smatr 3– an R package for estimation and inference about allometric lines

Abstract

Summary1. The Standardised Major Axis Tests and Routines (SMATR) software provides tools for estimation and inference about allometric lines, currently widely used in ecology and evolution. 2. This paper describes some significant improvements to the functionality of the package, now available on R in smatr version 3. 3. New inclusions in the package include sma and ma functions that accept formula input and perform the key inference tasks; multiple comparisons; graphical methods for visualising data and checking (S)MA assumptions; robust (S)MA estimation and inference tools.Key-words: common slope testing, model II regression, principal component analysis, robust estimation, standardised major axis Biologists often wish to estimate how one variable scales against another and to test hypotheses about the nature of this relationship and how it varies across samples. The most common example of this is allometry (Reiss 1989); hence, we refer to this problem as one of estimation and testing about allometric lines. An example is given in Fig. 1a, where we wish to understand how leaf lifespan (longev) scales against leaf mass per area (lma) and how this relationship changes across sites with different rainfall (rain). longev and lma are log-transformed prior to analysis and are approximately linearly related on the transformed scale. This is common in allometry, and it means that their relationship approximately follows a power law, longev¼ alma b . The 'scaling exponent' b is the slope on log-transformed axes, and the magnitude of this parameter describes how steep the leaf lifespan-leaf mass per area relationship is. The 'proportionality coefficient' a, related to the elevation on log-log axes, is needed to understand how longlived leaves of a given mass per area will be.Estimating a and b is not a simple linear regression problem because we are not interested in predicting one variable from another -we are interested in estimating some underlying line of best fit (Warton et al., 2006 ). Another way to understand this is to see that the problem is symmetric -the basic problem does not change if we plot lma on the Y axis instead of the X axis (Smith 2009). Hence, the appropriate methods for analysis have more in common with principal component analysis, a multivariate approach, than with linear regression (Warton et al., 2006). Common approaches to estimating the line of best fit are standardised major axis (SMA) and major axis (MA) estimation, which will be collectively referred to as (S)MA, and which are widely used in ecology and evolution.Warton et al. (2006) reviewed (S)MA techniques, proposed routines for comparing the parameters a and b amongst groups and developed software to implement the methods. The Standardised Major Axis Tests and Routines (SMATR) software, available in both R (R Development Core Team 2010) and C++, has since been used in over 200 publications. We have made significant improvements to the software in the recently released version 3 of the smatr R package, and this paper briefly describe...

Activity rhythm and action range of workers of the invasive hornet predator of honeybees Vespa velutina, measured by radio frequency identification tags

“…First, the sessions 1 and 2 for the release distances of 3,000, 4,000, and 5,000 m were compared using either Fisher's exact test (3,000 and 5,000 m) or Pearson's χ 2 test (4,000 m). The standardized mass (i.e., the body condition) of the hornets was assessed with the scale mass index developed by Peig and Green (2009) based on standardized major axis regression using “ smart” package (Warton, Duursma, Falster, & Taskinen, 2012). The effect of the release distance on the probability of returning to the nest was tested using a Cox proportional hazards regression model from “ survival” package (Therneau, 2014).…”

Spatial variability of soil microbial biomass and its relationships with edaphic, vegetational and climatic factors in the Three-River Headwaters region on Qinghai-Tibetan Plateau

“…Unlike the ordinary least-squares regression, the SMA regression technique fits the slope and intercept for a linear model by assessing the "best fit bivariate line" between two variables instead of predicting one variable from the other (Warton et al, 2006(Warton et al, , 2012. If the slope does not significantly differ from one, two variables are described to follow an isometric relationship which indicates that they would change with the same pace.…”

“…In this study, stoichiometric relationship was analyzed on a log-log scale because only did the log-transformed soil nutrient and microbial biomass related variables follow the normal distribution (Log(Y) = a + b * Log(X)). The SMA regression analysis was conducted using the SMATR 3 package in the R 3.1.0 environment (R development Core Team, 2014; Warton et al, 2012).…”

Antibiotic‐induced effects on scaling relationships and on plant element contents in herbs and grasses

“…Packages used were geoR (Ribeiro & Diggle, 2015), car (Fox & Weisberg, 2011), nortest (Gross & Ligges, 2015), and smatr (Warton, Duursma, Daniel, & Taskinen, 2012). …”

“…This analysis summarizes the relationship between two variables by minimizing the residuals in both variables (Kerkhoff et al., 2006; Warton, Wright, Falster, & Westoby, 2006), rather than predict one variable from the other (e.g., Y from X ), which would be best described by ordinary least squares regression (Niklas, 2006). To test for significant deviations from isometric scaling (slope ~1) between the element contents of the plant organ combinations, we used the function sma( y ~ x , slope.test=1) (R package smatr, Warton et al., 2012). …”