Metrics for dominance interactions 2: Fighting success, Clutton-Brock et al. (1979)

dominance_iconThis is the second in a series of blog entries exploring the metrics used for assessing dominance hierarchies: see the introductory post for the rationale behind doing this, with other metrics visible through the index page.

Clutton-Brock et al. (1979) were interested in giving a metric to fighting success in red deer stags, where individuals were studied over long periods of time. Studying any network system over longer periods of time is going to cause a problem, as the status of individuals may change during that period (see Rands 2014 for some discussion of this problem), and the authors of this paper were aware that a male’s dominance could change within a mating period as his energy levels flagged or he became injured. Simply counting the number of fights won and lost will not give a very accurate reflection of how an individual is placed within the herd, as his success is also going to depend upon the idntities of the individuals he beats: a male who consistently fights and wins against weak opponents is not necessarily going to be of similar quality to a male who consistently fights and wins against strong opponents. So, Clutton-Brock and colleagues designed a simple metric that takes account of the quality of opponents individuals win and lose against.

I’ll illustrate how this is calculated with by considering the fighting ability metric of two individuals (labelled black and blue) within the following group structure:

Figure 1: all winner/loser interactions recorded. As depicted in the box, the arrow denotes which individual is the winner (W) or loser (L) in a connected pair.
Figure 1: all winner/loser interactions within a group. As depicted in the box, the arrow denotes which individual is the winner W or loser L in a connected pair.

To gauge an individual animal’s fighting success, you need to calculate B, the number of other animals that the focal individual has won against, and note the identities of all the losers. For each of these marked losers, you also need to calculate the number of individuals that they in turn have beaten, and sum these to give Σb. Because we define one individual in an interacting pair as a winner, and the other a loser, this means that none of the summed interactions contributing to Σb are against the focal individual.

As well as assessing wins, you also need to calculate L, the number of other individuals that the focal loses against. These winning animals are marked and the summed number of animals that they themselves lose against is calculated, giving Σl.

Having collated these numbers, the fighting success of a focal individual (which I will refer to as DCB) is calculated as

DCB = (B + Σb + 1)/(L + Σl + 1),

where the “+1” term on both the top and bottom of the equation allows a meaningful metric to be calculated for individuals that are either never seen to win or lose.

Using the group interactions given in Figure 1, we calculate DCB for the individual coloured black using the following reasoning:

Figure 2: Calculating black's win (left panel) and loss (right panel) statistics
Figure 2: Calculating black’s win (left panel) and loss (right panel) statistics

Following Figure 2, we see that B = 8, Σb = 2 + 2 + 2 + 1 + 1 + 0 + 0 + 0 = 8, L = 3, and Σl = 2 + 2 + 0 = 4. So, DCB = (8 + 8 + 1)/(3 + 4 + 1) = 2.125 for the black individual. Similarly, using the reasoning given in Figure 3, DCB =1.167 for the blue individual.

Figure 3: Calculating blue's win (left panel) and loss (right panel) statistics
Figure 3: Calculating blue’s win (left panel) and loss (right panel) statistics

A larger value of DCB will notify a greater fighting ability, and the maximum size of the statistic within an observed group is going to depend on both the size of the group and the maximum number of other animals that each individual in the group interacts with.   In their original paper, Clutton-Brock and his colleagues found DCB for red deer ranged between 0 and a little over 3.

This is a simple statistic to compute, but I would caution that it should really only be used for comparing individuals within a group, given that it is dependent upon both group size and number of interactions recorded. The metric is also dependent upon observed relationships being fixed: an individual that wins an interaction will always win future interactions with the same opponent. This suggests that caution should be used if this metric were to be transferred to observed interactions where the dynamic between a dyad could change over time.

Further reading

Clutton-Brock TH, Albon SD, Gibson RM & Guinness FE (1979). The logical stag: adaptive aspects of fighting in red deer (Cervus elaphus L.). Animal Behaviour 27: 211-225 | pdf

Rands SA (2014). We must consider dynamic changes in behavior in social networks, and conduct manipulations: comment on Pinter-Wollman et al. Behavioral Ecology 25: 259-260 | full text | pdf

Technical Note: The network diagrams were drawn on a Mac with Dia Diagram Editor (open source freeware), and coerced into nice smooth images with GIMP (GNU Image Manipulation Program: open source freeware).

Pollinator movement through fragmented landscapes

beeMany pollinators live in complex and changeable environments. The location of of their food sources changes with time of year (as plants flower), time of day (as flowers open and close or nectar flows) and physical location (for although plants may not move very much during a flowering season, the places that flowers may be found may differ dramatically with time). Natural selection has shaped the behaviours of pollinators so that they have a suite of behaviours that allow them to exploit their environment: although it is unlikely that they know exactly when and where food will be available, they are able to couple clues from the environment with a repertoire of behaviours that will allow them to find food.

Agriculture and other human-generated change is altering the enviroment that pollinators live within, and it is very likely that the rules they are following are not ideal for the changed landscape. Because pollinators are essential for crop production, agricultural policies often dictate that there is some concession to the pollinators. This could be through leaving set-aside ‘wild’ land for nests and wild flowers, or by adding corridors of uncropped land or hedgerows where beneficial species can travel between environments. However, the pollinators will still be following their evolved rule sets, which means that we need to consider whether our concessions to them are of any use. This is something that is difficult to measure, and we need to use a wide range of techniques to ask whether particular manipulations are of benefit to some or many helpful species.

As a behavioural ecologist, I’m interested in how the behavioural decisions made by individual animals allow them to interact with the environment. For most animals, the environment that they live in is highly complex and frequently unpredictable, and it is often a challenge for us to understand how a particular decision gives the animal an advantage over an alternative behaviour. As well as conducting experiments and making observations of behaviour, we can also use theoretical techniques for exploring how simple behaviours could be the best solutions for dealing with complex environments. Simulation techniques are particularly useful for understanding how particular sets of decision allow an animal to cope with changes at the landscape level (bringing together two very different disciplines: landscape ecology and behavioural ecology).

In a paper that has just been published in PeerJ (Rands 2014), I describe a series of models describe a framework for considering how landscape alterations affect the foraging success of a pollinator nesting within the environment. These models build on earlier ideas presented by Rands and Whitney (2010, 2012, discussed in an earlier blog entry), where we simulated landscapes with simple geometries and allowed pollinators to forage within them. In the new PeerJ paper, I describe how hedgerow removal and set-aside field creation may affect the movement of pollinators. The models demonstrate that decreasing either landscape connectivity (be removing hedges) or wild land availability (through having lots of fields of unusable crops) affect how often pollinators have to switch between different environmental types. This may be important for how they find and collect food: for example, swapping between habitats may lead to a temporary reduction in nectar uptake if the pollinator has to work out how to collect it from a newly-encountered shape of flower.

The models are a first step, and are presented as a means of discussing how we can manipulate the environment in a reproducible way within a model. What needs to be done now is to identify a suitable set of behavioural rules to follow (for those presented in the models are basic, and are very likely to be improved upon!). Ongoing work should be able to demonstrate whether particular environmental manipulations are of value to some of our threatened pollinator species.

Further reading

Rands SA (2014). Landscape fragmentation and pollinator movement within agricultural environments: a modelling framework for exploring foraging and movement ecology. PeerJ 2: e269 | full text | pdf

Rands SA & Whitney HM (2010). Effects of pollinator density-dependent preferences on field margin pollination in the midst of agricultural monocultures: a modelling approach. Ecological Modelling 221: 1310-1316 | abstract | pdf (postprint version)

Rands SA & Whitney HM (2011). Field margins, foraging distances and their impacts on nesting pollinator success. PLoS One 6: e25971 | full text | pdf

Metrics for dominance interactions 1: Zumpe and Michael’s ‘Dominance Index’ (1986)

dominance_iconThis is the first in a series of blog entries exploring the metrics used for assessing dominance hierarchies. The previous introductory post explains the rationale behind doing this. An index page will give detailed links to other metrics within this blog.

I’ll start with giving details for how to calculate the Dominance Index metric described by Zumpe & Michael (1986), which uses counts of agonistic encounters to generate individual scores, which can then be used to suggest a hierarchy. Using this technique is possible with pen and paper, so I may be giving a bit more detail of the nuts and bolts than I will with some of the more complex metrics. This technique is intended to give the user a ‘cardinal ranking’ – rather than just sorting the interacting individuals into a ranked order, this technique provides a way of assigning each individual a weighting statistic. The authors suggest that this could be useful for assessing how individual dominance changes over time, if different datasets are used.

The agonistic data required for this statistic are the counts of aggressive/dominant and submissive behaviours between all possible pairings of the group members. These should be collected in two tables. So, for an example group with four individuals (identified as A, G, H, and K), we tally the number of aggressive behaviours committed by each individual to each of its three group members:

Table 1

For example, A directs aggression towards H on seven occasions. Note also that no aggressive interactions are observed between G and K.

Similarly, we tally the number of submissive behaviours directed towards each individual by the other three group members:

Table 2
Table 2

For example, H displays submissive behaviours to G on 11 occasions. Note also that no submissive behaviours were recorded between H and K.

Having collected this information, we now calculate the percentage of the aggressive actions between pairs of individuals that each individual directs at the other. For example, within the pairing of A and G, nine aggressive acts are recorded (five by A, and four by G). A is aggressive towards G in 55.6% of their aggressive interactions (= 5 / 9), and G is aggressive towards A for 44.4% (= 4 / 9). If we work out these two percentages within each pairing, we can build up a table giving the percentages of aggressive behaviours given by each individual. If no aggression is seen within a pair, the two corresponding table entries for the pair should be marked as ‘null’, as is given for the two entries between G and K here:

Table 3
Table 3

Similarly, the percentages of submissive actions received by individuals within each pairing should also be calculated. Again ‘null’ values should be recorded where no submissive actions within a pair were observed, as seen between H and K here:

Table 4
Table 4

The aggression/submission percentages are then combined by calculating an average aggression/submission score for each possible pairing of group members. For example, the average score for A when it interacts with G is

65.3% = (55.6% + 75.0%) / 2.

If no aggressive actions are recorded for a pair, this average is simply given the value of the percentage of submissive actions (calculated in table 4). So, the average score for G when it interacts with K is 90.9%. Similarly, if no submissive actions are recorded between pair members, the average is assumed to be the percentage of aggressive actions committed by an individual (recorded in table 3). So, the average score for H when it interacts with K is 71.4%. Calculating all possible pairing, we get:

Table 5a
Table 5a

Finally, the Dominance Index for each of the group members is calculated as the mean of the averages calculated for each focal individual, as given in table 5b. For example, the dominance index for A is calculated as 73.4% = (65.3% + 69.2% + 85.7%) / 3.

Table 5b
Table 5b

From this, we can use the Dominance Index rankings to construct a hierarchy. In this case, A > G > H > K.

The metric falls apart when there are no aggressive or submissive acts recorded within a pairing, which means that no average score can be recorded in table 5a. This could potentially be remedied by observing the interacting individuals until some agonistic interaction is recorded, but it may be that the non-interacting individuals are able to assess each other without needing to interact (using alternative cues, or through recognising each other from earlier unrecorded interactions). This metric is therefore not ideal if some individuals do not interact with others.

Similarly, a dataset which records few interactions between individuals may be biased by a few anomalous recorded encounters. However, using mean percentages (as calculated in table 5b) removes biases that could be introduced by simply scoring the overall number of ‘wins’ in dyadic agonistic encounters for each individual, which may be incorrectly inflated by many interactions with a small subset of the group members. I’m also curious to see what happens when a group consists of two or more subgroups where interactions tend to be within rather than between subgroups.

Further reading

Zumpe D & Michael RP (1986). Dominance index: a simple measure of relative dominance status in primates. American Journal of Primatology 10: 291-300 | doi: 10.1002/ajp.1350100402

Metrics for dominance interactions: introduction

dominance_iconMany interactions between group-living individuals can be influenced by hierarchies that exist between the interactors. These interactions can be measured in lots of different ways, and once measured, whatever has been scored needs to be processed to give a reproducible estimate of the shape of these interactions.

What this means in practice if you’re starting a new project with a new study organism is that you spend a lot of time thinking about what behaviours to record, and how to record them, but don’t really give consideration to the means of crunching these numbers down to something meaningful at the end. Good experimental design implies that the analysis has been considered during the design of the experiment, but this intermediate stage of generating ‘raw’ information about any hierarchies that are in place may be left out, meaning that something has to be cobbled together post hoc after the work has been done. This is never ideal!

Having supervised a fair number of projects where exactly this has been done, I’ve decided to try and get my head around the various statistics out there that are designed for assessing and ranking hierarchies. Some of these are fairly straightforward, and some are slightly more involved, dipping into social network analysis and other emerging fields in animal behaviour. To make this a useful exercise, I’ll attempt to put together a how-to guide for using them, aimed at researchers with a mixed range of skills in manipulating numbers, and where time permits, I’ll try and add in some practice examples. How well this works depends upon both my own understanding, the time I have available, and the limitations of inputting maths into a WordPress blog!

What I won’t be doing (at least, initially) is being particularly critical about which techniques work best: this is a voyage of discovery for me too! I also won’t be focussing on what dominance is for, why it exists, and how it does or doesn’t drive particular group behaviours (but I do discuss how leadership decisions don’t necessarily depend upon the hierarchy present in Rands et al. 2008 and Rands 2011). This series of blog postings will take a little time to put together (An index page will give detailed links to other metrics within this blog), so if you’re looking for general advice on the sort of indices that are out there, I strongly recommend hunting down a copy of the excellent book by Hal Whitehead (pages 186-195 in particular).

Further reading

  • Rands SA, Cowlishaw G, Pettifor RA, Rowcliffe JM & Johnstone RA (2008). The emergence of leaders and followers in foraging pairs when the qualities of individuals differ. BMC Evolutionary Biology 8: article 51 | abstract | pdf | full text
  • Rands SA (2011). The effects of dominance on leadership and energetic gain: a dynamic game between pairs of social foragers. PLoS Computational Biology 7: e1002252 | full text | pdf
  • Whitehead H (2008). Analyzing animal societies: quantitative methods for vertebrate social analysis. Chicago: University of Chicago Press

How do pollinators respond to the shape of agricultural landscapes?

beeThe global debate rumbles on about pollinator decline. In the UK, the recent European Commission directive banning neonicotinoid pesticides has at least partly been a catalyst for some very public debate on why decline is happening, and what could be done about it (with the BBC rushing out a nicely-balanced edition of their science programme Horizon, exploring a few of the factors that may be driving the disappearance of pollinators).

This posting ties in with my talk at INTECOL 2013 in London (if you’re there, it’s in the Ecosystem Services session in Capital Suite 13 on Wednesday 21st at 2.15pm).

Aside from disease and poisoning, one factor that is frequently pointed to is the huge changes that have been made to the landscape in recent years.  The intensification of agriculture has meant that the ‘wild’ bits of the landscape have been taken away through changes in field management, and the steady creep of urbanisation.  These wild bits, even if they’re simply hedgerows and the other untidy bits at the edges of fields, are hugely important for providing nesting sites, refuge and food for wild pollinators and the other beasties that contribute to making agricultural systems work.  If we take these messy little spaces away, not only do we remove the resources that these beneficial species use, but we also make it much more difficult for those existing beneficial species already present to gain access to the parts of our managed agricultural species that are not close to these refuge areas.

Working with Heather Whitney (University of Bristol), I’ve done some work looking at how the shape of the agricultural environment affects the ability of pollinators to access it. In a paper published in Ecological Modelling, we considered a simple case where the environment was considered to be a square grid of hedgerows, with pollinators nesting in the hedgerows. The pollinators were considered to only fly a set distance from their nest (realistic, since many solitary bees fly a maximum  of about a kilometre from their nest), and the model demonstrated that if this distance was small, and kind of environmental manipulation that increased the size of fields beyond a certain point may have a detrimental effect upon the amount of wild space available to a pollinator.

However, the model was extremely simplistic.  Although I believe very strongly in keeping exploratory models as simple as possible, it felt like there was too many rigid assumptions made when we assumed that the landscape was a square grid.  In order to make the landscapes more realistic, we took two approaches: firstly, simulating random landscapes filled with hedgerows, and secondly, using landscape data from the UK, where there is a large amount of variation in wild refuge space within the landscape, as you can see from the four sample landscapes given below.

Examples of British field structures used within the model
Examples of British field structures used within the model

These landscape-informed models, published in PLoS One, demonstrated again that pollinators that only fly short distances from their nest (less than about 125 metres, which is relevant for some solitary bees such as Andrena hattorfiana) are affected heavily by landscape manipulations, but are unlikely to benefit from having wild land added to the environment unless it is targetted specifically for them (the equivalent of trying to help an isolated island community by building a new hospital for them on the mainland.  For species travelling more than 125 metres, adding wild space into the (British) landscape is a good thing, regardless of the exact distance the species travels.

So, we should maybe consider how far specific pollinators are able to travel when we are considering their conservation.  Lots of work is being conducted by  research groups across the world to quantify and observe the lengths of these commuting distances, and many research teams are finding that pollinators are thriving in response to many unexpected resources such as urban gardens. We still have a lot of work to do to explore how different species choose to move through the environment, and how this can be manipulated to benefit them and us.

Further reading

Rands SA & Whitney HM (2010). Effects of pollinator density-dependent preferences on field margin pollination in the midst of agricultural monocultures: a modelling approach. Ecological Modelling 221: 1310-1316 | abstract | pdf (postprint version)

Rands SA & Whitney HM (2011). Field margins, foraging distances and their impacts on nesting pollinator success. PLoS One 6: e25971 | full text | pdf