Gene expression data preprocessing.

We present an interactive web tool for preprocessing microarray gene expression data. It analyses the data, suggests the most appropriate transformations and proceeds with them after user agreement. The normal preprocessing steps include scale transformations, management of missing values, replicate handling, flat pattern filtering and pattern standardization and they are required before performing any pattern analysis. The processed data set can be sent to other pattern analysis tools.

Territorial intrusion risk and antipredator behaviour: a mathematical model.

In territorial animals that hide to avoid predators, a predatory attack creates a conflict because a hiding animal cannot defend its territory from conspecific intruders. When intruders are persistent, a past conspecific intrusion informs a territorial resident that future intrusions by the same animal are likely. Using a mathematical model, I examine the effects that past territorial intrusions can have on antipredator behaviour. Past territorial intrusions rarely affect a resident animal's time to hide (the optimal behaviour is to hide as soon as the predator initiates its attack). In contrast, past intrusions should shorten the length of time during which territory holders remain in hiding, with the magnitude of this effect depending on the time of the predator's attack, the re-intruder's pattern of return, and the intrusion rates of other conspecifics. The results of the model show that we need more information on patterns of re-intruders' behaviour, and emphasize that a similar functional explanation could underlie other behavioural changes following territorial and/or aggressive encounters (such as winner/loser effects or changes in display frequency and territorial vigilance). Differences between my findings and those from previous studies suggest that the trade-off between antipredator behaviour and territorial defence can involve different costs from the trade-off between antipredator behaviour and foraging.

Polytomies and phylogenetically independent contrasts: examination of the bounded degrees of freedom approach.

We examined the effect of soft polytomies on the performance (Type I error rate and bias) of Felsenstein's (1985; Am. Nat. 125:1-15) method of phylogenetically independent contrasts for estimating a bivariate correlation. We specifically tested the adequacy of bounding degrees of freedom, as suggested by Purvis and Garland (1993; Syst. Biol. 42:569-575). We simulated bivariate character evolution under Brownian motion (assumed by independent contrasts) and eight other models on five phylogenetic trees. For non-Brownian motion simulations, the adequacy of branch-length standardization was checked with a simple diagnostic (Garland et al., 1992; Syst. Biol. 41:18-32), and transformations were applied as indicated. Surprisingly, soft polytomies tended to have negligible effects on Type I error rates when models other than Brownian motion were used. Overall, and irrespective of evolutionary model, degrees of freedom were appropriately bounded for hypothesis testing, and unbiased estimates of the correlation coefficient were obtained. Our results, along with those of previous simulation studies, suggest that independent contrasts can reliably be applied to real data, even with phylogenetic uncertainty.

Anti-predator behaviour changes following an aggressive encounter in the lizard Tropidurus hispidus

Avoiding predators may conflict with territorial defence because a hiding territorial resident is unable to monitor its territory or defend it from conspecific intrusions. With persistent intruders, the presence of an intruder in the near past can indicate an increased probability of future intrusions. Therefore, following a conspecific-intrusion, territorial residents should minimize costs from future intrusions at the cost of higher predation risks. I conducted experiments with males of the territorial lizard Tropidurus hispidus recording approach distance (distance between predator and prey when the prey escapes) and time to re-emergence from a refuge after hiding. Past aggressive interactions affected anti-predator behaviour: lizards re-emerged sooner (compared to a control) when the predator attacked 5 min after an aggressive encounter. If the predator attacked while an aggressive encounter was ongoing, there was also a reduction in approach distance. The results are consistent with an economic hypothesis which predicts that T. hispidus incur greater predation risks to minimize future territorial intrusion; additionally they show that the effects of past and ongoing aggressive interactions are different, consistent with the minimization of present intrusion costs. These results are relevant for studies of the changes in aggressive behaviour due to changes in the social environment and for studies of the costs and (co) evolution of aggressive and anti-predator strategies.

Effects of branch length errors on the performance of phylogenetically independent contrasts.

We examined Type I error rates of Felsenstein's (1985; Am. Nat. 125:1-15) comparative method of phylogenetically independent contrasts when branch lengths are in error and the model of evolution is not Brownian motion. We used seven evolutionary models, six of which depart strongly from Brownian motion, to simulate the evolution of two continuously valued characters along two different phylogenies (15 and 49 species). First, we examined the performance of independent contrasts when branch lengths are distorted systematically, for example, by taking the square root of each branch segment. These distortions often caused inflated Type I error rates, but performance was almost always restored when branch length transformations were used. Next, we investigated effects of random errors in branch lengths. After the data were simulated, we added errors to the branch lengths and then used the altered phylogenies to estimate character correlations. Errors in the branches could be of two types: fixed, where branch lengths are either shortened or lengthened by a fixed fraction; or variable, where the error is a normal variate with mean zero and the variance is scaled to the length of the branch (so that expected error relative to branch length is constant for the whole tree). Thus, the error added is unrelated to the microevolutionary model. Without branch length checks and transformations, independent contrasts tended to yield extremely inflated and highly variable Type I error rates. Type I error rates were reduced, however, when branch lengths were checked and transformed as proposed by Garland et al. (1992; Syst. Biol. 41:18-32), and almost never exceeded twice the nominal P-value at alpha = 0.05. Our results also indicate that, if branch length transformations are applied, then the appropriate degrees of freedom for testing the significance of a correlation coefficient should, in general, be reduced to account for estimation of the best branch length transformation. These results extend those reported in Díaz-Uriarte and Garland (1996; Syst. Biol. 45:27-47), and show that, even with errors in branch lengths and evolutionary models different from Brownian motion, independent contrasts are a robust method for testing hypotheses of correlated evolution.