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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.


Comparison of allometric sample size distributions between extant and extinct taxa (A) and between invertebrates and vertebrates (B).Extinct taxa show a systematically smaller sample size in both invertebrates and vertebrates. Conversely, the sample sizes between invertebrates and vertebrates, for both extinct and extant taxa, are similar. “*” indicates significance of results of Kolmogorov–Smirnov tests for differences in distributions.
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fig-4: Comparison of allometric sample size distributions between extant and extinct taxa (A) and between invertebrates and vertebrates (B).Extinct taxa show a systematically smaller sample size in both invertebrates and vertebrates. Conversely, the sample sizes between invertebrates and vertebrates, for both extinct and extant taxa, are similar. “*” indicates significance of results of Kolmogorov–Smirnov tests for differences in distributions.

Mentions: A survey of the literature reveals a wide range of sample sizes (n = 542, range = 3–1,449) used for quantifying intraspecific allometry. When these studies are segregated based on their taxa of interest (i.e., vertebrate vs. invertebrate) and age/nature (i.e., extant/recent vs. extinct/fossil), distinct patterns are clear (Fig. 3 and Table 2). Samples from extant invertebrates and extant vertebrates illustrate very similar distributions, which are not significantly different from each other (KS test, p-value = 0.4381) (Fig. 4 and Table 3). In contrast, those studies examining extinct taxa use systematically smaller sample sizes than those of extant taxa, a pattern that is consistent for both vertebrates and invertebrates (p-values <0.001) (Fig. 4 and Table 3). Although not nearly as distinct as the pattern between extinct and extant (for either group), the difference between extinct vertebrate and extinct invertebrate samples is significant (p-value = 0.0375). The mean, median, minimum, and maximum of the extant samples (both vertebrate and invertebrate) are all larger than those of the extinct samples. The systemic use of smaller datasets for extinct taxa can be illustrated in that only 5.6% (invertebrate) and 3.0% (vertebrate) of the extant samples are based on 10 specimens or fewer, while 20.1% (invertebrate) and 34.7% (vertebrate) of the extinct samples are of this size.


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

Brown CM, Vavrek MJ - PeerJ (2015)

Comparison of allometric sample size distributions between extant and extinct taxa (A) and between invertebrates and vertebrates (B).Extinct taxa show a systematically smaller sample size in both invertebrates and vertebrates. Conversely, the sample sizes between invertebrates and vertebrates, for both extinct and extant taxa, are similar. “*” indicates significance of results of Kolmogorov–Smirnov tests for differences in distributions.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig-4: Comparison of allometric sample size distributions between extant and extinct taxa (A) and between invertebrates and vertebrates (B).Extinct taxa show a systematically smaller sample size in both invertebrates and vertebrates. Conversely, the sample sizes between invertebrates and vertebrates, for both extinct and extant taxa, are similar. “*” indicates significance of results of Kolmogorov–Smirnov tests for differences in distributions.
Mentions: A survey of the literature reveals a wide range of sample sizes (n = 542, range = 3–1,449) used for quantifying intraspecific allometry. When these studies are segregated based on their taxa of interest (i.e., vertebrate vs. invertebrate) and age/nature (i.e., extant/recent vs. extinct/fossil), distinct patterns are clear (Fig. 3 and Table 2). Samples from extant invertebrates and extant vertebrates illustrate very similar distributions, which are not significantly different from each other (KS test, p-value = 0.4381) (Fig. 4 and Table 3). In contrast, those studies examining extinct taxa use systematically smaller sample sizes than those of extant taxa, a pattern that is consistent for both vertebrates and invertebrates (p-values <0.001) (Fig. 4 and Table 3). Although not nearly as distinct as the pattern between extinct and extant (for either group), the difference between extinct vertebrate and extinct invertebrate samples is significant (p-value = 0.0375). The mean, median, minimum, and maximum of the extant samples (both vertebrate and invertebrate) are all larger than those of the extinct samples. The systemic use of smaller datasets for extinct taxa can be illustrated in that only 5.6% (invertebrate) and 3.0% (vertebrate) of the extant samples are based on 10 specimens or fewer, while 20.1% (invertebrate) and 34.7% (vertebrate) of the extinct samples are of this size.

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.