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The relationship between engorged female weight and egg number in ixodid ticks: a biological interpretation of linear regression parameters

Uspensky, I. and Ioffe-Uspensky, I.

1999 - Volume: 40 Issue: 1 pages: 9-17


Ixodidae engorged female weight egg number linear regression


The relationship between the weight of engorged females of ixodid ticks and the number of eggs they produce is considered, using both our own data and numerous literature data. There are three critical weights during female engorgement, which are followed by a change in the relationship of female weight/egg number. When the females acquire an initial weight (W-) after which they are able to lay eggs, they produce a constantly increasing number of eggs per unit weight (partially-engorged females). After the females acquire weight W2, they produce a constant number of eggs per unit weight (fully-engorged females), and after reaching the weight W3, they produce a diminishing number of eggs per unit weight (over-engorged females). In the linear regression between female weight (x) and egg number (y) (y= a + bx), used in most studies of tick life history, the X-axis not only expresses the whole range of weights (thus mixing together females of all groups, even those which do not produce eggs at all), but also includes non-existing weight values, from 0 to the mean weight of an unfed female. Under these conditions, the parameters a and b have no biological meaning, since the linear dependence between female weight and egg number is only valid for fully-engorged females. This means that 0 on the X-axis must correspond to the very beginning of the linear dependence. The regression should only be computed over the part of the X-axis with weights of fully engorged females, where the relationship of female weight/egg number is truly linear (Y, X; W2, 0), thus making both parameters informative: a corresponds to the number of eggs laid by a fully engorged female with a minimal possible weight (W2) and b is the number of eggs produced per unit of weight increase. Hence, this is a simple way to take into account the real limits of the linear relationship between y and x values and to transform the regression, such that its parameters can be interpreted biologically.

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This work is licensed under a Creative Commons Attribution 4.0 International License
1999 Uspensky, I. and Ioffe-Uspensky, I.
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