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Marine Environmental Research 71 (2011) 145–146

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Marine Environmental Research

journal homepage: www.elsevier .com/locate/marenvrev

Letter to editor

Effect of incorrect interpretation of population statistics in the description of coralpopulation dynamics: Response to Crabbe 2009

In an article recently published in this journal (Crabbe, 2009),the author studied the dynamics of several demographic parame-ters of different coral populations in Jamaica between 2002 and2008. Among the response variables studied, the coefficient ofskewness was calculated as an estimate of colony-size frequencydistribution. The article states that the coefficient was calculatedfollowing Zar (1999). Unfortunately, the interpretation of the signof the coefficient was incorrect. Crabbe (2009) states that “Negativevalues for the skewness indicate data that are skewed left (more smallcolonies than in a normal distribution) and positive values for theskewness indicate data that are skewed right (more large coloniesthan in a normal distribution)”. Following Zar (1999), or any othertext book that describes symmetry in distributions, the meaningof the sign of the coefficient is the opposite. Negative skewnessimplies more large colonies than expected and positive skewnessimplies more small colonies than expected (e.g. Zar, 1999;Fig. 1B). In fact, Meesters et al. (2001, an article cited in Crabbe,2009) specifically states “Most coral-size distributions were notsymmetrical around the mean, but negatively skewed (48 out of52: Table 1). This indicates colony-size distributions with relativelyfewer colonies in the smaller size classes and a preponderance oflarger colonies”. Even though this seems a simple technical issue,it strongly influences the discussion of the article, as the authorrepeatedly states incorrectly that more large colonies were foundthan expected in a normal distribution through the entire article.A clear example can be seen in Fig. 1A where the size frequencydistribution histogram shows graphically that there are more smallcolonies than expected in a normal distribution, and accordinglythe skewness value cited in the text are positive for all the sites.Nevertheless, the author interprets these values as an indication

Fig. 1. Interpretation of skewness coefficients. A: size frequency distribution of Siderastrea sitext that the skewness was positive for all sites representing more large colonies than a normskewness “i” and negative skewness “ii”. The skewness for the corals populations in Crabbe

0141-1136/$ – see front matter � 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.marenvres.2010.12.001

that distribution is “skewed to the left with more large coloniesthan in a normal distribution”.

There are twomain consequences of the incorrect interpretationof the sign of the coefficient: firstly the author acknowledges in twoseparate sections of the discussion that the relationship betweenthe number of small colonies vs. large colonies in a population canbe an indicator of the status of the population. It is generallyaccepted that a healthy, viable population has a size frequencydistribution dominated by small colonies (positive skewness; Bakand Meesters, 1998; Meesters et al., 2001; Smith et al., 2005;McClanahan et al., 2008) while populations with low proportionof small colonies can potentially be less resilient (Connell, 1978).Yet, the author suggests thatmost of the populations hadmore largecolonies than expected in a normal distribution in the first timepoint (2002), that some had more small colonies than expected,and that this trend changed in 2008. This would imply that mostof the populations were in a degraded state and that some ofthem actually ‘improved’ (became more dominated by small colo-nies). Nevertheless, because the skewness coefficient was inter-preted inversely, what the actual data shows is the opposite, withmost of the populations being in a relatively “healthy” state (moresmall colonies than in a normal distribution) and some being dete-riorated over time. This correction is critical for the understandingof the response of coral populations to disturbances.

Secondly, the incorrect interpretation of the coefficient leads tocontradicting results between the different response variablesstudied. In addition to skewness, the author also studied thenumber of colonies in the smallest size class for each species persite over time. This result should, at least partially, coincide withthe change in skewness over time, although this was not discussed

derea in 2008 for 5 sites in Jamaica. (Taken from Crabbe, 2009). The author states in theal distribution. B: diagram modified form Zar 1999 showing distributions with positive(2009) is positive, clearly showing more small colonies than in a normal distribution.

Letter to editor / Marine Environmental Research 71 (2011) 145–146146

in the article. For example, in the results section and in Fig.1g–h(Crabbe, 1999) the authors reported that “C. natans skewnesschanged from �0.07 to 0.68 at Rio Bueno from 2002 to 2008 (adecrease of small colonies in relation to a normal distribution), andat Dancing Ladies from �0.31 to 0.38.” Then in Fig. 5d it is shownhow in both populations the number of colonies in the smallestsize class actually increased from 4 to 7 between 2002 and 2008(Crabbe, 2009, Fig. 5d). If the interpretation of the sign of the coef-ficient of skewness used by the author was right, this informationwould be contradictory as an increase in the number of small colo-nies would have lead to a value of skewness showing a reduction inthe dominance of small colonies. In contrast, if the skewness coef-ficient is interpreted correctly following Zar (1999), then there is nocontradiction, as the skewness would have shown a shift fromnegative (more large colonies than expected) to positive (moresmall colonies than expected), in accordance with the increase inthe number colonies of the smallest size class.

In addition, given the fact that the skewness coefficient isexplained in the methods section explicitly (with the incorrectinterpretation of the sign) this can lead to authors not familiarwith skewness coefficients repeating the same mistake and inter-preting their results incorrectly. The use of sensitive indicators ofthe status of coral populations like size frequency distribution hasbeen identified as crucial for the understanding of the dynamicsof complex systems like coral reefs (Gilmour, 2004; Smith et al.,2005). Proper application of the basic ecological concepts is crucialfor the future inclusion of this type of variable in long term studies

and monitoring programs that can help scientists, managers andpolicymakers design and evaluate the effectiveness of differentmanagement approaches.

References

Bak, R.P.M., Meesters, E.H., 1998. Coral population structure: the hidden informationof colony size-frequency distributions. Marine Ecology-Progress Series 162,301–306.

Connell, J.H., 1978. Diversity in tropical rain forests and coral reefs - high diversity oftrees and corals is maintained only in a non-equilibrium state. Science 199,1302–1310.

Crabbe, M.J.C., 2009. Scleractinian coral population size structures and growth ratesindicate coral resilience on the fringing reefs of North Jamaica. Marine Environ-mental Research 67, 189–198.

Gilmour, J.P., 2004. Size-structures of populations of the mushroom coral Fungiafungites: the role of disturbance. Coral Reefs 23, 493–504.

McClanahan, T.R., Ateweberhan, M., Omukoto, J., 2008. Long-term changes in coralcolony size distributions on Kenyan reefs under different management regimesand across the 1998 bleaching event. Marine Biology 153, 755–768.

Meesters, E.H., Hilterman, M., Kardinaal, E., Keetman, M., de Vries, M., Bak, R.P.M.,2001. Colony size-frequency distributions of scleractinian coral populations:spatial and interspecific variation. Marine Ecology Progress Series 209, 43–54.

Smith, L.D., Devlin, M., Haynes, D., Gilmour, J.P., 2005. A demographic approach tomonitoring the health of coral reefs. Marine Pollution Bulletin 51, 399–407.

Zar, J.H., 1999. Biostatistical Analysis, fouth ed. Prentice Hall, Upper Saddler River, NJ.

Juan Carlos OrtizSchool of Biological Sciences, The University of Queensland,

St Lucia QLD 4072, AustraliaE-mail address: j.ortiz@uq.edu.au