in the tropics , cattle can be afflicted by various tick species and the diseases they transmit , possibly leading to significant loss in production systems . among these , rhipicephalus ( boophilus ) microplus is outstanding . apart from the reduction in production , infection can even be mortal to more susceptible animals . regarding losses caused by boophilus microplus , frisch et al . ( 2000 ) estimated that an animal with an average of 40 ticks per day could lose weight equivalent to 20 kg / year , whereas furlong et al . ( 1996 ) calculated a reduction of 23% in the daily milk yield , when crossbred holstein - zebu cows were infested by 105 ticks , on an average . thus , the control of infestation is of extreme importance for the dairy and beef industries . an important and interesting alternative in the control of tick infestation in cattle is to select resistant animals , and identify those specific quantitative trait loci ( qtls ) and dna markers , which could be useful in marker - assisted selection ( mas ) or introgressive strategies , as a part of inbreeding programs . although costly and time consuming , this could be better than control by acaricides , in which misuse has given rise to tick - resistance against pesticides , as well as increased environmental contamination . in the search for markers of tick - resistance in bovines , martinez et al . ( 2006 ) found associations between certain bola class ii microsatellite alleles and susceptibility to r. microplus . furthermore , it was shown that b. indicus cattle are generally more resistant to parasite challenges than b. taurus . ( 1998 ) found that genetic variability among subspecies can be exploited when mapping populations for qtl analysis , e.g. taurus  indicus f2 animals . the major concern regarding qtl mapping for tick - resistance refers to its statistical analysis . as opposed to most qtl studies , which consider continuous phenotypes and normal assumptions , the number of ticks / animal is characterized as a discrete trait , more specifically as a counting variable , which could potentially follow poisson distribution . however , if there is an excess of zeros in empirical phenotype distribution , for example due to several noninfected animals , zero - inflated poisson distribution ( zip ) ( lambert , 1992 ) may provide a better description of the data . zero inflation of ticks on any specific animal may be due to either animal resistance , or simply their absence . consequently , there are two different kinds of zeros , whose probability of occurrence must be modeled separately in qtl analysis . although poisson and zip models are potentially more appropriate statistical alternatives for qtl detection of the number of ticks per animal , it is , as yet , not clear whether these strategies are better than certain classical alternatives in data transformation . in agreement with cui et al . ( 2010 ) , although the problem of zero excess can be solved by zip modeling , when the assumption that trait variance is equal to its mean is not proved , i.e. in the presence of over / under dispersion , the zip model can be further improved by the addition of a new parameter , thereby characterizing the generalized zip ( gzip ) model . in view of the above mentioned issues , the aim was to compare , by way of simulation studies , poisson and zip models ( simple and generalized ) with classical approaches , as applied to qtl mapping , with counting phenotypes under different scenarios , and to apply these approaches to a qtl study of tick - resistance in f2 cattle ( gyr  holstein ) population . the qtl mapping methodologies discussed here , besides being based on the regression approach described by haley et al . ( 1994 ) , were further extended to the context of generalized linear models ( glm ) for count data ( mccullagh and nelder , 1989 ) , more specifically to poisson , zero - inflated poisson ( zip ) and generalized zip ( gzip ) regression models . in the next few sections , the implementation of qtl regression interval mapping for approaches presenting normally distributed traits is presented , together with data transformation strategies that will be compared to the glm methods . in addition , the simulation study and motivating data - set of tick counting in gyr  holstein cows are described . the classical regression approach for interval mapping in outbred f2 populations ( haley et al . , 1994 ) can be described as : where yi is the observed trait ( phenotype ) relative to the ith f2 individual ,  a general mean , qi the additive qtl coefficient for the ith individual ,  the additive effect of putative qtl , and ei a residual term , assumed as normally distributed with mean 0 and variance  , i.e. , ei ~ n(0 ,  ) . the co - efficient qi is given in terms of the probability of line - origin combination , conditional on the marker s genotypes ( haley et al . , 1994 ) , whose values were obtained by qxpak software ( prez - enciso and misztal , 2004 ) . the likelihood ratio test ( lrt ) is usually employed ( baret et al . , 1998 ) for evaluating the significance of the additive qtl effect . here , for every 1 cm on the chromosome , maximum likelihood ( ml ) estimates were obtained using the simplex method proposed by nelder and mead ( 1965 ) , whereby lrt was applied to compare the full model ( 1 ) against a reduced model with no qtl . given the normality assumption in model ( 1 ) , it is evidently not optimal for analyzing counting data , such as the number of ticks per cow . their results showed that , on analyzing nontransformed data , gaussian - based methods can lose around 50% of qtl detection potential . a flexible methodology for data transformation , when the phenotypic data is not normally distributed , as proposed by box and cox ( 1964 ) , is given by : where zi is the transformed variable , yi the original variable , and  the transformation factor , which can be inferred using , for example , maximum likelihood techniques . box - cox transformation has already been successful applied to qtl mapping with continuous data traits and skewed distribution ( yang et al . , in addition to the box - cox transformation , which includes searching for the value of  which best approximates the data to a normal distribution , here we used also the classical square root transformation , this being traditionally considered as a suitable transformation when the data follow a poisson distribution . the square root is equivalent to a specific type of the box - cox transformation , where  = 1/2 , given by : however , according to yamamura ( 1999 ) , the box - cox transformation has serious limitations , when the response - variable contains zeros . in such cases , the addition of a small constant c to each observation is generally recommended , to so assure the most nearly constant variance possible . specifically for poisson data , the value c = 3/8 is optimal , in the sense that variance converges more rapidly as the mean increases ( ascombe , 1948 ) . ( 2 ) and ( 3 ) . here , the analysis using data transformations were performed using transreg procedure of sas 9.1.3 . this procedure was chosen especially for the box - cox transformation , as it allows simultaneous estimation of  and model fitting . an alternative to data transformation is direct modeling of the data in its original scale using a more general model . under this approach , we considered a poisson regression as an extension of model ( 1 ) . in this case , it is assumed that each observation yi is drawn from a poisson distribution , whose probability function is given by : where mi is the mean of this distribution , i.e. , e(y ) = mi , which , according to glm theory ( mccullagh and nelder , 1989 ) , can be related to model ( 1 ) by a linear predictor given , in this case , by i =  + qi . the relationship between the linear predictor ( i ) and the mean ( mi ) is provided by a link function . in the case of a poisson distribution , thus , to enable use of the poisson means with the linear predict of model ( 1 ) it is necessary to obtain the inverse of the link function ; i.e. , mi = exp(i ) = exp( + qi ) . as mentioned earlier , tick - counting data can present an excess of zeros , since a cow may have no ticks , either through being resistant ( so called  true zero  ) , or , although susceptible , for any other reason , e.g. by chance or because no tick has touched her ) . to accommodate such a scenario , a zero - inflated poisson ( zip ) model the zip model can be formulated as a mixture of probability  of  true zero ( tick - resistance ) and a probability distribution of the number of ticks ( which would also include zero ) , according to a poisson process ( lambert , 1992 ) . in order to define the zip probability density function , wi = 1 if the cow is resistant and wi = 0 if the cow is susceptible . thus , considering wi as a latent variable , p(wi = 1 ) = i and p(wi = 0 ) = 1  i , whereby : where 0 = i = 1 and mi is the expected number of ticks on cow i , given this cow is susceptible . in agreement with cui et al . ( 2010 ) , the zip model can be improved by the addition of a new parameter (  ) , to so describe the occurrence of under ( if 0 < this model is denominated generalized zip ( gzip ) , which is given by : poisson regression was implemented using the genmod procedure of sas , using the log link - function . the zip model was fitted using the nlmixed procedure , according to syntax described by liu and cela ( 2008 ) , and the gzip using countreg sas macro ( chow and steenhard , 2009 ) with the statement method = 2 ( generalized poisson ) and zindep = ( name of the independent variables used in the zero - inflated model ) . all the sas codes used are available , direct from the authors . simulations consisted of a single 45 cm long chromosome based on real data , with 5 non - evenly spaced markers ( 0 , 14.8 , 29.9 , 37.4 , 43.3 cm ) , for an f2 population with a sample - size equal to 263 , mean (  ) equal to 2 , and qtl additive effect given by  = 0.05 , 0.1 , 0.2 . although the putative qtl that affects the phenotype of interest is located at 20 cm from the first marker on the linkage group , a data set with no qtl was also simulated to account for false positive and negative rates . simulation settings were chosen to mimic real data sets , while real pedigree structure was used to calculate the probability of line - origin combination , conditional on marker genotypes . phenotypic data from poisson and zero - inflated poisson were generated , with two different  true - zeros  probability ( 0.2 , 0.5 ) , using sas iml . in each simulation scenario , 1000 monte carlo repetitions are performed , and five different models of analysis were tested for each monte carlo sample . the original count data and two different transformation approaches ( box - cox and square - root ) were analyzed with the gaussian model ( 1 ) , whereas for the glm approach , the poisson ( 4 ) , zero - inflated poisson ( 5 ) and generalized zero - inflated poisson ( 6 ) were considered . the following measures were used for evaluating the performance of each model : variance ( var ) of the additive effect (  ) calculated from 1000 repetitions ; bias of  estimates , calculated as the sum of the difference between estimated and true values divided by 1000 ; the mean of absolute distances ( mad ) , defined as the absolute values of the difference between true and estimated qtl position ( the position with the highest log - likelihood ) ; false positive rates ( fpr ) , given by the percentage that a qtl was considered significant ( p < 0.05 ) in any position , when the simulation did not include the additive qtl effect ; and false negative rate ( fnr ) , defined as the percentage of a qtl not presenting a significant ( p < 0.05 ) effect , when considered in the simulation . dairy cattle research center , from four holstein sires  28 gyr dams to obtain f1 animals , among which five sires and 68 dams were intercrossed to form an f2 population . this population was challenged for tick infestation with no tick control until 1014 months of age . these infestations were carried out by placing tick larvae on the dorsal - lumbar region of the animals . counting took place on the morning of the 21 day after infestation , before detachment of mature female ticks . the classical regression approach for interval mapping in outbred f2 populations ( haley et al . , 1994 ) can be described as : where yi is the observed trait ( phenotype ) relative to the ith f2 individual ,  a general mean , qi the additive qtl coefficient for the ith individual ,  the additive effect of putative qtl , and ei a residual term , assumed as normally distributed with mean 0 and variance  , i.e. , ei ~ n(0 ,  ) . the co - efficient qi is given in terms of the probability of line - origin combination , conditional on the marker s genotypes ( haley et al . , 1994 ) , whose values were obtained by qxpak software ( prez - enciso and misztal , 2004 ) . the likelihood ratio test ( lrt ) is usually employed ( baret et al . , 1998 ) for evaluating the significance of the additive qtl effect . here , for every 1 cm on the chromosome , maximum likelihood ( ml ) estimates were obtained using the simplex method proposed by nelder and mead ( 1965 ) , whereby lrt was applied to compare the full model ( 1 ) against a reduced model with no qtl . given the normality assumption in model ( 1 ) , it is evidently not optimal for analyzing counting data , such as the number of ticks per cow . their results showed that , on analyzing nontransformed data , gaussian - based methods can lose around 50% of qtl detection potential . a flexible methodology for data transformation , when the phenotypic data is not normally distributed , as proposed by box and cox ( 1964 ) , is given by : where zi is the transformed variable , yi the original variable , and  the transformation factor , which can be inferred using , for example , maximum likelihood techniques . box - cox transformation has already been successful applied to qtl mapping with continuous data traits and skewed distribution ( yang et al . , in addition to the box - cox transformation , which includes searching for the value of  which best approximates the data to a normal distribution , here we used also the classical square root transformation , this being traditionally considered as a suitable transformation when the data follow a poisson distribution . the square root is equivalent to a specific type of the box - cox transformation , where  = 1/2 , given by : however , according to yamamura ( 1999 ) , the box - cox transformation has serious limitations , when the response - variable contains zeros . in such cases , c to each observation is generally recommended , to so assure the most nearly constant variance possible . specifically for poisson data , the value c = 3/8 is optimal , in the sense that variance converges more rapidly as the mean increases ( ascombe , 1948 ) . ( 2 ) and ( 3 ) . here , the analysis using data transformations were performed using transreg procedure of sas 9.1.3 . this procedure was chosen especially for the box - cox transformation , as it allows simultaneous estimation of  and model fitting . an alternative to data transformation is direct modeling of the data in its original scale using a more general model . under this approach , we considered a poisson regression as an extension of model ( 1 ) . in this case , it is assumed that each observation yi is drawn from a poisson distribution , whose probability function is given by : where mi is the mean of this distribution , i.e. , e(y ) = mi , which , according to glm theory ( mccullagh and nelder , 1989 ) , can be related to model ( 1 ) by a linear predictor given , in this case , by i =  + qi . the relationship between the linear predictor ( i ) and the mean ( mi ) is provided by a link function . in the case of a poisson distribution , thus , to enable use of the poisson means with the linear predict of model ( 1 ) it is necessary to obtain the inverse of the link function ; i.e. , mi = exp(i ) = exp( + qi ) . as mentioned earlier , tick - counting data can present an excess of zeros , since a cow may have no ticks , either through being resistant ( so called  true zero  ) , or , although susceptible , for any other reason , e.g. by chance or because no tick has touched her ) . to accommodate such a scenario , a zero - inflated poisson ( zip ) model true zero ( tick - resistance ) and a probability distribution of the number of ticks ( which would also include zero ) , according to a poisson process ( lambert , 1992 ) . in order to define the zip probability density function , wi = 1 if the cow is resistant and wi = 0 if the cow is susceptible . thus , considering wi as a latent variable , p(wi = 1 ) = i and p(wi = 0 ) = 1  i , whereby : where 0 = i = 1 and mi is the expected number of ticks on cow i , given this cow is susceptible . in agreement with cui et al . ( 2010 ) , the zip model can be improved by the addition of a new parameter (  ) , to so describe the occurrence of under ( if 0 < this model is denominated generalized zip ( gzip ) , which is given by : poisson regression was implemented using the genmod procedure of sas , using the log link - function . the zip model was fitted using the nlmixed procedure , according to syntax described by liu and cela ( 2008 ) , and the gzip using countreg sas macro ( chow and steenhard , 2009 ) with the statement method = 2 ( generalized poisson ) and zindep = ( name of the independent variables used in the zero - inflated model ) . simulations consisted of a single 45 cm long chromosome based on real data , with 5 non - evenly spaced markers ( 0 , 14.8 , 29.9 , 37.4 , 43.3 cm ) , for an f2 population with a sample - size equal to 263 , mean (  ) equal to 2 , and qtl additive effect given by  = 0.05 , 0.1 , 0.2 . although the putative qtl that affects the phenotype of interest is located at 20 cm from the first marker on the linkage group , a data set with no qtl was also simulated to account for false positive and negative rates . simulation settings were chosen to mimic real data sets , while real pedigree structure was used to calculate the probability of line - origin combination , conditional on marker genotypes . phenotypic data from poisson and zero - inflated poisson were generated , with two different  true - zeros  probability ( 0.2 , 0.5 ) , using sas iml . in each simulation scenario , 1000 monte carlo repetitions are performed , and five different models of analysis were tested for each monte carlo sample . the original count data and two different transformation approaches ( box - cox and square - root ) were analyzed with the gaussian model ( 1 ) , whereas for the glm approach , the poisson ( 4 ) , zero - inflated poisson ( 5 ) and generalized zero - inflated poisson ( 6 ) were considered . the following measures were used for evaluating the performance of each model : variance ( var ) of the additive effect (  ) calculated from 1000 repetitions ; bias of  estimates , calculated as the sum of the difference between estimated and true values divided by 1000 ; the mean of absolute distances ( mad ) , defined as the absolute values of the difference between true and estimated qtl position ( the position with the highest log - likelihood ) ; false positive rates ( fpr ) , given by the percentage that a qtl was considered significant ( p < 0.05 ) in any position , when the simulation did not include the additive qtl effect ; and false negative rate ( fnr ) , defined as the percentage of a qtl not presenting a significant ( p < 0.05 ) effect , when considered in the simulation . dairy cattle research center , from four holstein sires  28 gyr dams to obtain f1 animals , among which five sires and 68 dams were intercrossed to form an f2 population . this population was challenged for tick infestation with no tick control until 1014 months of age . these infestations were carried out by placing tick larvae on the dorsal - lumbar region of the animals . counting took place on the morning of the 21 day after infestation , before detachment of mature female ticks . fnrs and fprs obtained from the simulation study are respectively presented in tables 1 and 2 . in the case of the probability of zeros being equal to zero ( poisson distribution ) , the percentage of false negative rate ( fnr ) would be around 74% and 25% , if the qtl effect were 0.05 and 0.1 , respectively , and almost none when 0.2 ( table 1 ) . the box - cox transformation performed better with a slightly smaller fnr than the other approaches , although interestingly , the zip and gzip models presented the best results . thus , it seems that inclusion of the extra parameters  and  , respectively relative to perfect zero occurrence probability and under / over dispersion , bears a small penalty , if the data has poisson distribution with no inflation , and in the absence of under / over dispersion , especially in situations with reduced qtl effect . with moderate zero inflation , and only slight qtl effect , the zip and gzip models presented slightly higher fnrs than the poisson , and almost twice as high as the gaussian approach , with or without data transformation . however , with greater qtl effects ( 0.1 and 0.2 ) , the zip and gzip models performed much better than all the other approaches . finally , with extreme zero inflation ( p(0 ) = 0.5 ) , the poisson model performed the best in situations with small to moderate qtl effects , and the zip second best . nonetheless , with greater qtl effects , the zip and gzip models surpassed all the other methods . in terms of fpr ( table 2 ) , since defined by any significant statistical test for qtl effects , without any addition , all the models presented roughly the same rates in the absence of zero inflation . however , even with moderate zero inflation , the poisson model presented almost three times fpr than the remainder , thus indicating it to be the less conservative . interestingly , either with or without data transformation , the gaussian model presented very similar results to the zip and gzip . in general , the gaussian models had higher fnrs and were even in the fprs . the poisson model showed the same fprs when compared to the zip and gzip models and performed a little better than this one in terms of fnrs , when the qtl effects were small . however , when the qtl effect was moderate to high , the zip and gzip models overall fnrs and fprs were smaller than with the other approaches . finally , when working with count - data , a previous descriptive - data analysis is always advisable . in the case of zero inflation , the zip and gzip models are indicated , the latter being an alternative , when solving the problem of under / over dispersion as called for . with zero inflation , either the poisson model or a transformation approach the disadvantage is that when using data transformation , interpretation of the results is not straightforward . the well - known results of sqrt transformation working fine with poisson distribution data , are here confirmed . however , in the event of not wishing to rely on a poisson assumption , a more general data transformation ( box - cox , for example ) is advised . var , bias and mad values ( table 3 ) indicate that , notwithstanding the scenario , the gaussian model without transformation presented the worst results for var and bias , with transformations , more precisely by box - cox and sqrt , assuming a better stance , whereas with assumed normal sqrt transformation , the simplest and most used for count data , performance was the best . as expected , the superiority of glm approaches was eminently clear , especially of zip and gzip models , whose performances , although practically the same as poisson when p(0 ) = 0 , were far superior when p(0 ) = 0.2 and p(0 ) = 0.5 . as to mad with a small additive qtl effect (  = 0.05 ) , values were very similar for all the models . however , with an increase in qtl effect , zip and gzip performances improved substantially compared to the other models . generally speaking , all presented good values for mad when  = 0.2 , explainable by the higher the qtl effect the higher the probability for detecting this qtl in the right position . in summary , in view of the results ( tables 1 , 2 and 3 ) , it is possible to conclude that when there is moderate or extreme inflation of zeros , the best option is to adopt either the zip or gzip models , since both are appropriate when reckoning with the simultaneous occurrence of true zeros and zeros from poisson distribution . furthermore , with both , final results were very similar in all scenarios , since in the simulation studies under / over dispersion was disregarded , i.e.  = 1 . thus , as could be expected , gzip can be characterized as a zip model . in any case , sqrt transformation proved to be an interesting and easy alternative to qtl detection in the presence of count data . qtl profile - plots from five different models applied to first and second tick - count phenotypes in holstein  gyr cows , appear in figure 1 . as there were less zeros in the data used for the first count than for the second , this could be used as a parameter for checking how the different models perform in the presence of zero - counts and real zero - inflated counts . from the set of graphs related to the first count , it can be inferred that only simple ( figure 1i ) and generalized ( figure 1k ) zip models had come close to the 0.5% threshold , and that this was the only model that presented a qtl  like curve . for the second set of graphs , except for that of box - cox transformation as there apparently was a qtl around 21 cm , the zip models ( figure 1j and l ) showed that the curve had reached close to the 0.5% threshold . through being compatible with those obtained with the simulated data set , the results revealed the superior performance of zip models when working with counting data in the high presence of zeros . furthermore , the zip and gzip models presented similar results in both tick counts , since in the gzip fit , the estimated  parameter came close to one , thereby indicating the absence of under / over dispersion . in summary , we conclude that when working with nonormal distribution data , such as count data , prior descriptive analysis is always advisable . if working with zero - inflated data , it is recommended to use both simple and generalized zip models for data analysis . if working with data with zeros , but not zero inflated , either the poisson model or a data transformation approach , such as square - root transformation , can be employed . square - root transformation can be used for poisson distribution data , although in the case of uncertainty as to this being the case , a more general transformation , as box - cox , should be used instead . fnrs and fprs obtained from the simulation study are respectively presented in tables 1 and 2 . in the case of the probability of zeros being equal to zero ( poisson distribution ) , the percentage of false negative rate ( fnr ) would be around 74% and 25% , if the qtl effect were 0.05 and 0.1 , respectively , and almost none when 0.2 ( table 1 ) . the box - cox transformation performed better with a slightly smaller fnr than the other approaches , although interestingly , the zip and gzip models presented the best results . thus , it seems that inclusion of the extra parameters  and  , respectively relative to perfect zero occurrence probability and under / over dispersion , bears a small penalty , if the data has poisson distribution with no inflation , and in the absence of under / over dispersion , especially in situations with reduced qtl effect . with moderate zero inflation , and only slight qtl effect , the zip and gzip models presented slightly higher fnrs than the poisson , and almost twice as high as the gaussian approach , with or without data transformation . however , with greater qtl effects ( 0.1 and 0.2 ) , the zip and gzip models performed much better than all the other approaches . finally , with extreme zero inflation ( p(0 ) = 0.5 ) , the poisson model performed the best in situations with small to moderate qtl effects , and the zip second best . nonetheless , with greater qtl effects , the zip and gzip models surpassed all the other methods . in terms of fpr ( table 2 ) , since defined by any significant statistical test for qtl effects , without any addition , all the models presented roughly the same rates in the absence of zero inflation . however , even with moderate zero inflation , the poisson model presented almost three times fpr than the remainder , thus indicating it to be the less conservative . interestingly , either with or without data transformation , the gaussian model presented very similar results to the zip and gzip . in general , the gaussian models had higher fnrs and were even in the fprs . the poisson model showed the same fprs when compared to the zip and gzip models and performed a little better than this one in terms of fnrs , when the qtl effects were small . however , when the qtl effect was moderate to high , the zip and gzip models overall fnrs and fprs were smaller than with the other approaches . finally , when working with count - data , a previous descriptive - data analysis is always advisable . in the case of zero inflation , the zip and gzip models are indicated , the latter being an alternative , when solving the problem of under / over dispersion as called for . with zero inflation , either the poisson model or a transformation approach the disadvantage is that when using data transformation , interpretation of the results is not straightforward . the well - known results of sqrt transformation working fine with poisson distribution data , are here confirmed . however , in the event of not wishing to rely on a poisson assumption , a more general data transformation ( box - cox , for example ) is advised . var , bias and mad values ( table 3 ) indicate that , notwithstanding the scenario , the gaussian model without transformation presented the worst results for var and bias , with transformations , more precisely by box - cox and sqrt , assuming a better stance , whereas with assumed normal sqrt transformation , the simplest and most used for count data , performance was the best . as expected , the superiority of glm approaches was eminently clear , especially of zip and gzip models , whose performances , although practically the same as poisson when p(0 ) = 0 , were far superior when p(0 ) = 0.2 and p(0 ) = 0.5 . as to mad with a small additive qtl effect (  = 0.05 ) , values were very similar for all the models . however , with an increase in qtl effect , zip and gzip performances improved substantially compared to the other models . generally speaking , all presented good values for mad when  = 0.2 , explainable by the higher the qtl effect the higher the probability for detecting this qtl in the right position . in summary , in view of the results ( tables 1 , 2 and 3 ) , it is possible to conclude that when there is moderate or extreme inflation of zeros , the best option is to adopt either the zip or gzip models , since both are appropriate when reckoning with the simultaneous occurrence of true zeros and zeros from poisson distribution . furthermore , with both , final results were very similar in all scenarios , since in the simulation studies under / over dispersion was disregarded , i.e.  = 1 . thus , as could be expected , gzip can be characterized as a zip model . in any case , sqrt transformation proved to be an interesting and easy alternative to qtl detection in the presence of count data . qtl profile - plots from five different models applied to first and second tick - count phenotypes in holstein  gyr cows , appear in figure 1 . as there were less zeros in the data used for the first count than for the second , this could be used as a parameter for checking how the different models perform in the presence of zero - counts and real zero - inflated counts . from the set of graphs related to the first count , it can be inferred that only simple ( figure 1i ) and generalized ( figure 1k ) zip models had come close to the 0.5% threshold , and that this was the only model that presented a qtl  like curve . for the second set of graphs , except for that of box - cox transformation as there apparently was a qtl around 21 cm , the zip models ( figure 1j and l ) showed that the curve had reached close to the 0.5% threshold . through being compatible with those obtained with the simulated data set , the results revealed the superior performance of zip models when working with counting data in the high presence of zeros . furthermore , the zip and gzip models presented similar results in both tick counts , since in the gzip fit , the estimated  parameter came close to one , thereby indicating the absence of under / over dispersion . in summary , we conclude that when working with nonormal distribution data , such as count data , prior descriptive analysis is always advisable . if working with zero - inflated data , it is recommended to use both simple and generalized zip models for data analysis . if working with data with zeros , but not zero inflated , either the poisson model or a data transformation approach , such as square - root transformation , can be employed . square - root transformation can be used for poisson distribution data , although in the case of uncertainty as to this being the case , a more general transformation , as box - cox , should be used instead .
now a days , an important and interesting alternative in the control of tick - infestation in cattle is to select resistant animals , and identify the respective quantitative trait loci ( qtls ) and dna markers , for posterior use in breeding programs . 
 the number of ticks / animal is characterized as a discrete - counting trait , which could potentially follow poisson distribution . however , in the case of an excess of zeros , due to the occurrence of several noninfected animals , zero - inflated poisson and generalized zero - inflated distribution ( gzip ) may provide a better description of the data . 
 thus , the objective here was to compare through simulation , poisson and zip models ( simple and generalized ) with classical approaches , for qtl mapping with counting phenotypes under different scenarios , and to apply these approaches to a qtl study of tick resistance in an f2 cattle ( gyr  holstein ) population . 
 it was concluded that , when working with zero - inflated data , it is recommendable to use the generalized and simple zip model for analysis . on the other hand , 
 when working with data with zeros , but not zero - inflated , the poisson model or a data - transformation - approach , such as square - root or box - cox transformation , are applicable .