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Small sample sizes in the study of ontogenetic allometry; implications for palaeobiology.

Brown CM, Vavrek MJ - PeerJ (2015)

Bottom Line: Across a variety of subsampling techniques, used to simulate different taphonomic and/or sampling effects, smaller sample sizes gave less reliable and more variable results, often with the result that allometric relationships will go undetected due to Type II error (failure to reject the hypothesis).This may result in a false impression of fewer instances of positive/negative allometric growth in fossils compared to living organisms.No mathematically derived minimum sample size for ontogenetic allometric studies is found; rather results of isometry (but not necessarily allometry) should not be viewed with confidence at small sample sizes.

View Article: PubMed Central - HTML - PubMed

Affiliation: Royal Tyrrell Museum of Palaeontology , Drumheller, Alberta , Canada.

ABSTRACT
Quantitative morphometric analyses, particularly ontogenetic allometry, are common methods used in quantifying shape, and changes therein, in both extinct and extant organisms. Due to incompleteness and the potential for restricted sample sizes in the fossil record, palaeobiological analyses of allometry may encounter higher rates of error. Differences in sample size between fossil and extant studies and any resulting effects on allometric analyses have not been thoroughly investigated, and a logical lower threshold to sample size is not clear. Here we show that studies based on fossil datasets have smaller sample sizes than those based on extant taxa. A similar pattern between vertebrates and invertebrates indicates this is not a problem unique to either group, but common to both. We investigate the relationship between sample size, ontogenetic allometric relationship and statistical power using an empirical dataset of skull measurements of modern Alligator mississippiensis. Across a variety of subsampling techniques, used to simulate different taphonomic and/or sampling effects, smaller sample sizes gave less reliable and more variable results, often with the result that allometric relationships will go undetected due to Type II error (failure to reject the hypothesis). This may result in a false impression of fewer instances of positive/negative allometric growth in fossils compared to living organisms. These limitations are not restricted to fossil data and are equally applicable to allometric analyses of rare extant taxa. No mathematically derived minimum sample size for ontogenetic allometric studies is found; rather results of isometry (but not necessarily allometry) should not be viewed with confidence at small sample sizes.

No MeSH data available.


The 23 linear morphometric variables of A. mississippiensis skulls used in this study.For description of measurement see Table 1. Figure modified from Dodson (1975a).
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fig-1: The 23 linear morphometric variables of A. mississippiensis skulls used in this study.For description of measurement see Table 1. Figure modified from Dodson (1975a).

Mentions: Twenty-three cranial measurements were taken from each skull (see Fig. 1 and Table 1). The measurements were taken following Brown, Arbour & Jackson (2012), which were modified from Dodson (1975a). These osteological measurements represent functional complexes as opposed to dimensions of individual bones, and have biomechanical and behavioral correlates (see Dodson, 1975a). Measurements were taken from the left side, unless this side was either incomplete or damaged, in which case the right side was used. Measurements smaller than 150 mm were taken with digital calipers, and those greater than 150 mm with a fiberglass measuring tape. All measurements were taken to the nearest millimeter.


Small sample sizes in the study of ontogenetic allometry; implications for palaeobiology.

Brown CM, Vavrek MJ - PeerJ (2015)

The 23 linear morphometric variables of A. mississippiensis skulls used in this study.For description of measurement see Table 1. Figure modified from Dodson (1975a).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4358694&req=5

fig-1: The 23 linear morphometric variables of A. mississippiensis skulls used in this study.For description of measurement see Table 1. Figure modified from Dodson (1975a).
Mentions: Twenty-three cranial measurements were taken from each skull (see Fig. 1 and Table 1). The measurements were taken following Brown, Arbour & Jackson (2012), which were modified from Dodson (1975a). These osteological measurements represent functional complexes as opposed to dimensions of individual bones, and have biomechanical and behavioral correlates (see Dodson, 1975a). Measurements were taken from the left side, unless this side was either incomplete or damaged, in which case the right side was used. Measurements smaller than 150 mm were taken with digital calipers, and those greater than 150 mm with a fiberglass measuring tape. All measurements were taken to the nearest millimeter.

Bottom Line: Across a variety of subsampling techniques, used to simulate different taphonomic and/or sampling effects, smaller sample sizes gave less reliable and more variable results, often with the result that allometric relationships will go undetected due to Type II error (failure to reject the hypothesis).This may result in a false impression of fewer instances of positive/negative allometric growth in fossils compared to living organisms.No mathematically derived minimum sample size for ontogenetic allometric studies is found; rather results of isometry (but not necessarily allometry) should not be viewed with confidence at small sample sizes.

View Article: PubMed Central - HTML - PubMed

Affiliation: Royal Tyrrell Museum of Palaeontology , Drumheller, Alberta , Canada.

ABSTRACT
Quantitative morphometric analyses, particularly ontogenetic allometry, are common methods used in quantifying shape, and changes therein, in both extinct and extant organisms. Due to incompleteness and the potential for restricted sample sizes in the fossil record, palaeobiological analyses of allometry may encounter higher rates of error. Differences in sample size between fossil and extant studies and any resulting effects on allometric analyses have not been thoroughly investigated, and a logical lower threshold to sample size is not clear. Here we show that studies based on fossil datasets have smaller sample sizes than those based on extant taxa. A similar pattern between vertebrates and invertebrates indicates this is not a problem unique to either group, but common to both. We investigate the relationship between sample size, ontogenetic allometric relationship and statistical power using an empirical dataset of skull measurements of modern Alligator mississippiensis. Across a variety of subsampling techniques, used to simulate different taphonomic and/or sampling effects, smaller sample sizes gave less reliable and more variable results, often with the result that allometric relationships will go undetected due to Type II error (failure to reject the hypothesis). This may result in a false impression of fewer instances of positive/negative allometric growth in fossils compared to living organisms. These limitations are not restricted to fossil data and are equally applicable to allometric analyses of rare extant taxa. No mathematically derived minimum sample size for ontogenetic allometric studies is found; rather results of isometry (but not necessarily allometry) should not be viewed with confidence at small sample sizes.

No MeSH data available.