The annual probability of survival of the average adult individual is a critical parameter for demographic projections of long-lived animal populations. Indeed, small changes to this adult survival rate can yield large changes in the rate of population growth or decline. Yet this parameter was still unknown for the Gyrfalcon, an iconic raptor living in boreal and arctic ecosystems. In a recent PeerJ article¹, Ólafur K. Nielsen and I estimate adult as well as juvenile survival rates for the Icelandic population of gyrfalcons.

The Gyrfalcon is the largest of all extant falcons, slightly larger and heavier than a buzzard. Gyrfalcons used to be exported in past centuries from Iceland to mainland Europe (and beyond) for use in the falconries of kings. For this reason, we have detailed information about long-term trends, and therefore know that the Icelandic gyrfalcon and its main prey (rock ptarmigan) both have oscillations in population size². But surprisingly, basic components of ecological knowledge such as survival rates of this famous bird (now protected) were still lacking, not only in Iceland, but also all over the gyrfalcon’s circumpolar population range.

We estimate annual survival rates to be on average 83% [79%; 87%] for adults and 40% [34%; 45%] for juveniles³. A linear regression of annual survival rates in raptors with body mass⁴ yields a predicted 81% for adults: we therefore confirm that adult survival rates in long-lived birds are quite predictable. However, although the average adult survival rate is predictable, there is broad variability around the mean: the individuals that live the longest do so for 15 years or so, while the expected average lifespan is around 8 years. These differences are likely due to human-induced mortality (1 in 4 x-rayed dead falcon had embedded shotgun pellets). Juvenile survival was about half that of adult survival, again a relatively expected result for birds, and was - a little more surprisingly - neither related to weather nor main prey (rock ptarmigan) density. We suspect that this is because these variables had to be spatially averaged, as we model the survival rates of the average individual while in fact juveniles do move around within Iceland (but we do not know their detailed locations).

We used a multistage hidden Markov model combining capture-mark-recapture (from live individuals) and mark-recovery data (from dead individuals). Most capture-recapture models that estimate survival and detection probabilities for plant and animal species belong to hidden Markov models⁵. These models are called hidden because some states of the animals cannot be directly observed, only inferred. This particular model is called multistage because it uses three hidden states to combine information from encounters of observers with both live and dead individuals⁶. This “data fusion” technique helps to get survival estimates when data is scarce. In the model, we define observed states L: seen or captured alive; D: recovered dead; U: neither seen, captured nor recovered, which leads to a time series of observed states such as LUUULUUDUUUUU for each individual in the dataset⁷. These observed states are then related through probabilities to the true states of an individual (1: alive; 2: recently dead; 3: long dead) - an individual may very well be alive but unobserved, or recently dead but not yet found. State 2 helps to differentiate dead individuals that have some probability to be found from individuals in state 3 whose corpses are probably long decomposed. A Markov chain then specifies transition probabilities between the true states, to which adult and juvenile annual survival survival probabilities belong to, eventually modelling the dynamics of survival for each individual bird.

There are multiple ways to adjust these complex hierarchical models to data. One option is a full Bayesian analysis using a variant of the Gibbs sampler, where we would estimate directly the probabilities of each latent state (i.e. the probability that individual 347 is alive in 1994). As we have about 1500 individuals monitored for more than 10 years, this option would be a bit cumbersome (more than 15000 parameters to estimate) and early trials revealed that such models did not converge very well. Another option is to fit the model through the classical maximum likelihood framework, using the Forward algorithm⁸, a popular algorithm to fit hidden Markov models to data, which estimates Markov chain transition parameters without estimating each latent state. We used an in-between between those two options, using the Forward algorithm in a Bayesian framework in Stan⁹, a software implementing Hamiltonian Monte-Carlo^10,11, which helped to provide reliable credible intervals for parameter estimates.

Ironically, the sad fact that there is substantial variation in realized lifespan of falcons - likely due to humans - helped us keep the model simple, since Markov models assume geometrically distributed lifespans (the geometric distribution has such broad variability). If all adults had died at roughly the same ages, we would have been constrained to use more complex semi-Markov models¹².

These analyses have resulted not only from the efforts of the researchers (one of whom did a large portion of the captures starting in 1981) but also from the efforts of many others who were involved at various stages during the four decades of data collection. In recent years, more and more “recaptures” have in fact been re-sightings of birds by volunteers through photography, a fact made possible by improvement in camera technology. These ornithologists cannot be thanked enough for their critical contribution to knowledge.

This project is part of a long-term study started in 1981 in North-East Iceland where, in addition to the captures for survival estimation, gyrfalcons territories are mapped and fecundity at the nest is evaluated. Our hope is then to combine the survival estimates produced here with the rest of the data into demographic models predicting the Icelandic gyrfalcon population’s trends, and its possible trophic linkages to its prey, the rock ptarmigan.

– Frédéric Barraquand

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