planners to identify variations in smoking rates within small areas, as such data is currently not available in health surveys. Further collaborative investigations could explore possible additional reasons for higher and lower smoking rates in certain municipalities. In addition, current policy initiatives around smoking prevention could be analysed and what-if scenarios for future modelling could be defined so that specific population groups are targeted. Possible links to the location of stop smoking services are of high interest: for instance, ‘how many smokers reside within a certain distance of stop smoking services?’ Where would be the optimal set of locations for the provision of such services? Non-spatial initiatives, for example increasing cigarettes prices, could also be tested to see if these would be effective, especially in localities with lower income residents (using any data which might be a good proxy for income)? see also , 26. Suc


When animal behavior is studied in a laboratory environment, the animals are often extensively trained to shape their behavior. A crucial question is whether the behavior observed after training is part of the natural repertoire of the animal or represents an outlier in the animal’s natural capabilities. This can be investigated by assessing the extent to which the target behavior is manifested during the initial stages of training and the time course of learning. We explored this issue by examining smooth pursuit eye movements in monkeys naïve to smooth pursuit tasks. We recorded the eye movements of monkeys from the 1st days of training on a step-ramp paradigm. We used bright spots, monkey pictures and scrambled versions of the pictures as moving targets. We found that during the initial stages of training, the pursuit initiation was largest for the monkey pictures and in some direction conditions close to target velocity. When the pursuit initiation was large, the monkeys mostly continued to track the target with smooth pursuit movements while correcting for displacement errors with small saccades. Two weeks of training increased the pursuit eye velocity in all stimulus conditions, whereas further extensive training enhanced pursuit slightly more. The training decreased the coefficient of variation of the eye velocity. Anisotropies that grade pursuit across directions were observed from the 1st day of training and mostly persisted across training. Thus, smooth pursuit in the step-ramp paradigm appears to be part of the natural repertoire of monkeys’ behavior and training adjusts monkeys’ natural predisposed behavior. Studying any behavior in the lab creates a conflict between the need to control behavior precisely and the advantages of observing natural behavior. Field studies reveal a great deal about natural tendencies but make it difficult to standardize experiments, manipulate the environment and measure behavior accurately. On the other hand, training animals in the lab on a very specific task with associated specific demands may recruit specialized mechanisms that might not generalize to other environments. The conundrum between natural and restricted environments is especially critical in neuroscience where the goal is to probe the neural basis of behavior. Recording neural activity imposes strong constraints on the experimental environment. For example, in many studies the head is restrained to record neural activity at high temporal and spatial resolution . Thus, nThe rationale for studying the neural basis of behavior in animals is to be able to observe and deduce principles that generalize within and across species . UltimatWe used the smooth pursuit eye movement system to study how monkeys learn to track moving targets in a lab setup. The eye movement generally  and the Recent studies have shown that in the initial phase of training, the smooth eye movements are small and that across weeks of training monkeys’ performance improves markedly. We monitored the monkeys’ behavior during the initial days of training. We found that in some conditions the monkeys could track targets with fast smooth eye movements as early as the 1st day of training. In these conditions the monkeys tracked the target primarily through pursuit accompanied by small corrective saccades. Pictures of monkeys were tracked with the highest eye velocity. The small spot stimulus evoked slow eye movements in the initial days but improved markedly over 12–14 days of training . ExtensiInstitutional Animal Care and Use Committees of the Hebrew University of Jerusalem and were in strict compliance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals. Monkeys were first trained to sit calmly in a primate chair (Crist Instruments) and to consume food from a tube in front of them. To prepare the monkeys for recording eye movements, we implanted a headholder on the skull to allow us to restrain the monkeys’ head movements. The location of the eye was measured with a high temporal resolution camera  and collected for further analysis.Data were collected from two male Macaca fascicularis monkeys . All procedures were approved in advance by the Visual stimuli were displayed on a CRT monitor  at 45–60 cm from the monkeys’ eye. The stimuli appeared on a dark background in a dimly lit room. A computer performed all real-time operations and controlled the sequences of target motion. We used three types of targets: a bright white circle measuring 0.5° in diameter, pictures of monkeys, and a scrambled version of the same monkey pictures. Initially we trained the monkeys on a single picture and verified the results in later sessions using additional pictures. In monkey B we used a 2° × 2° picture and switched between different pictures with the same size on the 13th day. In monkey C we switched from a 2° × 3° to a different 3° × 2° picture on the 6th training day and confirmed the results in a later session with a 2° × 2° picture (not shown). To scramble the pictures, we randomly shuffled the picture pixels. The shuffling procedure preserved the picture size, luminance and colors but removed all spatial correlations between pixels and left no noticeable objects in the picture.During the initial training the monkeys learned to direct their gaze toward a still target to obtain a liquid food reward (baby food mixed with water and infant formula). In these initial stages the target was presented in different locations on the screen, typically along the horizontal and vertical axis at locations with eccentricities of 0, 5, 10, and 15 degrees. We trained the monkeys for 5–7 days until they fixated for up to 2 s on the target. We used spots and pictures to train the monkeys to associate the fixation with reward. For monkey B we also used the scrambled pictures for training and employed them from Day 1 of the step-ramp paradigm. For monkey C we only used the scrambled pictures during Day 2 of training on the step-ramp paradigm. To calibrate the eye signal we adjusted the horizontal and vertical offset and gain while presenting the stimulus in the center of the screen and at locations 15° eccentric to the horizontal and vertical axis. The window and duration of fixation during calibration varied across days; namely, the window was typically around 5° and the duration was around 1–2 s. We used either pictures or spots for calibration. Using large stimuli for calibration might lead to inaccurate calibration, which could be detected by large differences in the center of fixation for large and small stimuli. However, we found that there was only a small difference between the center of gaze for spots and pictures. Specifically, the average distance between the center of gaze for spots and pictures was 0.6°  and 0.43°  for Monkeys C and B. The small differences in center of gaze of the different targets indicated that we could calibrate the equipment with either stimulus, thus ensuring sufficient accuracy for the smooth pursuit experiment.At the start of each step ramp trial, a stationary target appeared in the middle of the screen and the monkeys were required to fixate within an invisible 4° × 4° window. This large window allowed the monkeys to fixate on features in the picture that were not in the center of the screen. Although the window was large, the monkeys typically fixated on the target and made only small fixational movements. For monkey C the standard deviation of the eye position was 0.3° and 0.4°  for the spot condition and 0.65° and 0.58° for the picture condition. For monkey B the values were 0.47° and 0.75° for the spot and 0.46° and 0.78° for the picture. Further, the eyes were directed outside a 2° × 2° window around the center of fixation for less than 5% of the time . Prior to motion the target appeared in the center of the screen for 700–1500 ms and then the same target jumped to a location 4° eccentric to the center of the screen (step) and then moved at 20°/s (ramp) toward the center of the screen . In the We used large windows to avoid restricting the monkeys’ behavior to accurate pursuit. The large window (>3°) only led to failures after the initiation of pursuit, thus confirming that we could collect data from trials in the period just after target motion onset even when the pursuit was substantially slower than target velocity. The window was limited in size (<7°) to force the monkeys to move their eyes to complete a trial successfully. Including or excluding trials in which the monkeys failed to match the accuracy requirements did not change any of the findings. The target continued to move at a constant speed for 700 ms (except for the first session for monkey C when the motion duration was 900 ms) and then stopped. The monkeys were required to continue to fixate for 400–600 ms and then received a liquid food reward (0.15–0.25 ml).2, eye velocity crossing 15°/s during fixation or eye velocity crossing 50°/s while the target moved. To calculate the average of the smooth pursuit initiation we first removed the saccades and treated them as missing data. We also used the detected saccades to calculate the fraction of pursuit displacement on a trial. In each trial we calculated overall eye displacement as the amplitude of the eye position in the direction of target motion. The pursuit displacement was calculated as the sum of eye position displacements between the times of the saccades. The fraction of pursuit displacement was then calculated as the ratio of the pursuit displacement to the total eye displacement. Using the target displacement  with u=f cos φ and v=f sin φ. The average power was calculated across all frequencies in bins of 1 cycle/image. We present the power spectrum of the grayscale image. We confirmed that for the features we extracted from the pictures there was not any substantial difference between the different pictures we used or between different color components of the same picture.For image power spectral analysis, we calculated the Fourier transform of the picture and the scrambled stimulus , F . After a short delay the target jumped to a position 4° eccentric to the center of the screen (step) and started to move at 20°/s toward the center of the screen (ramp). We presented the moving stimuli after the monkeys were trained to fixate on targets (5–7 days of training).We recorded eye movements from the 1st day of training on a step-ramp paradigm . At the Figure 1B). Figures 1C–F present examples of traces of eye positions from the first training session for monkey C and after extensive training for 6 months. When the tracking target was a spot, movement was mostly composed of large saccades . When the monkey tracked a moving picture, the eye continuously followed the picture and only small saccades were required to correct for errors . After extensive training the monkey followed the target continuously both when tracking the spot and the picture . Thus, the examples in Figure 1 show differences in the tracking of a picture of a monkey and a spot as early as the 1st day of recording.To study eye movements during the initial steps of training, we recorded eye movements from the 1st day of training on the monkey picture stimulus, the scrambled version of the picture and the bright spots  and then the full target motion epoch . In these sections we focus on the spot and picture stimuli. We then compare pursuit in all three stimulus conditions including the scrambled version of the picture . In the last section of the results, we show how training affects variability in these movements .In the following results sections, we first analyze the differences in pursuit initiation  or a picture (black), for both monkeys. To calculate the eye velocity, we smoothed the eye position with a Gaussian kernel with a standard deviation of 5 ms and digitally differentiated the position signal. On the first training day the average eye velocity was the slowest for the spot target . For the picture target, the eye accelerated markedly and almost reached target velocity , indicating that as early as the 1st day of pursuit, the monkeys could track the target in the step-ramp paradigm. The monkeys were trained on various pursuit paradigms for half a year, after which we reexamined pursuit behavior. After this extensive training period, pursuit initiation was enhanced markedly when tracking a moving spot  and improved for the picture target as well . However, even after extensive training, acceleration was still lower for the spot target . Note that the examples in Figure 2 show one direction of movement; in later sections, we analyze eye movements in different directions separately. Thus, the examples indicate that the monkeys could track some stimuli with a large gain (speed/target velocity) as early as the 1st day of training and that even after extensive training there was still a difference in the pursuit of a picture and a spot target.The improvement across training was highly apparent in the smooth pursuit initiation. Figures 3A,B,E,F. As training progressed the gain increased, as shown in Figure 3 by the tendency of the green and red traces to lie above the blue traces. After the initial training, the monkeys were engaged in a variety of different tasks for several months  and 850  trials per day. In both the picture and spot conditions the monkeys tended to have lower gains during the initial training days, as indicated by the average eye velocity depicted by the blue traces in Figure 3A). In the picture condition, there was an increase in the pursuit velocity between the 1st and 2nd day of training, but in further training the increase tapered off . Extensive training led to a small additional increase . For Monkey B there was a gradual increase in eye velocity in both stimulus conditions . Monkey B showed larger gains for pursuit in the picture vs. spot condition; however, the difference was not as pronounced as for Monkey C.Both monkeys exhibited similar trends in terms of improvement across days; however, there were some differences between them. For Monkey C the gradual increase was the most pronounced for the spot condition  and the latency from motion onset . The increase in the eye velocity traces across days of training  resulted from an increase in eye acceleration  and a decrease in the latency of the movement . In both monkeys the acceleration was larger for the picture than for the spot target . The effect of the latency was inconsistent across the two monkeys. For Monkey B we found longer latencies for the picture vs. the spot  whereas for Monkey C there were no consistent differences . The latency values for Monkey B might seem inconsistent with the larger overall gain of the pursuit for picture vs. spot . Note, however, that the overall effect of constant acceleration on the eye velocity was much larger than the effect of latency, since acceleration but not latency accumulates in time.To quantify the improvement across days we decomposed the average eye traces into a linear increase in eye velocity (constant acceleration) after initiation . In both monkeys and in all conditions the pursuit velocity was the lowest for upward movement . With a few exceptions, across training, the anisotropies were consistent. This is indicated by the tendency of the different traces in Figure 4 not to intersect. One exception to the overall consistency of the anisotropies was the crossover of the traces in conditions where target velocity was close to the eye velocity . In these conditions, the ceiling effect of the target velocity probably masked the anisotropies. Another minor exception to the overall tendency of the anisotropies to be the same across training was that after extensive training the order of the gain changed in Monkey C . This could be a result of the extensive training schedule. During the initial training, we equalized the number of trials for the different directions; hence, we can be confident that we did not confound the anisotropies with biases that might arise from unbalanced training. Later the anisotropies could have been affected to some extent by the training schedule where we did not attempt to equalize the direction of movement.There were clear anisotropies in eye velocity from the 1st day of training . In monkey B the opposite trend was observed; i.e., on the day we switched pictures (day 13) there was a small decrease in eye velocity . Interestingly for both monkeys eye velocity rebounded the day after the switch: it decreased for monkey C and increased for monkey B. Future work utilizing a series of pictures while probing pursuit could systematically explore the effects of picture content and novelty on pursuit.Analyzing the eye traces separately for each direction also revealed a potential effect of switching the picture stimulus. In monkey C we switched pictures at the start of the 6th day. Immediately after the switch there was an increase in eye velocity for upward movement . A previous study showed that on the 1st day of training the fraction of movement with pursuit corresponded to approximately 20% of the overall target displacement . Hence next we tested whether the stimuli we used could drive tracking with pursuit from Day 1, or as was found previously, that tracking is initially accomplished mostly through saccades.Up to this point we have focused on the initiation of pursuit that corresponds to the open loop period. Because saccades have longer latency than pursuit in the period we have analyzed so far, there were few saccades; however, later in the trials the monkeys often made saccades to compensate for inapt pursuit gain . This difference between the picture and the spot on Day 1 was very large for Monkey C. Although smaller, there still was a substantial increase in pursuit displacement for Monkey B. For example, when the stimulus moved to the left , on the 1st day Monkey B tracked 20% of the displacement with pursuit in the spot condition and 42% for the picture condition. Across all motion directions, on the 1st day the average pursuit displacement for the spot was 21 and 10% for monkeys B and C, respectively. The values for the picture targets were 37 and 72% for Monkeys B and C. Thus, these results are consistent with previous reports that displacement of small spots are tracked initially primarily by saccades but also indicate that a lack of pursuit tracking is not the result of an inherent limitation of the pursuit system.To quantify how much of the tracking involved smooth pursuit, for each trial we calculated the fraction of displacement through pursuit vs. the total eye displacement . Values Figure 4) and the fraction of pursuit displacement . For each training day we calculated the average fraction of pursuit displacement separately for different target direction conditions and stimulus conditions. In both monkeys the fraction of pursuit displacement increased across days of training . The improvement was substantial for both monkeys in the spot condition. In the picture condition, the fraction of pursuit displacement in Monkey C reached a plateau of around 75% as early as the 1st day of measurements , whereas Monkey B required a few more days of training to achieve values close to 75% for horizontal movement and longer training was required for vertical movement . Again, this is consistent with the lower gain observed for Monkey B in the vertical movement and the lower gain for Monkey B compared to C for the picture stimulus.Overall, the findings thus indicate that the effects of training, stimulus condition and motion direction were similar for pursuit initiation  and 5.72° (±2.8) for Monkeys B and C. The values for the picture targets were smaller; 3.1°(±1.8) and 2.6° (±1.6) for Monkeys B and C. Training reduced the amplitude of the first saccade. After extensive training the average amplitude of the first saccade for the spot condition was 1.94° (±0.81) and 1.2° (±0.63) for Monkeys B and C. The values for the picture targets were smaller; 1.29° (±0.71) and 0.77° (±0.54) for Monkeys B and C.Figure 1B). Note that the main aim of the current study was to optimize stimuli for enhancing tracking from the 1st day. Therefore, the number of conditions we could test was limited and we did not attempt to perform an extensive study to explore the properties of the monkey picture that drove faster pursuit.The differences in pursuit between the monkey picture and the spot could be attributed to either the difference in the relevance of the stimulus to the monkey prior to training, and/or the low level properties of the stimulus such as its size  or its sFigure 6A). To quantify the effect, we calculated the eye velocity 250 ms after target motion onset. In both monkeys we found a significant difference between the stimulus conditions (repeated-measure ANOVA p < 0.01). Post hoc comparisons (Tukey’s post hoc comparison p < 0.01) revealed that the eye velocity was indeed the fastest for the picture condition, slightly slower for the scrambled picture, and the slowest for the spot . This order of eye speeds was maintained across first 12–14 training days . An exception to this order was that after extensive training, pursuit in monkey C for the scrambled picture was slightly greater than the velocity for the picture . Note as well that we did not present the scrambled condition on the 1st day of training for Monkey C .We found that eye velocity was the fastest for the picture condition, slightly slower for the scrambled picture, and the slowest for the spot  was 88 and 90% for Monkeys B and C. The velocity ratio between the spot and the picture condition was smaller for Monkey C (spot/picture eye velocity = 50%) than Monkey B (spot/picture = 76%). Thus, the faster pursuit for scrambled vs. spot indicates that the pursuit enhancement we found in the picture condition was not only related to the object in the picture. The faster pursuit for the picture vs. the scrambled stimulus suggests that the object (monkey picture) potentiated the pursuit, but other explanations are possible. Nevertheless, one crucial difference between the picture and scrambled stimuli has to do with their spectral frequency components.Figure 7 compares the power spectrum of the picture and scrambled targets. We calculated the power spectrum  of the picture and the scrambled version that are shown in Figure 1B. For each frequency in the 2-dimensional spectrum, we calculated the ratio between the power of the picture and scrambled targets. The larger power spectrum of the picture at low frequencies is shown by the tendency of the pixels to plot in yellow and red around the center of Figure 7A. The smaller power spectrum of the picture in the higher frequencies appears in the tendency of the pixels close to the margins of Figure 7A to plot in cyan and blue. We transformed the power spectrum into polar coordinates  and averaged the power across all spatial frequencies . In the frequency range between 1 and 8 cycles per image, the power of the picture was greater whereas in frequencies above 8 cycles per image the power of the scrambled stimuli was greater. We return to these points in the discussion.The picture had greater power at low frequencies whereas the scrambled target had greater power in the higher frequency range. Figures 6A, 8A). The standard deviation increased when the eye started to move and was larger for pictures and scrambled targets than for the spot. This pattern is consistent with the signal-dependent noise that is often observed in motor control . The values after extensive training tended to lie below the values during training, indicating that conditions with similar average velocity tended to have lower standard deviations after extensive training. The regression through the origin  had a smaller slope after extensive training . The slope estimates the coefficient of variation for the eye velocity before and after extensive training . Thus, training increased the precision of eye velocity since there was less variability per average eye velocity after extensive training. Note that because of the substantial noise in the analysis of the coefficient of variation, especially when the signal is very small, we focused on comparison before and after extensive training and not on the modulation of the coefficient of variation during the initial training.To test whether training affected the variability beyond the effect it had on average eye velocity we compared the average and standard deviation of the eye velocity at 250 ms after motion onset. To focus on the pursuit component, we subtracted the standard deviation prior to the movement from the standard deviation during movement. We analyzed the eye movements of monkeys from the 1st day of training on a step-ramp task to assess the conditions that enabled them to exhibit pursuit from the initial days of training. The results show that under the appropriate conditions, the monkeys had a high pursuit gain in the step-ramp paradigm as early as the initial days of training. When the monkeys tracked a picture, the pursuit gain was high, and training rapidly enhanced the gain. Tracking of small spots was associated with lower gain, but increased substantially over the 12–14 days of training. We conducted control experiments which showed that the difference between the picture and the spot was influenced by the low-level properties of the stimulus such as its size, but some of the effect could have been due to the object in the picture.There are crucial differences between smooth pursuit in the laboratory and in the natural environment. In natural environments gaze shifts are obtained by coordinating head and eye movements , whereasPrevious work has indicated that training markedly enhances smooth pursuit eye movements  and oculThe consistency between the current and previous experiments further validates the approach we and others have taken. One potential confounding factor affecting previous experiments on monkeys has to do with the mechanical interference of the eye coil, which could affect eye movements and lead to anisotropies. In the current study, we used camera-based eye tracking. The consistency of the current findings with other studies with respect to movement anisotropies  indicateFigure 7). Since the goal of this study was to study whether and to what extent monkeys learn to pursue in a laboratory setup, our ability to characterize the features of the pictures that led to the high gain was limited. These could be low level features such as the overall energy in different frequency channels . The enhancement in pursuit initiation could partly have been due to the preparatory mechanism (Another possibility is that the enhancement in the pursuit initiation was related to the subjects’ state at the time of pre-motion fixation. In the current experiment the object appeared before the target motion (echanism . These cechanism  might heWe found that monkeys can perform a step-ramp task relatively well from the initial days of training. Even when the initial gain was small, the monkeys adjusted rapidly over the 12–14 days of training. This indicates that this paradigm does not require highly specialized mechanisms that might be generated by extensive training. Thus, it is likely that the results obtained from the step-ramp paradigm generalize across animals and from monkey to humans.YB carried out the experiments with support from MY. MJ analyzed the data with support from YB. MJ wrote the manuscript with support from YB and MY. MJ conceived the original idea and supervised the project.The 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.


Femoral component malrotation is a common cause of patient dissatisfaction after total knee arthroplasty. The sulcus line (SL) is more accurate than Whiteside’s line as it corrects for variation in the coronal orientation of the groove. The hypothesis is that averaging the SL and posterior condylar axis (PCA) will reduce femoral malrotation.The component was inserted at a position between the SL and PCA in 91 patients. An intraoperative photograph was taken showing the landmarks. These were compared to the component position achieved relative to the surgical epicondylar axis (SEA) on a postoperative CT scan. The component position was compared to the position achieved using the individual landmarks.p < 0.05) for the average position (2/84) when each was compared to the SL (16/84) and PCA (14/84) individually. In 21/84 (25%) of cases, there was more than 4° of divergence between the SL and PCA.Relative to the SEA, the final component position was 0.6° , the coronally corrected SL position was −0.7° , the PCA position was 0.9° . Averaging the landmarks significantly decreased the variance of the component position compared to using the SL and PCA individually. The number of outliers (>3° from SEA) was also significantly less (Averaging the SL and the PCA decreases femoral component malrotation. Femora are frequently asymmetrical in the axial plane. Referencing posterior condyles alone to set rotation is likely to cause high rates of patellofemoral malalignment. Femoral component rotation in total knee arthroplasty (TKA) continues to be a contentious issue. Femoral component malrotation is associated with patella maltracking –7, increThese landmarks have been extensively studied to determine how they relate to each other and to the flexion-extension axis (FEA) of the knee. The SEA has been recommended as a closer approximation of the FEA of the knee than the AEA –15. HoweReferencing the posterior condyles during either mechanical alignment or KA techniques relies on the assumption that the flexion-extension axis of the posterior condyles has a consistent relationship with the axis of rotation of the patella and trochlear groove. There is some research to suggest that on average, the axes are close to parallel , 19. HowA new technique for measuring the rotational alignment of the trochlear groove has recently been developed , 26. TheThe aims of this study were to (i) determine the clinical accuracy of the SL and STAG technique, (ii) assess the benefit obtained by averaging the SL and PCA, and (iii) characterise the relationships between the SL, SEA and posterior condyles.Approval to conduct the study was gained from the local Human Research Ethics Committee.A prospective study of a consecutive series of 91 TKAs was conducted. There were no preoperative exclusion criteria. All operations were performed by one surgeon using a standardised technique. Conventional instruments were used. The distal femoral cut was produced at 6° from the anatomical axis of the femur using an intramedullary rod. The tibial cut was produced perpendicular to the long axis of the tibia using an extramedullary jig.The femoral rotation was determined by averaging the SL and the PCA. The SL was drawn on the distal femur using diathermy after dislocation of the patella and before any bony cuts were made. This was done by carefully palpating the deepest points of the trochlear groove starting at the intercondylar notch and leading anteriorly. The most proximal section of the trochlear groove was not incorporated into the SL as it has been shown to be prone to excessive variability due to arthritic damage, osteophyte formation and anatomical variation , 28. MulThe STAG intramedullary rod was inserted and the STAG block placed over the rod. The block was then orientated to match both the rotational Fig.  and the The PCA was determined with the use of a standard sizing guide. Paddles were placed under the posterior condyles, and an additional 3° of external rotation was added to compensate for the average proximal tibia joint line obliquity. The PCA is defined as 3° of external rotation to the posterior condylar line (PCL). A 3.2-mm drill was used to produce two holes on the distal cut surface which match the rotation of the PCA. In order to report reproducible technique which does not rely on surgeon experience and to allow the calculation of an accurate PCL, no adjustment was made for posterior condylar bone loss.A sizing guide was used which allowed variation in the rotation from the posterior condyles in 1° increments between 0° and 6° of external rotation. The rotation of the SL (STAG pin-holes) and the PCA PCL + 3°) were compared. These landmarks are able to be accurately compared by placing a sizing guide on the distal cut surface of the femur and dialling the rotation between the two sets of pin-holes. Therefore, the rotational angle between the PCA and SL was able to be accurately determined. When they were different, an average position was produced as accurately as possible by altering the rotation of the sizing guide in 1° increments. This average position was marked with a further set of pin-holes, and the 4-in-1 cutting block was inserted into these pin-holes. The prosthesis was therefore inserted in the average position. Therefore, the relationship between the PCA or SL and the actual component position was able to be determined from the photograph. An intraoperative photograph was taken of the three sets of pin-holes using a camera set in the overhead light . Both components have symmetrical posterior condyles.A postoperative computed tomography (CT) scan was performed prior to discharge from hospital. A low-dose scanner (GE Optima 660) produced 1.25 mm slices from the proximal end of the femoral component to the tip of the tibial stem.Measurements were taken of both the intraoperative photographs and the CT scan by two observers (one orthopaedic resident and one orthopaedic surgeon). The first ten cases were measured twice at an interval of 1 week to assess interobserver and intraobserver reliability. Internal rotation was recorded as a negative angle and external rotation as positive. The angles between the three sets of pinholes were measured on the photographs using Adobe Photoshop CS6. The angle between the posterior condyles of the femoral component and the SEA was measured using InteleViewer 4-3-4. The SEA was defined as a line from the most prominent point on the lateral epicondyle to the deepest point of the medial sulcus posterior to the medial epicondyle. Multiple axial slices were referenced when necessary to determine the landmarks. If either observer found that the sulcus was not able to be accurately determined, the scan was excluded. The data was collected using a purpose-designed Excel spreadsheet. Statistical analysis was performed using SPSS (22.0.0.0).calculated mean PCA and SL to SEA)  Table  was measA) Table  was alsoA definition of trochlear condylar divergence (TCD) was developed to identify cases in which the PCL and SL were not perpendicular. This is a measure of femoral rotational asymmetry. A difference of 4° was deemed clinically significant based on the evidence that more than 3° of femoral malrotation is associated with adverse patellofemoral outcomes , 3, 6.Subgroup analysis was performed based on the predominant pattern of arthritis detected on preoperative knee X-rays and intraoperative findings. They were classified as predominantly medial, lateral, patellofemoral or tricompartmental osteoarthritis.Of the 91 cases, one was excluded as the SL could not be clearly delineated. This patient had a patellectomy 30 years prior to TKA and the groove was grossly deformed. Six cases were excluded due to a poorly visible medial epicondylar sulci on the postoperative CT scans, leaving 84 cases for analysis. Slightly, more female  than male  participants were included in the study. More TKAs were conducted on the right side .SL  or the PCA   or the PCA .The SL 0.7° internally rotated to the SEA . The PCL was 2.1° internally rotated . The actual component position achieved was 0.6° externally rotated . The calculated mean PCA and SL was 0.1° externally rotated . There was a significant decrease in variance between the calculated mean PCA and SL to SEA to either the p < 0.05).There was a significant difference between the means for both the SL and PCA when compared to either the actual component position or the calculated mean PCA and SL to SEA (p < 0.05). There was no significant difference between the SEA and the calculated mean PCA and SL to SEA (p > 0.05).There was a significant difference between the means for the SL, PCA and actual component position compared to the SEA  (Table p < 0.05).Outliers were considered to be measurements more than 3° from the SEA. By combining the SL and PCA, the rate of outliers decreased from 19% for the SL, 17% for the PCA to 2% for the calculated mean PCA and SL .Interobserver and intraobserver reliability was excellent for all measurements .The STAG device removes parallax errors which occur when referencing APA . These eThe combination of the SL and PCA produced fewer outliers than predicted by the findings of the 3DCT study suggesting that the intraoperative technique using the STAG is at least as accurate and reproducible as the virtual technique using the CT scans.On average, the SL was slightly internally rotated to the PCA and SEA, and externally rotated to the PCL. Referencing the SL using the STAG device produced a landmark with a narrow range and a level of variability which was similar to the PCA. This is an improvement compared with published results using APA –32 whichThe comparison of the means revealed that the only technique to produce no statistically significant difference from the SEA was the calculated mean PCA and SL to SEA. While this would support the hypothesis that combining the two landmarks is likely to result in a closer average position relative to the SEA, it is the decrease in variability and outliers which is more important. In addition, the size of the difference in the means relative to the SEA was less than 1° for each of the techniques, which may not be clinically significant. It is the size of the potential variation using each technique which is important. This changes from up to 5.5° for the SL and 6.1° for the PCA down to 4.0° for the actual component position and 3.7° for the calculated mean PCA and SL to SEA. Averaging the SL and PCA . When severe trochlear arthritis is present, there are often parallel grooves in the bone surface which allow easy identification of the SL. In knees with lateral arthritis, there was on average 0.9° of internal rotation of the PCA compared to the medial group. This difference was not significant. There was no difference in the SL between medial and lateral groups.Analysis of the relationship between the SL and PCL revealed a high percentage of cases in which the two landmarks were not perpendicular to each other . Overall, there was only a weak negative correlation between the SL and PCL Fig. . The relIn 21 of 84 knees, there was more than 4° of difference between the PCL and SL. We have coined the term trochlear condylar divergence to describe this group. In 19 of these 21 knees, the SL shifted, relative to the SEA, in the opposite direction to the PCL. This suggests an anatomical variation in which the rotational alignment of the SL and the PCL may be linked. The direction of this divergence was not influenced by the diagnosis of medial or lateral osteoarthritis. In two of four knees with lateral arthritis and nine of 14 knees with medial arthritis, the divergence occurred in the opposite direction to that anticipated if the variation was due to posterior condylar bone loss. For example, in nine knees with medial arthritis, the PCL was more than 4° internally rotated to the SL. This is despite posterior condylar cartilage and bone loss tending to externally rotate the PCL. Therefore, if the surgeon in these nine cases had internally rotated the femoral component relative to the PCA in order to compensate for posterior medial condylar bone loss the degree of internal malrotation relative to the SEA and SL would have increased. This would indicate that it is a true anatomical variation rather than the effect of arthritic bone loss. Further studies are planned to assess this variation and determine if it is linked to proximal tibial coronal alignment.These findings are consistent with the findings of Iranpour et al. . This stIranpour et al.  also pubBoth studies by Iranpour and colleagues are quoted by proponents of posterior referencing and kinematic alignment as evidence of a consistent rotational relationship between the posterior condyles and the patellofemoral joint . This coThis is also consistent with several recent studies which measured the relationship between the posterior condyles, the epicondyles and the trochlear groove using a variety of techniques. Jones et al.  used MRIThe results of this study raise concerns regarding any technique which solely references the posterior condyles to determine rotation. Twenty-five percent of femora have more than 4° of rotational asymmetry, and yet our femoral components are symmetrical. Therefore, referencing solely the posterior condyles may produce a well-balanced tibiofemoral joint but change the rotation of the patellofemoral joint relative to its original position. This may be particularly pertinent in cases of kinematic alignment in which the native knee has a combination of proximal tibial varus and external rotation of the SL relative to the PCL. This combination may lead to an exaggerated internal rotation of the trochlear groove of the femoral component relative to the native position.One limitation of this study is that we did not attempt to compensate for posterior condylar bone loss when determining the PCA. This was done to maintain a consistent technique and to avoid subjectivity involved in compensating for bone loss intraoperatively. Nam et al.  determinIntraoperatively, the ability to perfectly average the SL and PCA was limited by the sizing guide which had 1° or 1.5° rotational increments. In cases where the difference between the SL and PCA was less than the 1° the guide was left at the PCA landmark. Therefore, a measurement based on perfect averaging of the angles from the intraoperative photographs was also calculated. This is why there are "actual" and "calculated" measurements for the average of the SL and PCA. The difference between the two results was minor.Further limitations of the study involve the exclusion of several cases due to difficulty finding the medial epicondylar sulcus; however, our exclusion rate is similar to other studies , 22.Due to the lack of preoperative long leg X-rays, data on mechanical alignment or severity of deformity was not available. Preoperative knee X-rays and intraoperative assessment of the location of the arthritis were used to produce subgroup data. There are only 11 cases with predominantly lateral compartment osteoarthritis. The results in this group suggest that combining the two landmarks may be a reliable technique; however, the numbers are too small to draw firm conclusions. Further studies assessing non-arthritic knees are planned.Measurement errors could occur with the identification of the SL and measurement of the intraoperative photographs and the CT scans. However, the very high interobserver and intraobserver reliability makes it unlikely to account for the degree of variation we have identified. Likewise, the measurement error associated with the use of the STAG device was shown to be small (mean 1° for both interobserver and intraobserver measurements) in the previously published cadaver study .A high proportion of femora have axial asymmetry with different rotational alignment of the trochlear groove and posterior condyles. By using a trochlear alignment guide that corrects for the coronal alignment of the trochlear, the rotational alignment of the groove can be more accurately identified during surgery than by using APA. It also allows direct comparison between the anterior and posterior landmarks. Averaging the SL of the trochlear groove and the PCA significantly decreases femoral component malrotation.


Plant density and its non-uniformity drive the competition among plants as well as with weeds. They need thus to be estimated with small uncertainties accuracy. An optimal sampling method is proposed to estimate the plant density in wheat crops from plant counting and reach a given precision.Three experiments were conducted in 2014 resulting in 14 plots across varied sowing density, cultivars and environmental conditions. The coordinates of the plants along the row were measured over RGB high resolution images taken from the ground level. Results show that the spacing between consecutive plants along the row direction are independent and follow a gamma distribution under the varied conditions experienced. A gamma count model was then derived to define the optimal sample size required to estimate plant density for a given precision. Results suggest that measuring the length of segments containing 90 plants will achieve a precision better than 10%, independently from the plant density. This approach appears more efficient than the usual method based on fixed length segments where the number of plants are counted: the optimal length for a given precision on the density estimation will depend on the actual plant density. The gamma count model parameters may also be used to quantify the heterogeneity of plant spacing along the row by exploiting the variability between replicated samples. Results show that to achieve a 10% precision on the estimates of the 2 parameters of the gamma model, 200 elementary samples corresponding to the spacing between 2 consecutive plants should be measured.This method provides an optimal sampling strategy to estimate the plant density and quantify the plant spacing heterogeneity along the row. Plant density at emergence is governed by the sowing density and the emergence rate. For a given plant density, the uniformity of plant distribution at emergence may significantly impact the competition among plants as well as with weeds , 2. PlanCrops are generally sown in rows approximately evenly spaced by seedling devices. Precision seedling systems mostly used for crops with plants spaced on the row by more than few centimeters  distribute seeds relatively evenly along the row. Conversely, for most crops with short distances among plants on the row, e.g. wheat, barley or canola, seeds are distributed non-evenly along the row. This can be attributed both to the mechanisms that free, at a variable frequency, the seed from the seed tank, and the trajectory of the seed that may also vary in the pipe that drives it from the seed tank to the soil. Further, once reaching the soil, the seed may also move with the soil displaced by the sowing elements penetrating the soil surface. Finally, some seeds may abort or some young plants may die because of pests or too extreme local environmental conditions . The population density and its non-uniformity are therefore recognized as key traits of interests to characterize the canopy at the emergence stage. However, very little work documents the plant distribution pattern along the row, which is partly explained by the lack of dedicated device for accurate plant position measurement . Electro2 quadrats corresponding roughly to a total of 6.7 m length of rows (assuming the rows are spaced by 0.15 m). In this case, quadrats may be considered as a set of consecutive row segments with the same length when the quadrat is oriented parallel to the row direction or with variable lengths when the quadrat is oriented differently. Although these recommendations are simple and easy to apply, they may not correspond to an optimal sampling designed to target a given precision level. They may either provide low precision if under sampled or correspond to a waste of human resources in the opposite case.Manual field counting in wheat crops is still extensively employed as the reference method. Measurements of plant population density should be completed when the majority of plants have just emerged and before the beginning of tillering when individual plants start to be difficult to be identified. Plants are counted over elementary samples corresponding either to a quadrat or to a segment . The eleThe sample size required to reach a given precision of the plant density will depend on the population density and the heterogeneity of plant positions along the row that may be described by the distribution of the distances between consecutive plants. This distribution is more likely to be skewed, which could be described by an exponential distribution or a more general one such as the Weibull or the gamma distributions. Fitting such random distribution functions provides not only access to the plant density at the canopy level, but also to its local variation that may impact the development of neighboring plants as discussed earlier.The objective of this study is to propose an optimal sampling method for plant density estimation and to quantify the heterogeneity of plant spacing along the row. For this purpose, a model is first developed to describe the distribution of the plants along the row. The model is then calibrated over a number of ground experiments. Further, the model is used to compare several plant counting strategies and to evaluate the optimal sampling size to reach a given precision. Finally, the model was also exploited to design a method for quantifying the non-uniformity of plant distribution.Three sites in France were selected in 2014  [A Sigma SD14 RGB camera with a resolution of 4608 by 3072 pixels was installed on a light moving platform  . For eacn (noted −2) was computed simply as the number of plants counted on the segments, divided by the product of the length of the segments and the row spacing.The coordinates The autocorrelation technique was used to explore the spatial dependency of spacing between successive plants: the linear correlation between p value of Chi square test  as follows:a and b may lead to the same plant density, but with variations in their distribution along the row . The sample size can be expressed either as a given length of the segments where the (variable) number of plants should be counted, or as a (variable) length of the segment to be measured corresponding to a given number of consecutive plants. The two alternative sampling approaches will be termed FLS (Fixed Length of Segments) for the first one, and FNP (Fixed Number of Plants) for the second one.L, where plants need to be counted. The optimal L value for a given target precision quantified by the CV will mainly depend on the current density as demonstrated in Fig. b, that controls the plant density drives therefore the optimal segment length L  provides a precision better than 10% for densities larger than 150 plants·m−2 for the most common conditions characterized by a shape coefficient a > 0.9. These figures agree well with the usual practice for plant counting as reviewed in the introduction [L to be sampled  is extensively used to estimate the plant density. The 600 cm segment length recommended by , 14 agreThe previous sections demonstrated that the scale and shape parameters could be estimated from the observed distribution of the plant spacing. However, the measurement of individual plant spacing is tedious and prone to errors as outlined earlier. The estimation of these parameters from the variability observed between small row segments containing a fixed number of plants will therefore be investigated here. This FNP approach is preferred here to the FSL one because there will be no additional uncertainties introduced by the position of the first and last plants of the segment with the corresponding start and end of the segment. These uncertainties may be significant in case of small segments in the FLS approach.n corresponding to n plant spacing between (n + 1) consecutive plants with n · a as shape parameter and the same scale parameter b as the one describing the distribution of ∆X.The probability distribution of a gamma distribution can be expressed as the sum of an arbitrary number of independent individual gamma distributions . This pra and b will therefore be estimated by adjusting the gamma model described in Eq. n + 1 consecutive plants.The parameters a and b parameters estimation was further investigated. A numerical experiment based on a Monte-Carlo approach was conducted considering a standard case corresponding to the average of the 14 plots sampled in 2014 with a = 1.10 and b = 2.27. The sampling size is defined by the number of consecutive plants for the FNP approach considered here and by the number of replicates. For each sampling size 300 samples were generated by randomly drawing in the gamma distribution  to 250 within 12 steps. This allows describing the variation of the coefficient of estimated values of parameters a and b as a function of the number of replicates and the number of plants  to keep the same precision on estimates of a and b parameters.Additional investigations not shown here for the sake of brevity, confirmed the independency of the number of replicates to the number of plants per segment when parameters A method was proposed to estimate plant density and sowing pattern from high resolution RGB images taken from the ground. The method appears to be much more comfortable as compared with the standard outdoor methods based on plant counting in the field. Images should ideally be taken around Haun stage 1.5 for wheat crops when most plants have already emerged and tillering has not yet started. Great attention should be paid to the geometric correction in order to get accurate ortho-images where distances can be measured accurately. The processing of images here was automatic except the last step corresponding to the interactive visual extraction of the plants’ coordinates in the image. However, recent work , 25 suggThe method proposed is based on the modeling of the plant distribution along the row. It was first demonstrated that the plant spacing between consecutive plants are independent which corresponds to a very useful simplifying assumption. The distribution of plant spacing was then proved to follow a gamma distribution. Although the Weibull distribution showed similar good performance, it was not selected because of the comparatively heavier tails of the distribution that may create artefacts. Further the Weibull model does not allow to simply derive the distribution law of the length of segments containing several consecutive plants . The gam−2 over the 14 plots available. The model performs better for the low density with a RMSE of 21 plants m−2 for density lower than 400 plants m−2. These discrepancies may be mainly explained by the accuracy in the measurement of the position of individual plants (around 1–2 mm). Uncertainties on individual plant spacing will be high in relative values as compared to that associated with the measurement of the length of the segment used in the simple method to get the ‘reference’ plant density. Hence it is obviously even more difficult to get a good accuracy in plant spacing measurements for high density, i.e. with a small distance among plants. In addition, small deviations from the gamma-count model are still possible, although the previous results were showing very good performance.The adjustment of the gamma-count model on the measured plant spacing using a maximum likelihood method provides an estimate of the plant density Eq. . The comThe model proposed here concerns mainly relatively nominal sowing, i.e. when the sowing was successful on average on the row segments considered: portions of rows with no plants due to sowing problems or local damaging conditions . The sowing was considered as nominal on most of the plots investigated in this study, with no obvious ‘accidents’. However, it is possible to automatically identify from the images the unusual row segments with missing plants or excessive concentration of plants . Rather This study investigated the sampling strategy to estimate the plant density with emphasis on the variability of plant spacing along the row, corresponding to the sampling error. However additional sources of error should be accounted for including measurement biases, uncertainties in row spacing or non-randomness in the sample selection – 29. Unl−2) and shape parameter (a > 0.9) usually experienced, a segment length of 6 m will ensure a precision better than 10%. The second approach (FNP) appears generally more optimal: it aims at measuring the length of the segment corresponding to a number of consecutive plants that will depend mainly on the targeted precision. Results demonstrate that in our conditions, the density should be evaluated over segments containing 90 plants to achieve a 10% precision. The sampling size will always be close to optimal as compared to the first approach where optimality requires the knowledge of the plant density that is to be estimated. Further, the FNP approach is probably more easy to implement with higher reliability: as a matter of facts, measuring the length of a segment defined by plants at its two extremities is easier than counting the number of plants in a fixed length segment, where the extremities could be in the vicinity of a plant and its inclusion or not in the counting could be prone to interpretation biases by the operator. The total number of plants required in a segment could be split into subsamples containing smaller number of plants that will be replicated to get the total number of plants targeted. This will improve the spatial representativeness. Overall, the method proposed meets the requirements defined by [Optimal sampling requires a tradeoff between minimum sampling error obtained with maximum sampling size and minimum cost obtained with minimum sampling size . The optfined by , 33 for The gamma-count model proved to be well suited to describe the plant spacing distribution along the row over our contrasted experimental situations. It can thus be used to describe the heterogeneity of plant spacing as suggested by . This ma


Species phenotypic traits affect the interaction patterns and the organization of seed‐dispersal interaction networks. Understanding the relationship between species characteristics and network structure help us understand the assembly of natural communities and how communities function. Here, we examine how species traits may affect the rules leading to patterns of interaction among plants and fruit‐eating vertebrates. We study a species‐rich seed‐dispersal system using a model selection approach to examine whether the rules underlying network structure are driven by constraints in fruit resource exploitation, by preferential consumption of fruits by the frugivores, or by a combination of both. We performed analyses for the whole system and for bird and mammal assemblages separately, and identified the animal and plant characteristics shaping interaction rules. The structure of the analyzed interaction network was better explained by constraints in resource exploitation in the case of birds and by preferential consumption of fruits with specific traits for mammals. These contrasting results when looking at bird–plant and mammal–plant interactions suggest that the same type of interaction is organized by different processes depending on the assemblage we focus on. Size‐related restrictions of the interacting species  were the most important factors driving the interaction rules. Our results suggest that the structure of seed‐dispersal interaction networks can be explained using species traits and interaction rules related to simple ecological mechanisms. This plA salient feature of interaction networks is the fact that some potential interactions never occur; they are the so‐called forbidden interactions  and Barranco Alto farms . Both sites are private areas located close to one another in one of Pantanal's most pristine areas, collectively comprising 18,500 ha. The vegetation consists of a mosaic of seasonally flooded savannah and semi‐deciduous and gallery forests, with average annual precipitation of 1,192.5 mm and mean monthly temperature of 26°C.Geochelone carbonaria), and some terrestrial birds were recorded using camera traps . This information was complemented with the analyses of 716 scats from mammals, rheas, and red‐footed tortoises. Seed‐dispersal by the pacu fish (Piaractus mesopotamicus) was recorded by examining intact seeds found in their intestine . This sampling procedure was found to be the most appropriate for a system with such a diverse group of dispersers from different taxa  and 46 plant species  that represent species niche dimensions. Within each axis, species are assigned a i interacts with species j depending on whether ni is larger or smaller than nj. We used a probabilistic version of the Cascade model ,  isIn the Cascade model Cohen, , a specii,j encodes the relationship between ni and nj so that ϕi,j equals 1 if ni > nj or zero otherwise. α and β are parameters that determine how the relationship between ni and nj shape interaction probabilities. α determines the probability of interactions when ni < nj  and β determines how Pij changes when ni > nj . To be consistent with the original Cascade model α was constrained to be <1 and β is constrained to be >1 so that the probability of interaction is larger when ni > nj. In this probabilistic version of the Cascade model Pij is always greater than zero  allowing the computation of the model likelihood (see below). The Cascade model can be used to identify a passive mechanism because, for each species, we identify a threshold after which its interaction with the species in the other axis is not possible .The term ϕi and resource species j is defined bynd,j is the position of the resource j on the trait axis, cd,i represents the center of the diet of consumer i, and rd,i determines the range of the diet of species i. Parameters are defined for each niche dimension of D (we use D = 1 in this study); γ controls the cut‐off rate of the probability function and ν is the maximum probability of interaction . Therefore, the rules of the Niche model are related to more behavioral mechanisms and can be related to Optimal Foraging Theory predictions, which propose that diet is determined by foraging decisions that depend on characteristics of the resource and the consumer.In the probabilistic Niche model  of each of the animal and plant species on the axes are free parameters in the models and are estimated using empirical data on interactions. We initially assigned species positions and other model parameters (see below) randomly and then used an optimization algorithm, the simulated annealing . We repeated the optimization procedure estimations 30 times per model, starting from different points in the parameter space in order to have more reliable estimates of the parameters. All the models were implemented in MATLAB . We used the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). The BIC introduces a higher penalty than the AIC . Thus, to allow comparisons with other studies, we discuss the results based on the AIC, which is the standard method used for model selection based on the likelihood approach, but we also report the BIC values. To establish a reference point for the goodness‐of‐fit measures, we also calculated the fit of a random model in which all interactions are in principle possible with the same probability and with no systematic constraint on interactions. In this model n MATLAB . Codes fSus scrofa). However, we did not include this species in our analysis because we wanted to make the results transferable to other sites in the tropics where there are no exotic species that could potentially take over seed‐dispersal services of locally extinct native species.As the interaction rules for mammals and birds may be different because of differences in body size and their preferences for different fruit traits Jordano, , we firs2.3We gathered information on the traits of plants and animals to identify the potential biological drivers behind the network interaction rules. For each species of plants, we used the information in Donatti et al.  and Dona2.4ni) when the interaction rules followed the Cascade model by means of AIC, and the interaction center  and range  when they followed the Niche model. For plants, we used the species position (nj), which is the only parameter related to the resources in all models. As explanatory variables, we used all the plant and animal traits described in the section animal and plant traits. We evaluated the significance of the variables in question by a random permutation of the dependent variables  and re‐running GLM tests using the randomized variables. We repeated this procedure 1000 times and checked if the GLM coefficient estimates were within or outside the 95% confidence interval of the distribution of the same coefficients based on the randomizations. We used univariate models in all analyses . R codes for this GLM analysis are available as Appendix To identify which biological attributes perform better in explaining the interaction rules identified with model selection, we examined the relationship between the values of model parameters obtained after optimization and the animal and plant traits described above, using generalized linear models (GLM). We performed all analyses in R  and so on. The advantage of this procedure is that we do not make any assumption on the specific relationship between model parameter and traits, except that there is a correlation between them. We performed simulations constraining the distribution of parameters , one at each time, and all combinations of constrained and unconstrained parameter distributions. We obtained MLEs using simulated annealing and used the AIC to compare the fit of the models. These models constrained by species traits are expected to perform worse than the unconstrained model, because the latter allows any parameter distribution. However, by comparing the fit of the different constrained models we can tell whether there are traits that better predict the observed network structure than others. We could only perform these simulations for those species traits that did not have missing values. This included body mass and the degree of frugivorous diet for animals, and seed and fruit size for plants.As a validation procedure, we also ran the model selection routine while considering the information on species traits. Instead of parameterizing the model using the interaction data, which would impose a certain functional relationship between model parameters and traits, we used trait values to rank species and, at each iteration of the optimization used to find the maximum likelihood estimates (MLEs), we reassigned parameter values according to the trait rank. For example, to test how good was animal body mass in describing the interaction patterns, we ranked the species according to body mass and we kept this order when assigning the species position in the Cascade Model or the parameters of the Niche Model in the simulations, so that the animal with largest body mass always had the largest Finally, we wanted to gauge if we could reproduce our interaction network using the interaction rules. To do so, we use the MLEs to create a matrix with the probability for each interaction to occur. Using these probabilities, we created 1000 random matrices and we compared each of them with our empirical interaction network. For each matrix, we calculated the proportion of correctly predicted interactions (both presence and absence of interactions) as the total number of interactions in the simulated matrix that were equal to the interactions in the empirical matrix, divided by the total number of possible interactions . Then, we calculated the average proportion of correctly predicted interactions in the 1000 matrices. Finally, we also calculated for each species the proportion of simulations where its interactions were correctly predicted by the model. We performed this analysis for the complete matrix, and for matrices with only birds and only mammals.33.1Of the three models considered, the Cascade model outperformed the other models in reproducing the structure of the analyzed seed‐dispersal interaction network Table , suggestp < .001, Fig. p < .001, Fig. Next, we used the MLEs of model parameters obtained from optimization to generate theoretical networks and test whether the models are indeed capable of reproducing the empirical interaction network. The models accurately predicted an average of 86.6% (±0.6) of the interactions (both the presence and the absence of interactions) in the matrix including all the species. Moreover, the mean percentage of correctly predicted links at species level when analyzing the network for the birds was similar to the mean proportion of correctly predicted links when analyzing the matrix with only the bird species . However, the analyses including only mammals and under the premises of the Niche instead of the Cascade model, increased the mean proportion of correctly predicted links for the mammal species . Also, the proportion of correctly predicted links increased with seed diameter for the entire matrix and for the matrix with only birds , which translates in being dispersed by a contingent of fewer species, corresponding to large‐bodied animals. Accordingly, dispersers with small body size and body length presented lower values for model parameters, being able to disperse a smaller contingent of plant species. When we examined birds and mammals separately, we found that none of the animal characteristics analyzed correlated with the model parameters corresponding to each species, yet both fruit and seed size for the bird network and fruit size for the mammal network were important drivers of the interaction patterns  and fruit size was different for the bird and mammal networks. While birds dispersed preferentially small fruits , mammals dispersed preferentially the largest ones .GLMs indicated that the interaction rules are mainly driven by fruit, seed, and animal sizes Table . When wes Figure , Table 2The results were similar for the analyses where model parameters were constrained by species traits Tables . For bot4There is an ongoing discussion regarding the prevalence of passive vs. behavioral interaction rules in determining mutualistic interaction patterns, with some studies supporting preferential foraging  tree do not fit the mouth of the small six‐banded armadillo Euphractus sexcinctus (mouth size = 15.3 mm). Also, several studies have already shown that fruit selection follows a hierarchical decision‐making process , limiting the suite of behavioral mechanisms simulated. One possible alternative would be to increase the dimensions of the niche model (Eklöf et al., From a conservation science perspective, the detected interaction rules can be used to reconstruct interaction networks in areas where the information on species interactions is not available and the gathering of interaction data is difficult (Pires et al., The authors declare that they have no conflict of interest.ESG, PRG, and RD conceived the idea. CD and RD designed the field data gathering. CD performed the fieldwork. MMP wrote Matlab codes; ESG analyzed the data. ESG wrote the manuscript; all authors edited and commented on the manuscript and provided editorial advice. Click here for additional data file.