Socializing in experimental streams: crayfish groups exposed to cues, refuges, and day-night conditions

Abstract

We initiated the use of a replicated, remote-video, artificial stream system to determine the effects of conspecific cue, refuge availability, and day/night conditions on movement, aggression, dominance, downstream preference, and refuge use by the crayfish Procambarus clarkii. In line with previous research, we found that walking on the gravel substrate was greatly increased and refuge use decreased in the dark. Conspecific cue (macerated crayfish filtrate) increased walking, contrary to our prediction but consistent with cue as a signal of food availability or of risk either from cannibalism or from visual predators. Exposure to conspecific cue in the streams resulted in a reduced degree of dominance in subsequent pairwise dominance trials. We developed and implemented a new and broadly applicable way of determining the extent of linearity (consistency of dominance ranks) for incomplete dominance; for our data, this method found a lack of evidence for linear hierarchies in these stream systems. Our results suggest that streams may tend to feature weaker dominance and reduced linearity of social hierarchies, relative to standing-water systems, a hypothesis that requires further testing.

Appendix A

Linearity of the pairwise dominance trials

Our experimental design, based on twelve groups of five crayfish in separate stream channels, enables us to evaluate the dominance relationships among individuals. We addressed this directly after the week of within-channel group interactions by performing dominance trials among all possible pairs within each group; procedures for these and the results are described in the text.

A key feature of the dominance-trial results is that relatively few (26 of 89, or 29%) of the 5-minute trials for each pair were “resolved”, in the sense of a clear dominant and submissive established for the pair. This unexpected feature of the results, along with the loss through mortality of 9 of the initial 60 individuals, has necessitated a careful interpretation of the dominance patterns we found. Previous work with P. clarkii has generally found a high proportion of dominance trials resolved (Dickey 2004; P. Crowley and K. Shenoy, unpublished), making the characterization of the interaction structure more straightforward.

The probability that a fully resolved dominance hierarchy is linear L(i,j) = $i!$ / 2^j, where i is group size and the number of pairwise interactions $j = \frac{i!}{{2!\left( {i - 2} \right)!}}$ (Appleby 1983). In the L(i,j) equation, the numerator $i!$ is the possible number of different linear outcomes (i.e. the number of ways i individuals can form consistent ranks), and the denominator 2^j is the total number of different outcomes. This can be used to assess the statistical support for linearity in empirical data. For example, in completely resolved results in groups of 5, L(5,10) = 5! / 2¹⁰ = 0.117 for each individual group. This means that linear results obtained in two independent groups could happen by chance with probability 0.00513, which would constitute strong statistical support for an interpretation of dominance linearity in groups of 5. But suppose one of four groups of five violates linearity. The probability of a result with this many linear outcomes or more by chance (i.e. the appropriate benchmark in this case) is 4(0.117)³(0.883) + (0.117)⁴ = 0.0059. This would still constitute strong evidence for an overall pattern of linearity.

Since so many of our pairwise interactions were unresolved and some individuals were missing, we determined the probability of linearity in partially resolved dominance hierarchies λ(i,j,k), where k is the total number of resolved outcomes (k < j). This required tedious probability calculations based on contingencies taking account both of possible outcomes and of possible inclusion of each possible pairwise interaction in the set of resolved outcomes. Table 1 summarizes these results.

One example of the way these probabilities were calculated is described here for λ(i,j,k) = λ(4,6,3), the case in which 4 of the original 5 individuals survived to participate in the dominance trials and resolved 3 of their 6 pairwise interactions. With 3 resolved interactions, the only possible non-linearity is a strict 3-loop (see Table 1). The first interacting pair and outcome is arbitrary, so we imagine that individual 1 dominates 2. For the second possible interaction, there are 5 choices for the 4 individuals (i.e. 1 vs 3, 1 vs 4, 2 vs 3, 2 vs 4, and 3 vs 4). Of these, all but 3 vs 4 would still allow for a strict 3-loop, so the chance of a 3-loop compatible choice is 0.8; but for that choice, only 1 of the 2 possible outcomes is consistent with the strict 3-loop. For example, if 1 vs 3 were chosen, only 3 dominating 1 could help produce the loop, resulting in the chance of a compatible second interaction of 0.4. Then for the third choice, only 2 vs 3 (one of the remaining 4 interactions), with 2 dominating 3, would complete the loop. Thus the probability of strict-3-loop-compatible second and third outcomes is (4/10)(1/8) = 0.05, and λ(4,6,3) = 0.95. Most of the other λ(i,j,k) calculations were more complicated, particularly with 4 or 5 resolved outcomes, because more possible patterns of non-linearity and more ways of achieving them come into play (see Table 1). Further details of these calculations are available from the authors on request.

Note in Table 1 that for the observed interactions with their limited resolution, the overall probability of consistent linearity by chance is 0.4575. This indicates that even fully consistent linearity in the results would provide only weak statistical evidence for an overall tendency toward linearity in these dominance hierarchies. To see how infrequent resolution of the interactions influences this result, consider the corresponding calculation if all seven of the observed groups of size 4 and 5 had resolved all of their interactions. L(4,6) = 4! / 2⁶ = 0.375; from two of these and five of L(5,10), we have the overall probability for the seven fully resolved groups as (0.117)⁵(0.375)² = (3.08)10^–6.

Because we did observe one non-linear outcome in our results, it is also useful to determine the chance of one non-linear outcome or better (i.e. none) by chance as (3.08)10^–6 + 5(0.883)(0.117)⁴(0.375)² + 2(0.117)⁵(0.625)(0.375) = 0.00013. Thus a fully resolved set of interactions among the surviving individuals in our study would have provided very strong evidence for overall linearity of the dominance hierarchies if all of the additionally observed interactions were consistent with linearity. (We can show that one additional non-linearity would still support linearity in this fully resolved case.) We calculate the probability of linearity as strong or better than we actually observed in our own data (i.e. with the one non-linearity we obtained) in an analogous way, resulting in the probability 0.4575 + (0.1937)(0.9137)(0.9792)³(0.8083)(0.9500) + (0.8063)(0.0863)(0.9792)³(0.8083)(0.9500) + 3(0.8063)(0.9137)(0.0208)(0.9792)²(0.8083)(0.9500) + (0.8063)(0.9137)(0.9792)³(0.1917)(0.9500) + (0.8063)(0.9137)(0.9792)³(0.8083)(0.0500) = 0.8230. This result clearly indicates that our empirical results provide only very weak evidence for linearity and are consistent with outcomes determined entirely by chance.