Parasite Ingestion by Fish

Transcription

1 Data Set 5: Parasite Ingestion by Fish Background Pink spot disease of Porites corals is caused by infection by the digenetic trematode * Podocotyloides stenometra. The pink spots are individual coral polyps which have been infected by immature stages of the parasite, which form cysts inside the coral tentacles and cause the polyp to swell and become pink colored. One step in the very complex life-cycle of this parasite occurs when a fish feeds on an infected polyp and ingests parasite cysts, after which the larval parasites are released from the cysts and develop into adults which infest the digestive tract of the fish. Greta Aeby, a Ph.D. graduate of the Zoology Department, studied the interactions between the trematode and its coral and fish hosts. The fish hosts she worked with were Chaetodon multicinctus, the same species as in Ernie Reese s study of size-assortative mating (Data set #4). These fish actually prefer to feed on infected polyps rather than uninfected ones, so part of Greta s research was aimed at explaining this behavior by measuring the benefits and costs to the fish. There was a substantial benefit in that the swollen infected polyps were easier to feed on. The first part of measuring the costs was to quantify the rate of ingestion of cysts when fish feed on infected colonies, as well as the success rate of ingested worms in establishing themselves in the host s gut; the data from this study are the subject of this handout. In a subsequent study Greta found that infected fish suffer no detectable decrease in body condition or energy reserves; combined with the results presented in this handout, her conclusion was that there is essentially no cost to the fish for feeding on infected polyps. The questions: When a fish feeds on an infected coral colony, how many cysts does it ingest? When cysts are ingested, what fraction of them produce adult worms in the fish gut? *. Trematodes, commonly called flukes, are a class in the animal phylum Platyhelminthes (flatworms). All trematodes are parasitic, several species causing serious human diseases. Many species use two or more host species at different stages of their life cycles.

2 The data Procedure Adults of C. multicinctus were held in the lab without food for hours, to empty their guts of any parasite cysts or juveniles. They then were allowed to feed on infected coral for 30 minutes, during which the number of bites on the coral was recorded. After this 30 minute observation period, they were held another 24 hours without food. They were then allowed to feed on infected coral for 30 minutes, while the number of bites was recorded. Immediately after this second 30 minute period the fish were sacrificed and the numbers of cysts and of young adult trematodes in their guts were counted; the cysts would have been infested during the second feeding period (immediately before dissection), while the young adults would have been from cysts ingested the previous day. Nine fish were used. The variables (1) Ingestion rate, cysts / bite: The number of cysts divided by the number of bites during the second 30 minute period. (2) Establishment rate, adults / cyst: The number of young adult worms divided by the number of ingested cysts, the latter estimated by multiplying the ingestion rate by the number of bites in the 30-minute period the previous day. The data Ingestion rate: Establishment rate: Data Set 5: Parasite Ingestion by Fish (rev. October 19, 2005) 2

3 Data exploration Displays of the distributions Histograms and boxplots ingestion rate establishment rate ingestion rate establishment NQQ plots ingestion rate (cysts / bite) establishment rate (adults / cyst) Normal Distribution Normal Distribution With such a small sample size it is difficult to say much about the distributions. One clear pattern is that the distribution of establishment rates is skewed, with most values very low (<10%), no left tail, and a somewhat elongated right tail; this asymmetry is seen in all three plots. Ingestion rates also were low (most considerably less than one cyst per bite); the distribution of ingestion rates is more symmetrical than that of establishment rates, but is fairly bumpy. Neither distribution is grossly non-normal. Data Set 5: Parasite Ingestion by Fish (rev. October 19, 2005) 3

4 Statistical summary ingestion rate establishment rate Minimum: Q1: Median: Q3: Maximum: IQR: Mean: Std Dev.: Typical ingestion rates were a little less than 0.3 cysts per bite, with the middle five observations (out of nine) ranging from 0.21 to The distribution is only moderately spread out, with the standard deviation about half the mean and the IQR a little less than half the median. The mean and median are fairly close, reflecting the rough symmetry of the distribution. Establishment rates were very low, with typical values less than 10% and the middle five observations ranging from to only This distribution is quite spread out, with the standard deviation almost equal to the mean and the IQR actually greater than the median. The mean and median are quite similar, but the much greater difference between the maximum and Q3 than between Q1 and the minimum indicates the asymmetry of the outer parts of this distribution. Data Set 5: Parasite Ingestion by Fish (rev. October 19, 2005) 4

5 Inference The purpose of the study was to estimate two rates, so the appropriate inferences are single-sample estimates with confidence intervals. There were no hypotheses to test. Scope of inference The fish and the infected corals used in this study were collected haphazardly from Kaneohe Bay. To generalize from these data to the interaction between these three species generally we must assume that the animals and how they interacted were representative of their species and interactions, without being able to assert this based on having a random sample of some sort. This also entails the assumption that being in captivity did not affect these phenomena. I expect that these assumptions are at least roughly true. It seems very safe to assume that however Greta chose the corals and fish, it was not directly related to the two variables measured in the study. I am less comfortable assuming there were no effects from being in captivity for instance, the low establishment rate could have been partly due to the parasites being unhealthy in the lab but the basic result that both rates were low probably is accurate. Ingestion rate Rather than go through the different methods of estimation one at a time, I present them together. method parameter estimate confidence interval level t mean , % sign median , % signed-rank median , % bootstrap percentiles mean , % BCa mean , % tilting mean , % t w/ bootstrap se mean , % Data Set 5: Parasite Ingestion by Fish (rev. October 19, 2005) 5

6 The confidence intervals generated by all these methods are generally similar. The nonparametric estimates of the median are somewhat larger than the sample mean, the sign estimate more so than the signedrank estimate. The sign CI is considerably wider than the others, as is to be expected. The various bootstrap CIs all are somewhat narrow than the standard t CI. Which interval to use? The distribution of ingestion rates is not grossly non-normal, but it also was not strikingly normal, and the sample size is too low for the Central Limit Theorem to have a strong effect. I therefore would be cautious about using the standard t procedure. The bootstrap distribution the distribution of sample means from 1000 resamplings of the data is slightly asymmetric but basically fairly close to normal. In addition the various bootstrap CIs are close to symmetric. These results suggest that the standard t procedure in fact is acceptable for these data. The nonparametric procedures also are valid, with the signed-rank procedure being more powerful. Estimating the median, though, is not as useful in this setting as is estimating the mean: multiplying the mean rate by a Density t sign sign-rank%ile BCa tiling t boot se number of bites estimates total ingestion, while this cannot be done with the median rate. I therefore would report the sample mean together with the standard t CI; the bootstrap CIs should be valid, but using the wider t interval is both conservative as a sort of compensation for my concerns about the realism of these lab results and easier to explain Param bootstrap : trematodes : mean(cysts.bite) Observed Mean Param Quantiles of Standard Normal Data Set 5: Parasite Ingestion by Fish (rev. October 19, 2005) 6

7 Establishment rate method parameter estimate confidence interval level t mean , % sign median , % signed-rank median , % bootstrap percentiles mean , % BCa mean , % tilting mean , % t w/ bootstrap se mean , % These confidence intervals again are generally similar. There is less difference between the nonparametric estimates of the median and the sample mean than was the case for the ingestion rate, but again the nonparametric CIs, especially the sign CI, are somewhat wider than the others. The various bootstrap CIs all are somewhat narrow than the standard t CI. Which interval to use? The distribution of establishment rates is somewhat skewed and the sample size is small. For these reasons, if the only aim was to estimate this rate, I would be inclined to use the nonparametric methods, in particular the signed CI. The bootstrap distribution of resample means, however, again is only slightly asymmetric and the various bootstrap CIs are close to symmetric. These results suggest that the standard t procedure probably is acceptable for these data.as was the case with the ingestion rate, estimating the mean has the advantage that it could be used to estimate the total number of worms becoming established. I therefore again would report the sample mean together with the standard t CI. Density Param t sign sign-rank %ile BCa tiling t boot se bootstrap : trematodes : mean(establishment) Observed Mean Param Quantiles of Standard Normal Data Set 5: Parasite Ingestion by Fish (rev. October 19, 2005) 7

8 Conclusions When a fish feeds on an infected coral colony, how many cysts does it ingest? Just over one-fourth of a cyst per bite (or one cyst per four bites): the mean ingestion rate is estimated to be cysts/bite. Due primarily to the small sample size, this is not a very precise estimate: the 95% margin of error is , a fairly large fraction of the mean. When cysts are ingested, what fraction of them produce adult worms in the fish gut? Probably less than one in ten: the mean fraction of ingested cysts successfully establishing as adults is estimated to be worms/cyst. This estimate is even less precise than the one for ingestion rate, with a 95% margin of error of , approaching the magnitude of the mean. The indirect method of measuring establishment rate probably contributes to this uncertainty. Combining these two results, a fish that feeds on an infected coral colony will acquire, on average, one adult worm for every 43.7 bites. [0.272 cysts bite worms cyst = worms bite, or = 43.7 bites worm.] This supports Greta s conclusion that the fish pay little if any cost for feeding on infected polyps, since the risk of infection is so low. Data Set 5: Parasite Ingestion by Fish (rev. October 19, 2005) 8