A new index of interactivity in parasite communities

International Journal for Parasitology 29 (1999) 915±920

A new index of interactivity in parasite communities Alistair D.M. Dove Department of Microbiology and Parasitology, The University of Queensland, St Lucia, Queensland 4072, Australia Received 1 October 1998; received in revised form 19 March 1999; accepted 19 March 1999

Abstract A new index of interactivity which allows objective evaluation and comparison of interactivity in communities between di€erent host species is presented. The index is derived from the equations for species-accumulation curves generated using non-linear regression (with the Levenberg±Marquardt algorithm) of sample infracommunity richness data. It is advantageous in that it requires only presence/absence data to calculate, is applicable to all parasite taxa (including asexual species), is largely independent of sample size and allows objective comparison of parasite communities while correcting for di€erences in total richness. Iterative randomisation of infracommunity richness values to generate a mean value for the index avoids spurious results which may be generated by heterogeneity in infracommunity richness and the variation this produces in the non-linear regression results. # 1999 Australian Society for Parasitology Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Community; Index; Interactivity; Richness

1. Introduction It is really only since the works of Dogiel and colleagues in the 1940s that community studies have been undertaken in earnest by parasitologists. Recently, however, many interesting hypotheses have been proposed, and some tested, by parasitologists, concerning the structure, nature and dynamics of parasite communities (see for example [1±11]). The degree of interactivity in communities of parasites is a central theme of current parasite ecology. The isolationist/interactive community concept was postulated by Holmes and Price [12] and has since achieved practical recognition (see for example [13±17]) as well as attracting a degree of controversy [18±20]. Generally, interactive communities are species-rich, have many

core species (often specialists), a large degree of niche overlap between parasite species and a dominance of inter-speci®c interactions over individualistic responses, resulting in predictable infracommunities [12]. Isolationist communities generally have few species, have a higher proportion of rare (satellite) generalist species, large amounts of available niche space and a dominance of individualistic responses over interspeci®c interactions, resulting in communities which are dicult to predict and largely stochastically-determined [12, 18]. The point along the cline from interactive to isolationist at which a given community lies has often been a matter of subjective judgement in the past. The use of statistical evaluation of the proportion of negative or positive pair-wise species associations has been used to examine

0020-7519/99/$20.00 # 1999 Australian Society for Parasitology Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 0 - 7 5 1 9 ( 9 9 ) 0 0 0 5 8 - 2

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interactivity objectively [14, 15] but has the logistical and ethical disadvantage of requiring a large host sample size. In addition, this approach is dependent to a degree on the richness of communities in each host species [14] making comparative studies dicult without some way of correcting for di€erences in richness. Furthermore, the need to measure relative densities complicates the data collection process [15]. This paper presents a new index allowing objective estimation of interactivity in parasite communities using data from relatively few hosts and correcting for di€erences in component community richness.

2. An index of interactivity The native Queensland freshwater ®sh species, the glass perchlet, Ambassis agassizi, has a species-rich component community and a reasonably high mean infracommunity richness (Fig. 1A). An exotic species occurring in the same habitat, the green swordtail, Xiphophorus helleri, on the other hand, has a species-poor component community and a low mean infracommunity richness (Fig. 1B) (data not shown). Generalist species of parasites are common in A. agassizi and rare in X. helleri, whereas rare species form a greater proportion of the total richness in X. helleri than they do in A. agassizi. These characteristics would normally lead to a hypothesis that A. agassizi has an interactive and X. helleri an isolationist component community. In the past, however, the objective measurement of the degree of interactivity has not been possible. The increase in sample component community richness with sample size follows a modi®ed Weibull growth curve with the following form: y ˆ a ÿ ae…ÿbx† where the ®rst term a determines the asymptote (the total component community richness), the second term ae(ÿbx) de®nes the shape of the curve and drives it through the origin and b is the gradient of the curve. The term b can be related to

Fig. 1. Increase of parasite component communty richness with increasing sample size (after Dove, submitted). (A) the Australian native ®sh Ambassis agassizi; (B) the exotic poeciliid Xiphophorus helleri.

the mean infracommunity richness; with larger bvalues, the slope of the curve becomes steeper and the mean infracommunity richness approaches the total component community richness. Examples of the e€ects of varying values of a and b are shown in Fig. 2A±D. The gently sloping curves of low b-values represent communities where many individuals must be examined before the component community has been fully accounted for (i.e. there are many rare species of parasites). The steep curves with high b-values represent communities where relatively few individuals need be examined before all parasite species infecting that host species have been found (i.e. there are few rare species of parasites). It is clear from these examples that the two quantities a and b describe a great deal about community structure and function. Between

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has a value in the tens of species, while b has a value between 0 and 1 and their product typically gives a value between 0 and 5 across the range of biologically meaningful values, a seemingly convenient range for a biological index. G ˆ ab

Fig. 2. E€ects of changing the equation parameters a and b on the form of Weibull growth curves. (A) a = 10, b = 0.01; (B) a = 10, b = 0.1; (C) a = 50, b = 0.01; (D) a = 50, b = 0.1. The interactivity index, G, is given for each graph.

them, they describe the mean infracommunity richness and the total component community richness which may be expected from that host. Aside from the practical implications they carry for ecient sampling strategies, these properties are likely to re¯ect the degree of interactivity in a community. Mean infracommunity richness (here measured as b) describes to a degree the niche overlap between parasite species in a community. Obviously the realised overlap depends on the tendency of the parasites to restrict their niche in the presence of other parasite species, but it may be stated generally that richer infracommunities will tend to have greater a degree of niche overlap than poorer communities. When related to b, the total component community richness, a, allows the relative contributions of rare and common parasite species to the community structure and function to be determined; communities where common species dominate are likely to show higher degrees of interactivity than those where rare species form a greater proportion of the total richness. The product of a and b, therefore, is an index which can be used to estimate the degree of interactivity in a component community. The product is used because a typically

The values of G for each host represented in Figs. 1 and 2 are given on each graph. Ambassis agassizi has a more interactive community than its introduced counterpart (see above), X. helleri, and this is re¯ected in its higher G-value. Thus, the index supports intuitive assessment of interactivity in this system. Similarly, Fig. 2A and 2D are obviously at opposing ends of the spectrum of interactivity, which is once again re¯ected in the values of their indices. The index is most useful, however, for comparing communities such as those represented by Fig. 2B and 2C; the graph in Fig. 2B has a far steeper rate of increase, but that of Fig. 2C has a higher total richness. Which one is more interactive? If the index is to be trusted, then the more species-poor illustrated in Fig. 2B is more interactive. This suggests that the high mean infracommunity richness and high prevalence of each parasite species in the host represented by Fig. 2B are more important for generating an interactive community than the high component community richness but low mean infracommunity and species prevalence represented in Fig. 2C. Intuitively, this conclusion seems sound because a high degree of similarity of infracommunities indicates that most parasites have a high prevalence (and are therefore core parasite species), are distributed evenly in resource space, and are likely to be engaged in interactive community processes [12].

3. Advantages of the index approach A great advantage of the index approach is that it requires a small host sample size relative to other methods of assessing interactivity. Parasite species-accumulation curves for Australian freshwater ®shes (from which this technique was derived) show high r 2-values (data

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not shown), which also means that relatively few hosts are needed for the non-linear regression algorithm to generate an equation which converges with the data. Once such a curve has been produced, estimates of a and b can be obtained and the interactivity index calculated. This extrapolative technique relieves to a degree the dependence on large sample size for reliable results. Statistical assessment of pair-wise non-zero associations between parasite species, for example, is a particularly data-intensive analysis [14, 15]. If non-linear regressions of this nature do not ®t the Weibull model with high correlation coecients, the estimates of the index parameters may be unreliable (but see comments on randomising below). For this reason, r 2-values (and their signi®cance levels) should be provided with the index. For the data presented here, the r 2-values were 0.9893 for A. agassizi (P < 0.001) and 0.9061 for X. helleri (P < 0.001) (both n = 30). Another major advantage of the index is that it requires only presence/absence data to calculate. This has major practical implications in that valuable time need not be spent counting parasites for later analysis. In addition, the index is not a€ected by the reproductive mode of the parasite; both sexually- and asexually-proliferating species need only be measured as `present' to calculate the index and the problems inherent in trying to quantify the intensity of infections with the latter species are removed. The need for fewer hosts than other methods, the need for only presence/absence data rather than intensity information, and the ability to incorporate all parasite taxa rather than only helminths, make the index useful for comparative studies. Because of the relative ease of calculating the index, a number of host species can be examined at once and conclusions drawn about di€erences in interactivity. The index may be most useful for examining interactivity di€erences in guilds of hosts such as waterfowl, ungulates or any of the many species ¯ocks of reef ®shes.

4. Disadvantages of the index Although the high r 2 of most species-accumulation curves are largely una€ected by sample size, very small samples can still cause problems. When ®tting curves (the technique used for generating the index), using only the ®rst few data points before the curve begins to ¯atten out will overestimate interactivity by projecting an extremely large value for a. The risk of this error depends on the intrinsic value of b and the degree of noise in the data (the r 2-value). Higher bvalues and lower r 2-values give gross errors if the sample size is small enough to completely precede the plateaux of the curves. As is usually the case, the bigger the sample size, the stronger the predictive powers and the less the chance of the model generating a spurious answer. One other drawback with the technique used to derive the index is that the curve ®tted by the Marquardt±Levenberg algorithm is susceptible to heterogeneity in infracommunity richness values. If richness values are aggregatedÐthat is, if most hosts have few parasite species and a few hosts have manyÐthen the order of examination will a€ect the shape of the curve produced. If an unusually rich host is examined early, then the curve will project an unnaturally high b-value. If, on the other hand, many species-poor hosts are examined before a rich one is encountered, then a low b-value will be projected and, most likely, a poor ®t (low r 2-value) will result. The solution to this problem is to randomise the order of host examinations over a number of iterations and to determine the mean values for the terms a and b of the Weibull curve. The resulting estimations should be far more accurate while avoiding potentially spurious results from heterogeneous richness values. It should be noted that the index presented here does not directly measure the extent of interactivity in a parasite community; it is correlated with it. It makes no measure of the extent to which species' niches overlap, the rates at which parasites are recruited to the infrapopulations, the infrapopulation sizes, or the number of positive or negative species associations, all of which are factors which determine the interactivity in a

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system [12, 18]. Instead, the index uses easily-collected richness data and exploits the tendency of the relationship between infracommunity richness and component community richness to re¯ect the degree of interaction occurring in the system. There are, conceptually at least, communities for which the index will not re¯ect the interactivity of the system. A rich community, for example, where species have strongly delineated and nonoverlapping potential niches, or a poor community composed of unusually prevalent generalists with overlapping potential niches, are communities for which values of the index may not correlate with interactivity. Nonetheless, it would appear that such communities are rare in nature and that the index should be a useful measure of interactivity for the majority of parasite communities.

associations [14, 18, 19]. The two approaches may provide interesting results for comparison. The ability to quantify interactivity, if indirectly, provides new opportunities for rigorous comparative community studies between di€erent host species. Because the index may be used for any subset of a community, gastro-intestinal helminths for example, it is important that the community being assessed is clearly identi®ed in the study. As long as this is addressed along with the drawbacks outlined above, however, the index should allow critical comparison of the degree of interactivity in parasite communities of di€erent host species, correcting for di€erences in total component community richness.

5. A note on utility

Prateep Bandharangshi wrote the UNIX program for randomised iteration of richness values and I am hugely indebted to him for that and for many discussions of randomisation and computing issues in general. I thank Joan Hendrikz and Hugh Dove, who both provided a great deal of help with curve ®tting assumptions and algebra. I also thank John Holmes for planting the seeds of the idea for an interactivity index and Di Barton for creative and critical discussions. Ingo Ernst and Clinton Chambers provided comments on drafts of the manuscript.

An analogue of the index may be generated using the ratio of the sample mean infracommunity richness to sample component community richness instead of the product of a and b. Because of the non-linear nature of the relationship between the cumulative richness of a component community and the sample size, however, sample size-dependence is an inherent problem with this approach. Small samples will underestimate interactivity because the mean infracommunity richness is independent of sample size but the cumulative component community is obviously not and will be smallest (but growing fastest) at small sample sizes. For this reason, the analogue is not recommended for anything but the largest of sample sizes; the non-linear regression approach should produce far more reliable estimates. Perhaps the best approach is to combine the index with other methods of assessing interactivity, to give a more detailed picture of the community structure and to redress some of the drawbacks of each. For example, a useful approach may be to compare the index with the proportion of the total parasite pairwise species comparisons showing non-zero statistical

Acknowledgements

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