Volume 10, Issue 12 p. 2195-2202
Free Access

VoCC: An r package for calculating the velocity of climate change and related climatic metrics

Jorge García Molinos

Corresponding Author

Jorge García Molinos

Arctic Research Center, Hokkaido University, Sapporo, Japan

Global Station for Arctic Research, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Japan

Graduate School of Environmental Science, Hokkaido University, Sapporo, Japan


Jorge García Molinos

Email: [email protected]

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David S. Schoeman

David S. Schoeman

Global-Change Ecology Research Group, School of Science and Engineering, University of the Sunshine Coast, Sunshine Coast, QLD, Australia

Department of Zoology, Centre for African Conservation Ecology, Nelson Mandela University, Port Elizabeth, South Africa

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Christopher J. Brown

Christopher J. Brown

Australian Rivers Institute – Coast and Estuaries, School of Environment and Science, Griffith University, Nathan, QLD, Australia

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Michael T. Burrows

Michael T. Burrows

Scottish Association for Marine Science, Scottish Marine Institute, Dunbeg, UK

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First published: 07 September 2019
Citations: 33



  1. Climate change is a primary global driver of biodiversity reorganization. The velocity of clisecondary functions, or to produce output for display (see mate change and related metrics describe the spatial change of climatic variables over time, allowing quantification of climate change exposure and connectivity, facilitating insights into the potential scope of species’ range-shift responses. These metrics have been extensively used in climate-change ecology research and provide useful information for conservation. Multiple extensions to the original concept of climate velocity have been proposed since first presented nearly a decade ago. However, despite its utility, no software application is currently available that brings all these methods together.
  2. The r package VoCC fills this gap by providing a comprehensive collection of functions that calculate climate velocity and related metrics from their initial formulation to the latest developments. Here, we introduce the core package functionality through a series of applied examples.
  3. The collection of functions in the VoCC package represents a new, useful addition to the existing portfolio of tools with which to assess risks posed by climate change to species and ecosystems.

Foreign Language Abstract


  1. El cambio climático es un factor global de reorganización de la biodiversidad. La velocidad del cambio climático y otros índices relacionados describen el cambio espaciotemporal de variables climáticas, proporcionando medidas de exposición y conectividad climáticas relacionadas con los cambios potenciales de la distribución de especies. Estos índices han sido usados profusamente en estudios de ecología del cambio climático y proporcionan información útil en materia de conservación. Múltiples extensiones han sido propuestas desde que la velocidad del cambio climático se presentó hace ya una década. Sin embargo, y a pesar de su utilidad, todavía no existe ninguna aplicación informática que incluya todos estos métodos e índices.
  2. El paquete de R VoCC viene a llenar este vacío proporcionando una colección exhaustiva de funciones para el cálculo de la velocidad de cambio climático e índices relacionados. Este artículo introduce la funcionalidad principal del paquete a través de una serie de ejemplos prácticos.
  3. El conjunto de funciones disponibles en el paquete VoCC representa una nueva y útil adición al conjunto de herramientas existentes para la estimación de los riesgos asociados al cambio climático para especies y ecosistemas.


Anthropogenic climate change is recognized as a main global driver of biodiversity change. Altered climatic conditions can trigger a plethora of biotic responses, ranging from impaired individual performance and changes in population abundance to alterations in the phenology and geographical distribution of species (Parmesan & Yohe, 2003). Thus, there is a growing need to assess the exposure of species to climate change and associated risks to their persistence. In response, modelling techniques are becoming increasingly more realistic and sophisticated (Yalcin & Leroux, 2017). But process-based models require detailed physiological and behavioral data, which are not available for most species. Further, even commonly used approaches, such as correlative species distribution models, are vulnerable to bias from insufficient or inadequate occurrence data (Platts et al., 2014; Yates et al., 2018).

In response to data paucity, climate–landscape metrics have become popular for rapidly assessing the exposure of large numbers of species to climate change (Brito-Morales et al., 2018; Garcia, Cabeza, Rahbek, & Araújo, 2014). They provide information on the magnitude, direction, and timing of changes in local climatic conditions across a region of interest as well as changes in their availability (i.e. area). Though lacking explicit ecological or biological connotation, they can be readily interpreted in terms of exposure to climatic change (Burrows et al., 2011; Loarie et al., 2009) and, with caveats (Dobrowski & Parks, 2016; García Molinos, Takao, et al., 2017; Hamann, Roberts, Barber, Carroll, & Nielsen, 2015), linked to potential biological responses (Burrows et al., 2014; Ordonez, Williams, & Svenning, 2016). Among the multiple existing metrics (Garcia et al., 2014), the velocity of climate change (VoCC), representing the rate of movement of climatic isopleths across a landscape (Loarie et al., 2009), is one of the most widely used in climate-change ecology and conservation (Table 1; Brito-Morales et al., 2018), and referred to in policy documents (IPCC, 2014; MCCIP, 2015).

Table 1. Functions provided in the VoCC package and reference examples for ecological applications. Secondary functions accept outputs from primary functions. Auxiliary functions are used to preprocess data for primary and/or secondary functions, or to produce output for display (see Figure 1)
Function Description Type Examples Application
A – Gradient-based climate velocity
tempTrend Long-term local climatic trends Primary n/a  
spatGrad Local spatial climatic gradients Primary n/a  
gVoCC Gradient-based climate velocity Secondary Kumagai et al. (2018) Range shifts marine taxa
Comte and Grenouillet (2013) Range shifts freshwater taxa
VanDerWal et al. (2013) Range shifts terrestrial taxa
Sandel et al. (2011) Terrestrial endemism patterns
VoCCTraj Climate-velocity trajectories Secondary Hiddink et al. (2015) Range shifts marine taxa
shiftTime Shift in timing of seasonal climatology Primary Poloczanska et al. (2013) Phenological shifts marine taxa
trajClas Classification of climate-velocity trajectories Secondary Fogarty et al. (2017) Early detection of range shifts
resTime Climatic residence time within a polygon Secondary Loarie et al. (2009) Climatic turnover terrestrial biomes
sumSeries Summarize climatic series to coarser temporal resolution Auxiliary n/a  
trajLine Spatial lines traced by climate-velocity trajectories Auxiliary n/a  
B – Distance-based climate velocity
dVoCC Distance-based velocity from the geographically closest climate analogue Primary Carroll et al. (2017) and García Molinos, Takao, et al. (2017) Identification of climate refugia and connectivity in relation to terrestrial and marine protected areas, respectively
climPCA Reduce dimensionality of climate predictors via Principal Component Analysis Auxiliary n/a  
climPlot Binned scatter plot for two-dimensional climate space Auxiliary n/a  

Here, we aim to make VoCC calculations more accessible to ecologists through the development of a VoCC r package. We expand upon earlier definitions of VoCC to add additional features to the algorithms. This will improve the ability of users to customize the algorithms to specific systems or locations. Finally, we demonstrate some of the features for several applied case-studies in climate-change ecology and conservation.


Since its formal definition nearly a decade ago as a measure of climatic exposure (Loarie et al., 2009), two main forms of climate velocity have evolved. The first form stems from calculating velocity based on local climatic gradients (herein gradient-based VoCC), the second form from distance-to-analogue climates (distance-based VoCC) (Brito-Morales et al., 2018). The VoCC package collectively gathers both formulations (Table 1 and Figure 1).

Details are in the caption following the image
Flow chart showing the relationship between the different functions (in red) of the VoCC package for the (a) gradient-based and (b) distance-based approaches
A gradient-based approach (Figure 1a) calculates the velocity of climate change gVoCC as the ratio of the long-term temporal trend, s, described as the simple linear regression slope of the local (cell-wise) climatic time series, to the local spatial climatic gradient, g, based on a 3 × 3 cell neighbourhood (Burrows et al., 2011):

Other than exposure, gradient-based velocities can also inform on climatic connectivity by building climate-velocity trajectories (voccTraj; Figure 1a) using local velocity rates and directions to propagate isotherms over time from a starting location (Burrows et al., 2014). These trajectories show paths connecting present local climates with their future locations through the most direct route as dictated by the local spatial climatic gradient.

Distance-based approaches (Figure 1b) use climate-analogue algorithms to identify local environments having future climatic conditions analogous to the reference conditions at a location of interest, and then to estimate the distance and direction between the reference location and its future analogue (Hamann et al., 2015; Ohlemüller, Gritti, Sykes, & Thomas, 2006). Distance-based climate velocity dVoCC is calculated as the distance, d, to the geographically closest climate analogue for each focal cell divided by the time elapsed, t, between baseline and future periods:
Different options are available regarding the analogue search algorithm (Figure 1b). The choice of climatic threshold for matching analogous climates is especially important. Given a focal cell, i, with a baseline climate at time t defined by urn:x-wiley:2041210X:media:mee313295:mee313295-math-0003 for each climatic variable, k, the climatic departure at time, tꞌ, at any target cell, j, is calculated as:
Cell j is a climate analogue of i if the change in climate conditions between tꞌ and t remains within certain bounds:
Selecting meaningful thresholds, Ck,th, is an important but subjective task, particularly when using synthetic climatic variables (e.g. principal components). Constant, single thresholds are often defined for each climate variable; pragmatically selected as small as possible yet avoiding artefacts from excessive precision that would otherwise render all future climates non-analogues (Hamann et al., 2015). An alternative, which may provide more ecologically meaningful results (García Molinos, Takao, et al., 2017), is to use local thresholds defined by reference to the baseline climatic variability at each focal cell. The definition of a climatic analogue then becomes cell-specific:
where urn:x-wiley:2041210X:media:mee313295:mee313295-math-0007 is the standard deviation (or any other metric of variability) of variable k at focal cell i over the baseline period t. This can be approached in dVoCC by passing the thresholds as an extra variable in the input data frame (see function documentation).


In the following section, we introduce some of these functions using two applied examples. Given space limitations, we focus here on discussing the main functions and their significance in an ecological context. Step-by-step code to reproduce these examples and further details on the functions are available with vignette('VoCC_Tutorial'). The reader is also referred to the package's help documentation and references in Table 1 for a full description of all the functions and further examples. Installation of the package and dependencies from our github repository is straightforward using the r package devtools:

  • > devtools::install_github("JorGarMol/VoCC", dependencies = TRUE, build_vignettes = TRUE)

  • > library(VoCC)

Alternatively, to save installation time, the html and pdf versions of the vignette can be viewed directly from the repository (https://github.com/JorGarMol/VoCC/tree/master/doc).

3.1 Example 1: Prediction of biogeographical shifts

Species distribution shifts are among the most frequent, ubiquitous responses to climate change observed in marine, freshwater and terrestrial biota (Parmesan & Yohe, 2003; Poloczanska et al., 2016). Several global (Brown et al., 2016; García Molinos, Burrows, & Poloczanska, 2017; Poloczanska et al., 2013) and regional (Comte & Grenouillet, 2013; Hiddink, Burrows, & García Molinos, 2015; Kumagai et al., 2018; VanDerWal et al., 2013) analyses have investigated whether patterns of species’ range shifts follow climate expectations using climate velocity. Here we reproduce a global meta-analysis of observed distances of range shifts in marine species over given time periods (Poloczanska et al., 2013) using gradient-based and distance-based velocities. The ‘marshift’ dataset provided with the package contains the most up-to-date version of the meta-data set as provided in Brown et al. (2016). We use annual mean monthly sea surface temperatures (SSTs), which is consistent with the original study, however, we note that annual means are not always the most ecologically relevant metric. The sumSeries function allows for other statistics to be used, such as seasonal means, monthly maximum, minimum or user-defined functions (see function documentation for details). As shown in Figure 1a, the workflow for computing gradient-based velocities use the SST time series to produce the long-term temporal trend (function tempTrend), local spatial thermal gradients (spatGrad), and finally compute the velocity (gVoCC). Calculation of distance-based velocities is performed with dVoCC and requires information on both the baseline and future climatologies to be compared for detection of climate analogues.

Gradient-based velocities can result in large over/underestimations of true migration requirements where local climatic gradients do not capture the availability of neighbouring analogous climates, as may be the case in very flat gradients (Hamann et al., 2015). They are also more difficult to interpret than distance-based velocities when using multivariate climatic indices. On the other hand, distance-based velocity requires specific decisions that should be driven by adequate knowledge of the study system and the research question at hand (Figure 1b). First, the user needs to decide whether to limit the analogue search area by specifying a search radius (argument geoTol) or conduct an unrestricted search. When relevant ecological information is available, search distances can be used to make the metric more realistic (e.g. by reflecting a species' dispersal capacity) (Carroll, Parks, Dobrowski, & Roberts, 2018; García Molinos, Burrows, et al., 2017). Second, the algorithm used for measuring the distance between the focal cell and its geographically closest analogue needs to be selected (argument distfun), which can be any of the Euclidean (Cartesian coordinate system), geographical (great-circle), or least-cost path distances. These options can be used to make the distance-based velocity more relevant to its application, such as the use of least-cost distances to account for important factors such as barriers to species dispersal (García Molinos, Takao, et al., 2017) or avoidance of dissimilar climates (Dobrowski & Parks, 2016).

By definition (Equation 2), distance-based velocities are strictly positive, whereas gradient-based velocities take their sign from the temporal trend, s, in Equation 1. However, for comparison, the sign of dVoCC can be changed simply by inverting the sign of those velocities where future local (cell) climatic conditions are cooler than current conditions (but note that signs are meaningless for multivariate velocities). The resulting spatial patterns and range of values are comparable between both velocity formulations (Figure 2a,b). However, note that whereas gradient-based velocities always report a value, distance-based velocities can return no value (NA) for those cells not having a future climate analogue within the specified search radius and climatic threshold (green marine regions in Figure 2a,b); that is, disappearing climates sensu Williams, Jackson, and Kutzbach (2007).

Details are in the caption following the image
Global patterns of (a) gradient-based and (b) distance-based climate velocities for mean annual sea surface temperatures for 1960–2009, and resulting scatter plots of observed versus (c) gradient-based and (d) distance-based predicted shift values with their corresponding linear regression lines (response and predictor variables fourth-root transformed). Green regions in (b) correspond to cells not having a future climate analogue within the specified search radius and climatic threshold

Using the extracted mean velocity estimates for each reported observed shift, as the average of all grid cell values within a circle of radius equal to the reported range-shift distance, we can then fit a simple climate expectation model to distribution shift rates (fourth-root transformed km/decade) using VoCC (same units) as predictor (Figure 2c,d). For both velocity estimates, the climate-expectation model detects a statistically significant effect of climate velocity (p < .0001), though the proportion of explained variance is modest (adjusted-R2 = 0.12 and 0.15 for gradient- and distance-based velocities, respectively). Indeed, this simple climate expectation model can be greatly improved (66% of variance explained) by incorporating other predictors like taxonomic identity, location of the shift within the distribution range (leading edge, trailing edge or centre of distribution) and the directional agreement between warming and ocean current flow (García Molinos, Burrows, et al., 2017). Similarly, accounting for methodological differences between studies explained by itself 22% of the variation in range shifts (Brown et al., 2016).

3.2 Example 2: Analysis of climate exposure and connectivity in the Western Pacific Ocean

Understanding how present and future climates are spatially connected is as important as estimating how fast those climates move and where they end up. Here, we analyse climate connectivity over the period 1990–2009 for Western Tropical Pacific countries, located in a region that is expected to be affected by large-scale climate-induced range shifts in both its fisheries species and marine biodiversity (Bell et al., 2013). See vignette('VoCC_Tutorial') for reproducible code for the calculation of the 1960–2009 mean SST trajectories, trajectory classes and exclusive economic zone (EEZ) residence times used in this example.

Climatic connectivity can be represented with climate-velocity trajectories, which follow tracers through time as they travel over the velocity field (Burrows et al., 2014). The function voccTraj calculates trajectories and requires the input of the magnitude and angle of the climate velocity, and the annual mean of the climatic variable averaged over the study period of length (see ?voccTraj for examples). The resulting table containing the coordinates for each trajectory can then be easily converted into a spatial lines data frame using trajLine for representation or further spatial analysis. Trajectories for the period 1960–2009 based on mean annual SST show widespread migration of isotherms out of the EEZ's belonging to most of the island nations towards the poles (Figure 3a), because of the prevailing high velocities in the tropical region. For instance, the Federated States of Micronesia is predicted to be particularly affected by northward migration of its current climate out of its EEZ, a result aligning with predictions that this country may lose access to migratory fish stocks (tuna) in the future (Bell et al., 2013).

Details are in the caption following the image
Maps of the western central Pacific island nations showing (a) the climate velocity trajectories (arrows) over the period 1960–2009 overlaid on the mean sea surface temperatures, and (b) the resulting trajectory categories and residence times for each exclusive economic zone

These trajectories can be further classified (sensu Burrows et al., 2014) with trajClas to identify locations disconnected from cooler (sinks) or warmer (sources) climates, as well as regions funnelling trajectory movement, where individual trajectories converge, flow-through and diverge again. Under the assumption of climate-niche tracking, this categorization can be useful to infer potential conservation implications to biodiversity (Brito-Morales et al., 2018; Burrows et al., 2014). Trajectory classes can be combined with indices of climate exposure to give a better indication of the potential risk to biodiversity posed by climate change. For example, the function resTime calculates the climate residence time associated with a polygon as temporal climatic turnover, or the average time required for an isopleth to cross a circle of equivalent area (Loarie et al., 2009). Together, these metrics offer a contrasting view of the climate-warming hazard to the Western tropical Pacific nations (Figure 3b). Westernmost nations have seen over the past 50 years a rapid emigration of their local climates, as suggested by their short residence times and, being disconnected from warmer regions, experienced little or no climate immigration (i.e. these regions are dominated by climate sources). Brunei represents an extreme case, with its EEZ fully covered by climate source zones and presenting a thermal turnover of <10 years. The anticipated result is that its biodiversity is at high risk becasue species lost to warming are not replaced. On the other hand, nations occupying the eastern half of the region incorporate areas that both have been exposed to comparatively lower velocities, resulting in much longer residence times, as well as incorporate zones where trajectories concentrate (i.e. corridors, convergence and emergence). High rates of emigration and immigration in these latter regions imply that local communities should face greater reshuffling of species and novel ecological interactions (Lurgi, López Bernat, & Montoya José, 2012).

The package VoCC also contains other auxiliary and secondary functions related to both gradient- and distance-based velocities (Table 1). shiftTime calculates changes in the timing of seasonal temperatures (or other climatic variables) relevant to the phenological response of species to climate change (Burrows et al., 2011). climPCA can be used to reduce dimensionality of a large set of climate variables via Principal Component Analysis, extracting PCs as synthetic variables to be used for the calculation of climate analogue velocity. Finally, climPlot generates binned scatter plots of cell counts in climate space. It can be used to visualize the effect of a given climatic threshold (bin size) on the density and distribution of present and future local climates, and the proportion of novel (i.e. without present analogue) and disappearing (i.e. without future analogue) climates (Williams et al., 2007). Details and examples for all these functions can be found in the corresponding function documentation.


The VoCC package provides all major gradient- and distance-based algorithms for calculation of the velocity of climate change and related metrics. This comprehensive set of functions, together with the flexibility provided by the choice of algorithms, climatic thresholds and distance measures should provide a useful tool for the assessment of climate change exposure and climatic connectivity.


J.G.M. is supported by the ‘Tenure-Track System Promotion Program’ of the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and the JSPS KAKENHI Grant Number 19H04314. C.J.B. was supported by a Discovery Early Career Researcher Award (DE160101207) from the Australian Research Council. D.S.S. is supported by ARC Discovery Grant DP170101722. The authors declare that there is no conflict of interest regarding the publication of this article.


    J.G.M., M.T.B. and D.S.S. wrote the original code, with contribution from all authors to the final package. J.G.M. wrote the first draft of the manuscript and all authors contributed to subsequent revisions.


    The code and data used for the examples presented in this study are available respectively from the vignette included in the r package, (https://doi.org/10.5281/zenodo.3382092) and the GitHub Data Repository (https://doi.org/10.5281/zenodo.3382084) (García Molinos, Schoeman, Brown, & Burrows, 2019).