The quantitative study of marked individuals relies mainly on the use of meaningful biological models. Classical inference is then conducted based on the model likelihood, parameterized by parameters such as survival, recovery, transition and recapture probabilities. In classical statistics, we seek parameter estimates by maximising the likelihood. However, models are often overparameterized and, as a consequence, some parameters cannot be estimated separately. Identifying how many and which (functions of) parameters are estimable is thus crucial not only for proper model selection based upon likelihood ratio tests or information criteria but also for the interpretation of the estimates obtained. In this paper, we provide the reader with a description of the tools available to check for parameter redundancy. We aim to assist people in choosing the most appropriate method to solve their own specific problems.

Seabirds are subject to the influences of local climate variables during periods of land-based activities such as breeding and, for some species, moult; particularly if they undergo a catastrophic moult (complete simultaneous moult) as do penguins. We investigated potential relationships between adult penguin survival and land-based climate variables (ambient air temperature, humidity and rainfall) using 46 years of mark-recapture data of little penguins Eudyptula minor gathered at a breeding colony on Phillip Island in southeastern Australia. Our results showed that adult penguin survival had a stronger association with land-based climate variables during the moult period, when birds were unable to go to sea for up to 3 weeks, than during the breeding period, when birds could sacrifice breeding success in favour of survival. Annual adult survival probability was positively associated with humidity during moult and negatively associated with rainfall during moult. Prolonged heat during breeding and moult had a negative association with annual adult survival. Local climate projections suggest increasing days of high temperatures, fewer days of rainfall which will result in more droughts (and by implication, lower humidity) and more extreme rainfall events. All of these predicted climate changes are expected to have a negative impact on adult penguin survival.

Tagging is essential for many types of ecological and behavioural studies, and it is generally assumed that it does not affect the fitness of the individuals being examined. However, the tagging of birds has been shown to have negative effects on some aspects of their lives. Here we investigate the influence of tagging on apparent survival. We examined the effects of flipper bands and injected transponders on the apparent survival of adult Little Penguins by comparing the survival probabilities of 2483 Little Penguins marked at Phillip Island, Australia, between 1995 and 2001 in one of three ways: with bands, with transponders or with both. The design of the study and our method of analysis allowed us to estimate tag loss and ensured that tag loss did not bias the survival estimates. Birds marked with flipper bands had lower survival probabilities than those marked with transponders (with apparent survival probabilities in the first year after tagging of 75% for banded birds and 80% for birds fitted with transponders, and in subsequent years of 87% for banded birds and 91% for birds fitted with transponders). We estimated both band and transponder loss probabilities for the first time, and found that transponder loss probabilities were substantially higher than band loss probabilities, particularly in the first year after marking when the tag loss probability was 5% for transponders and 0.7% for bands. Survival probabilities were lower in the first year after marking than in subsequent years for all birds. Studies of penguins that have used flipper bands to identify individuals may have underestimated annual adult survival probabilities, as banded penguins were likely to have lower than average survival probabilities than those of unbanded birds. The higher annual survival probabilities of individuals marked with transponders indicate that this should be the preferred marking technique for Little Penguins. However, future studies will, like ours, need to consider the higher rates of transponder loss when estimating survival, possibly by double-tagging some birds.

Ocean temperature has been shown to be related to various demographic parameters in several seabird species, but ultimately its influence on breeding success and survival are paramount. The timing and success of breeding of little penguins Eudyptula minor in south-eastern Australia have been shown to correlate with local sea-surface temperatures (SST) and the east-west sea-temperature gradient across Bass Strait several months earlier. However, the causal links between ocean temperature and these demographic variables are not readily apparent due to their lagged nature. Using 41 yr of data on little penguins in south-eastern Australia, we carried out a mark-recapture analysis to examine if the changing SST and sea-temperature gradient (east-west difference between 2 locations in Bass Strait) are associated with survival probability in the first year of life. First-year survival is correlated with (1) an east-west sea-temperature gradient in Bass Strait in the winter after fledging, with an increased temperature gradient associated with decreased survival and (2) the mean SST in the autumn after fledging, with warmer seas associated with increased survival. SST alone does not provide the best model for explaining first-year survival. Projections suggest that SST in south-eastern Australia and sea-temperature gradient in Bass Strait will both increase due to global warming. The net effect of an increased sea-temperature gradient in winter (which has a negative influence) and increased SST in autumn (which has a positive influence) on first-year survival is uncertain, given the current lack of knowledge concerning the relationship between the sea-temperature gradient and SST in Bass Strait.

We live in an age of increased awareness of climate change and its potential effects on our ecosystems. Here we look at the effect of one aspect of climate, directional wind components, on the survival of Little Penguins Eudyptula minor on Phillip Island in south-eastern Australia, using mark-recapture data gathered over a 42 year period since 1968. We apply biologically realistic age structures for the survival and recapture probabilities, and use mean seasonal wind magnitudes from the four cardinal compass directions as covariates in our modelling of the survival probability. Results indicate that first year survival is most affected by southerly winds in the winter prior to the chick's birth, which increase survival, and by easterly winds in the summer of hatching/fledging, which decrease survival. Adult survival is most affected by increasing northerly winds in the autumn following moult (positively) and by easterly winds in the preceding summer (negatively). For both first-year and adult birds, increasing easterly summer wind is associated with decreased survival, possibly due to reduced flows of nutrient rich waters from western Bass Strait. References D. G. Ainley, J. Russell, S. Jenouvrier, E. Woehler, P. O. Lyver, W. R. Fraser, and G. L. Kooyman. Antarctic penguin response to habitat change as earth's troposphere reaches $2^{\circ }$C above preindustrial levels. Ecological Monographs, 80:49--66, 2010. http://www.esajournals.org/doi/pdf/10.1890/08-2289.1 C. J. Brown, E. A. Fulton, A. J. Hobday, R. J. Matear, H. P. Possingham, C. Bulman, V. Christensen, R. E. Forrest, P. C. Gehrke, N. A. Gribble, S. P. Griffiths, H. Lozano-Montes, J. M. Martin, S. Metcalf, T. A. Okey, R. Watson, and A. J. Richardson. Effects of climate--driven primary production changes on marine food webs: implications for fisheries and conservation. Global Change Biology, 16:1194--1212, 2010. doi:10.1111/j.1365-2486.2009.02046.x K. Burnham and D. Anderson. Model selection and multimodel inference: a practical information-theoretic approach. Springer Verlag, 2002. E. A. Catchpole, S. N. Freeman, B. J. T. Morgan, and M. P. Harris. Integrated recovery/recapture data analysis. Biometrics, 54:33--46, 1998. doi:10.2307/2533993 L. E. Chambers, C. A. Devney, B. C. Congdon, N. Dunlop, E. J. Woehler, and P. Dann. Observed and predicted effects of climate on Australian seabirds. Emu, 111:235--251, 2011. doi:10.1071/MU10033 M. Collins, J. M. Cullen, and P. Dann. Seasonal and annual foraging movements of Little Penguins from Phillip Island, Victoria. Wildlife Research, 26:705--721, 1999. doi:10.1071/WR98003 R. M. Cormack. Estimates of survival from the sighting of marked animals. Biometrika, 51:429--438, 1964. doi:10.1093/biomet/51.3-4.429 J. M. Cullen, L. E. Chambers, P. C. Coutin, and P. Dann. Predicting onset and success of breeding in little penguins Eudyptula minor from ocean temperatures. 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McCutcheon, P. Dann, M. Salton, L. Renwick, A. J. Hoskins, A. M. Gormley, and J. P. Y. Arnould. The foraging range of Little Penguins (Eudyptula minor) during winter. Emu (online first), 2011. doi:10.1071/MU10078 M. J. Mickelson, P. Dann, and J. M. Cullen. Sea temperature in Bass Strait and breeding success of the Little Penguins Eudyptula minor at Phillip Island, South-eastern Australia. Emu, 91(5):355--368, 1992. doi:10.1071/MU9910355 I. C. T. Nisbet and P. Dann. Reproductive performance of little penguins in relation to year, age, pair-bond duration, breeding date and individual quality. Journal of Avian Biology, 40:296--308, 2009. doi:10.1111/j.1600-048X.2008.04563.x P. N. Reilly and J. M. Cullen. The Little Penguin Eudyptula minor in Victoria. {II}: Breeding. Emu, 81:1--19, 1981. doi:10.1071/MU9810001 Y. Ropert-Coudert, A. Kato, and A. Chiaradia. Impact of small-scale environmental perturbations on local marine food resources: a case study of a predator, the little penguin. In Proceedings of the Royal Society B, volume 276, pages 4105--4109, 2009. doi:10.1098/rspb.2009.1399 P. A. Sandery. Seasonal variability of water mass properties in Bass Strait: three-dimensional oceanographic modelling studies. PhD thesis, Flinders University, Adelaide, 2007. http://catalogue.flinders.edu.au/local/adt/public/adt-SFU20070831.093503 G. A. F. Seber. A note on the multiple recapture census. Biometrika, 52:249--259, 1965. doi:10.1093/biomet/52.1-2.249 L. A. Sidhu. Analysis of recovery-recapture data for Little Penguins. PhD thesis, School of Physical, Environmental and Mathematical Sciences, The University of New South Wales at the Australian Defence Force Academy, 2007. L. A. Sidhu, E. A. Catchpole, and P. Dann. Mark-recapture-recovery modeling and age-related survival in Little Penguins Eudyptula minor. The Auk, 124:815--827, 2007. doi:10.1642/0004-8038(2007)124[815:MMAASI]2.0.CO;2 L. A. Sidhu, E. A. Catchpole, and P. Dann. Modelling banding effect and tag loss for Little Penguins Eudyptula minor. In W. McLean and A. J. Roberts, editors, Proceedings of the 15th Biennial Computational Techniques and Applications Conference, CTAC-2010, volume 52 of ANZIAM Journal, pages C206--C221, 2011. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/3941 [June 6, 2011].

Web Appendix A: Extended Models In the main paper we considered models with a separate survival probability for animals in their first year of life. We may wish to consider the survival probability separately for longer than a year, for example if an animal is juvenile for longer than a year. To include such cases we extend the models examined to consider survival separately for the first J years of their life. The animal would then be considered an adult for years J +1 onwards. A similar x/y/z notation is used. Here x represents the first J years of life with the following options: (i) Dependent on age for years 1 to J (A1:J). (Note that A1:1 is equivalent to C.) (ii) Dependent on age and time for years 1 to J (A1:J ,T). (Note that A1:1,T is equivalent to T.) The options for y, the adult survival probability, are: (i) Constant (C). (ii) Dependent on time (T). (iii) Dependent on age (A). (iv) Dependent on age and time (A,T). The options for z, the recovery probability, are: (i) Constant (C). (ii) Dependent on time (T). (iii) Dependent on age (A). (iv) Dependent on age for years 1 to J with separate adult recovery (A1:J+1). (v) Dependent on time and age for years 1 to J with separate adult recovery (A1:J+1,T). (vi) Dependent on age and time (A,T). ∗Corresponding author: e-mail:d.j.cole@kent.ac.uk, Phone: +44-1227-823664

We present a framework for using Matlab to analyse mark-recapture data arising from studies that use more than one type of tag to mark animals for later identification. We consider life history data collected for groups of single and double tagged animals. We include tag loss probabilities in the likelihood function, which removes a common source of bias in the estimation of survival rates. We show how the formation of appropriate summary statistics, and use of vectorisation, vastly improves speed in computing the likelihood function. We illustrate our methods by analysing seven years of mark-recapture data for 2483 Little Penguins Eudyptula minor on Phillip Island in south-eastern Australia. References D. G. Ainley, R. E. LeResche, and W. J. L. Sladen. Breeding Biology of the Adelie Penguin. University of California Press, Berkeley, 1983. A. N. Arnason and K. H. Mills. Bias and loss of precision due to tag loss in Jolly--Seber estimates for mark-recapture experiments. Canadian Journal of Fisheries and Aquatic Sciences, 38:1077--1095, 1981. doi:10.1139/f81-148 R. J. H. Beverton and S. J. Holt. On the dynamics of exploited fish populations. Fishery Investigations Series II, 19:1--533, 1957. doi:10.2307/1440619 C. J. A. Bradshaw, R. J. Barker, and L. S. Davis. Modeling tag loss in New Zealand fur seal pups. Journal of Agricultural, Biological and Environmental Statistics, 5(4):475--485, 2000. doi:10.2307/1400661 E. A. Catchpole. Ted Catchpole's Personal Home Page. http://pems.unsw.adfa.edu.au//staff/profiles/catchpole_t. E. A. Catchpole, S. N. Freeman, B. J. T. Morgan, and M. P. Harris. Integrated recovery/recapture data analysis. Biometrics, 54:33--46, 1998. doi:10.2307/2533993 E. A. Catchpole, B. J. T. Morgan, and G. Tavecchia. A new method for analysing discrete life-history data with missing covariate values. Journal of Royal Statistical Society, B, 70(2):445--460, 2008. doi:10.1111/j.1467-9868.2007.00644.x P. B. Conn, W. L. Kendall, and M. D. Samuel. A general model for the analysis of mark-resight, mark-recapture, and band-recovery data under tag loss. Biometrics, 60:900--909, 2004. doi:10.1111/j.0006-341X.2004.00245.x B. M. Culik, R. P. Wilson, and R. Bannasch. Flipper-bands on penguins: what is the cost of a life-long commitment? Marine Ecology Progress Series, 98:209--214, 1993. doi:10.3354/meps098209 P. Dann and J. M. Cullen. Survival, patterns of reproduction and lifetime reproductive output in the Little Blue Penguins (Eudyptula minor) on Phillip Island, Victoria, Australia. In L. S. Davis and J. T. Darby, editors, Penguin Biology, pages 63--84. Academic Press, San Diego, 1990. P. Dann, J. M. Cullen, and R. Jessop. Cost of reproduction in Little Penguins. In P. Dann, F. I. Norman, and P. N. Reilly, editors, The Penguins: Ecology and Management, pages 39--55. Surrey Beatty, Sydney, 1995. P. Dann, L. A. Sidhu, R. Jessop, L. Renwick, M. Healy, P. Collins, B. Baker, and E. A. Catchpole. The effects of flipper bands on the survival of adult Little Penguins Eudyptula minor. The Auk. In review. G. Froget, M. Gauthier-Clerc, Y. Le Maho, and Y. Handrich. Is penguin banding harmless? Polar Biology, 20:409--413, 1998. doi:10.1007/s003000050322 M. Gauthier-Clerc, J.-P. Gendner, C. A. Ribic, W. R. Fraser, E. J. Woehler, S. Descamps, C. Gilly, C. Le Bohec, and Y. Le Maho. Long-term effects of flipper bands on penguins. Proceedings of the Royal Society of London B (Supplement), Biology Letters, 271:423--426, 2004. doi:10.1098/rsbl.2004.0201 S. R. Johnson, J. O. Schiek, and G. F. Searing. Neck band loss rates for lesser snow geese. Journal of Wildlife Management, 59:747--752, 1995. doi:10.2307/3801951 R. King, S. P. Brooks, and T. Coulson. Analyzing complex capture-recapture data in the presence of individual and temporal covariates and model uncertainty. Biometrics, 64:1187--1195, 2008. doi:10.1111/j.1541-0420.2008.00991.x J.-D. Lebreton, K. P. Burnham, J. Clobert, and D. R. 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An extensive set of wind-tunnel fires was burned to investigate convective heat transfer ahead of a steadily progressing fire front moving across a porous fuel bed. The effects of fuel and environmental variables on the gas temperature profile and the ‘surface wind speed’ (gas velocity at the fuel bed surface) are reported. In non-zero winds, the temperature of the air near the fuel bed surface decays exponentially with distance from the fire front. In zero winds, the temperature decreases rapidly within a very short distance of the flame front, then decays slowly thereafter. The maximum air temperature decreases as the free stream wind speed, packing ratio and fuel moisture content increase. The characteristic distance of the exponential decay increases strongly with the free stream wind speed and decreases with the packing ratio and surface area-to-volume ratio of the fuel. The surface wind speed depends strongly on the free stream wind speed, and to a lesser extent on packing ratio, fuel bed depth and fuel moisture content. There are three general regimes for the surface flow: (1) a constant velocity flow of approximately half the free stream flow, far from the flame front; (2) an intermediate zone of minimum flow characterised by low or reversed flow; and (3) a region near the flame front where the velocity rises rapidly almost to the free stream velocity. The boundaries between the three regions move further from the flame front with increasing wind speed, in a way which is only slightly affected by fuel geometry.

SummaryRegular censusing of wild animal populations produces data for estimating their annual survival. However, there can be missing covariate data; for instance time varying covariates that are measured on individual animals often contain missing values. By considering the transitions that occur from each occasion to the next, we derive a novel expression for the likelihood for mark–recapture–recovery data, which is equivalent to the traditional likelihood in the case where no covariate data are missing, and which provides a natural way of dealing with covariate data that are missing, for whatever reason. Unlike complete-case analysis, this approach does not exclude incompletely observed life histories, uses all available data and produces consistent estimators. In a simulation study it performs better overall than alternative methods when there are missing covariate data.

We analyzed yearly mark-recapture-recovery information collected over a 36-year period for the Little Penguins (Eudyptula minor) of Phillip Island in southeastern Australia. We show that it is feasible to model age-dependence for the survival, recapture, and recovery probabilities simultaneously, and that such a modeling scheme yields biologically realistic age structures for the model parameters. We provide illustrations of potentially erroneous results that may arise when researchers fail (1) to consider simultaneous age-dependence or (2) to detect annual variations that may mask age-dependence. From 1968 to 2004, 23,686 chicks were flipper-banded; 2,979 birds were encountered after fledging, and 1,347 were ultimately recovered dead. We found low survival of 17% in the first year of life, increasing to 71% in the second year of life, 78% in the third year, and 83% thereafter, and declining gradually after nine years of age. A population model allowing for immigration of birds from areas surrounding the study sites fits the observed stable population in the study sites. Modelado de Marca-Recaptura-Recuperación y Supervivencia Relacionada con la Edad en Eudyptula minor

Evaluating models to estimate flame characteristics for free-burning fires using laboratory and field data Wendy Anderson , Elsa Pastor , Bret Butler , Edward Catchpole , Jean-Luc Dupuy , Paulo Fernandes , Mercedes Guijarro , Jose-Miguel Mendes-Lopes , Joao Ventura g a UNSW@ADFA, Northcott Drive, ACT 2600, Australia b CERTEC, Technical University of Catalonia, Diagonal 647, E08028 Barcelona, Catalonia, Spain c USDA Forest Service, Rocky Mountain Research Station, Fire Sciences Laboratory, 5775 Hwy 10 west Missoula, MT 59802, USA d I.N.R.A., Unite de Recherches Forestieres Mediterraneennes, Equipe de Prevention des Incendies de Foret, Avignon, France e UTAD, CEGE/Department Florestal. Apartado 1013, 5001-801 Vila Real, Portugal f Centro de Investigacion Forestal, INIA, Apartado 8111, 28080 Madrid, Spain g Mechanical Engineering Department and IN+, Instituto Superior Tecnico, P-1049-001 Lisbon, Portugal

Necessary and sufficient conditions are established for the parameter redundancy of a wide class of nonlinear models for data distributed according to the exponential family. The likelihood surfaces for parameter-redundant models possess completely flat ridges. Whether a model is parameter redundant can be established by checking the rank of a derivative matrix, using a symbolic algebra package. A feature of contingency table applications is the need to extend conclusions from particular to general dimensions. We meet this via an extension theorem. Examples are given from the area of animal survival estimation using mark-recapture/recovery data.

Summary Key ecological studies involve the regular censusing of populations of wild animals, resulting in individual case history data which record when marked individuals are seen alive and/or found dead. We show how current conditional methods of analysing case history data may be biased. We then show how a correction can be applied, making use of results from a mark–recovery–recapture analysis. This allows a simple investigation of the effect of time-varying individual covariates such as weight that often contain missing values. The work is motivated and illustrated by the study of Soay sheep in the St Kilda archipelago.

A detailed and extensive mark-recapture-recovery study of red deer on the island of Rum forms the basis of the modeling of this article. We analyze male and female deer separately, and report results for both in this article, but use the female data to demonstrate our modeling approach. We provide a model-selection procedure that allows us to describe the survival by a combination of age-classes, with common survival within each class, and senility, which is modeled continuously as a parametric function of age. Dispersal out of the study area is modeled separately. Survival and dispersal probabilities are examined for the possible influence of both environmental and individual covariates, including a range of alternative measures of population density. The resulting model is succinct and biologically realistic. We compare and contrast survival rates of male and female deer of different ages and compare the factors that affect their survival. We demonstrate large differences in the rate of senescence between males and females even though their senescence begins at the same age. The differences between the sexes suggest that, in population modeling of sexually size-dimorphic species, it is important to identify sex-specific survival functions.

We show how random terms, describing both yearly variation and overdispersion, can easily be incorporated into models for mark-recovery data, through the use of Bayesian methods. For recovery data on lapwings, we show that the incorporation of the random terms greatly improves the goodness of fit. Omitting the random terms can lead to overestimation of the significance of weather on survival, and overoptimistic prediction intervals in simulations of future population behavior. Random effects models provide a natural way of modeling overdispersion-which is more satisfactory than the standard classical approach of scaling up all standard errors by a uniform inflation factor. We compare models by means of Bayesian p-values and the deviance information criterion (DIC).

A major recent development in statistics has been the use of fast computational methods of Markov chain Monte Carlo. These procedures allow Bayesian methods to be used in quite complex modelling situations. In this paper, we shall use a range of real data examples involving lapwings, shags, teal, dippers, and herring gulls, to illustrate the power and range of Bayesian techniques. The topics include: prior sensitivity; the use of reversible-jump MCMC for constructing model probabilities and comparing models, with particular reference to models with random effects; model-averaging; and the construction of Bayesian measures of goodness-of-fit. Throughout, there will be discussion of the practical aspects of the work-for instance explaining when and when not to use the BUGS package.