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closeconcerns with ISP/ISH Indices
Posted by devindrown on 17 Apr 2007 at 17:50 GMT
In Malpica et al (2006), the authors propose two indices, based on Cramer’s C, which measure the degree of association between pathogens and hosts. One index proposed is called the index of selectivity of the pathogen (ISP) which measures the selectivity of the pathogen among hosts. They also describe the analogous index, ISH, from the point of view of the host. ISP and ISH range from 0 (representing complete homogeneity in infection) to 1 (representing maximum heterogeneity).
In the discussion of the paper, the authors imply their measures of selectivity are measures of specialization. However, because these indices are based upon contingency chi-squared tests, they actually reflect whether infection status is independent of host species (ISP) or parasite species (ISH). This has little to do with whether a host or pathogen is selective or a specialist. We have picked several test cases that illustrate how these indices (ISP and ISH) are problematic and do not represent a summary of the selectivity of the pathogen or host. Here is a link to a table of the example pathogens and related ISP values (http://www.wsu.edu/~drown...)
As a first test case, imagine two pathogens (A and B) which infect the same set of five hosts. Pathogen A has a high prevalence on only a single host and low prevalence on the remaining hosts (90%, 10% respectively). Pathogen B has a high prevalence on two hosts and a low prevalence on the remaining three hosts. Which is more selective? From our point of view, the pathogen that has a high degree of success on a smaller number of hosts (pathogen A). However, pathogen B has a slightly higher ISP value indicating a higher selectivity under the definition of Malpica et al (2006).
As another test, imagine another two pathogens (C and D). In this case, one pathogen (C) can only infect one host with 100% prevalence and the other pathogen (D) infects two hosts with 100% prevalence. In this case, it is obvious which pathogen is the more selective, the specialist pathogen (C). However, the ISP values fail to capture this distinction at all, indicating the maximum value of 1.0 for both pathogens. This is again troubling as it represents a case where the same index value summarizes two very different pathogen strategies.
As a final test case, we were interested in how the sampling strategy may impact the index value. The authors claim the index is a measure of the lack of homogeneity of the prevalence among hosts (for ISP). In this case, we compared two situations (E and F) which differ only in the number of hosts sampled, but not in the prevalence of the pathogen on each host. If the ISP index is measuring the lack of homogeneity of prevalence, then a difference in host counts should not affect the value of the statistic. However, for the case with a larger number of hosts sampled the ISP value is higher. This final case reveals another troubling point for the proposed indices.
Devin M. Drown and Ben J. Ridenhour
RE: concerns with ISP/ISH Indices
fegarciaarenal replied to devindrown on 09 May 2007 at 08:22 GMT
As Drown and Rindehour state, our indices are based upon contingency chi-squared tests, and they measure weather infection status is independent (or dependent) of host (ISP) or parasite (HSP) species. This, contrary to what they say, has much to do with a parasite or a host being generalist or specialist: a parasite selective or specialist is defined by having a prevalence dependent on the host, and if the parasite’s prevalence is independent of the host, the parasite will be a generalist, because it is able to infect any host with the same probability. So we can say that we measure the degree of association between pathogens and hosts by finding out if the presence of the pathogen is dependent or independent on the host.
Since these indices are based upon contingency chi-squared tests, they basically compare the distributions of frequencies in different samples (ie. pathogen’s prevalence in different host species). If frequencies are equally distributed in the samples, infection by that pathogen is independent of the host (it would be a generalist pathogen). If frequencies are different in the different host, we have a specialist pathogen. This comparison has especial sense in distributions with different sample sizes, which is the most common situation in random samplings. Therefore these tests are suitable to distinguish and rank the different degrees of selectivity of parasites infecting hosts that have different prevalences in the ecosystem.
The correlation between ISP and the absolute selectivity of the pathogen is not 100%, as you have shown with your simulations with examples A-B and C-D, because it does not discriminate between extreme situations. However, for a parasite with prevalences 0.30. 0.30. 0.30. 0.10. and 0.10 on five hosts of which 100 individual for each were sampled (as in D&R Table 1) the ISP is 0.24, indicating indeed a difference in selectivity. The sensitivity of these indices might therefore not be enough to determinate the most selective parasite of a given set of parasites tested on a few hosts. Anyway, this does not invalidate these tests for their actual aim: ranking the selectivity level of the different parasites in the complex ecosystems that constitute the real situations.
Finally, the last assessment of Drown and Ridenhour’s criticism, exemplified in simulation with pathogens E and F is not correct. In these examples different sample sizes are not compared, but populations with different host composition, as in population F the frequency of host I is twice that on population E. Obviously the host composition of the sampled ecosystem should not depend on the number of individuals sampled (sample size). Therefore, the distribution of frequencies of infected and non infected plants among hosts will be different for pathogen E than for pathogen F, which will be reflected on the ISPs.