- Quantitative parasitology
**Counting parasites**Quantifying parasites in a sample of hosts or comparing measures of infection across two or more samples can be challenging.

The parasitic infection of a sample of hosts inherently exhibits a complex pattern that cannot be adequately quantified by a single statistical measure. As the use of two or more separate indices is advisable, only two or more separate statistical tests can reliably compare infections different samples of hosts.

A few of the available statistical measures have markedly different biological interpretations, while others have more-or-less overlapping interpretations or no interpretations at all. Therefore, one should apply measures that have clear and separate biological interpretations thus do not predict each other.

Parasite individuals typically exhibit an aggregated (right-skewed) distribution among host individuals; most hosts harbour few if any parasites and a few hosts harbour many of them. This quantitative feature of parasitism renders many of traditional statistical methods obsolete and requires the use of advanced computer-intensive statistical methods.

**How to describe the parasitic infection of a sample of hosts**Always give the host

**sample size**. In most cases, this is expressed as the number of hosts individuals examined. (Exceptionally, other units may also be used for special cases.)Describe

**prevalence**. This is the proportion of infected hosts among all the hosts examined. Give theconfidence interval (CI) of prevalence (either as a Clopper-Pearson interval or as adjusted Wald/Sterne's interval) to indicate the accuracy of the estimation (use of the confidence intervals belonging to the 95% probability is advisable).Describe

**mean intensity**. This is the mean number of parasites found in the infected hosts (the zeros of uninfected hosts are excluded). Since sample size and prevalence are known, mean intensity defines the quantity of parasites found in the sample of hosts. Given the typical aggregated (right-skewed) distribution of parasites, its actual value is highly dependent on a few extremely infected hosts. Also give CI to indicate the accuracy of the estimation. Use bias-corrected and accelerated bootstrap (BCa Bootsrap) to get this confidence interval.Describe

**median intensity**. This is the median number of parasites found in infected hosts (the zeros of uninfected hosts are excluded). Median intensity shows a typical level of infection among the infected hosts. Use exact CI to indicate the accuracy of the estimation.In certain cases one may prefer to use

**mean abundance**instead of mean intensity. This is the mean number of parasites found in all hosts (involves the zero values of uninfected hosts). Give BCa Bootsrap confidence interval to indicate the accuracy of this estimation. This measure unifies two of the former ones: prevalence and mean intensity. Do not use it, unless you have a clearly specified a reason why to prefer it.Describing

**mean crowding**(intensity values averaged across parasite individuals) and its confidence interval is essential only for those who study density-dependent characters of parasites. BCa Bootsrap CI can be used to indicate the accuracy of the estimation.Finally, quantify

**levels of**of the parasites' distribution among hosts. There are 3 indices widely used for this purpose, but their interpretation is quite similar. They predict each other rather well, thus it is not necessary to use all the 3 of them.skewness **How to compare the parasite burdens across two or more samples**Compare

**prevalences by**. This will show whether the proportion of infected individuals differs significantly between the two (or more) samples. The time need of this test may increase dramatically when several samples are involved. The useFisher's exact test Chi-square test for the same purpose may be advisable in such cases.Compare

**mean intensities by a**. This will show whether parasite quantities differ significantly between the infected proportions of the two samples.Bootstrap t-test Compare

**median intensities by**. This will show whether the typical level of infection differs significantly between the infected proportions of the two samples.Mood's median test One can also compare the

**frequency distributions of intensities by a**. It compares several random pairs of individual values taken from the two samples to test whether or not there is a significant tendency to get higher values from one sample than from the other.Stochastic equality test In certain cases, one may also decide to compare

**mean abundances by a**. This will show whether parasite quantities differ significantly between two samples. This comparison unifies two of the former ones: the comparison of prevalences and the comparison of mean intensities.Bootstrap t-test Finally,

**mean crowding can be compared**across samples by a simple method: provided that the two 97.5%confidence interval s do not overlap, we conclude that the two values are different at a 95% level of significance.**Avoid typical mistakes**Do not use

geometric mean because this measure is hard to interpret biologically.Do not apply the usual form of "

arithmetic mean ±standard deviation (mean ± SD)" to describe levels of infection because this is useful only fornormal distribution s, and not for the aggregated (right-skewed) distributions that characterize parasites. Useconfidence interval s to quantify the accuracy of estimations.Avoid overstatements when interpreting the results.

**Literature*** Lotka AJ 1923. Contribution to quantitative parasitology. J. Wash. Acad. Sci, 13, 152-158. (a

population dynamics model, notbiostatistics )

* Morales G, Arelis Pino L 1987. Parasitología cuantitativa. Acta Científica Venezolana, p 132.

* Bush AO, Lafferty KD, Lotz JM, Shostak AW 1997. Parasitology meets ecology on its own terms: Margolis et al. revisited. Journal of Parasitology, 83, 575–583.

* Crofton HD 1971. A quantitative approach to parasitism. Parasitology, 62, 179-193.

* [*http://www.behav.org/qp/quant_large.pdf Rózsa L, Reiczigel J, Majoros G 2000. Quantifying parasites in samples of hosts. Journal of Parasitology, 86, 228-232.*]

* [*http://www.behav.org/qp/Reiczigel_conf_int.pdf Reiczigel J 2003. Confidence intervals for the binomial parameter: some new considerations. Statistics in Medicine, 22, 611-621.*]

* [*http://www.ncbi.nlm.nih.gov/pubmed/15357054?dopt=Abstract Neuhauser M, Poulin R 2004. Comparing parasite numbers between samples of hosts. Journal of Parasitology, 90, 689-691.*]

* [*http://www.behav.org/qp/j_parasitol_crowding.pdf Reiczigel J, Lang Z, Rózsa L, Tóthmérész B 2005. Properties of crowding indices and statistical tools to analyze crowding data. Journal of Parasitology, 91, 245-252.*]

* [*http://www.behav.org/qp/stochastic%20equality.pdf Reiczigel J, Zakariás I, Rózsa L 2005. A Bootstrap Test of Stochastic Equality of Two Populations. The American Statistican, 59, 156-161.*]**External links*** [

*http://www.behav.org/qp/qp.htm Quantitative Parasitology 3.0, a free statistical toolset for parasitologists*]

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