Two of Peter Schmidt’s many contributions to econometrics have been to introduce a simultaneous logit model for bivariate binary outcomes and to study estimation of dynamic linear fixed effects panel data models using short panels. In this paper, we study a dynamic panel data version of the bivariate model introduced in Schmidt and Strauss  that allows for lagged dependent variables and fixed effects as in Ahn and Schmidt . We combine a conditional likelihood approach with a method of moments approach to obtain an estimation strategy for the resulting model. We apply this estimation strategy to a simple model for the intra-household relationship in employment. Our main conclusion is that the within-household dependence in employment differs significantly by the ethnicity composition of the couple even after one allows for unobserved household specific heterogeneity. A large recent literature has been concerned with econometric models in which binary outcomes interact with each other. The papers by Bresnahan and Reiss  and TameAt the same time, a large econometric literature has been concerned with estimation of linear panel data models with fixed effects and lagged dependent variables. This literature dates back to Nickell  and AndeThis paper combines insights from these literatures by illustrating how the simultaneous binary outcome model in Schmidt and Strauss  can be mMethodologically, the paper fits into the literature that is concerned with estimation of standard nonlinear panel data models with fixed effects using short panels. This literature has a long history in econometrics. The main problem to be solved is that treating the fixed effects as parameters to be estimated will typically lead to inconsistent estimation of all the model parameters. The literature has developed a number of methods to deal with this. One approach for parametric models is to try to construct a non-trivial sufficient statistic for the fixed effect. If such a sufficient statistic exists, then conditional maximum likelihood  can typically be used to estimate the parameters of the model. This approach was, for example, taken by Rasch  and HausIn this paper, we study estimation of a dynamic fixed effects panel data version of the Schmidt–Strauss model. It turns out that although the conditional likelihood approach can be applied to identify and estimate some of the parameters of the model, it does not identify the key parameter that captures the dependence between the binary outcomes. On the other hand, it turns out that one can construct moment conditions that do depend on this parameter, which can therefore be estimated by generalized method of moments.As an empirical illustration of the models and methods studied in this paper, we investigate the joint determination of husbands’ and wives’ employment. In this context, it is natural to allow for the possibility that the outcome for each spouse is related to the outcome of the other, which makes it natural to consider the Schmidt–Strauss framework. The specific empirical question is how the parameter that captures the dependence between outcomes for husbands and wives differs by the ethnicity of the couple, and whether it varies over time. Since there is likely persistence in employment, and that some of this persistence might be due to heterogeneity as opposed to true state dependence, it is therefore natural to study this question using dynamic panel data versions of the model proposed by Schmidt and Strauss .The paper is organized as follows: In Sect. i are each distributed according to a logit model conditional on the other variable and on a set of explanatory variablesSchmidt and Strauss  proposed Strauss  show thaThe simultaneous logit model of Schmidt and Strauss  has beenThe conditional probabilities in Eq.  emerge fentclass1pt{minimai denotes the identity of the household, and Below, we apply the model of Schmidt and Strauss   Basic Monthly micro data from the 40 years between January of 1982 and December of 2021. The data are sourced from We define four race/ethnicity groups: White, Black, Hispanic, and Other. Below we interchangeably refer to these groups as “race,”“ethnicity” or “race/ethnicity”. The couples are then grouped into five groups based on the race/ethnicity of the two partners: White, Black, Hispanic, Other, and Mixed Race. For example, White will refer to a couple, where both spouses are White, and “Mixed” will refer to a couple where the wife and husband have different ethnicity. We refer to these groups as the “ethnicity mix” (or sometimes just the “ethnicity”) of the couple.Table We start by presenting summary statistics for the joint probability of working by ethnicity. The first panel of Table Table The left panel of Fig. g of Eq. . The estIt is clear from the evidence in Sect. The dependent variable is working and the parameters are estimated by maximum likelihood. The data are from IPUMS CPS and cover a balanced panel of couples where each individual’s age is between 25 and 65. The data cover the period between 1982 and 2021. Coefficients on year dummies, husband’s and wife’s age, their interaction and their squares are not reported. Standard errors are clustered at the household levelThe estimates of The dependent variable is working and the parameters are estimated by maximum likelihood using the same specification as in Table Figure In the Schmidt–Strauss models estimated in Table In order to investigate the role of dynamics, we first estimate the Schmidt–Strauss model in the last two columns of Table The dependent variable is working and the parameters are estimated by maximum likelihood. The data are from IPUMS CPS and cover a balanced panel of couples where each individual’s age is between 25 and 65. The data cover the period between 1982 and 2021. Coefficients on year dummies, husband’s and wife’s age, their interaction and their squares are not reported. Standard errors are clustered at the household levelSince controlling for the lagged employment status of both partners dramatically change the estimate of The dependent variable is working and the parameters are estimated by maximum likelihood using the same specification as in Table The evolution of the estimates of the parameters that govern the dynamics and the interdependence is shown in Figs. It is well-understood that it can be difficult to disentangle state dependence  from unobserved heterogeneity. Intuition suggests that it is also difficult to distinguish between the effect of Honoré and Kyriazidou  adapt th Strauss , needs tFollowing Schmidt and Strauss , it can riazidou  show tha in Eqs.  and 6)..\documenHonoré and Kyriazidou  also conT. The conditional likelihood approach is then illustrated empirically by obtaining estimates of the Honoré and Kyriazidou  show than in Eq.  with a tρ in Eq.  to be inriazidou  to show i in Eq.  will alss in Eq.  in the cThe traditional approach to estimating nonlinear fixed effects models is to find a sufficient statistic for the fixed effects, and then to construct a conditional likelihood function conditioning on the sufficient statistic. By construction, this conditional likelihood function will not depend on the fixed effects and it may or may not depend on some or all of the parameters of interest. In this subsection, we consider the conditional likelihood approach for the model in Eq. . This exT periods. We also assume that the initial condition, We consider a situation in which a pair of outcomes4from Eq.  are obseWith this, the probability of a particular sequence isT. Also note that the conditional likelihood is constant if In the numerator, the We finally note that the argument above is unchanged if one replaces In Table The dependent variable is working and the parameters are estimated maximizing the conditional likelihood in Eq. . The datIn this subsection, we investigate whether additional identification can be obtained by assuming that T periods . Again, we use the notation a’s cancel in the ratio of the probabilities of two different sequences with the same initial conditions. In the numerator, the As before, we consider a situation in which a pair of outcomes from Eq.  are obseThe conditional likelihood function  isIn Table Figure The dependent variable is working and the parameters are estimated maximizing the conditional likelihood in Eq. . The datIn panel data models with fixed effects, it is sometimes possible to construct moment conditions that do not depend on the fixed effects. When that is the case, one can consider estimating the common parameters of the model by generalized method of moments. The dynamic linear panel data model is a simple example of this; see, for example Anderson and Hsiao  or HoltzWe consider two versions of the modelT.Table T we report Results from the numerical counting of moment conditions for the dynamic simultaneous logit are reported. Four different model specifications are considered: additional exogenous regressors are present  which all depend on In this subsection, we illustrate how the method of moments approach discussed above can be used to estimate The results of the estimation of The dependent variable is working. The parameter Figure The calculations reported above establish that oldridge  has prop Mundlak  and Cham Mundlak  and is k Mundlak . If the Table The dependent variable is working and the parameters are estimated by maximizing the likelihood function conditional on the initial conditions and under the assumption that s in Eq. . The datThe estimates of Figures Correctly specified:  where Discrete, but approximately normal: Discrete, asymmetric: Heteroskedastic: Very heteroskedastic:The results are in Table The fact that the correlated random effects approach is associated with less sampling uncertainty than the conditional likelihood approach comes at a price: If the parametric form for the individual specific effect is misspecified then the estimator can be inconsistent. For a given simple data generating process, one can gauge the importance of this by calculating the maximizer of the limiting (the expected) log-likelihood function for the conditional random effects model. This is especially easy if the data generating process for the fixed effects is discrete because the limiting objective function becomes a sum rather than an integral in that case. This maximizer of the limiting log-likelihood function will be the probability limit of the conditional random effects estimator. To illustrate this, let  assumes  under thmentclasspt{minimaThe table gives the probability limit of the correlated random effects estimator for various distributions of the fixed effect when The probability limits in Table Two of Peter Schmidt’s many contributions to econometrics have been to introduce an econometric model for simultaneous binary outcomes and to study the estimation of dynamic linear fixed effects panel data models using short panels. In this paper, we combine aspects of this research by studying panel data versions of the model introduced in Schmidt and Strauss  that allOn the methodological side, we first use the conditional likelihood approach of Honoré and Kyriazidou  to const Weidner  to studyOn the empirical side, we apply existing methods like those developed in Schmidt and Strauss , as well


This paper reports the development of novel surface parameters which can be used to characterise the scale structure of wool fibres obtained from different breeds. Scanning electron microscopy and subsequent image analysis technique were used to study wool fibres from Leicester, Dartmoor, Ryeland and Herdwick breeds of sheep. Novel scale parameters related to wool fibre’s effective chemical diffusion pathway were developed. Namely, the total scale perimeter per 100 µm fibre length and scale perimeter index, which is the total scale perimeter per 100 µm length divided by the fibre diameter. Wool fibres obtained from different breeds showed significant differences in their scale pattern with the change in fibre diameter. The scale perimeter per 100 µm length increased with the fibre diameter and showed a polynomial correlation. It was also demonstrated that an increase in the diameter of the wool fibre resulted in an increase in the apparent dye diffusion coefficient, which contrasts the established theory that finer fibres are associated with a higher dyeing rate. The increase in effective diffusion pathway  for the wool fibres (among different breeds) resulted in a higher dye diffusion rate at the initial phase of dyeing (liquor to surface). Wool products are used in diverse applications, not only in garments but also in other technical application areas including filtration, composites, furnishings and construction engineering10. The unique properties of wool fibres originate from the macroscopic and microscopic features of their structure.Wool is a multi-functional natural fibre which is valued in the twenty-first century fibre market due to its unique properties such as high elongation, thermal insulation, capacity to absorb and hold moisture and high ignition temperature11. The cuticle layer has a high cystine content, making it chemically resistant (highly crosslinked structure) and is further subdivided into epicuticle, exocuticle and endocuticle. The outmost epicuticle consists of a hydrophobic F-layer made of polar and nonpolar long chain fatty acids13.Wool fibre typically contains two main types of morphological components, the outer cuticle  and the inner cortex, which makes up almost 90% of the fibre16. The diffusion of water molecules into the fibre core is strongly dependent on the intercellular gaps present between the scales18. Similarly, other chemicals can also follow a similar path of diffusion assuming that the molecules are small enough to diffuse through the intercellular gaps. It has been hypothesised that these intercellular gaps can control both the amount of diffused chemicals and the rate of diffusion and therefore, are expected to have strong influence on the fibre properties19.Wool fibres from different sheep breeds exhibit significant difference in properties  and in surface morphology 20. Image analysis of different animal fibres has also been performed using various methodologies21 to study their scale structures. For example, Blyth categorised wool scales into two types—coronal and reticulate forms22. The edges of the scales in the coronal pattern face away from the fibre axis and tend to grow around the fibre in a semi-circle. Wool fibres with a diameter of less than 25 µm show coronal pattern of scales23. Reticulate type scales are irregular in size and shape and appear randomly distributed on the surface of the fibre. Later studies discovered the coronal-reticulate scale pattern which is observed in the form of a network and divided into bands around the fibres running diagonally on the surface  between the cuticle and fibre surface, as shown in Fig. 29. Robson et al. included more parameters related to the scales  in their study that was carried out using the fibre casting method and an image analysis algorithm. There are, however, not much literature on how the scale gap could influence the diffusion of chemicals into the core of wool fibre, or could be related to different fibre properties30.Several studies have been reported in the literature to characterise different parameters related to the scale structure of wool fibres. Hausman et al. analysed several wool fibres obtained from different parts of the world  to determine the average scale gap between two scales and reported that the number of scales increased with the increase in the diameter of the fibre31 including dye molecules32. The first path of entrance of dye molecules into the fibre structure has also been confirmed by fluorescence microscopy as the intercellular gaps33. The total scale perimeter per 100 µm, used in this work signifies the total length of the cracks or opening present on the surface of a wool fibre. It can be hypothesised that higher the value of this parameter, more will be the intercellular gaps and chances for the dye molecules to penetrate inside the fibre, resulting in a higher diffusion coefficient. Diffusion coefficient (D) is defined as the change in mass of a substance that diffuse through a unit surface per unit concentration gradient. Such understanding about the diffusion coefficient value of different chemical reagents associated with wool fibre can be helpful for understanding the chemical sorption property of wool fibre and can be further utilised to manufacture filtration fabrics or materials which show high absorption of certain chemicals. The diffusion of dyes into fibre has been explained with the help of Fick’s law of diffusion34. But wool fibre in its diffusion curve follows a non-fickian diffusion at its very early stage of dyeing due to presence of surface barrier effect32. The calculation of D is a direct representation of rate of dyeing (kinetics). Diffusion in wool fibre occurs in three stages (i) from solution to the surface (ii) adsorption on surface and (iii) diffusion of dyes from surface to the core of the fibre34.The intercellular gaps present between the scales are considered to be the main diffusion pathway for chemical reagents (e.g. dyes) to penetrate into the fibre structure. This is because the rest of the outer cuticle is hydrophobic and relatively non-reactive towards many chemical reagents due to its highly crosslinked structure. Hence, the intercellular gaps influence the diffusion coefficient of these chemicals36. Mainly Hill’s equation was used for the calculation of the diffusion coefficient, with time this equation has been modified by several researchers to make the models more accurate40. The Hills equation for the current research work represents an apparent diffusion coefficient which is assumed to stay constant for the initial phase of dyeing (i) Ref.41. There are multiple factors that affect the dye diffusion coefficient among them hydrodynamic boundary layer can have a significant impact on the dyeing kinetics34. As the dye molecules approach the fibre there is a ≈ 99% decrease in the velocity of the dye before it reaches the surface. At this point the diffusion of the dye molecules becomes an influencing factor. The distance at which this change in velocity is observed is called the hydrodynamic boundary layer. This layer can be effected by the circulation velocity of the liquor and the shape of the fibre42.The mathematical equations for diffusion were developed based on the fact that it is constant , or it changes with the concentration of dye . Diffusion coefficient of dyes has been reported to be dependent on factors like shape of the fibre, concentration gradient, time, temperature, rate of agitation and also, on the structure of the dye molecules37. The knowledge of scale perimeter and SPI and its inclusion in the mathematical models of diffusion might make them more representative of real dyeing conditions.Most of the models consider wool fibre to be an infinite cylinder with no edges, but in a practical scenario wool fibre diameter varies within a single fibre and also the scales change their pattern from fibre to fibre. This may affect the hydrodynamic boundary layer thus influencing the diffusion coefficient. Theoretical modelling has always been modified from time to time to make the models more aligned with the experimental findings of dyeing. However, for natural fibre like wool it has always been very difficult to obtain an exact value for the diffusion coefficient and to conclude which theory is more suitable44. Scale height was observed to increase by 21%, on an average, in wet conditions as compared to dry conditions and the scale dimensions measured in dry conditions were more reproducible43. In wet conditions, there was swelling of wool fibre which was associated with the swelling of the cuticle, causing a change in the dimension of the scales. Therefore, the scale parameters measured using most of the previous methods were strongly dependant on the testing conditions . Moreover, the studied scale parameters have been mostly used for the identification of wool fibres and differentiate them from other hair fibres, but not for investigating the influence of surface morphology on the fibre functionality or properties. To bridge that gap in the existing literature, the present research reports novel scale parameters related to the intercellular gaps of wool fibre and discusses how these parameters can be correlated with fibre diameter as well as dye diffusion coefficient and fibre functionalities.Till date, research studies were mainly focused on the scale height which is the distance between the projected-out scale and the edge of the scale see Fig. d. TechnoWool fibres from four different UK sheep breeds were provided by Fleet Green Farm in the form of fleece. The breeds were Bluefaced Leicester (Leicester), Greyface Dartmoor (Dartmoor), Ryeland and Herdwick. Wool fibres were taken from the fleece randomly to avoid preferential sampling. Also, Welsh mountain wool fibre was obtained from British Wool and characterised to verify the experimental correlations achieved using the above four breeds of wool fibre.2CO3) supplied by Sigma Aldrich, and ULTRAVON JUN (a nonionic detergent) manufactured by Huntsman Textile Effects (Germany) GmbH and supplied by Town End (Leeds). For dyeing of wool fibres, CI Acid Violet 90, sulphuric acid and sodium sulphate (Na2SO4) were used (supplied by Sigma Aldrich).Before analysis, wool fibres were scoured using sodium carbonate  and ULTRAVON JUN (2.0 g l–1) in a liquor ratio of 1:20. The pH of the solution was 1.2. The wool fibres were immersed in the solution for 2 h at 20 ± 2 °C. The fibres were then removed, rinsed in cold water, dried and baked at 100 °C for 10 min. This was done so that all the vegetable matter present in wool could be removed as it becomes brittle. The fibres were manually crushed between two rollers so that the impurities were crushed and manually shaken to remove them. The wool fibres were rinsed once in an excess of cold water and then washed in a solution (1:20 liquor ratio) of sodium carbonate (53.0 g l–1) at room temperature. They were rinsed once again in an excess of cold water, squeezed and then dried overnight at room temperature. Damage to the F-layer of the wool fibres were evaluated by dyeing the fibres with Acid Red 1 at 2% omf, before and after carbonising. The wool fibres did not show any observable difference, hence no potential damage to the F-layer was confirmed.The scoured wool samples were carbonised based on a recipe reported by Park2SO4 and 5% Glauber’s salt. The pH of the bath was maintained at 2.7 ± 0.2, dyeing temperature was kept 90 °C and the MLR  was maintained at 1:50. The dyeing time was varied from 5 to 240 min.Pre-treated wool fibre samples from Leicester, Ryeland and Dartmoor (1 g) were dyed using a CI Acid Violet 90. The dyeing was carried out using laboratory-based Roaches Pyrotec IR dyeing machine using 2% CI Acid Violet 90 dye (on mass of fibre), 1% Ht (mg g–1) at time t was determined by the equation below.o is the initial dye concentration (mg ml–1) in the solution, Ce is the left-over dye concentration in the solution after dyeing (mg ml–1), V is the initial volume of the solution (ml) and W is the weight of wool fibre (g).The amount of dye adsorbed M47.e is the amount of dye adsorbed (mg g–1) at equilibrium, r is the radius of the fibre and D is the apparent diffusion coefficient. According to Eq.  is valid only for a finite bath. The average of two sets of repeat for dyeing kinetics study was performed and the standard error of the calculated diffusion coefficient is reported in Table The dye diffusion coefficient was calculated using the modified version of Hill’s equation for a finite bathSEM images were taken using Quanta FEG 250 scanning electron microscope (FEI Instruments) at different magnification levels ranging from 100 to 1000x. The samples were sputter coated with gold before measurement. The accelerating voltage was kept between 5 and 10 kV. The SEM images were used to evaluate different scale patterns, number of scales and the distribution of fibre diameter. For the measurement of diameter, a mean value of 50 readings for each breed was calculated and reported. Measurement of diameter for thousands of fibre via SEM images is a very tedious approach. For the mean fibre diameter, it will be beneficial to opt for an optical fibre diameter testing to have a better distribution and representation of the diameter data. The purpose of this research work was to test the initial feasibility of how scale structures of wool fibre could affect dyeing kinetics.The scale analysis methodology employed in this work possesses some key advantages to preserve the structural properties of the fibres. The fibres were not immersed in a resin or any solvent which could influence the scale arrangement. The fibres did not undergo any kind of extension (to remove the crimp). Also, the measurement was performed in a dry condition. The fibres were scoured to remove contaminants such as dirt and wool grease so that the scales were perfectly visible under the microscope, but no additional pre-treatments (e.g. bleaching) were performed which could influence the scale arrangement.Although in this method wool fibre samples were sputter coated with gold and measured in a vacuum, no previous literature indicated that this coating might change fibre and/or scale arrangement, and any changes that may occur are likely to be minimal as compared to immersion in a liquid. However, like most image analysis techniques reported earlier, this methodology characterised only one side of each fibre (a 2D image) rather than the entire 3D surface advanced technologies such as 3D SEM can be combined with the proposed method in future work for a more accurate measurement of scale morphology.The measurement of scale perimeter was performed from the SEM images using ImageJ software. Straight fibres were selected for measurements to eliminate errors caused by bending of fibres, as shown in Fig. Further, another scale parameter, namely scale perimeter index (SPI) was also calculated. SPI is a dimensionless parameter which is defined here as the total perimeter of all the visible scales on a 100 µm long 2D image of a single fibre divided by the diameter of that fibre. Therefore, SPI is defined as:max) as deduced from the calibration curve of the dye . The absorbance of the residual dye solution was calculated at 535 nm  wool showed a higher number of scales than Leicester (mean diameter 22 µm) due to the finer diameter of Leicester wool. Thus, the number of scales in the studied wool fibres per 100 µm increased with the fibre diameter. This can be clearly observed from the correlation curve plotted between the number scales and fibre diameter, as discussed in section “Total scale perimeter and scale perimeter index (SPI)”.The observations confirmed that the changes in the scale pattern of wool fibres are related to the fibre diameter. The number of scales and the scale pattern in Merino wool51. As per the discussion in Section “52. This in turn may result in different chemical absorption behaviours for different breeds of wool fibre. To investigate this further and to use effective diffusion pathway for categorising wool fibres according to their chemical adsorption property, a new scale parameter, called total scale perimeter per 100 µm, was calculated as a measure of the total diffusion paths present on the surface within a fibre length of 100 µm.It is hypothesised that the number of active molecules entering into the core of the fibre depends on the dimension of the diffusion pathway between the scales. As the number of gaps increases for a specific length of fibre (e.g. 100 µm), the amount of chemical uptake by the fibre should also increase. This is in agreement with the earlier observation that the generation of cracks on the surface of wool fibres improved the colour yield by allowing more spaces for the dye molecules to enterThe total scale perimeter per 100 µm length of fibre, SPI and number of scales were calculated for all the four wool types  with the fibre diameter, and the nature of the curve was hyperbolic  the wool fibre will exhibit depending on its diameter. Both the parameters can be used to characterise and understand the surface morphology of wool fibres.As shown in Fig. The scale pattern observed for Welsh Mountain wool fibre was coronal-reticulate, which was expected as the measured diameter of the fibre was 36 µm between 25 and 60 µm Fig. . SPI of –8 (cm2 sec–1) (respectively) using Hill’s equation (Table t/Me) curve against time1/2 and using Eq.  shows highest diffusion coefficient followed by Ryeland and Leicester.Further the D values of Acid Violet 90 were correlated to the average total scale perimeter per 100 µm and average number of scales per 100 µm, represented in Fig. The rate of increase of D between Leicester and Ryeland was significantly less compared to the rate of increase between Leicester and Dartmoor. This can be supported with the findings made earlier that Ryeland showed the presence of both coronal and coronal reticulate scale pattern. Ryeland with coronal reticulate pattern have a higher avg. total scale perimeter per 100 µm than Leicester whereas presence of two different kind of scale pattern within the same wool fibre might be the possible reason for the rate of increase in D to be less.It can be summarised from the earlier discussion that total scale perimeter per 100 µm have influenced the diffusion coefficient of Acid Violet 90 dye in the solution phase. This confirmation can have further impact on the overall rate of dyeing at the same time the amount of dye adsorbed on the fibre. Thus, further research can be performed in this area to correlate the scale parameters with dyeing thermodynamics and kinetics parameters.61. Thus, the studied scale parameters could be useful to understand the functionalities and end use of different varieties of wool fibre.Chemical properties of wool fibres  are significantly influenced by the effective diffusion pathway between the scales. The current study have opened up the possibility to investigate the effect of scale morphology on these essential properties of wool fibre44. The effect of the permanganate salt was limited to the scales of the wool fibre, modifying the cuticle, and removing the hydrophobic scales. This change in scale structure resulted in a higher value of water absorption and an improvement in the surface roughness44. In the present research paper, new scale parameters related to the effective diffusion pathway of wool fibre  have been characterised, leading to the possibility of better correlating scale morphology with important fibre properties and predicting various applications of different varieties of wool fibres:Previous literature related to surface morphology of wool fibre mainly focused on characterising the scale height Fig.  and only62. This is attributed firstly to the presence of hydrophilic groups in the protein structure of the fibre and secondly, to the surface structure of the wool fibre64. When wool fibre absorbs water, the fibre swells and creates a path for the water molecules to diffuse through the intercellular gaps and breaks the hydrogen bonds in the amino acid structure. This in turn creates more interaction sites and increases the absorption of water molecules65. In both dyeing and water sorption phenomena, the surface morphology is likely to have a very high impact on the final uptake values. A fibre with more scale perimeter per 100 µm is expected to have a higher tendency to absorb water. This parameter, therefore, can be useful for the manufacturing of technical textile products such as medical textiles where high water or liquid sorption is a key requirement.Wool has a very high-water absorption property and can absorb more water as compared to any other natural fibre66. Thus, it is expected that more is the number of diffusion paths present on the surface of wool fibre more it will be susceptible to enzymatic hydrolysis or microbial attack, leading to a faster degradation rate67. This will potentially allow wool products to be tailored with specific degradation properties.The hydrophobic crosslinked epicuticle of wool fibre also resists biodegradation of wool fibre by the action of bacteriaTherefore, with further research and experimental verifications, the studied scale parameters can be used to classify different varieties of wool fibre according to their properties and end usage. This approach and knowledge will be very important for the wool industry in terms of using different breeds of wool fibre in diversified technical textile applications like filtration , geotextiles, medical textiles, composites, garments and so on.In this research, wool fibres collected from four different British sheep breeds  were characterised using SEM to study their scale pattern and number of scales, and two novel scale parameters, namely total scale perimeter per 100 µm and SPI were calculated. The studied varieties of wool exhibited differences in their scale pattern, number of scales, scale perimeter and SPI. The patterns of scales visible on the surface were identified as coronal for Leicester and reticulate for Dartmoor wool, whereas Herdwick and Ryeland fibres showed more than one scale pattern due to their wider diameter distribution.The change in scale pattern from coronal to reticulate was associated with the change in the fibre diameter and was attributed to the increase in number of scales within a specific fibre length. Total scale perimeter per 100 μm length showed a polynomial correlation with the fibre diameter. On the other hand, SPI values were observed to decrease with the increase in fibre diameter and showed specific ranges for finer, medium and coarser fibres.The characterised scale parameters showed a good correlation with the apparent diffusion coefficient of Acid Violet 90 dye. The D values showed a steady increase with the increase in mean fibre diameter, avg. total scale perimeter per 100 µm and avg. number of scales per 100 µm. Wool fibre with highest avg. total scale perimeter per 100 μm (due to increased effective diffusion pathway) has shown the highest apparent diffusion coefficient (D) of Acid Violet 90. This clearly suggests that the effective diffusion pathway is an influencing factor during the early stage of dye diffusion.This correlation between the fibre properties and the surface morphology can be utilised to design various technical textile products . This can also contribute towards developing a framework where wool fibres obtained from an unutilised or new breed can be studied and used in the application fields mentioned above. This research work, therefore, opens up further opportunities to investigate into the correlation of dyeing and other properties of wool fibre with the scale morphology.Supplementary Information.


Domestic dogs have been shown to engage in interspecific communication with their owners using a flexible repertoire of signals . This ability is influenced by ontogenetic development as well as breed selection. Different aspects of this phenomenon have been studied using the out of reach/hidden object task in which a piece of food is shown to the dog and then hidden in an unreachable spot by the experimenter. Dogs’ behavioral displays toward the target and the owner (ignorant about the location of the food) have been observed. The complex communicative behavior dogs exhibit in this context is defined as showing behavior and includes attention-getting components directed toward the owner, and directional components directed toward the target. No study has investigated the ontogenetic development of this behavior. In the current study, we compared the showing behavior in 4–6 month old puppies and 2–11 year old adults in an out of reach task involving the hiding of a food reward in one of two cabinets. Dogs were exposed to three conditions: (1) Owner with Food (OF), (2) Owner No Food (ONF), and (3) Alone with food (AF). Dogs showed more gaze alternations when both the food and the owner were present confirming the intentional and referential nature of this behavior. Contrary to our expectations, we found no differences between the showing behaviors of 4–6 month old puppies and adult dogs. This study provides interesting preliminary evidence of showing behavior in puppies. Further studies are needed to gain a deeper understanding of the factors influencing this communicative behavior . Furthermore, longitudinal studies should be performed from the age of 2 months up to 1 and 2 years to better clarify the influence of development and experience on showing behavior in domestic dogs.The online version contains supplementary material available at 10.1007/s10071-023-01744-7. Canis familiaris) comprehension and use of different human communicative signals as well as their capacity to engage in communication with humans, attracting and directing their attention toward a desired goal  in an object choice paradigm, using the information provided by pointing, gazing, and head orientation toward a target  is initially shown to the dog by an experimenter and then in the absence of the owner, hidden out of reach . In this task, the owner ignores the presence and location of the food/toy and the dog can inform them with behavioral cues.This test allows researchers to assess the intentional and referential nature of dogs’ communication with humans. It evaluates whether  and how  dogs direct owners’ attention toward the hidden reward Gaunet .The term showing was introduced by Miklósi et al.  to descrIn a pilot study by Hare et al. , they reThe out of reach/hidden object task has allowed for further evaluation of which contexts and situations this behavior takes place  and adult dogs (2–11 years old). A testing procedure was adopted from Miklósi et al.  and CavaBased on previous findings  between 4 and 6 months of age (mean age = 4.83 SD ± 0.71), and 23 adult dogs  between 2 and 11 years of age (mean age = 4.63 SD ± 3.09). Data from 7 dogs (6 adults and 1 puppy) were omitted due to errors in the procedure or camera failures. Therefore, the final sample included 17 puppies  and 13 adults  .All subjects were recruited either via social networks and word of mouth or with the support of two dog centers that hosted us for the study and helped us to recruit subjects with just basic training and a high motivation toward food. All subjects lived as companion animals within the household, had no visual or hearing problems, no behavioral problems, and were used to meeting strangers. None of the adults had received specific training but just basic training . Some puppies attended a puppy class or had just started to attend it. Owners provided information about dogs’ favorite food and were instructed not to feed the dogs for at least 3 h before the test.Canis Sapiens Lab” at the Università degli Studi di Milano, the “Green Dog Club” at Zibido San Giacomo, and the “Al Mulino” dog center in Sozzago. The two dog centers’ rooms were private rooms in which dogs were not allowed and closely reproduced the “Canis Sapiens Lab” room (2.5 m × 3.5 m): an unfamiliar indoor environment illuminated by both natural and artificial light, without furniture other than the equipment needed for the test, quiet, and without distractions. Figure Dogs were tested in three different locations: “Two small opaque rectangular plastic bowls 13 × 8 cm) were used as food containers and placed on two different cabinets, so that the dogs could see and smell the food but not reach it. The two cabinets were located opposite to each other on the long side of the room and equally distant from the chair where the owner sat , with an upside-down wooden box  fixed on the top with an opening in which the food container was placed. The second one consisted of five black plastic fruit boxes which were tied together  and fixed on a wooden support. In this case, the food container was inserted into the space between the top two boxes. Both cabinets were fixed to the floor to make them stable.The use of two cabinets differing in shape and material could help, especially in pups, to remember in which cabinet the food was hidden. The owner, while in the test room, sat on a chair placed in front of the door, equally distant from the two cabinets. The food used in the test ranged from small pieces of sausage, dried beef, or the dog's favorite snack brought by the owner.The test was recorded using a wide-angle video camera (Sony HDR-PJ410) placed on a tripod on the opposite side of the owner’s chair to capture the full view of the room. The experimenter used her smartphone to precisely monitor the timing for each part of the task.The test procedure was similar to the one used in the previous studies  Owner with Food (OF), (2) Owner No Food (ONF), and (3) Alone with food (AF). The AF condition was always the last presented, since a pilot study revealed that both puppies and adult dogs could show signs of distress when remaining alone in the room after the owner exited. The remaining two conditions were counterbalanced, so that half of the subjects were exposed to the OF followed by the ONF condition and vice versa.Each condition consisted of four consecutive phases, with Phase 1 and Phase 4 being the same in all conditions see Fig. . Before Dog and owner were in the room and the owner sat on his/her chair and read for 1 min.The experimenter entered and asked the owner to leave. Then, in the conditions OF and AF, she called the dog and said in Italian “Do I have something for you? What is it?”, while showing the dog a piece of food . After that, she took the bowl from one of the two cabinets and put the food in it, while the dog was looking and placed it back in its original place. In the condition ONF, after calling the dog, she also said “Do I have something for you? What is it?” while showing empty hands and gently interacting with the dog. Finally, she left the room.In the conditions OF and ONF, the owner entered the room and, as in Phase 1, sat down reading for 1 min, giving no attention to the dog. In the condition AF, the dog remained alone in the room for 1 min.This phase lasted 30 s and was included to evaluate the effect of the owners’ attention on dogs’ showing behavior .Two coders (GP and ET) analyzed 26% of the videos to assess intercoder reliability. The Spearman correlation score revealed good reliability for all the behaviors coded  (function “glmmTMB”) was used to compare puppies’ and adults’ behaviors in the different phases of the different conditions. We adopted a “poisson” error distribution for frequency response variables  and a “beta” error distribution for proportion . The frequency or proportion of the behavioral variables were modeled in the function of the interaction between the group (puppies/adults), the condition , and the phase (Phase 1/Phase 3/Phase 4). For the behavioral variables directed toward the cabinet with food , we included the behaviors directed toward the cabinet with food for the phases in which food was present and we considered a randomly selected cabinet for the phases in which no food was present. In the models for the “gaze alternations”, we included the duration of the phase as an offset term to account for its variability. In all the models, we included sex and area of testing as fixed effects as well as subject ID as a random effect to account for repeated observations of the same individual.For testing the impact of the interaction between the group and the other two predictors (group*condition*phases), we compared the full model with a null model lacking the factor group (puppies/adult) and its interaction with the other two predictors. If the three-way interaction did not have a significant impact on the behavioral variable, the predictor group (puppies/adults) was included in the model as a fixed effect, without the interaction with the other two predictors.Then, as an overall test of the impact of the fixed effects and to avoid “cryptic multiple testing” . A significant effect of the factor group was found for the behavior looking at the door (p = 0.044), but not for interaction with the door (p = 0.571), with puppies looking for less time at the door compared to adults.The full-null model comparisons revealed no significant impact of the three-way interaction (group*condition*phase) neither of the fixed effect “group”, revealing no significant differences between puppies and adults in showing related behaviors . In particular, dogs performed more gaze alternations in Phase 3 compared to Phase 1 in the condition OF. No such difference was present in the conditions ONF and AF. Dogs performed more gaze alternations in Phase 4 (when the owner gave attention to them) compared to Phase 3 of the condition OF. This effect was present also in the condition AF where the dogs performed more gaze alternations in Phase 4 (when the owner re-entered the room) compared to between the chair and the cabinet with food in Phase 3 (when the owner was outside the room). No differences in gaze alternations were found between the phases of the condition OF . In the condition, OF dogs looked more at the cabinet with food in Phase 3 compared to both Phase 1 (no food present) and Phase 4 (food present and owner giving attention to the dog). This effect was not present in the other two conditions  (interaction: full-null model comparison: p = 0.000). Only in the condition OF, dogs interacted with the apparatus more in Phase 3  compared to both Phase 1 (food absent and owner ignoring the dog) and 4 (food present and owner giving attention to the dog).In regard to the interaction with the cabinet with food, a significant interaction between the factor condition and phase was found (interaction: full-null model comparison: p = 0.000). Dogs looked more toward the owner in Phase 4  and then in Phase 1 and 3: this effect was present in all the experimental conditions but clearly significant in the condition AF . Dogs were looking toward the door for longer in Phase 3 compared to Phase 1 and 4 in the AF condition, when the owner stayed outside the room. No such effect was found in the other two conditions. No significant impact of the factor phase or condition was found for the behavior “interaction with the door”.Looking toward the door was influenced by the interaction between the condition and the phase (full-null model comparison: p = 0.000). In particular, dogs wagged their tail significantly more in Phase 4 compared to Phases 1 and 3 in the condition AF. This significant effect was not present in the other conditions, even if there was a tendency for longer duration of tail wagging in Phase 4 .Tail wagging was influenced by the interaction between the condition and the phase (full-null model comparison: p = 0.002). Dogs whined for longer duration in Phase 3 compared to the other two phases.The time dogs spent whining was influenced by the phase, regardless of the condition (full-null model comparison: p < 0.001). Nine out of 13 adult dogs’ owners  correctly reported both the presence and location of food; however, this result was not above chance level . In the AF condition, only 6 pups’ owners  and 4 adult dogs’ owners  succeeded in the task.At the end of the conditions in which food was hidden  the experimenter asked the owners whether they thought there was any food hidden inside the room and, if there was any food, where it was located. In the OF condition, 16 out of 17 pups’ owners (94%) reported both the presence and location of food above chance level .Differences in success between puppy and adult owners in either condition were not significant  looked significantly more at the cabinet with food in Phase 3 of the OF condition compared to one cabinet chosen randomly in Phase 1. Furthermore, in Phase 3, both adults and pups looked significantly more at the cabinet with the food in the “Owner with food” condition compared to the other conditions (ONF and AF). Thus, gazing at a cabinet was strictly linked to the presence of food in it, and was triggered by the presence of both owner and hidden food, as previously reported  than in Phase 4 . This result is in line with that reported by Henschel et al. . They foThis study is the first investigating showing behavior, as described by Miklosi et al. , in puppSupplementary file1 (DOCX 628 KB)Below is the link to the electronic supplementary material.


R, may remain poorly identifiable with these models. Here we show that this identifiability issue can be resolved by taking into account disease-specific characteristics of the transmission process in closer detail. Using tuberculosis (TB) in the San Francisco Bay area as a case study, we consider a model that generates genotype data from a mixture of three stochastic processes, each with its own distinct dynamics and clear epidemiological interpretation. Earlier research has suggested that approximate Bayesian computation (ABC) makes it possible to fit simulator-based intractable birth–death models to investigate communicable disease outbreak dynamics with accuracy comparable to that of exact Bayesian methods. However, recent findings have indicated that key parameters, such as the reproductive number     R related to the primary underlying transmission process is estimated to be nearly three times larger than previous estimates, which has a substantial impact on the interpretation of the fitted outbreak model. We show that our model allows for accurate posterior inferences about outbreak dynamics from aggregated annual case data with genotype information. As a byproduct of the inference, the model provides an estimate of the infectious population size at the time the data were collected. The acquired estimate is approximately two orders of magnitude smaller than assumed in earlier related studies, and it is much better aligned with epidemiological knowledge about active TB prevalence. Similarly, the reproductive number Under circumstances where a disease outbreak occurs but where daily, weekly or even monthly incidence counts are not directly applicable or available, the estimation of key epidemiological parameters, such as the reproductive numberR, has to be based on alternative sources of information. This can be the case when the disease demonstrates large variability between the times of infection and onset, such as withMycobacterium tuberculosis, or in retrospective analyses where some information is no longer available. In such situations, aggregate measures of the clusteredness of cases  can be used as alternative sources of information. In the case of tuberculosis, which generally mutates on a timescale much longer than that of a single outbreak, it is reasonable to assume that new cases arising from transmission during that outbreak will all belong to a single cluster. Likelihood-based inference could provide an alternative to standard outbreak investigations relying solely on incident count data, but it is often considerably more challenging.Birth–death processes are flexible models used for numerous purposes, in particular for characterizing the spread of infections under the so-called Susceptible–Infectious–Removed (SIR) formulation of an epidemic processet al. proposed fitting birth–death (BD) models to tuberculosis (TB) outbreak data using approximate Bayesian computation (ABC). Later on, the same setting was used in numerous ABC studies while the ABC methodology was being developed. Stadler and Aandahlet al. also tested the ABC procedure against an exact Bayesian inference method based on an elaborate Markov Chain Monte Carlo (MCMC) sampling scheme. These investigations considered TB outbreak data from the San Francisco Bay area originally collected by Smallet al., who reported results from extensive epidemiological linking of the cases, as well as from the corresponding classical IS6110 fingerprinting genotypes. Such genetic data from the causative agentMycobacterium tuberculosis are natural to characterize using the infinite alleles model (IAM), where each mutation is assumed to result in a novel allele in the bacterial strain colonizing the host. When lacking precise temporal information about the infection and the onset of the active disease, the numbers and sizes of genotype clusters can be used to infer the parameters of the BD model, as shown by Tanakaet al. and Aandahlet al..As a solution to such a setting, Tanakaet al. demonstrated an issue with the nonidentifiability ofR for the TB outbreak model in cases when both the birth and the death rates were unknown in the underlying birth–death process. This was visible as a nearly flat approximate likelihood over the parameter space ofR. Additionally, they found that in cases whenR was identifiable, the acquired estimate was dependent on the assumed population sizen. In an earlier investigation by Tanakaet al., a large infectious population size ofn = 10,000 was required for the BD simulator to produce similar levels of genetic diversity to those observed in the San Francisco Bay data. Because it has not been observed, this assumption is difficult to justify when the acquired estimates depend on it.LintusaariR.Here we introduce an alternative formulation of the BD model that resolves the identifiability issue ofet al., we see that both the significantly reduced infectious population sizen and the increasedR for the main driver component of the model make good sense. Our model thus provides a drastically different interpretation of these parameters than the ones offered by earlier studies.The proposed model does not require any assumptions about the underlying infectious population size, instead providing an estimate for that value as a byproduct of the inference. The model incorporates epidemiological knowledge about the TB infection and disease activation processes by assuming that the observed genotype data represent a mixture of three birth–death processes, each with clearly distinct characteristics. The new formulation depends on partially different parametrization, for which estimates can be found in the literature. By evaluating the ABC inference results of our model against the backdrop of the epidemiological information available in Small. Through this and other epidemiologically motivated modelling choices, we show that the model becomes identifiable. Due to the rather modest requirements for the available data and the flexibility of modelling in ABC, our BD model could be applied to many similar settings beyond the case study considered in this article.In the new model, we consider latent and active TB infections separately, as only the latter lead to new transmission events. Transmission clusters are formed by recent infections that rapidly progress to active TB and spread further through the host population. Due to the rapid onset of symptoms in a new active case, the fingerprint of the pathogen remains the same throughout the transmission process, and its patients consequently form an epidemiological cluster. If, on the other hand, an infection remains latent, the pathogen undergoes mutations and thus acquires a new genetic fingerprint over the yearsOur model is based on a birth–death (BD) process in which a birth event corresponds to the appearance of a new case of active TB and a death event corresponds to any event that makes an existing host non-infectious. Such events include death, sufficient treatment, quarantine, and relocation away from the community under investigation. The model incorporates two BD processes and one pure birth process that have epidemiologically based interpretations. As in a standard BD process, these events are assumed to be independent of one another and to occur at specific rates. The time between two events is assumed to follow the exponential distribution specified by the rate of occurrence, causing the number of events to follow the Poisson distribution. The timescale considered here is one calendar year. The evolution of the infectious population is simulated by drawing events according to their rates.Building upon the BD process, the simulated population carries auxiliary information. At birth, each case is assigned a cluster index that represents the specific genetic fingerprint of the pathogen and determines the cluster the case belongs to. The simulated output includes the cluster indexes that are recorded when cases are observed.et al..We will now explain our model in more detail and point out differences between it and the model of Tanaka. Observations are collected from the simulated process after a sufficient warmup period so that the process can be expected to have reached stable properties. This procedure is visualized inFirst, we assume that observations are collected within a given time interval that matches that of the observed data. In the case of the San Francisco Bay data, the length of this interval is two yearsobsp. Our model makes the simplifying assumption that both being observed and ceasing to be infectious are combined under the death event in the simulation. This is based on the assumption that a typical patient is treated promptly after being diagnosed, but we still allow for the possibility that some patients do not comply with treatment and remain infectious (see below). In contrast to the model of Tanakaet al., there is no separate observation sampling phase, nor is there a prior estimate for the underlying population size.In the figure, the dashed lines are the balance values. The population sizes fluctuate around them after the process has matured. Both populations surpass their balance values at least once by the 22-year mark. The observation period is the green patch. The grey line shows the number of observations collected during each year of the simulation. The number of observations from the observation period and the clustering structure of the observations are used in the inference of the epidemiological parameters. A patient becomes observed in the study with probabilityβ that reflects the rate at which new active TB cases with a previously unseen pathogen fingerprint appear in the community. This is the pure birth process of the model, and it represents reactivation of TB from latent cases as well as new pathogen fingerprints introduced by immigration. In the simulation, each such case receives a new cluster index that has not been assigned to any earlier case. Unlike Tanakaet al., we do not explicitly model mutations. Instead, we assume they occur during the latent phase of infection over the years. This decision was partially motivated by the fact that Aandahlet al. found the mutation rate parameter fromWe introduce a burden parametercompliant ornon-compliant with treatment. These birth–death processes are parametrized with birth ratesiτ and death ratesiδ, wherei = 1 denotes the non-compliant population andi = 2 the compliant population. A significant number of cases in the largest clusters observed by Smallet al. corresponded to non-compliant patients who stayed infectious for several months and belonged to subgroups under increased risk of rapid development of active TB due to conditions such as AIDS and substance abuse. Patients who are compliant with therapy typically cease being infectious quickly and do not transmit the disease as effectively as before diagnosis and treatment. Meta-analysis of typical time delays before diagnosis can be found in Sreeramareddyet al..We introduce two distinct birth–death processes for cases that are eitherp1. At transmission (birth event in the simulation), this probability is used to determine the patient type of the new case. We also assume that the epidemic is at a steady state , wheren1 andn2 are the current subpopulation sizes andp1 is the probability of a case being non-compliant. The corresponding death rate isδ1n1. Using this approach, we can determine the balance sizesb1 andb2 of the subpopulations—that is, the values ofn1 andn2 that make the birth rate equal to the death rate in each subpopulation. In this steady state, the subpopulation sizes neither shrink nor grow. We obtain expressions forb1 andb2 by solving the following set of linear equations:Let subscriptp2 = 1 –p1 is the probability of a new case being compliant. The linear equations yield the following solution:whereb1 andb2 exist whenGiven this solution, the balance valuesp2 = 0.95   software3.1.1 Priors. We set priors over the burden rateβ, reproductive numbersR1 andR2, and the net transmission ratet1 =τ1− δ1 of the non-compliant subpopulation. For the compliant population, we fix the death rate to an estimatedδ2 = 5.95 . Given the severity of the symptoms of active TB and bearing in mind the stringent protocols followed by public health officials, it is expected that virtually all active cases in the San Francisco Bay area were documented during the outbreak described inobsp = 0.8. We set the probability of a new case being non-compliant top1 = 0.05 . The pairwise sample clouds seem reasonably concentrated, do not extend to the edges of the axes, and are located inside the support of the prior  of the mean as well as the coverage propertysee e.g. caused bβ) and the reproductive number of the non-compliant population (R1) have the smallest relative MAEs: 4.0% and 14.9%, respectively. The reproductive number of the compliant population (R2) and the net transmission rate of the non-compliant population (t1) have MAEs of 29.5% and 44.2%, respectively. The MAE of the latter seems rather high. The 95% percentile indicates that in 5% of the trials, the error was substantial. Further investigation of this issue shows that for some of the synthetic datasets,t1 is not identifiable, meaning that the synthetic data in those cases is not informative enough to produce a clear mode for the parameter.R2 suffered slightly from the same problem. This kind of situation, where some of the synthetic datasets turn out uninformative, is rather common when little data is available. Because of these exceptions, the MdAE might be a more appropriate measure than the MAE, as the former is not as heavily influenced by the results of non-identifiable datasets in trials. The relative MdAE errors forR2 andt1 were 21.9% and 32.1%, respectively.t1 is only weakly identifiable, the results of our simulations indicate that the set of epidemiological parameters we have analyzed is identifiable for the San Francisco Bay dataset. Our simulations suggest that a structural model issue could be at fault for the weak identifiability oft1, as this can arise as a consequence of the generating stochastic process producing a relatively flat cluster distribution. Fortunately,β ,R1 andR2, all of which provide more valuable epidemiological insight thant1, are robust against this identifiability issue.Though is used to assess the reliability of the inference by checking whether the spreads of the acquired posterior distributions are accurate. Given a critical levelα, the true parameter value should be outside the 1−α credible interval of the posterior with probabilityα. We carried out our coverage analysis as follows.The coverage propertyFirst, we used rejection sampling to produce a sample for the posterior from the observed data. From this posterior, we sampled 1000 parameter vectors (with replacement) for the trials. For each of these 1000 vectors, we simulated synthetic data and performed rejection sampling in order to acquire posterior samples for that data. We then calculated the MAE for these 1000 trials. Finally, we applied the coverage property by determining in how many of the 1000 trials the original parameter was in the credible interval of the marginal posterior acquired from the synthetic data.α values from the 1000 marginal posteriors with known true parameter values appear satisfactory  = . The overall performance for different values ofα was similar to this case in the sense thatβα suffered from a larger error than the other parameters’ estimates . This assumption has a considerable effect on the estimate of the reproductive numberR. However, epidemiological knowledge of TB does not support the existence of such a large infectious population in the study region during the observation period. Under our model, a prior estimate of the infectious population size is not needed. This model has a different parametrization for which estimates can be found from the literature. As a byproduct of the inference, the model also yields estimates for the infectious population size at the end of the data collection period. For the San Francisco Bay data, we found that the mean and median sizes of the compliant subpopulation were 48.4 and 48, respectively. The equivalent estimates for the non-compliant subpopulation were 13.5 and 11. These values are consistent with the findings of Smallet al..Earlier approachesR1 orR2) represents the average number of infections caused by a single infectious case that rapidly progresses to active TB. This value excludes latent infections, which are indirectly captured via the burden rate parameterβ. We estimate that the basic reproductive number of non-compliant patients isR1 = 5.88 with a 95% credible interval (CI) of ; seeet al. with the same data,R1 = 2.10, which served as a blanket estimate for the whole infectious population (a distinction was not drawn between patient types). Our larger value would reasonably explain the formation of large clusters over a short time period. We estimate the reproductive number of the compliant subpopulation to beR2 = 0.09 with a 95% CI of .For each subpopulation, the basic reproductive number  before they cease to be infectious, which implies that this simulator model deviates slightly from the real-world observation process. However, considering that this discrepancy applies to only roughly 5% of all observed cases, we do not expect it to cause significant bias. Furthermore, our summary statistics do not depend on exact diagnosis times: they rely instead on the span and the rate at which diagnoses occur.R1 was 14.9% . However, as discussed earlier, it is probably more sensible to use the median error  forR2. Coverage property analysis suggests that the credible intervals produced by this model are reasonable. In future work, it would be interesting to evaluate the sensitivity of the model to other choices of literature-based parameter estimates.Our model’s identifiability was found to be satisfactory for the San Francisco Bay dataset . The relR and removing the dubious assumption of ana priori known infectious population size by extending the BD model with relevant epidemiological knowledge from the literature, it would be interesting to generalize this approach to other pathogens for which the sampling process or other factors make simulator-based inference the most promising estimation method.As IS6110 typing remains in use despite advances in whole-genome sequencing of TB isolates, our model could be especially useful for investigations in middle- and low-income countries, where TB burden is often the highest. For example, the acquired estimates of epidemiological parameters could be used to gain insight into the relative efficacy of control programs across multiple communities. Given the apparent success of resolving the non-identifiability issue forThe observed data are available inhttps://doi.org/10.6084/m9.figshare.7578728.v1.Figure S1 is available atSource code:https://github.com/jlintusaari/tb-modelArchived source code at time of publication:https://doi.org/10.5281/zenodo.2540933License:3-Clause BSD license The authors have very carefully addressed my comments, and I am happy with the current version.Is the rationale for developing the new method (or application) clearly explained?PartlyIs the description of the method technically sound?YesAre the conclusions about the method and its performance adequately supported by the findings presented in the article?PartlyIf any results are presented, are all the source data underlying the results available to ensure full reproducibility?YesAre sufficient details provided to allow replication of the method development and its use by others?YesReviewer Expertise:Statistical population geneticsI confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. i.e. the flow of individuals between different states while pointing out individual rates, e.g. see Figure 1 athttps://institutefordiseasemodeling.github.io/Documentation/general/model-seir.html for SEIR model) would help the readers to grasp quickly the mathematical model.While adding a workflow of the study helps greatly, we think that adding a flow diagram of the model  should be kept.“It should be noted that the summaries chosen here do not consider global sufficiency. In cases where the dataset is very different from the San Francisco data, a modified set of summaries should probably be considered.” With respect to this remark, we believe an extensive list of the summary statistics that you tried before identifying the final set, would help further research and adaptation of your method to similar studies. Such a list might be added as Supplementary Material.The authors have made changes that further improved the clarity and the flow of the manuscript and addressed our comments and suggestions. We propose final approval of the paper. We would like to suggest several minor changes not requiring any further analysis. Hope this helps, sincerely, Jakub Voznica, Anna Zhukova and Olivier GascuelIs the rationale for developing the new method (or application) clearly explained?YesIs the description of the method technically sound?YesAre the conclusions about the method and its performance adequately supported by the findings presented in the article?YesIf any results are presented, are all the source data underlying the results available to ensure full reproducibility?YesAre sufficient details provided to allow replication of the method development and its use by others?YesReviewer Expertise:NAI confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. This interesting paper covers an area - TB epidemiology - that has been the subject of a number of papers that have used approximate Bayesian computation (ABC). These studies have also involved some full-likelihood MCMC solutions for the same models. The present paper carries out an ABC analysis with an alternative modelling framework, which provides some satisfactory solutions to some problems that had been previously noted.et al. paper explicitly emphasised the importance of modelling the mutational structure of clusters (3rd paragraph of the introduction). By contrast the present paper gives no justification for dropping the mutational modelling. My reason for querying this is that, as I understand it, Tanaka had a previous history of detailed work on TB epidemiology, prior to the 2006 paper, including co-authorship with Peter Small, and so presumably was able to put in the benefit of that experience into the paper. Therefore I recommend that this aspect be much better justified and discussed. I generally have few quibbles with the ABC analysis. My only main query with the paper, in my ignorance of TB epidemiology, is to what extent the new modelling framework gives a reasonable representation of the underlying biology. I note that the original Tanaka On the ABC side, my main query is to what extent the authors are confident about identifiability of their parameters. Particularly, since they seem to suggest one of their parameters is not identifiable (discussed more in specific points below). In a model-free setting, identifiability is demonstrated through simulation, rather than analytically. Obviously, if non-identifiability is shown this naturally leads to some questions about the summary statistics etc. as well as the structure of the model itself. But, with informative priors, some parameters that are only jointly identifiable can appear to be identifiable marginally - in a population genetics context the apparent identifiability of N and \mu with informative priors is a case in point, when only their product is identifiable. Again, this needs a bit more discussion than in the present paper.Specific Comments:et al. is that multiple outbreaks can involve the same cluster, and that different clusters (due to mutation?) could arise from the same outbreak.Introduction, first paragraph: "genotype fingerprints". Some more discussion of this would be useful with regard to my point above. Presumably what concerned TanakaModel, 4th paragraph: “p_{obs}” - does the assumption of being observed lead to ceasing to be infectious fit with the compliant/non-compliant distinction, two paragraphs further down?Model, 5th paragraph: Note my main query.Summary statistics, paragraph 2: It might be helpful to emphasise that a 'cluster' here is assumed to be a new active TB case. Presumably many of these summary statistics are highly correlated with the parameter \beta?Figure 2/3: I wonder whether these might be better in the supp. text, and replaced with a single figure with HPD contours for the prior and posterior.), which are generally straightforward to apply? I think there are good reasons  for expecting the optimal number of summary statistics to be the same as the number of parameters, thus reducing the effect of the 'curse of dimensionality'.Summary statistics, last paragraph: "It is good to note". Do the authors mean that? Or rather do they mean "It should be noted"? Presumably it is not good to be not sufficient. More generally, is there an argument to use projections as in Fearnhead and Prangle  in Prangleet al. (2014) .Results, 3rd paragraph: coverage property. The analysis seems fine, but the authors skirt some details, worth noting. They use 'true' values from the ABC posterior. The WegmannResults, 4th paragraph: non-identifiability of t_1. This observation seems at variance with what is stated in the abstract. Is this a summary statistic issue? Or a structural model issue?).Figure 5: These results look convincing. Note that because of the need for a tolerance interval ABC coverage is not expected to be perfect  clearly explained?PartlyIs the description of the method technically sound?YesAre the conclusions about the method and its performance adequately supported by the findings presented in the article?PartlyIf any results are presented, are all the source data underlying the results available to ensure full reproducibility?YesAre sufficient details provided to allow replication of the method development and its use by others?YesReviewer Expertise:Statistical population geneticsI confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. We thank the reviewers for their useful comments that allowed us to improve the paper. Below we provide detailed responses to the issues brought up. Our responses are written in italics.This interesting paper covers an area - TB epidemiology - that has been the subject of a number of papers that have used approximate Bayesian computation (ABC). These studies have also involved some full-likelihood MCMC solutions for the same models. The present paper carries out an ABC analysis with an alternative modelling framework, which provides some satisfactory solutions to some problems that had been previously noted.I generally have few quibbles with the ABC analysis. My only main query with the paper, in my ignorance of TB epidemiology, is to what extent the new modelling framework gives a reasonable representation of the underlying biology. I note that the original Tanaka et al.paper explicitly emphasised the importance of modelling the mutational structure of clusters (3rd paragraph of the introduction). By contrast the present paper gives no justification for dropping the mutational modelling. My reason for querying this is that, as I understand it, Tanaka had a previous history of detailed work on TB epidemiology, prior to the 2006 paper, including co-authorship with Peter Small, and so presumably was able to put in the benefit of that experience into the paper. Therefore I recommend that this aspect be much better justified and discussed.This is a very relevant point. However, the subsequent joint work by the Tanaka et al. authors and Tanya Stadler notified that the mutation parameter appears non-identifiable from the fingerprint data and used a fixed value obtained from the literature in their most recent paper. We have now included a discussion about this and the rationale for excluding an explicit mutation rate parameter in our model. On the ABC side, my main query is to what extent the authors are confident about identifiability of their parameters. Particularly, since they seem to suggest one of their parameters is not identifiable (discussed more in specific points below). In a model-free setting, identifiability is demonstrated through simulation, rather than analytically. Obviously, if non-identifiability is shown this naturally leads to some questions about the summary statistics etc. as well as the structure of the model itself. But, with informative priors, some parameters that are only jointly identifiable can appear to be identifiable marginally - in a population genetics context the apparent identifiability of N and \mu with informative priors is a case in point, when only their product is identifiable. Again, this needs a bit more discussion than in the present paper.We agree that an additional discussion is in place and have added such in the revision. Our simulation experiments reported in the paper suggest that the key epidemiological parameters are indeed identifiable for the SF Bay data set, even if the net transmission rate may remain only weakly identifiable. Specific Comments:    Introduction, first paragraph: "genotype fingerprints". Some more discussion of this would be useful with regard to my point above. Presumably what concerned Tanaka et al. is that multiple outbreaks can involve the same cluster, and that different clusters (due to mutation?) could arise from the same outbreak.We have added further discussion. Noting the slow mutation rate of TB, it is highly unlikely that multiple clusters would arise from the same outbreak within a relatively short timespan.        Model, 4th paragraph: “p_{obs}” - does the assumption of being observed lead to ceasing to be infectious fit with the compliant/non-compliant distinction, two paragraphs further down?th paragraph. We have now revised the text to be in line with the later paragraph.Good point, there was a sloppy phrasing in the 4         Model, 5th paragraph: Note my main query.As noted in our response to the main query item, we have now edited the text accordingly.        Summary statistics, paragraph 2: It might be helpful to emphasise that a 'cluster' here is assumed to be a new active TB case. Presumably many of these summary statistics are highly correlated with the parameter \beta?Excellent remarks, we have added further clarification about this.        Figure 2/3: I wonder whether these might be better in the supp. text, and replaced with a single figure with HPD contours for the prior and posterior.We do appreciate this suggestion, however, as noted in the response to R1,the first author who had the main responsibility for all aspects of the presented work has already graduated and left academia, as has the second author, so neither of the two are able to contribute to further work related to this paper. We would thus prefer keeping the two figures as in their current versions.        Summary statistics, last paragraph: "It is good to note". Do the authors mean that? Or rather do they mean "It should be noted"? Presumably it is not good to be not sufficient.The reviewer has a correct interpretation, this was a typo and is now fixed.1), which are generally straightforward to apply? I think there are good reasons  for expecting the optimal number of summary statistics to be the same as the number of parameters, thus reducing the effect of the 'curse of dimensionality'.More generally, is there an argument to use projections as in Fearnhead and Prangle  .They use 'true' values from the ABC posterior. The Wegmann et al. paper, following Cook et al., simulated 'true' values from the prior, for which coverage is indeed uniform. It is not so obvious that coverage from the ABC posterior should also be uniform, but this is demonstrated (I think for the first time) in Prangle et al. .    Figure 5: These results look convincing. Note that because of the need for a tolerance interval ABC coverage is not expected to be perfect  with a pure-birth process that creates new TB transmission clusters . This pure-birth process replaces mutation in Tanaka’s model and corresponds to migration or reactivating of a latent TB. The rate corresponding to the pure-birth process is referred as the burden rate. At each (non-burden) birth event (i.e. TB transmission) the compartment of the newly infected individual is assigned to non-compliant or compliant with the probability p1 or (1 - p1) correspondingly. At each death (i.e. becoming non-infectious) event the individual is sampled with the probability p-obs. The article describes a new model of TB outbreak in San Francisco Bay area that overcomes the non-identifiability/dependency on the assumed population size of the reproductive number R in the generic birth-death-mutation model by Tanaka Overall, the proposed model has 7 parameters: the burden rate, 2 birth rates, 2 death rates, and 2 probabilities (p1 and p-obs). However, 3 of them  were fixed based on the estimates from the literature, therefore leaving 4 parameters to be estimated, expressed in terms of two reproductive numbers, i.e. birth to death rate ratios for the corresponding compartments, the non-compliant net transmission rate (difference between the birth and the death rates), and the burden rate. Priors and additional constraints on the rates were set to avoid biological meaningless of the simulations. The simulator was implemented for the proposed model and parameter estimation was performed for the data collected in SF Bay area in 1991-92  with ABC, based on 1000 parameter values sampled with rejection from 6M simulations, using 8 (weighted) summary statistics:   1.    the number of observations 2.    the total number of clusters 3.    the relative number of singleton clusters 4.    the relative number of clusters of size two 5.    the size of the largest cluster 6.    the mean of the successive difference in size among the four largest clusters 7.    the number of months from the first observation to the last 8.    the number of months when at least one observation was made.  The new model not only allowed for estimation of the aforementioned parameters (posteriors are well concentrated within but far from the edges of the priors) but also of the balance subpopulation sizes (at the equilibrium state when infected subpopulations neither shrink nor grow). The estimates differ from those done with the birth-death-mutation model, and are potentially better aligned with the epidemiological knowledge on TB in the area. The coverage property (accuracy of the spread of the acquired posterior) of the estimator was further tested on 1000 parameter values drawn from the posterior, giving satisfactory results for the critical level of .05 .General comments The article reads well, the model, rationale behind it, its assumptions and advantages over the previous TB model are explained in a clear and convincing way. It is a valuable addition to TB research, and we believe that the article should be accepted. Having little knowledge on TB (but on ABC), we feel like the article could benefit from a more detailed discussion of the obtained estimates. For example, is there any literature/other data supporting the estimated subpopulation sizes? We also point out a few technicalities that could be explained in more detail (see below).Technical comments A flow diagram of the model could facilitate the model understanding for the reader. Additional sensitivity analysis of the model while varying pre-fixed parameter values  might add confidence in author’s findings.Figure 1).”“The observations are collected from the simulated process after a sufficient warm-up period, so that the process can be expected to have reached stable properties ...” Page 5: The authors might detail what kind of inference was used: Is it a pure distance/rejection-based approach? Or do you use some regression tool, random forest, LASSO, neural network or other? How was the technique selected? “Based on the details in Small et al. describing the San Francisco Bay area TB data, there were 585 confirmed cases of TB of which 487 were included in the study. To account for the cases that were not included in the study, we fix the probability of becoming observed to p-obs = 0.8” Page 5: If we understand correctly the p-obs is calculated as 487/585, but what about potentially unknown cases of TB in the SF Bay area? Is it assumed that all the existing TB cases are known?“the mean of the successive difference in size among the four largest clusters” Page 5: It is not very clear why these particular summary statistics were selected, e.g. Why not 3 or 5, etc.? Were for example other statistics tested, which performed worse?“the number of months when at least one observation was made”) is rather confusing. In table 1 it has a slightly different name:“the number of months that at least one observation was made from the largest cluster”. Does it meanthe time when the first observation from the largest cluster was made? The name of the last statistic  clearly explained?YesIs the description of the method technically sound?YesAre the conclusions about the method and its performance adequately supported by the findings presented in the article?YesIf any results are presented, are all the source data underlying the results available to ensure full reproducibility?YesAre sufficient details provided to allow replication of the method development and its use by others?YesReviewer Expertise:NAWe confirm that we have read this submission and believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however we have significant reservations, as outlined above. We thank the reviewers for their useful comments that allowed us to improve the paper. Below we provide detailed responses to the issues brought up. Our responses are written in italics.R1:The article describes a new model of TB outbreak in San Francisco Bay area that overcomes the non-identifiability/dependency on the assumed population size of the reproductive number R in the generic birth-death-mutation model by Tanaka et al.  The new model considers two compartments, for compliant and non-compliant subpopulations, and combines two birth-death processes (for each of the compartments) with a pure-birth process that creates new TB transmission clusters . This pure-birth process replaces mutation in Tanaka’s model and corresponds to migration or reactivating of a latent TB. The rate corresponding to the pure-birth process is referred as the burden rate. At each (non-burden) birth event (i.e. TB transmission) the compartment of the newly infected individual is assigned to non-compliant or compliant with the probability p1 or (1 - p1) correspondingly. At each death (i.e. becoming non-infectious) event the individual is sampled with the probability p-obs.Overall, the proposed model has 7 parameters: the burden rate, 2 birth rates, 2 death rates, and 2 probabilities (p1 and p-obs). However, 3 of them  were fixed based on the estimates from the literature, therefore leaving 4 parameters to be estimated, expressed in terms of two reproductive numbers, i.e. birth to death rate ratios for the corresponding compartments, the non-compliant net transmission rate (difference between the birth and the death rates), and the burden rate. Priors and additional constraints on the rates were set to avoid biological meaningless of the simulations.The simulator was implemented for the proposed model and parameter estimation was performed for the data collected in SF Bay area in 1991-92  with ABC, based on 1000 parameter values sampled with rejection from 6M simulations, using 8 (weighted) summary statistics: 1.    the number of observations2.    the total number of clusters3.    the relative number of singleton clusters4.    the relative number of clusters of size two5.    the size of the largest cluster6.    the mean of the successive difference in size among the four largest clusters7.    the number of months from the first observation to the last8.    the number of months when at least one observation was made.The new model not only allowed for estimation of the aforementioned parameters (posteriors are well concentrated within but far from the edges of the priors) but also of the balance subpopulation sizes (at the equilibrium state when infected subpopulations neither shrink nor grow). The estimates differ from those done with the birth-death-mutation model, and are potentially better aligned with the epidemiological knowledge on TB in the area.The coverage property (accuracy of the spread of the acquired posterior) of the estimator was further tested on 1000 parameter values drawn from the posterior, giving satisfactory results for the critical level of .05 .General commentsThe article reads well, the model, rationale behind it, its assumptions and advantages over the previous TB model are explained in a clear and convincing way. It is a valuable addition to TB research, and we believe that the article should be accepted.We thank the reviewers for their highly positive comments about our work.Having little knowledge on TB (but on ABC), we feel like the article could benefit from a more detailed discussion of the obtained estimates. For example, is there any literature/other data supporting the estimated subpopulation sizes?The estimates are well aligned with the epidemiological discussion in the original NEJM paper introducing the fingerprint data. We now point this out more carefully in the revised version.We also point out a few technicalities that could be explained in more detail (see below).Technical commentsA flow diagram of the model could facilitate the model understanding for the reader.A flow diagram has been added as a supplementary figure to accompany the final version.Additional sensitivity analysis of the model while varying pre-fixed parameter values  might add confidence in author’s findings.We feel that the current sensitivity analysis is quite sufficient and fulfils its purpose to demonstrate stability of the estimates for data akin the San Francisco Bay observations. The first author who had the main responsibility for all aspects of the presented work has already graduated and left academia, so he is not able to contribute to further work related to this paper which limits our possibilities for performing extensive additional simulations. Page 4: “The observations are collected from the simulated process after a sufficient warm-up period, so that the process can be expected to have reached stable properties .”In Figure 1 the warm-up seems to be achieved already after 15 years, however the observation period is chosen around 45 years, where there is a drop of population sizes. Is it a coincidence? How is the start of the observation period selected?Figure 1 is intended only as a schematic numerical example to assist the reader in understanding the underlying logic of the model and the sampling assumptions. The drop is thus coincidental. This is now properly noted in the revision.Page 5: “We used the Engine for Likelihood-Free Inference (ELFI)...”The authors might detail what kind of inference was used: Is it a pure distance/rejection-based approach? Or do you use some regression tool, random forest, LASSO, neural network or other? How was the technique selected?As stated in the paper, we used pure rejection sampling . The main reasons for choosing this basic ABC approach were: 1) we implemented a computationally efficient vectorized Python version of the simulator which facilitated the use of a large number of simulations, 2) at the time the project was initiated, ELFI had yet no implementation of the Bayesian optimization procedure for non-uniform priors. Such a prior was essential for the model structure and straightforward to consider in a pure ABC rejection sampler, hence the choice for inference method was well motivated. These reasons are now more clearly stated in the revision.Page 5: “Based on the details in Small et al. describing the San Francisco Bay area TB data, there were 585 confirmed cases of TB of which 487 were included in the study. To account for the cases that were not included in the study, we fix the probability of becoming observed to p-obs = 0.8”If we understand correctly the p-obs is calculated as 487/585, but what about potentially unknown cases of TB in the SF Bay area? Is it assumed that all the existing TB cases are known?For epidemiological reasons it is unlikely that any substantial numbers of active TB cases were unknown to the public health officials, hence it is unlikely that these would have a non-negligible contribution to the observed outbreaks. Given the severity of TB and the protocols followed by public health officials most active cases are expected to have been traced. We have now stated this more explicitly in the revision.Page 5: It is not very clear why these particular summary statistics were selected, e.g. “the mean of the successive difference in size among the four largest clusters”Why not 3 or 5, etc.? Were for example other statistics tested, which performed worse?The name of the last statistic (“the number of months when at least one observation was made”) is rather confusing. In table 1 it has a slightly different name: “the number of months that at least one observation was made from the largest cluster”. Does it mean the time when the first observation from the largest cluster was made?We have edited the text to make the summary statistic definitions unambiguous. The summary statistics were iteratively defined by trialing inference on synthetic data from the model. The final set of statistics was settled on after extensive test simulations showing appropriate behavior. Note also that we had previous experience about the behavior of various summary statistics from the earlier Lintusaari et al. Genetics 2016 article examining inference for a different model but the same data.Page 7: “The chosen summary statistics and weights were found to perform well in the evaluation of the model in Subsection .”The subsection number is missing.The subsection number was missing due to the submission template and will be visible in the final typeset version.Page 7: “The resulting threshold for the acquired sample was ∈ = 31.7 with the smallest distance being 12.5.”How were the threshold and distance values selected?As for the summary statistics, the threshold was settled by extensive trialing of inference on synthetic data from the model to identify a threshold striking a good balance between runtimes and acceptance rate and the resulting Monte Carlo error rate. This is now more appropriately reported in the revision.