Measuring Up to Reality: Null Models and Analysis Simulations to Study Parental Coordination Over Provisioning Offspring

Abstract

Behavioral coordination when provisioning offspring, through alternation and synchrony, has been hypothesized to influence rearing success. However, studying coordination at the pair level presents two analytical difficulties. First, alternating or synchronous (i.e., simultaneous) feeding can occur randomly and be induced by a shared environment. Therefore, a null model must account for this apparent coordination that occurs by chance. Second, alternation and synchrony in provisioning are intrinsically linked to the rate of provisioning itself, and the effects of coordination and provisioning rate, for instance on fitness, need to be distinguished. In this paper, we explore several randomization procedures and simulation scenarios to tease apart true coordination from random alternation and synchrony, and to find an appropriate statistical model for analyzing coordination. First, to establish a baseline of alternated or synchronous visits expected by chance, we took data from a natural population of house sparrows and randomized inter-feeding intervals in various ways. Alternation and synchrony in the observed dataset were higher than expected by chance under any of our randomizations. However, it was impossible to exclude that alternation and synchrony patterns did not arise due to the pair's shared environment. Second, to identify a way of statistically modeling coordination without generating spurious effects due to intrinsic mathematical relationships between coordination and provisioning rates, we simulated data according to different scenarios. Only one out of five candidate models for analyzing alternation was deemed appropriate, and gave similarly appropriate results for analyzing synchrony. This work highlights the importance and difficulty of finding an adequate null model for studying behavioral coordination and other emergent behaviors. In addition, it demonstrates that analyzing simulated data, prior to analyzing empirical data, enables researchers to avoid spurious effects.

Environmental Effects on Parental Care Visitation Patterns in Blue Tits Cyanistes caeruleus

“…Synchrony at the nest may also be due to synchrony of foraging, possibly improving the probability of finding food in patchy environments expected in harsh environments Griffith, 2012, 2015). Short-term changes in weather might also cause correlated changes in the visit rates of both parents, which are not accounted for by randomisations, and hence are included in coordination scores (Ihle et al, 2019;Santema et al, 2019). In addition to weather, habitat tree diversity may also influence the quantity and quality of food available which in turn could impact patterns of parental feeding.…”

What Can We Quantify About Carer Behavior?

“…Theoretical work suggests that "turn-taking"-carers alternating contributions-can resolve sexual conflict efficiently (Johnstone et al, 2014), and provided the costs and benefits of care are time-dependent this does not require individuals to monitor each other perfectly (Johnstone and Savage, 2019). Empirical work has suggested that several species indeed alternate more than expected by chance, however questions remain over the mechanism of interaction and how strongly this turn-taking is driven by environmental variation vs. individual responsiveness (Ihle et al, 2019).…”

Do Parents Synchronise Nest Visits as an Antipredator Adaptation in Birds of New Zealand and Tasmania?

“…For all events except the first in each recording bout, we calculated the interval between it and the previous event. We considered synchronised events to be those that occurred within 120 s of the previous event (Mariette and Griffith, 2015;Ihle et al, 2019); as this window is somewhat arbitrary we also ran analyses using 90 and 150 s windows, which gave qualitatively similar results (see Ihle et al, 2019). The observed proportion of synchronised events (PSE obs ) for a nest watch can be calculated as the observed number of synchronised events (NSE obs ), divided by the total number of events (NTE) minus one for each recording bout (NR, usually 2 as we changed tapes once for most nests as described above), as we did not record the interval to the first event of the bout Equation 1.…”

“…It was particularly important to separate passive vs. active synchronisation, as our analyses compared multiple species and populations, which we knew or expected to differ in their provisioning rates (Massaro et al, 2008). Active and passive synchrony can be separated by comparing observed nest watches to simulated nest watches with similar properties, from which we can calculate how much synchrony we would expect to observe by chance (Ihle et al, 2019). We used simulations to estimate how much passive synchrony was expected to occur simply due to the provisioning rate for each nest watch, as follows: (1) we summed all intervals calculated for a nest watch, giving the total amount of time in seconds that occurred between events in recording bouts within the nest watch; (2) for each nest watch, we simulated a random sequence of the same number of events occurring over the same amount of time using the exponential distribution in R's basic stats package (R Core Team, 2018), giving a sequence of "expected" intervals between events; (3) we counted how many of the resulting intervals were <120 s, and (4) we repeated this process 100 times for each nest watch and took the median, to give an expected number of synchronised visits.…”

“…The interaction between this term and the effect of interest (e.g., whether species are native to New Zealand) then estimated whether the difference between observed and expected, i.e., the amount of active synchrony, was influenced by that effect. We used this model structure because it has an acceptable type-I error rate for this kind of data (Ihle et al, 2019). Details of each of our individual models are provided below.…”