The Avon Longitudinal Study of Parents and Children (ALSPAC) is a prospective population-based study. Initial recruitment of pregnant women took place in 1990-1992 and the health and development of the index children from these pregnancies and their family members have been followed ever since. The eligible sampling frame was constructed retrospectively using linked recruitment and health service records. Additional offspring that were eligible to enrol in the study have been welcomed through major recruitment drives at the ages of 7 and 18 years; and through opportunistic contacts since the age of 7. This data note provides a status update on the recruitment of the index children since the age of 7 years with a focus on enrolment since the age of 18, which has not been previously described. A total of 913 additional G1 (the cohort of index children) participants have been enrolled in the study since the age of 7 years with 195 of these joining since the age of 18. This additional enrolment provides a baseline sample of 14,901 G1 participants who were alive at 1 year of age. During the initial recruitment campaign (between 1990 and 1992) women with a total of 14,541 pregnancies were enrolled (some women had more than one eligible pregnancy during this period). The children resulting from these pregnancies and their parents have been followed up ever since, primarily via questionnaire, hands-on measurement at clinical assessment visits  including the provision and assaying of biological samples and through linkage to routine data. ALSPAC is now a three-generational study, comprising ‘G0’: the cohort of original pregnant women, the biological father and other carers/partners; ‘G1’: the cohort of index children and ‘G2’: the cohort of offspring of the index children. The study website contains details of all the data that is available through afully searchable data dictionary andvariable search tool.The Avon Longitudinal Study of Parents and Children (ALSPAC) is a geographically defined, longitudinal birth cohort that recruited pregnant women with an estimated date of delivery between April 1991 and December 19921 describes in detail how the families have been followed up until the age of 18 (G1) and describes how recruitment was extended to include members of families who were eligible to have taken part , did not initially enrol but who subsequently wanted to take part. Families were enrolled into the study inphase I between 1990 and 1992 during pregnancy and shortly after birth. Further enrolment occurred systematically inphase II in 1999 at the age 7 assessment clinic (child mean age: 7.5 years) and then opportunistically inphase III from 1999 until 2012 (child mean age: 17.8 years). Since 2012, ALSPAC has conducted an additional systematic recruitment drive and have continued to recruit additional families through opportunistic contacts and through recruitment of the G2 offspring of the index children (inphase IV recruitment). This data note provides an update on recruitmentphases II andIII and reports specifically onphase IV recruitment: that is, all those G1 participants who enrolled in the study from the age of 18 up to and including the clinic assessment held at age 24 (mean age 24.5 years). The 2012 G1 cohort profile paper1. This means that the study has a record of the identities  of most index children who are eligible to participate. This has allowed ALSPAC to respond to enquiries from both participants and the wider public, for example around eligibility to participate and use of an individual’s data in research projects. Forphase IV recruitment, since the age of 18 years, there were three ways in which eligible G1 index children (now adults) could enrol into ALSPAC. Firstly, all participants who could be traced were systematically invited to enrol in a postal exercise conducted by PEARL. This was part of their campaign to provide fair processing information to G1 as they reached legal adulthood and as ALSPAC started to systematically link to their health and routine administrative records. Secondly, during recruitment of the G2 participants, the study came into contact with individuals - either as the partner of an enrolled participant or through screening by midwives – who were eligible but had not previously enrolled. Thirdly, eligible participants proactively requesting to enrol are always welcomed and enrolled into the study.Through the Project to Enhance ALSPAC through Record Linkage (PEARL), ALSPAC has retrospectively defined the study’s eligible sampling frame through linking study recruitment records to NHS delivery records and child health recordsphase I). It should be noted that the G0 mothers of 69 pregnancies with unknown outcome have historically always been considered asPhase I enrolees, this is appropriate for the G0 cohort profile but not for G1 (since it is not clear how many foetuses were in each of these pregnancies and resulting offspring have not taken part in the study and therefore cannot be adequately quantified). G0 mothers of 456 G1 participants enrolled during the systematic campaign at age 7 (i.e. enrolled inphase II). A further 262 G1 participants enrolled through opportunistic contact between the ages of 8 and 18 (i.e. enrolled inphase III). This results in a total of 15,394 G1 participants who enrolled by the age of 18  are eligible to take part in the study. Of these pregnancies 116 had an unknown birth outcome. Of the eligible pregnancies, the G0 mothers of 14,676 G1 participants enrolled during the original recruitment campaign (i.e. enrolled inf 18 see. Please phase IV). Of these, 177 were recruited through systematic postal invitations during 2014. An additional 14 were recruited through the ALSPAC-G2 recruitment campaign: This means that an eligible member of the cohort enrolled after either: i) becoming pregnant, ii) their partner becoming pregnant or iii) they were already a parent. Finally, 4 enrolments resulted fromad hoc approaches from eligible participants during this period  G1 participants have enrolled who were not in the initial study sample (i.e. phase I enrolment). The total sample size for analyses is therefore 15,454 pregnancies, resulting in 15,589 foetuses. Of this total sample of 15,589 potential G1 participants, 14,901 were alive at 1 year of age (it should be noted that self-reported data are not available prior to the time of recruitment for those enrolled inphase II or later) and are considered the baseline sample for reporting purposes .A total of 913  which describes the process of accessing the data and samples in detail, and outlines the costs associated with doing so.Please read the ALSPAC access policy , which lists all research projects that have been approved since April 2011.You may also find it useful to browse our fully searchable research proposals database  for consideration by the ALSPAC Executive Committee. You will receive a response within 10 working days to advise you whether your proposal has been approved.Please submit your research proposal (The variables described in the cohort profile data file (ALSPAC reference: cp_2b) are provided as a matter of course with all data requests see. The denalspac-data@bristol.ac.uk.If you have any questions about the data or how to access it, please emailhttp://www.bristol.ac.uk/alspac/researchers/research-ethics/).Ethical approval for the study was obtained from the ALSPAC Ethics and Law Committee and the Local Research Ethics Committees. Informed consent for the use of data collected via questionnaires and clinics was obtained from participants following the recommendations of the ALSPAC Ethics and Law Committee at the time. Children were invited to give assent where appropriate. Study participants have the right to withdraw their consent for elements of the study or from the study entirely at any time. Full details of the ALSPAC consent procedures are available on the study website . As I understand from the note, these were individuals who would have been eligible to participate but did not actually enrol in the study until a later date. Summary details are given on the number of individuals, the broad stage at which they joined and how they were recruited – particularly given the most recent joiners between the ages of 18 and 24 years.Opinion The main points of the note are generally clearly described and benefit from the inclusion of the diagram in Figure 1, which breaks down the numbers joining and at what stage. There are two exceptions: (a) in Table 1, it is not clear whether the n for ‘known address’ and ‘linked to Primary health care data’ etc. are subsets of the 13,286 described as ‘currently active’ in row 1 or the full 14,901 participants in the final cell of Figure 1; (b) in the abstract, the term “additional offspring” implies later children who were born to the same mother could enrol but in the main note text that does not appear to be the case.Do we know why the late joiners did not originally participate? Had their mother initially refused or were they not identified as eligible at the start? The note suggests the latter might have been the case for some.A brief reminder of the eligibility criteria at the start would be useful. I assume, for example, that only people initially born in the Avon area be able to join the study later and not those who immigrated there at a later date, but I am not certain from reading the note in isolation.How similar is the demographic profile of the late-joiners to the originally enrolled sample ? And have the study weights been adjusted to account for the characteristics of the new joiners?The note makes brief mention of cohort ‘G0’, the mothers of the original children known as ‘G1’. If a data user were considering using G0 data, it would be good to know if (a) any of the mothers of the late joiners also entered the study in their own right and (b) if they stay in the study even if their G1 children leave. I have no particular criticisms of the note, and it should be a useful resource for those using (or considering using) the ALSPAC data. There are some additional points that would be ‘nice to know’ however. Perhaps the authors could consider either including them either (briefly) in the note or adding a reference to direct the reader to the relevant information elsewhere? They are as follows:I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. This is a useful paper for anyone using the ALSPAC resource, setting out how the additional participants have been included at different stages. The innovative methods have been reported in detail and we anticipate that the availability of this Data Note will enhance understanding. We do however have some suggestions that might aid clarity: We found the use of the term ‘index’ somewhat confusing. ‘Index’ to us rather implies the first children recruited. This paper describes the additional recruitment of children after the original (index) children had been recruited. Maybe stick to the term G1, where necessary, after defining it? Also we felt that there is a confusion in the title in that it implies that the additional children were all enrolled in 2019. Could it be reworded to say “a 2019 update on the enrolled sample of index children”? The abstract could do with a little clarification. The words ‘additional offspring’ is slightly confusing as it sounds as though it’s additional children born to the original mothers. As eligibility hasn’t been defined at this point, it’s not easy to follow what this means. Maybe the authors could define eligibility in the abstract and then make it clear that those children who would have been eligible, but who were missed originally, have later been included in the study. Also in the abstract it would be helpful if the word ‘additional’ could be inserted before ‘recruitment’ in the sentence: “This data note provides a status update on the recruitment of the index children since the age of 7 years with a focus on enrolment since the age of 18, which has not been previously described”. When you say that the original eligibility criteria were applied retrospectively, did you extract the expected date of delivery for all them to check this, or was it based on date of birth? It would be helpful if reference to Figure 1 was moved to near the top of the Study numbers section as it is useful to look at it while reading the subsequent paragraph. In the first paragraph on study numbers, there are these two sentences: “G0 mothers of 456 G1 participants enrolled during the systematic campaign at age 7 (i.e. enrolled in phase II). A further 262 G1 participants enrolled through opportunistic contact between the ages of 8 and 18 (i.e. enrolled in phase III).” At age 7, presumably the G1 participants were enrolled in addition to their mothers? In the enrolment between ages 8 and 18 were no G0 mothers enrolled or was it just the children? Also were any G0 participants enrolled in phase IV? In the sentence “As with previous phases, phase IV enrolment included two twin pregnancies where only one twin enrolled.” it is not clear whether both twins were ever included in any phase. The flowchart implies not, but it would be helpful if this could be clarified. We found the numbers in the top three boxes of the flowchart somewhat confusing. The 14,676 + 5,760 fetuses do not sum to 20,505 in the top box, whereas the 14,541+5,707 pregnancies do sum to the 20,248 in the top box. The 69 are included in the pregnancies but not in the fetuses in the left-most box, and this isn’t clear. At the end of the second paragraph of the Study numbers, it might be helpful to add something like “but will be included in subsequent data collection waves”. The following sentence was initially confusing: “The cohort profile data is provided in all data extracts, even where participants have formally withdrawn from the study or who are at high risk of disclosure, though it should be noted in these cases their data are supressed.” It seems odd to say that the profile data are provided for everyone but then to say that the data are suppressed for particular participants. It might help to modify the end of the sentence to say “… in these cases other data are suppressed”. (Please note that “suppressed” has been typed incorrectly). Minor comments: There seems to be an extraneous “(G1)” in the second line of the second paragraph of the introduction. At the end of the first paragraph of Study numbers section, reference number 1 should superscripted. The sentence in the last paragraph of the introduction that starts: “Since 2012, ALSPAC has conducted an additional systematic recruitment drive and have continued to recruit additional families through….” makes ALSPAC singular and plural. We suggest that ‘have’ should become ‘has’. Similarly there is inconsistent use of data as plural and data as singular in the last sentence of the first paragraph of the Cohort profile data file section. In Table 1, it’s pretty obvious that Qs stands for questionnaires but there is room to spell it out in full.We have read this submission. We believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.


For small ruminants, Gastrointestinal Nematodes (GINs) are responsible for severe economic losses and they are also an animal welfare problem. GIN use their host to reproduce and disperse eggs on the pasture, from where they can re-infect another animal. The high density of hosts on the pasture and the extreme tolerance of GIN to environmental constraints make GIN eradication almost impossible. In addition, significant resistance to anthelmintic treatment requires sustainable and integrated management to maintain the health and financial well-being of livestock farming. In this context, models of the complex interactions between host, GIN and environment can help us to design long term optimal management strategies. To build such models, quantitative information is needed but are generally very challenging to collect. In this article, we focus on the number of ingested larvae per animal, which we propose to characterise by using a simulation framework based on the estimation of the spatial distribution of the host over time. Our framework allows us to show that worm burden individual variation is not only explained by the host’s genetics, as is often the case, but is also a result of the grazing spatial process. For any grazing animals, infection by GINs is an almost inevitable event, but the severity during lifetime and the animal’s reaction varies. While the causes explaining this variability are mostly known–they can be intrinsic  and extrinsic –quantifying their effects on the success of an infection event and its consequences is very challenging.Gastrointestinal Nematodes (GINs) are a major threat to the health and welfare of small ruminants and they can be responsible for severe economic losses4. Parasitic stages (P) start when the host ingests infective L3, which eventually establish inside the host and develop into reproductive adult GINs. Reproduction of the species is only possible inside the host, where new eggs are laid with the feces and dropped on the pasture. Control and research efforts mostly focus on the parasitic stages, where it is possible to kill the GINs, either using chemicals or by improving host’s resistance. In this article, we are interested in the meeting point between (FL) and (P): the ingestion of L3 and more precisely to study the distribution of the ingested L3 among the individuals of a same flock.The life cycle of GINs is a succession of free living stages (FL) and parasitic stages (P). During (FL), GINs are found on the pasture, where they were dropped in the feces of infected animals. GINs start as eggs, and they eventually hatch and evolve into infective L3 that can survive for a relatively long period of time depending on meteorological factors, such as temperature and humidity5 and affect the population dynamic of parasites, as in the periparturient rise of fecal eggs count6. In addition, L3 are known to have a clumped distribution on the pasture7, which could be responsible for the aggregated distribution of parasites among the flock8 and helps to spread resistant parasites to anthelmintic treatments10. Although quantitative data can be useful to improve control, they are quite hard to collect. Indeed, estimating the spatial distribution of L3 on the pasture is highly time consuming and it is technically difficult to observe the quantity of ingested L3 during natural grazing11, to such an extent that a modeling approach is needed. The timing and quantity of ingested L3 are the result of two correlated spatial processes: (L) the spatial distribution of L3, resulting itself from (D) the spatial distribution of animals over time. Foraging behavior12 can explain part of (D) and has been used to define and parameterise models describing the displacement of small ruminants over time15. Even if it is possible to use these models to simulate animals displacement and feces deposit to study parasite transmission16, modeling an animal’s decision is inevitably a difficult task, particularly because not only feeding influence displacement over the day, but also environmental factors and social interactions, not accounted for in these models. In our study, instead of relying on foraging behavior theory, we proposed relying directly on (D), which is the flock’s spatial distribution over time.The timing and quantity of ingested L3 are important because they can drive the future resistance status of an individualWe used drone imagery to record the positions of goats, who were managed under rotational grazing. We recorded the position of two flocks  during their first week on their respective pasture. Making the hypothesis that the likelihood of dropping feces clump on a given position increases with the time that the animal spends on that position, we were able to simulate spatial distribution of L3 when the flock re-entered the pasture one month later. The individual positions were also recorded during this second week, which we used this time to estimate the ingestion risk, making the hypothesis that ingestion risk increases with the time spend on a position × the number of L3 present on the herbage. We hypothesised that ingestion risk and number of ingested L3 are proportional and that information on the risk distribution can also be used to characterise the distribution of the number of ingested L3. Our framework is entirely stochastic.a ∈  describes how a goat explore the pasture, spending many (few) times on few (many) quadrats when a is high (low). Second, we characterised the spatial distribution of the feces. We finally used our framework to discuss the effect of the number of individuals on a pasture.We first proposed to characterise the risk distribution at the individual and flock scales, starting by analyzing the effect of specificity on the individual risk distribution. The specificity parameter The simulation model is summarised in Fig. The model’s inputs are the feces parameters, elicited from the literature, the quadrats occurrence frequencies at the flock scale during the first and second grazing week (two replicas), as well as meteorological data, which were both recorded during a dedicated experiment. The model then simulated the individual time spent on each quadrat during the first and second grazing week, the feces deposit during first week and L3 spatial distribution at the beginning of the second grazing week. The model is finally used to simulate an individual L3 ingestion risk.r, p), that we used to simulate the FEC of each animal at the beginning of a simulation . We recall that initial mean FEC is equal to Unless otherwise specified, our conclusions are the same for the first and second flock. In the following, initial Fecal Eggs Count (FEC) distribution refers to the distribution, or more precisely parameters .The individual’s specificity seems to increase the Mean Individual Ingestion Risk (MIIR), as shown on Fig. g = 1, for a given initial FEC distribution, no matter the specificity value. The individual’s risk distribution is right-skewed with a long tail. In other words, an individual is generally exposed to low risk  but high exposure is still possible. Even after a logarithmic transformation, the individual’s risk distribution is still right-skewed and the normality hypothesis is generally rejected . We displayed the individual’s risk classes as a function of the initial FEC parameters on Fig. R2 > 0.9). For the first (second) flock, the MIIR increases by 0.20 (0.24) with the initial mean FEC.Our sample includes the 5,000 simulated risk values of the first goat R ≥ 0.9). For the first (second) flock, the mean simulated flock’s risk increases by 0.20 (0.23) with the mean initial FEC.We now study the risk distribution at the flock scale. A sample becomes the simulated risk of the entire flock for a given initial FEC distribution, therefore, there are 250,00 samples. The flock’s risk distribution is again right-skewed but this time a log transformation is sufficient to ensure normality of the sample in more than 99.8% of the cases . See Fig. The feces’ spatial distribution is highly aggregated, resulting in most quadrats having a low number of L3 and a few quadrats having a high value . The aggregation index generally increases with the mean of the initial FEC distribution but there is too much variation to fit a linear model.Statistically, the hypothesis of an aggregated dispersion is confirmed using the index of dispersion2 on a pasture. We first virtually divided the pasture into 25 zones of approximately 43 m2 and we then randomly selected n = 1, …, 5 sampling units (20 × 20 cm quadrats) per zone. The sampling units were chosen independently for each simulated spatial distribution of L3. Due to the aggregated nature of the feces’ spatial distribution, L3 are also highly aggregated on the pasture, which complicates sampling. Indeed, L3 are rarely found in the sample, which decreases the sample mean and in practice can lead us to mistakenly conclude that the pasture is not infected. The estimated average number of L3/m2 generally has a very poor quality, with more than 96% of error for each flock and all the tested number of samples. Note that increasing the number of samples has very little effect; for example, for the first flock, the average percentage of error is 96.7% with 25 samples and still 96.1% with 125 samples. The percentage of error is obtained as:x is the true number of L3/m2, 2 and |.| is the absolute value function.We used the simulated spatial distribution of L3 to study the efficacy of uniform random sampling to estimate the average number of L3 per m2 was small.For both flocks, in more than 43%, 19%, 9%, 4% and 2% of the simulations, no L3 were present in the 25, 50, 75, 100 or 125 sampled quadrats. In other words, in more than 43% of the cases, the pasture was mistakenly classified as not infected when using 25 samples. As one can see in Fig. Finally, we varied the number of goats in the pasture from 10 to 30 using simulation scheme S2. For a fixed pasture size, the average risk of the flock naturally increases with the number of goats present on the pasture. We fitted a linear model with interactions, explaining the average risk of the flock as a function of the number of goats and of the mean initial FEC:R2 = 0.997 for the first flock and R2 = 0.99 for the second flock. The estimated parameters are available in Table This model explains most of the variance with NbIg is the number of ingested L3 by goat g and NbL3q is the number of L3 on quadrat q. However, this framework does not allow us to compute the constants c1 or c2 but we believe that characteristics of the risk distribution and of the number of ingested L3 might be similar. In other words:The individual’s grazing behavior (here the specificity) influences the daily number of ingested L3.Distribution of the number of daily ingested L3 at the individual and flock scale is right-skewed and is in any case non-homogeneous.The average individual and flock daily number of ingested L3 increase with the average initial FEC and number of goats in a fixed pasture.on-ground sampling.The spatial distribution of L3 on the ground is highly aggregated and inhomogeneous, which certainly explains the risk distribution and makes estimation difficult via We studied the problem of L3 ingestion risk for goats managed under rotational grazing. As far as directly observing the number of ingested L3 is unmanageable, we proposed the first modeling approach to quantitatively characterise the ingestion risk distribution. This model is based on an estimation of the quadrat occurrence frequencies at the pasture scale and the hypothesis that the number of ingested L3 by an individual on a given position is proportional to the number of L3 on the ground and the time spent on this position:These conclusions echo the results from the literature that were described in introduction but our work brings quantitative informations that were missing for model design. More generally, our modeling framework shows that not only an animal’s body conditions and genetic but also mechanisms of infection  and grazing spatial process are responsible for individual variation. We believe that better quantifying timing and number of ingested L3 can improve the modeling of the host parasite interaction and will eventually improve the host’s management. In addition, models that simulate infection dynamic should benefit from our framework to link worm burden reduction and short/long term infection risk. We ran our model in a particular situation  and with a particular species (goats) and, therefore, the conclusions may change with other settings. In particular, it should be very interesting to compare the conclusions with sheep, who have a totally different behavior, or to compare with young animals who do not know the spatial distribution of food on the pasture.18, which will certainly provide a better estimation of the quadrats occurrence frequencies. Our framework can also benefit from higher resolution images, allowing individual detection and activity detection , which in turn will allow better risk estimation. We showed that individual time per quadrat can be approximated using occurrence frequencies but other materials, such as GPS19, can allow us to compute the individual time per quadrat and an accelerometer will allow us to record activity20. Other parameters can also be accounted for, such as the pasture topology combined with the daily precipitation to account for L3 movement via water21.To consolidate these conclusions, our modeling framework can be first combined with higher picture frequency22 or by mechanically removing the eggs or dry feces. This framework can also be used to better understand animal behavior and to identify areas that are more attractive for animals, and then enlarge these areas through agronomic improvement.Finally, this framework could also be used as a management tool. Indeed, if the time per quadrat can be recorded in real or near-real time and FEC are updated regularly, then one can follow the risk distribution per individual and concentrate management effort only on animals with higher risks. One can also identify areas in the pasture with the highest probability of having a large number of L3 and, for example, try to decrease the egg’s development with plant secondary metabolitesWe recorded the positions of the animals in the two flocks, who were managed under rotational grazing. Each flock alternates grazing on five different pastures of approximately 1.2 ha each , spending 7 days per pasture, from Friday until Thursday of the next week, before moving to the next adjacent pasture. For example, when a flock is on pasture P1 on a given day, it will be again on pasture P1 five weeks later. The first flock (F1) was composed of 21 goats and 27 kids, while the second flock (F2) was composed of 22 goats and 28 kids. Pastures are located  at the INRA-PTEA farm under a tropical climate. Each pasture is connected to a free access shelter where the animal can spend the night and have access to water. Every morning at around 8 am, a concentrate supply was distributed in the shelter.th 2017 to April 13th 2017. We replicated this study one month later, thus when each flock was back on the initial pasture, from May 15th 2017 to May 18th 2017. Due to losses in flock F2, each flock was composed of 27 kids during the second observation week while the number of adult goats remained constant.We recorded the positions of the goats on the two pastures during four consecutive days, from April 10We flew a drone (Phatom 3 of the Dji brand) every 15 to 30 minutes and take a picture of the two flocks, from 9 am to 6 pm at about 50 m from the ground. No photo was taken during a one-hour break around noon. In total, 122  and 120  photos were taken during the first week for the first and second flock; and 113 , 115  during the second week. The photos did not provide direct geographical information, so we used the QGis software v 2.18.5 to point on each of the goats (not the kids) present in the pasture and then extract their spatial coordinates. Note that we did not differentiate the activity of the animals  because this was too difficult based on a picture taken from behind. All of the statistical analyses were performed using Matlab.Panicum maximum, Digitaria Decumbens, Dichanthium sp., Paspalum dilatatu, Kyllinga sp., Brachiaria mutica purpuresens, Achyranthes aspera, Sida acuta, Digitaria swazilandensis, and Sporobolus indicus. Note that the zones are highly heterogeneous and several species, if not all, can be found inside a same zone. Meteorological data were collected from the nearest weather station 1 km away, from the on-line platform https://intranet.inra.fr/climatik_v2/ClimatikGwt.htmlClimatik .We virtually delimited several zones in the pastures, depending on the predominant grass species. We delimited the pasture of the first flock, denoted P1, into ten different zones and the pasture of the second flock, denoted P2, into seven different zones. The dominant grass species on each of the zone is provided in Supplementary Table We proposed a simulation framework because it allows us to describe the time that each animal spends on the different locations of the pasture during the first grazing week. From this, we simulated the number of eggs that were deposited on each of these locations and the effect of environmental factor on the development of eggs into infective L3. Finally, based again on the locations and time spend when the flock re-enter the pasture, we derived an infection risk for each animal. Schematic representations of our simulation frameworks are proposed in Supplementary Figs nQ and the number of goats on the pasture nG. Let us define tgq, the time  spent by goat number g ∈ {1, …, nG} on quadrat number q ∈ {1, …, nQ}. In addition, Tg is the total time spend on the pasture by individual number g, while Cq is the accumulated time spent on quadrat number q, such that we have:Notations: We virtually divided each pasture into a regular grid of square quadrats of 1 m each. The number of quadrats in a pasture is denoted g and q during week 2.We will use q is equal to g. Thereby, individuals are more likely to drop feces on the quadrats that they visited the most.Fecal deposit: We hypothesis that feces are deposited in clumps and that the probability of one fecal clump being deposited on quadrat et al.23 to estimate the number of fecal clumps per animal over a period of 11 hours, which follows a normal distribution with mean 8.5 and standard deviation 3.6. We used the work from Ortega-Jimenez et al.24 to estimate the weights of feces per individual over a period of 5 days (dry matter), which follows a normal distribution with mean 1900.2 grammes and standard deviation 688.11 grammes. We scaled these probability distributions to simulate a weight of feces and number of clumps per animal given the time spend on the pasture Tg. We hypothesis an equal weight distribution among clumps. Finally, we initialised the number of eggs per gram of feces  for each animal using the work from Mahieu et al.25, where they sampled 15 farms in Guadeloupe. We fitted a negative binomial distribution to each of the 15 farms to derive a realistic numerical domain for the r and p parameters of the negative binomial distribution. The domain for r is  and  for p.We used the work from Takeuchi Note that we divided each quadrat into smaller 20 cm square quadrats and recorded the locations of each clump to be used in other section.et al.26 to simulate the effects of environmental factors  on the development of eggs into infective L3. When the flock re-enters the pasture one week later, on average, only 0.1% of the eggs developed into infective L3 and survived at this time.Life cycle of the free living stages: We used the work from Rose Ez as the time needed for one goat to consume all the resources of a quadrat located zone z. We supposed that for each minute on a quadrat, a proportion q, a goat g is selected with probability Ingestion risk: Let define It is hazardous to interpret this quantity directly as the number of ingested L3 and we preferred to define it as a risk, which can nonetheless be a first approximation of the number of ingested L3. In our opinion, the number of ingested L3 is likely to be function of this risk. Note that risk can either be considered as a continuous variable or discrete variable when rounded.tgq are not directly observable and need to be estimated. We first estimated the cumulative flock grazing time for week 1 and 2 by taking the integral of the extrapolated number of goats as a function of time. This represents the sum of the grazing time of each goat over the 4 days of the experiment. We finally divide this cumulative grazing time by the number of goats to get the average grazing time per individual, denoted mgw, for week number w = 1, 2. Finally, to consider variation among individuals during the simulation, the grazing times Tg were drawn from a normal distribution of mean mgw and variance σ * mgw at the beginning of each run.The drone only provides the positions of individuals on a discrete time step, thus the fq denote the normalised frequency for quadrat q, such that We computed the frequency at which a goat was observed on a quadrat; i.e., the number of time a goat was detected on the quadrat divided by the number of pictures took from the drone. Let λg1, …, λgnQ} a set of normalised weights such that for all goat g:λgq is simply the proportion of time goat g spends on quadrat q. There are unfortunately no ways to estimate this weight using our dataset or any published data and, therefore, the weights will be drawn randomly. These weights depict some aspect of the animals’ behavior. For example, when they are all equal , the goat tends to explore all the quadrats. In contrast, when only a few of the weights are non-zeros, the goat is very specific and only spends time on a few quadrats. To simulate these different behaviors, we proposed to use a geometric distribution of parameter a ∈ . When a = 0.001, the time distribution is uniform and all weights are almost equal. When a = 0.1, the time distribution is highly heterogeneous, with the most visited quadrat monopolising 10% of the cumulative grazing time; and nearly 96% of the quadrats are visited for less than 1% of the cumulative grazing time . Once the weights are fixed, we simply used tgq = λgq * Tg. a will be called the specificity parameter.Let define {r, p) and specificity parameter a. We used a constant value of p, equals to the mean value estimated on the dataset from25. We selected five values of r such that the corresponding means of the initial FEC distributions cover the domain of the observed mean in the dataset. We used p = 32.55e−5, r =  and a = . For each of the parameter combination, we ran 1000 simulations. There is thus 5 * 5 = 25 parameter combinations and 125*1000 simulations were run in total. A simulated trajectory thus includes:r, p) and mean An individual initial FEC value, drawn from a negative binomial with parameter  = , we used a = 0.001 for the first goat g = 1 and drawn a randomly for the other goats g > 1. Simulated risk of the first goat will be used to analyze the risk distribution at the individual scale and the effect of the specificity parameter. See Fig. Note that for each run, parameter g ≥ 1. In this case, there are 5*1000 simulations.We used a simplified scheme for the other experiments by choosing specificity parameter randomly for all goats We used Matlab to run the simulation and all of the codes are available in the supporting information All mathematical notations are summarised in Supplementary Table The animals were already present at the farm and because the drone flew at an altitude of 50 m, the animals’ behavior and welfare were not impacted. Our experiment did not require any intervention of any type on the animals. The animals were manage under normal condition at the PTEA farm, respecting French and European laws.Supplementary tables and figures


We introduce a new dissimilarity measure between a pair of “clonal trees”, each representing the progression and mutational heterogeneity of a tumor sample, constructed by the use of single cell or bulk high throughput sequencing data. In a clonal tree, each vertex represents a specific tumor clone, and is labeled with one or more mutations in a way that each mutation is assigned to the oldest clone that harbors it. Given two clonal trees, our multi-labeled tree dissimilarity (MLTD) measure is defined as the minimum number of mutation/label deletions, (empty) leaf deletions, and vertex  expansions, applied in any order, to convert each of the two trees to the maximum common tree. We show that the MLTD measure can be computed efficiently in polynomial time and it captures the similarity between trees of different clonal granularity well. Here, each individual vertex represents a distinct clone and each mutation (i.e. its label) is placed as part of the label of clone where it occurs for the first time in evolutionary history. In this work we focus on trees built by the use of single nucleotide variants (SNVs), which represent the most widely used type of mutations in reconstructing trees of tumor evolution [One of the most widely used ways of depicting mutational heterogeneity and tumor progression over time is by the use of a volution . We alsovolution ) allow fmutation tree, a special case of the clonal tree, where the label of each vertex consists of exactly one mutation [u, v) and assume without loss of generality (WLOG) that a set of all mutations assigned to it is u, v) by a path with vertices k mutations assigned to it can be expanded to a chain of k vertices, each having exactly one mutation as its label, in k! different ways. Consequently, considering the numbers of mutations assigned to vertices of the clonal tree T and taking the product of factorials of these numbers gives a formula for computing the exact number of different mutation trees that can be obtained from T.A popular alternative to the clonal tree is the mutation , 5—thus There are additional tree representations  for tumoIn the past few years, we have witnessed rapid developments in computational methods for inferring trees of tumor evolution from both bulk and single cell high throughput sequencing (HTS) data –15.ground truth tree the true tree. Other studies, such as the Pan Cancer Analysis of Whole Genomes Project (PCAWG) compare trees inferred by participating methods on real tumor samples to reach a consensus tree. In order to compare clonal trees with varying granularity (granularity can be measured in terms of the average number of mutations assigned to a clone) the measure(s) used should be versatile enough to discriminate real topological differences between trees from those differences due to the type and coverage of the HTS data used by a method; e.g. such a “dissimilarity” measure should be equal to 0 between any clonal tree and its corresponding mutation tree (obtained using the procedure described above).In order to assess the accuracy of the proposed method, many of these studies use simulated HTS data extracted from synthetic tumor compositions. The inferred tree is then compared against the (synthetic) ground truth. We will call the Unfortunately, comparing trees of tumor evolution is a challenging problem and available measures fail to fully capture (dis)similarities between inferred and true trees. Many of existing measures only aim to compare the relative placement of pairs of mutations across two trees, e.g. whether the two mutations maintain an ancestor–descendant relationship in both trees . As such, it has a well established dynamic programming algorithm (e.g. ). The ru(nlog2n) —here n iNP-hard  .Extensions of edit distance measures for rooted trees have typically been defined for trees with ordered vertices, each with a single label, where the goal is to transform one tree to the other by the use of vertex deletions  and vertex label replacements . Based olargest common subtree [Motivated by the Levenshtein edit distance between strings, edit distances for trees with unordered vertices are defined in relation to the  subtree  between  subtree , this diIn this paper we consider a restricted version of the above notion of tree edit distance by allowing label (and implied node) deletions for leaves. This notion of distance can naturally be generalized to multi-labeled trees and the resulting “dissimilarity” measure  can be computed in polynomial time. More importantly, it successfully captures the differences between clonal trees: for example it satisfies a key condition that two clonal trees from which it is possible to produce two identical mutation trees have a dissimilarity of 0.Multi-labeled tree dissimilarity is the first polynomial time computable dissimilarity measure for vertex unordered trees.multi-labeled tree and use this term throughout the sections containing algorithms description ) and edges E ), with a particular vertex r identified as the root. For each non-root vertex v, any vertex u that lies on the simple path between v and the root is considered to be its ancestor; in particular, the vertex v is considered to be its parent. The depth of vertex v denoted d(v), is thus defined as the number of its ancestors. The lowest common ancestor of any pair of vertices u and v, denoted u and v whose depth is maximum possible. The structure of a tree induces partial order u is an ancestor of v.A rooted tree Multi-labeled treeT is a rooted tree in which each vertex v other than root has a subset u and v. We denote the set of all labels assigned to the vertices of T as L(T). In other words, deleting a label where one of the labels is removed from some set deleting an unlabeled leaf where a vertex is removed from the tree. This operation is allowed to be performed only for unlabeled leaves, i.e. vertices with no labels and no children,expanding a vertex where vertex v is replaced by two vertices v after this operation are children of v is the parent of A Common tree of arbitrary multi-labeled trees maximum common tree of Consider the following types of edit operations on multi-labeled tree:entclass1pt{minimaA (root vertex) and B (non-root vertex) (ii) tree B (root vertex) and A (non-root vertex) and (iii) a single vertex tree A and B, MLTD between As mentioned earlier MLTD defined above is not a metric since it is akin to the “inverse set intersection” and thus does not satisfy the triangle inequality. For example, given r represents population of healthy cells and each non-root vertex represents tumor clone. Universe v. The constraint u and v, ensures that each mutation appears at most once during the course of tumor evolution (this follows directly from the ISA).Formal definition of multi-labeled tree presented above is motivated by the clonal tree of tumor evolution discussed in "r is empty  and v is non-root vertex such that v would be, with respect to the set of mutations it harbors, identical to its parent which is atypical for clonal trees as it introduces unnecessary redundancy in representation of the process of tumor evolution. For the simplicity, in the figures of clonal trees presented in this work we do not show a root since its set of labels is empty hence such vertex would be non-informative.The main difference between multi-labeled and clonal tree is that in the latter we have constraint that the set of labels assigned to the root vertex Note that any multi-labeled tree can be converted to a unique clonal tree using the following steps: (i) merging each of non-root vertices having empty set of labels with its parent and repeating this until each non-root vertex has non-empty set of labels and (ii) in the case that root of the tree obtained after the first step has non-empty set of labels, add a new vertex without any mutational labels and connect it to the root of the modified tree (so that it becomes new root). In the applications, we first consider each clonal tree as a mutation tree and, once a common tree is obtained, it is converted to a clonal tree using the two of these steps.While the notion for the edit operation of label deletion is intuitively clear as in general case one would be unable to obtain a common tree without allowing this or any similar operation which removes some labels, the edit operation of expanding a vertex at no cost is directly motivated by the existing different ways of representing clonal trees of tumor evolution. More precisely, we introduce it in order to be able to capture differences between two clonal trees which are due to different levels of granularity in tree representation. An example of such trees is shown in Fig. a in the first tree and a in the second tree.We first demonstrate how maximum common tree is computed for a pair of trees where each tree is a path. Obviously in this case any common tree between the input trees is also a path. Let the ordered sequence of vertices of the first tree/path be It is easy to see that computing a maximum common tree in this special case is equivalent to the following generalized version of the string edit distance problem for a pair of ordered sets.et Alignment Problem. Our approach for computing dissimilarity between two arbitrary trees  into b we have that a and b belong to A but obviously they violate constraint A satisfied for all of its labels. This contradiction directly implies our latest claim. To finalize the proof of inequality A does not contain any label from For the second equation, we first prove that D between trees Lemma Total time and total space required for calculating number of labels in each of the setswhereandare bothf(u) and g(u). This can be implemented in the above time and space by using a hash table. If we know these indices, we can fill the table For each label from The Set Alignment Problem  is solvable intime and space.Follows straightforwardly from Lemma non-crucial vertices and all other vertices, i.e. leaves, and vertices with two or more children, as crucial vertices. Now consider the sequence of edit operations applied to a tree T with another tree We now describe an efficient algorithm for computing a maximum common tree. Note that in the remainder of the paper we call all vertices in a tree with exactly one child as Each edit operation applied to any vertex creates at most one (new) crucial vertex; no edit operation can increase the total number of crucial vertices.The edit operation of deleting a label does not change the topology of the tree or the set of crucial vertices in the tree.u does change the topology of a tree, but with respect to the set of crucial vertices, the only update is that u is lost, and, (i) provided that u was the only child of p(u), p(u) becomes crucial, or (ii) provided that u was one of the two children of p(u), p(u) becomes non-crucial, or (iii) provided that u was one of more than two children of p(u), p(u) stays crucial. All other vertices remain unaltered. See Fig. The edit operation of deleting a leaf v into v is non-crucial; however, (ii) if a vertex v is crucial, then Finally, the edit operation of expanding, i.e., splitting a vertex entclass1pt{minimaIn summary, after an arbitrary edit operation, at most one new vertex is added to the set of crucial vertices. However, in the case that new crucial vertex is added, at least one of such vertices is deleted implying that the total number of crucial vertices never increases. The proof is based on analyzing the effect that application of a given edit operation might have on the set of crucial vertices.u may create a new crucial vertex v. In that case, we say that the crucial vertex u in corresponds to a crucial vertex v in u in u corresponds to u, if p(u) which was originally non-crucial, became crucial, then we say that u in p(u) in v which remains unedited and crucial in v in tree v in the tree The observation above indicates that an edit operation applied to a crucial vertex v in T if for the sequence of trees i. We extend the notion of correspondence to Finally, we say that Thus we notice the following fact.We can construct the correspondence between a subset of crucial vertices inandand crucial vertices in the common tree. Such that each crucial vertex in the common tree corresponds to some vertex inandT and the vertices in T, it is straightforward to establish the edit operations to transform T. The algorithm to compute T makes use of this observation.Given trees Given two sets of crucial verticesandinandrespectively such thatandcorrespond to same crucial vertex in the common treeTfor eachi, we can reconstruct a common treesuch that the number of labels inis at least that inT.Here we describe the procedure of reconstructing the tree T in a trivial manner: let T will be deleted: if a vertex v does not belong to a path from the root to some crucial vertex in T, then any label from T. However, if any label in T that is in v which lies on a path from the root to a leaf w  then there must exist a pair of vertices w.In the first step we delete each label which cannot belong to Thus, starting from the leaf level, we can delete all vertices which do not belong to a path from the root to any T and Let In the second step, for each pair of vertices T. optimal pair of sequences of vertices The above observation implies that we can reduce the problem of computing a maximum common tree between two multi-labeled trees to the problem of finding an et Alignment Problem, which we compute in a preprocessing step.Our general algorithm for computing the “dissimilarity” between two multi-labeled trees requires constant time access to the solutions to many instances of the Set Alignment Problem  for all pairs of sequences Solving Set Alignment Problem  for all possible downward paths; we call this auxiliary problem Pairwise Alignments on a Tree.The algorithm for computing an optimal pair of sequences will need the solutions to Su, v such that u and v. Then we can define Pairwise Alignments on a Tree  problem formally as follows.Given a pair of vertices airwise Alignments on a Tree  which forms the basis of our dynamic programming algorithm.In the next lemma, we introduce equations for computing PGivenletbe the solution for the instanceof Set Alignment Problem. ThenIfandthenIfandthenIfandthenOtherwiseEach of the cases above holds true as a direct consequence of Lemma Through a straightforward application of the above lemma, we obtain the following.Ifanddenote the heights ofandrespectively, Pairwise Alignments on a Treeis solvable intime and space.a, b, c, d, which is bounded by The algorithm is a straightforward implementation of Observation T for v in w in T, such that v and w have the same crucial vertex in T.Given a common tree For any pair of verticesorwhich correspond to a vertex in the common tree the lowest common ancestor ofaandb, namelyhas a mapping, which is equal toFor any triplet of verticesorthe lowest common ancestor ofa, bis equal to the lowest common ancestor ofb, cif and only ifThe observation follows straightforwardly from the construction of correspondence. For that notice that the least common ancestor of vertices can correspond only the least common ancestor in the common tree because we may apply only operations of expanding for internal vertices. We now present our algorithm for computing the size of a maximum common tree, which is a combination of dynamic programming and an algorithm for finding a maximum cost matching.The mapping which corresponds to a maximum common tree can be computed in timex and let x. Let G be the size of the maximum common tree of a and b themselves). Notice that G is not necessarily equal to a and b do not correspond to each other x and y corresponds to the choice of vertices which are mapped to each other and has the minimal depth among all such vertices in For a, and b. The structure conditions on mapping provide the guarantee that all vertices which are leaves of downward paths from a without internal crucial vertices, lie in distinct subtrees. Using the Observation The key observation of our algorithm is that the computation of N between equal sized subsets of N thus trivially reduces to the well known maximum weighted bipartite matching problem, which can be solved in a polynomial time [nm edges) as a or b are leaves then Q. We provide an example of how our algorithm works in Appendix Consider now all possible bijections ial time . For thaentclass1pt{miniman vertices and m edges it takes a in b in The time to construct auxiliary graphs is bounded by There are number of measures in the literature that are being used to compare clonal trees. Two of the most widely used measures include: (1) Ancestor–Descendant Accuracy (ADA), measure which considers only mutations originating at vertices (clones) which are in ancestor–descendant relationship in the true tree and returns the fraction of pairs of such mutations for which the relationship is preserved in the inferred tree. (2) Different-Lineage Accuracy (DLA), defined analogously as ADA, where only pairs of mutations originating from different clones which are in neither ancestor–descendant nor descendant–ancestor relationship are considered. In addition to these two measures, used in –12, 35 aAll of the above mentioned are designed to compare inferred tree against the given true tree and no single measure can capture the overall similarity/difference between two arbitrary trees. Furthermore, for each of the measures there exist cases where it returns high similarity for topologically very different true and inferred trees. We will illustrate this below by presenting several examples using trees from Fig. For ADA measure, one needs to consider all pairs of labels in the true tree: a and b denote number of mutations in In order to facilitate the interpretation of results, for two arbitrary trees In this section we discuss similarity between true and inferred trees shown in Fig. ‘Inferred tree 1’ has relatively low score equal to 0.3 which rewards the proper placement of mutation A and correctly inferred phylogenetic relations for pairs of mutations originating from different clones, but penalizes for extensive branching which leads to the inaccurate placement to different branches of mutations originating from the same clone, as well as to significant topological differences between this and true tree. In contrast, and as expected based on our discussion from the introduction, ‘Inferred tree 2’ (which represents slightly refined version of ‘True tree’ where green and yellow clones are each split into two adjacent clones belonging to the same branch) and ‘Inferred tree 3’ (which represents fully resolved mutation tree that can be obtained from ‘True tree’) both have score 1. ‘Inferred tree 4’, having score 0.6, is rewarded for the proper placement of mutation A and large cluster of mutations appearing for the first time at green clone, but is penalized for inaccurate placement of yellow clone from where 4 out of 10 mutations originate.In order to demonstrate the application of measure developed in this work in real settings where true tree is usually not available, we analyzed two datasets obtained by sequencing real samples of triple-negative breast cancer (TNBC) and acute lymphoblastic leukemia (ALL). For each sample, we inferred trees of tumor evolution by the use of SCITE , SiFit  and PhIS


Publisher correction to: Military Medical Research, volume 6Military Medical Research. Several articles were published in volume 6 with a duplicate citation number.An error occurred during the publication of a number of articles in In this correction article the old and new citation metadata are published in Table The original articles have been updated. The publisher apologizes for the inconvenience caused to our authors and readers.


Distinct electrophysiological phenotypes are exhibited by biological cells that have differentiated into particular cell types. The usual approach when simulating the cardiac electrophysiology of tissue that includes different cell types is to model the different cell types as occupying spatially distinct yet coupled regions. Instead, we model the electrophysiology of well-mixed cells by using homogenisation to derive an extension to the commonly used monodomain or bidomain equations. These new equations permit spatial variations in the distribution of the different subtypes of cells and will reduce the computational demands of solving the governing equations. We validate the homogenisation computationally, and then use the new model to explain some experimental observations from stem cell-derived cardiomyocyte monolayers. Mathematical models are now available of the action potentials observed in many different species and cardiac cell types . The Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative has proposed a series of complementary cardiac safety assays to improve upon the current methods of assessing the arrhythmic risk associated with novel pharmaceutical compounds  action potential model FitzHugh  where7\dsing Eq. . For exai et al.  models oSet 1 This set of simulations is designed to test whether the action potentials of the PP model tend towards those of the HP model as the size of the unit that we homogenise over is decreased; that is, in the limit n, the number of repeating units that the domain is divided into. The layout of phenotypes is shown in Fig. Set 2 In a further stage of verification of the homogenisation, we use a small size of partitioned unit and alter the relative proportions of the two model phenotypes, Set 3 We will see later that the first two sets of simulations exhibit some localised behaviour in the vicinity of boundaries. Our third set of simulations investigates these effects through varying the distribution of phenotypes close to the boundary, as shown in Fig. Set 4 Until now, our investigations have assumed constant proportions of the two model phenotypes throughout the fibre at the macroscale. This assumption is, however, likely to be unrealistic. We therefore consider a fibre where the values of L is the length of the fibre, and A is the amount of variation in n units. In each unit, both Set 5 In these simulations, the values of n uniformly distributed random numbers, n is the number of partitioned units. Let x-coordinate of partitioned unit m. We then assign partitioned unit m as phenotype 1 ifA, we simulate 15 different arrangements of model phenotypes. Some example distributions of phenotypes are given in Fig. Set 6 Our final set of simulations closely follows the design of those in Set 5, but a physiological cell model is used rather than a phenomenological model. The first cell model is the ventricular-like model of Paci et al.  is unable to satisfy the boundary condition given by Eq. . This sAs the MDP is a property of the action potential during the hyperpolarised or resting phase, the influence of the pacemaker location on its value is smaller than for the There are, however, two exceptions to the smooth trends that we now explain. The first exception is in the two lower plots on the right-hand side of Fig. The second exception is in the third panel down on the right of Fig. In Fig. In the non-self-exciting stimulated fibres  with each of the excitable models . We alter the relative proportions of the two models,  with eacWe first examine the discrepancy in beat rate between the HP and PP models in both panels of Fig. n cases). In one of these, Model S1 is present at both boundary units, while in the other Model S3 is present at both boundaries. We test these three patterns of model phenotypes with partitioned units in a range of sizes.In Sect. We plot the activation times of every beat in each of the three cases in Fig. Throughout the simulations shown in Fig. A from Eqs.  acr acr\docuIn Sect. mentclasspt{minimaA is small), as the variations due to random error are then relatively large when compared to A. We note, however, that the gradients of all activation plots are very similar. Hence, although the pacemaker region may not be accurately located using the HP model, the conduction velocity is consistent. We return to this point when considering a physiological cell model in Sect. In contrast to the simulations for a regular variation in A, which sets the amount of variation in phenotype across the fibre.In this set of simulations, we extend the simulations in Sect. mentclass2pt{minimA. From left to right, the figure shows the activation times of fibres divided into 20, 30 and 120 partitioned units. As we are now dealing with a dimensional simulation, this corresponds to patches of cells that are approximately 500, 330 and 80 µm across. The typical size of a hSC-CM varies, but even the smallest size of partitioned unit that is tested here would correspond to at least two cells. As in the previous section, we decrease the amount of variability in phenotype from top to bottom of the figure, with parameter A set to 0.5, 0.3 and 0.1 in each row.In Fig. A. We make similar observations to those made in Fig. A is progressively increased, keeping n fixed, we see that the pacemaker region is accurately located by the HP model. Even if the pacemaker region is not accurately located, it is seen that the conduction velocity is accurately predicted, as can be seen by the gradient of the plot of activation times. We also observe that the pacemaker region is more accurately located as n increases, as expected. Finally, we note from the gradient of the activation plots that the conduction velocity is around A, which is similar to that discussed in Sect. In the previous section, we noted that the HP model is able to capture the overall behaviour of the PP model very well when there is substantial variation in phenotype, i.e. a high value of We have investigated two models for including multiple cellular phenotypes within simulations of cardiac tissue. In the partitioned phenotypes (PP) model, the simulated domain contains distinct regions where a single-model phenotype is present. The homogenised phenotypes (HP) model assumes a well-mixed sample of cells, which we represent as a homogenised system. We have verified that the electrical activity generated by the PP model tends towards that of the HP model as the size of the partitions decreases. The HP model is therefore a good approximation to the PP model when the length scale of regions containing a mixture of cell types is small.Use of the PP model requires that the mesh is sufficiently fine in order to capture the geometry of the partitioned regions as closely as possible. For realistic two- and three-dimensional simulations with small regions of distinct cell types, this will result in a very large number of nodes, and simulations using this mesh may not be computationally feasible. An advantage of the HP model is that it does not require the mesh to explicitly model the geometry of the partitioned regions, thus significantly reducing the number of nodes in the mesh and eliminating the need for customised versions of the mesh when simulating the same domain with different arrangements of cell types.Our simulations have demonstrated some experimentally observed properties of hSC-CM monolayers. The first two sets of simulations involved fibres with regularly repeating units of alternating phenotype, tending towards a fully mixed system. We observed that changes in values of e et al. , suggeste et al.  and Tixie et al.  propose The final three sets of simulations demonstrated how local spatial variability in the relative proportions of the two phenotypes introduced a stable pacemaker region in the HP and small-unit PP models. This observation provides a mechanism by which stable propagation of the activation wave can occur in hSC-CMs, even in cultures that only exhibit small amounts of variation in phenotype. The sixth set of simulations utilised physiologically based models of atrial-like and ventricular-like hSC-CM electrophysiology. We demonstrated similar conduction velocities in cases where both large and small amounts of phenotypic variation were simulated, in the region of values observed experimentally, which vary from approximately 1 cm/s to 20 cm/s depending on maturity (Mehta et al. In future work, we will compare two-dimensional simulation results using this model with experimental measurements from approximately two-dimensional monolayers of stem cell-derived cardiomyocytes. Such experiments typically use micro-electrode arrays to record extracellular potential at a number of sites in the centre of a monolayer in a circular well, and so provide some information on the direction and speed of propagating waves.In addition to our main focus of human stem cell-derived cardiomyocytes, the homogenised phenotypes model may also be useful in other types of cardiac simulation where two or more cell types are present, such as in sino-atrial node where cellular properties are reported to vary based on their position within the pacemaking region. The current interest in uncertainty quantification and variability in biological systems is driven by the need to understand how these factors can affect model output, thus influencing the utility of these models to complement experiments (Elkins et al.