Horn fly (Haematobia irritans) is an obligate blood-feeding parasite of cattle whose populations can build rapidly due to a dung-dependent life cycle (Gorden, 1964). Horn flies (HF) feed on multiple small blood meals from the host throughout the day. Each horn fly may take more than 30 blood meals per day, and during summer, burdens on a single animal can exceed 1,000 flies (Cupp and Kunz, 1998; Psota et al., 2021). Horn fly infestations impose physiological and behavioral stress on cattle, including increased respiratory and heart rates, and reduced feed efficiency. These effects are associated with depressed milk production and growth, and elevated risk of mastitis (Owens et al., 1998; Gillespie et al., 1999; Derouen et al., 2003; Boland et al., 2008; Anderson et al., 2012; Machtinger et al., 2021). These small blood-feeding parasites are some of the most damaging pests for cattle. Historic estimates put horn fly losses at $700 to $876 million per year (Arther, 1991; Kunz et al., 1991), and roughly $1.6 and $1.8 billion in 2018. Across all cattle ectoparasites, losses have been estimated at around $2.26 billion (Byford et al., 1992). Similar large losses were reported for Muscid stable flies (Taylor et al., 2012).

Horn flies are the principal external pest in pasture-based cow–calf systems in most of the southeastern and midwestern states in the US. Because resistance has reduced the effectiveness of many insecticides, producers face substantial economic losses (Hinkle, 2018). These combined effects underscore the urgent need for targeted strategies to mitigate the impact of horn flies on livestock. Despite the numerous available horn fly control methods, fly abundance on cattle remains a major challenge to the industry (Warner et al., 2022, 2023).

From a practical perspective, the mere presence of flies on an animal does not equate to an impact on its performance. Their impact on animal productivity and well-being occurs only when fly abundance exceeds a certain threshold. The fly load at which production or productivity starts to decay is commonly referred to as the economic injury threshold (EIT), and it is a measure of the ability of the animal to withstand a certain fly abundance without a noticeable negative impact on its performance (Headley, 1972; Gordon et al., 1984). It will be useful to evaluate horn fly tolerance, characterized as an animal’s capacity for maintaining productivity despite elevated Haematobia irritans abundance following the onset of established infestation (EIT), as measured by the decay of performance after onset (DPO).

Currently, there are no specific estimates for the onset of the economic injury threshold due to HF abundance. A threshold of 200 flies per side of an animal is traditionally used (Haufe, 1978; Kunz et al., 1991). Furthermore, there is no information about the decay in performance after the onset of the EIT (DPO). The lack of information regarding the onset of injury and the decline in performance after onset is due mainly to the absence of appropriate trait and fly abundance phenotypes, as well as the modeling approaches needed to estimate these parameters. The technique of changepoint identification enables inference regarding the specific thresholds at which systemic shifts occur, as well as potential alterations in the parameter values of the underlying statistical model. The changepoint techniques were first proposed by Stephens (1994) and later extended by Rekaya et al. (2000) to accommodate change in the dispersion parameters (heterogeneity of variances) and are well-suited for identifying the point at which horn fly infestations begin to cause measurable economic injury.

The objectives of this study were to develop an innovative approach based on changepoint techniques to identify the population-level onset of economic injury threshold and decay after onset due to horn fly abundance. Average daily gain (ADG) and the success of first insemination (SFI) collected on beef cattle heifers were analyzed using the proposed models.

Data Collection: The data used in this study were gathered in accordance with the guidelines outlined by the Animal Use and Care Protocol, as approved by the Institutional Animal Care and Use Committee (IACUC) at the University of Georgia (A2019 03- 034Y3-A0 and A2021 09-0140Y1-A0). This research was carried out at two distinct University of Georgia facilities: the Eatonton Beef Research Unit, Eatonton, Georgia and the Northwest Georgia Research and Education Center, Calhoun, Georgia.

Data for this study were collected from 2022 to 2024 during the horn fly season in Georgia (March to August), focusing on heifers, and it included 337 Angus beef heifers (all available replacement heifers). Animals grazed pasture most of the year, with hay/mineral supplementation as needed and no fly-removal treatments (e.g., washing, brushing, or other body-cleaning procedures) were applied immediately prior to data collection so that horn fly counts reflected natural infestation levels. The study timeline, including artificial insemination (AI), body-weight measurements, horn-fly assessments (image and subjective), and pregnancy checks, is shown in Figure 1. Growth and fertility traits, as well as subjective and image-based fly counts, were collected on each animal. Subjective assessment of horn fly count was carried out by trained agents. Image based fly count was assessed by counting flies directly of the collected digital images (Warner et al., 2023). Body weights were used to calculate average daily gain (ADG) at three-time intervals. The ADG at an interval j (j=1,2,3) for the animal i (i=1,2,…337) was calculated as:

Where Weighti,j is the weight of the animal i  at age j A summary description of the data used in this study is presented in Tables 1 and 2. Artificial insemination procedures were conducted between early March and mid-March each year at both Calhoun and Eatonton farms. Pregnancy status was assessed approximately 4 to 21 weeks after AI, depending on the group and year, as detailed in Table 1. Animals were weighed from March to August. All heifers were assessed for horn fly count using subjective and image-based methods (Table 2).

Data Analysis: To the best of our knowledge, there are no reported estimates of EIT and DPO in beef cattle due to horn flies. In this study, a new approach was developed to estimate both parameters for growth and fertility traits. Image-based horn fly counts were used to estimate the onset of the economic injury threshold (EIT) and the decay after onset (DPO) for three growth traits (ADG₁– ADG₃) and pregnancy status in heifers. A hierarchical Bayesian linear model was fitted for ADG and a threshold model for pregnancy status, extending the frameworks of Rekaya et al. (2000) and Sánchez et al. (2009a, 2009b). These are robust statistical approaches that allow the dissection of complex data generating processes into simpler components that can be assembled in a simple natural way. The approach assumes different sampling models for the data as a function of fly load. A reasonable assumption is that animal productivity will not be noticeably affected by fly abundance until the load reaches the EIT. After the EIT, production will keep decaying with the increase of fly load as presented in Figure 2A. It is reasonable to assume that the decay of performance of an animal could stop (or become very small) after the fly load reaches a certain threshold (insensitive threshold; IST). In such a case, the model will have two changepoints (EIT and IST) as indicated in Figure 2B.

The first stage of the Bayesian hierarchy describes the conditional distribution of the data (trait phenotypes) in each of the two intervals (before and after the onset threshold; EIT) given the parameters of the model:

where yi and μi are the observed phenotype (i.e., growth rate) and mean of the trait for animal i, EIT is the unknown onset threshold, and  f(αi) is the mathematical expression that describes the decay in performance as a function of HF abundance on heifer i (αi=fly load), and σe2 is the residual variance.

Although  μi it can be modeled as a function of fixed and random effects, in this study, it was assumed that μi=xiβ where β is a vector of systematic (farm and year) effects and  xi was the associated incidence vector, in order to estimate the population level EIT and DPO parameters. It was further assumed that f(αi)=(DPO)*αi. Although several functions can be used to model μi and f(αi), the choice in this study was motivated by the goal of estimating the population level of EIT and DPO.

In matrix notation and assuming μi=xiβ and f(αi)=DPO*αi, the model for n observations can be written as:

where y=(y1,y2…,yn)' is the vector of observed phenotypes, I is the identity matrix with the appropriate dimensions, and α=(α1, α2,…,αN)' is the vector of HF abundance.

Due to the requirement of continuity of the data at the changepoint ( EIT), the following equality needs to be satisfied:

Thus, the continuity of the data at the changepoint implies that DPO*α must be equal to zero at the changepoint ( EIT). After re-parameterization, the likelihood function of the data is proportional to:

where n=n1+n2 with n1 being the number of records with HF abundance is smaller or equal to the injury threshold ( EIT ).

At the second stage of the hierarchy, prior distributions were specified for β, σe2, EIT, and DPO. The classical normal and scaled inverse chi-square distribution priors were assumed for the systematic effects and residual variance, respectively. For the onset threshold and decay parameter, the following prior distributions were assumed:

DPO~U[−∞,0]

where  U[.,.] is the uniform distribution, and  αmin and αmax are the smallest and largest HF observed on the assessed heifers.

The conditional posterior distributions for β,  DPO and σe2 needed for the implementation of Gibbs sampling, were in closed form, being normal and scaled inverted Chi-square, respectively. The conditional distribution of the economic injury onset threshold (EIT) is proportional to:

Viewed as a function of  EIT, the above distribution is not in closed form. Sampling from such distribution was carried out using a Metropolis-Hastings algorithm, where candidate samples were generated from a truncated normal with mean 200 and variance equal to 2000 (Metropolis et al., 1953; Rekaya et al., 2000, 2001).

For the success of first insemination (success=1; failure=0), the same general algorithm was usedexcept that the sampling model presented in Equations 1 and 2 was at the liability scale as:

where l=(l1,l2,…,ln)' is a vector of unknown liabilities related to the observed binary responses (y, through:

In order to make the model in Equation 3 identifiable, the residual variance ( σe2) was set equal to 1.

When two changepoints were postulated (EIT and IST), the model presented in Equation 1 was extended as follows:

Implementation of the model in Equation 4 issimilar to the model in Equation 1, except an extra Metropolis-Hastings step was needed to sample the IST threshold.

Table 2 shows that body weight ranged from 400 to 471 kg. Average daily gain was 0.57 kg/day for ADG₁ (range −0.82 to 1.34), 0.38 kg/day for ADG₂ (range −1.17 to 1.84), and 0.52 kg/day for ADG₃ (range −0.21 to 1.15). These negative results for ADG were not expected and are a result of weight loss during March-June, likely due to extreme weather conditions (drought). There was sufficient variation between heifers as it related to body weights and growth rates, as indicated by the associated large standard deviations (Table 2). The average fly abundance was 561 and 315 for the subjective and image-based counts, respectively. Although the maximum number of fly counts was the same for both methods (1,800 flies), the image-based approach has a lower minimum observed count (0) than the subjective assessment (196). Given this range and precision, the image-based approach was used to obtain more accurate results. Table 3 presents the posterior mean (PM), posterior standard deviation (PS), and the 95% high probability density interval (HPD 95%) for the economic injury threshold (EIT) and decay after onset (DPO) for three growth traits using the one changepoint model. The PM for EIT was 261, 297, and 284 flies for ADG₁, ADG₂, and ADG₃, respectively. The 95% HPD interval for EIT ranged from 158 to 387 flies for ADG₁, 144 to 416 flies for ADG₂, and 149 to 402 flies for ADG₃, highlighting a slight variation in the fly load tolerance across different growth intervals. The estimated posterior means for DPO were -0.643, -0.584, and -0.614 g for each additional fly above the EIT for ADG₁, ADG₂, and ADG₃, respectively. The HPD 95% intervals for DPO ranged from -0.734 to -0.495 for ADG₁, -0.707 to -0.411 for ADG₂, and -0.709 to -0.487 for ADG₃.

For SFI with the one-changepoint model, the success rate of the first insemination was 51.2%. The estimated economic injury threshold (EIT) was 140 flies per animal (posterior mean = 140). The DPO estimate was −0.000108 per additional fly. All these intervals support the continuous decay of performance after the onset of EIT.

Table 4 presents the PM, PS, and the HPD 95% interval for the economic injury threshold, decay after onset, and the insensitivity threshold (IST) for the three growth traits using a two-changepoint model. For SFI, the two-changepoint model failed to converge; therefore, only the one-changepoint results are reported. This model extends the previous approach by estimating an additional threshold (IST) after which it was assumed that additional fly load will not induce further decline in performance (see Figure 2). The estimated EIT ranged between 293 and 322 flies across the three growth traits. These values are slightly higher than those obtained using the one-changepoint model presented in Table 3. A similar trend of declining performance after the onset of EIT was observed using the two-changepoint model, with the posterior mean of DPO estimates being -0.782, -0.578, and -0.685 for ADG₁, ADG₂, and ADG₃, respectively. These results indicated a loss of 0.578 to 0.782 g in average daily gain for each additional fly after the onset of EIT.

The introduction of the insensitivity threshold (IST) in the two-changepoint model provides additional insight into the heifers’ ability to tolerate increasing fly loads beyond the EIT. Estimates of the insensitivity threshold (IST) were 783, 1167, and 808 flies for ADG₁, ADG₂, and ADG₃, respectively. Despite the large variability associated with these estimates (Table 4), it seems that there is a load threshold after which the animal is no longer responsive to additional flies. The PSD values of 114, 136, and 129 indicate noticeable variability in this upper tolerance limit across growth traits. No sensitivity analyses (e.g., exclusion of data collected during the extreme periods) were carried out across the different models, mainly due to the small size of the dataset.

The average growth rate during the second (0.38 kg/day) and third time (0.52 kg/day) intervals (ADG₂ and ADG₃) was lower than the 0.57 kg/day observed in the first period. About 1.48% and 14.24% of heifers lost weight during the second and third period, respectively. Horn flies likely contributed to the observed weight loss during these time periods, as it coincides with extreme weather conditions and the peak of horn fly season in Georgia (June to August). Several studies provide evidence that decreased growth rate can be attributed to horn fly infestations. Research has shown that infested steers and heifers gained up to 17.7% and 14% less weight compared to those with horn fly control, respectively (Derouen et al., 2003). These studies support the observed impact of horn flies on ADG. The estimated economic injury thresholds for all the traits and changepoint models were substantially higher than the 200 flies currently accepted by the cattle industry. Using the one changepoint model, EIT ranged between 261 and 297 for the three growth traits (Table 3) and was equal to 140 for the success of first insemination. Based on these estimated thresholds, 49.26%, 43.04%, and 45.1% of heifers had their growth performance impacted by their fly load during the first, second, and third periods, respectively. Based on the current study, the fertility trait was more sensitive to horn flies than the growth trait: the EIT for SFI was 140 flies, while for the ADG it was 261–297 flies. This shows that thresholds can differ by trait, even within the same breed. Timed AI data were used for the fertility trait, and these results align with evidence that horn flies can elevate cortisol levels, which can negatively affect timed AI outcomes (Vitela-Mendoza et al., 2016; Fernandez-Novo et al., 2020; Faria et al., 2024). Because all heifers in this study were born between December and February, a large part of their early growth occurred during the following summer under high horn fly pressure, so those with low growth rates likely entered the breeding season with lower body condition, which can further reduce SFI.

Using the two-changepoint model, EIT estimates for the three growth traits were 309, 293, and 322 flies for ADG₁, ADG₂, and ADG₃, respectively. Using the two-changepoint model, the rate of decay was more pronounced, especially for the first (-0.782) and third (-0.685) growth periods, respectively. This could be due in part to the imposed insensitivity threshold after which additional fly load was assumed not to affect performance. The different DPO estimates suggest that some cattle cope better with horn flies and can maintain their performance even when fly numbers are high. This corroborate the data presented by Hinkle (2018), who suggested that some cattle are more resilient to horn flies and can stay productive even when infestations are high. These findings highlight the importance of genetic selection and targeted interventions for improving horn fly resistance in beef cattle production. The use of a two-changepoint model allowed us to estimate an insensitivity threshold. The IST estimates ranged from 783 to 1167 flies, a substantially higher threshold than previously considered. These estimates have large posterior standard deviations, partly because there are few animals with fly loads in this range, so the point estimates should be interpreted with caution.

Based on these results, using a fixed threshold of 200 flies may lead to unnecessary insecticide applications, increasing costs and environmental risks. Trait-specific economic injury thresholds (EIT) can make horn fly control more efficient. Because these metrics had not been quantified previously, trait-level EIT, the insensitivity threshold (IST), and the decay of performance after onset (DPO) were estimated for both growth and fertility traits. Taken together, these results indicate that the reproductive trait is more sensitive to horn fly burden than the growth traits and that fertility can be negatively affected at lower fly loads.

Knowing these trait-specific thresholds and their effects on animal performance can help improve horn fly management and support more effective herd-level decisions. Future research should validate these findings across different genetic lines, environments, and production systems to further refine precision-based EIT models. Additionally, the integration of image processing and automated fly counting methods with other phenotypic and physiological traits in future studies could enhance the accuracy and utility of EIT estimation. Overall, these findings establish a more precise, data-driven approach to horn fly management and offer a model that can be adapted in future research to enhance animal health, reproductive efficiency, and sustainable pest control strategies.