*Today’s post is a guest post by Rowan Christie, a RIT Bioinformatics BS student and RIT/NTID RISE research fellow. Rowan has been working for the past year on the NSF-funded ‘Managing Our Expectations’ project with Christie and Kaitlin. Check out Rowan’s work and progress on GitHub and FigShare. * This work updates Rowan’s earlier post, which you can read here.

Deer ticks are vectors of Lyme disease, a debilitating disease that can cause fever, muscle aches, facial paralysis, and other symptoms that can be really debilitating for many people.

@Global Lyme Alliance (https://globallymealliance.org/about-lyme/diagnosis/symptoms/)

In addition, deer ticks may also be spreading – CDC reports that the number of counties with the blacklegged ticks in the United States also has more than doubled over the past twenty years. You can learn more about the the CDC’s deer tick surveillance in their report here (https://www.cdc.gov/ticks/resources/TickSurveillance_Iscapularis-P.pdf).

Because of these reasons, deer ticks are a major public health concern. So to better understand risks to public health, it is important to study deer tick abundance and population trajectories.

Many studies have already been conducted to measure deer tick abundance trends and the occurrence of pathogen within them. However, one challenge is that most biological studies are mostly short term (~3 years). This can be problematic because the trends observed may not be indicative of longer-term patterns, and could only be a small variation on a much larger temporal scale. So you could assume that an upward trend could indicate a major increase in tick abundance. However, when the rest of the data is present…

Timeseries showing the density in m^{2} of *Ixodes scapularis* (deer ticks) by year in all grids (plots) of Cary Forest, NY.

You may find that the upward trend is not particularly significant compared to the rest of the data. So essentially, you are missing the big picture. Because of this, we decided to focus on long term datasets and investigate how the stability of patterns within the dataset responded to the number of years in the dataset.

Tick studies also vary in methodologies, making it difficult to weigh their relative quality of evidence. For example, many studies are focused on different sampling techniques such as: dragging (shown in the first picture for sampling method), which is where you take a large sheet and drag it around a site to pick up and measure the amount of ticks in a given location, and public surveys, an opportunistic sampling method where people send in reports of ticks found on themselves. Some studies focus on different life stages: larval (youngest), nymph (middle stage), and adults (final stage). Studies can also differ in geographic scope — for example, some studies collect data on a county level scale while other studies provide data on a more specific level like plot or state forest. Differences between study methods could be influencing the results we observe and conclusions we reach, so when you compare studies that vary between, say, sampling technique, it may be misconstrued to do so because using a standardized sampling techniques like dragging may provide rather different results than an opportunistic sampling technique like people sending in reports of ticks they found on themselves.

Thus, our objective was to investigate how study factors such as length, life stage, sampling technique, and geographic scope influenced deer tick abundance trends. Several studies have already investigated how study length impacts the ability to detect consistent differences between different samples/datasets. There is support for long term datasets being more likely to lead to stable patterns, according to this study.

To analyze the patterns between datasets, we need to consider statistics such as years to stability, which is the number of years it took for the dataset to reach a stable pattern, and reflects upon the consistency and strength of the trend. For example, the longer it takes for the dataset to reach stability, the more support it provides for long term datasets because they are more likely to reach stability. Similarly, other study factors can also influence how likely the dataset is to reach stability. So our hypothesis was:

- Longer deer tick datasets would have more consistent population trends, so they are more likely to reach stability;
- Studies using dragging will have more consistent population trends, so they are more likely to vary less by stability time.

First, we searched for publicly available datasets from observational studies from data repositories such as LTER, DataDryad, NCBI, DataOne, Google Datasets, and various department of health websites from different states in the US that measured count or density data of deer ticks at least annually for 10 or more years.

The datasets we collected were from states New York, Massachusetts, New Jersey, Iowa, and Connecticut, ranged from 9 – 24 years long between 1995-2017, included larvae, nymph, and adult life stage, and recorded at grid (plot), state forest, town, and county level scale.

To test what led to stable population trends, we used the ‘bad breakup’ algorithm in R developed by Dr. Christie Bahlai of Kent State University to model every subset of data greater than two years in the dataset and determine whether or not the subset was statistically significant, thus determining the number of years it takes for the dataset to reach a stable pattern.

First, data (an example dataset of tick count in Bethany county, CT, is shown below) is subjected to a standardization algorithm to normalize the data and to make it easier to compare tick count/density data with very different magnitudes and minimize the impact of using different units (such as # of ticks per meter squared and count of ticks people found on themselves) on the observed trends.

Then the algorithm iterates through data (as shown below) and each interval is run through a linear model. This linear model calculates the slope statistic, which is the change of standardized density over change in year – so say if the interval was this:

Year | stand.response |

1996 | 0.446773 |

1997 | -0.29591 |

1998 | 0.168265 |

The linear model will calculate the slope of the fitted line based on this interval, like this:

And the slope of that line (which is -0.139254) is the statistic we are using. The standard error of this slope, p-value, and r^{2} are also calculated.

The pyramid plot shown is a way to represent these summary statistics, where the slope and standard error per year are visualized. The red cross indicates insignificance (p-value>0.05) and black circle indicates significance (p<0.05).

We also needed a way to pull relevant metrics out of the computation: stability time, relative range, absolute range, proportion significant. You can see how these statistics are calculated in Dr. Christie’s bad breakup github repo.

Stability can be defined as greater than some percentage of slopes occuring within the standard deviation of the slope of the longest series, for a given window length.

The absolute range of significant findings and relative range, which is the absolute over and under estimate compared to the slope of the longest series, was also computed.

Proportion significant is the proportion of total windows with statistically significant values.

Proportion significantly wrong is ‘directionally wrong’ and represents the proportion of total windows where there is a significant relationship that does not match the direction of the true slope. We also included another statistic to study, proportion significantly right, which is essentially the inverse of proportion significantly wrong, equal to 1-proportion significantly wrong.

We calculated all of these metrics for each possible dataset we had collected, which includes all locations, life stages, and whether or not the dataset involved percentage of ticks infected with *Borrelia burgdorferi*. We recorded these stats in a dataset, and we ended up with 289 records. So basically, we had a dataset of stats we could analyze – stats on stats.

To analyze the results, we first looked at how the frequencies of the years to reach stability differ to see what years the datasets reached stability (i.e. the length of time needed for any given observation period to reflect the same trend as the longest time series) overall. We found that none of the studies we looked at reached stable patterns in under four years. This is critical to note because it indicates that studies with less than five years of data are unlikely to reach stable patterns- and may thus be insufficient to characterize tick dynamics. This provides support for our first hypothesis and for pursuing longer term studies, as they have been shown to be more likely to be more accurate and have more stable patterns.

*Figure 1: Line chart showing years to reach stability for all datasets. Most of our datasets reached stability within 5 to 10 years. None of the datasets reached stability under four years.*

To test our second hypothesis that dragging leads to more stable trends, we compared years to stability and the sampling techniques dragging (standardized) and reports from people having found ticks on themselves (opportunistic). We found that data produced by dragging varies less stability time (t(236.23)=-8.5346, p<0.05). This difference is largely explained by variability: opportunistic sampling techniques have a wider range, which means that it is more likely to vary in reliability, supporting our second hypothesis.

*Figure 3: Boxplot showing how the statistical stability time differs between two sampling techniques: dragging (standardized) and reports from people having found ticks on themselves (opportunistic). The opportunistic sampling technique appears to have a wider range times to reach stability.*

Another important factor to consider is the life stage of the tick. Many studies collect data for each life stage of the tick, but some focus on only nymphs or adults, or don’t record the life stage. Results may differ between different life stages, which could lead to studies obscuring patterns and inferring different conclusions as a result. To investigate this possibility, we looked at how life stages could differ in stability with the available data. We found that surveys for adults and nymphs, adults and larvae, and nymphs and larvae did not differ in stability time (t(126.84) = -5.9627, p<0.05; t(10.111) = -5.9627, p<0.05; t(10.54) = -5.5196, p<0.05 respectively). This suggests that all life stages behave similarly in regards to abundance.

*Figure 5: Line graph of the stability time between each of the different tick life stages (nymph, larvae, adult) by the number of datasets. Life stages are color coded (nymph is blue, larvae is orange, adult is green).*

Other analyses were also made in regards to geographic scope and the occurrence of pathogen that some studies recorded, and we also tested compared proportion significantly wrong and right.

Our main takeaway is that long term studies are very useful for understanding long term populations dynamics and are more likely to reach a stable pattern. We should be cautious with using short term studies (especially those less than 5 years) to interpret longer term population trends of deer ticks because they may lead to misleading results. In addition, dragging has proved to be a more reliable method for reaching consistent results, providing support for using standardized methods.

*Rowan is supported by the National Institute of General Medical Sciences of the National Institutes of the Health under Award Number R25GM122672. Kaitlin and Christie are supported by the Office of Advanced Cyberinfrastructure in the National Science Foundation under Award Number #1838807. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health or the National Science Foundation.*