Influence of behavioural tactics on recruitment and reproductive trajectory in the kittiwake

Many studies have provided evidence that, in birds, inexperienced breeders have a lower probability of breeding successfully. This is often explained by lack of skills and knowledge, and sometimes late laying dates in the first breeding attempt. There is growing evidence that in many species with deferred reproduction, some prebreeders attend breeding places, acquire territories and form pairs. Several behavioural tactics assumed to be associated with territory acquisition have been described in different species. These tactics may influence the probability of recruiting in the breeding segment of the population, age of first breeding, and reproductive success in the first breeding attempt. Here we addressed the influence of behaviour ('squatting') during the prebreeding period on demographic parameters (survival and recruitment probability) in a long-lived colonial seabird species: the kittiwake. We also investigated the influence of behaviour on reproductive trajectory. Squatters have a higher survival and recruitment probability, and a higher probability of breeding successfully in the first breeding attempt in all age-classes where this category is represented. The influence of behaviour is mainly expressed in the first reproduction. However, there is a relationship between breeding success in the first occasion and subsequent occasions. The influence of breeding success in the first breeding attempt on the rest of the trajectory may indirectly reflect the influence of behaviour on breeding success in the first occasion. The shape of the reproductive trajectory is influenced by behaviour and age of first breeding. There is substantial individual variation from the mean reproductive trajectory, which is accounted for by heterogeneity in performance among individuals in the first attempt, but there is no evidence of individual heterogeneity in the rate of change over time in performance in subsequent breeding occasions     

Testing the effect of conspecific reproductive success on dispersal and recruitment decisions in a colonial bird: Design issues

Factors affecting dispersal and recruitment in animal populations will play a prominent role in the dynamics of populations. This is particularly the case for subdivided populations where the dispersal of individuals among patches may lead to local extinction and 'rescue effects'. A long-term observational study carried out in Brittany, France, and involving colour-ringed Black-legged Kittiwakes (Rissa tridactyla) suggested that the reproductive success of conspecifics (or some social correlate) could be one important factor likely to affect dispersal and recruitment. By dispersing from patches where the local reproductive success was low and recruiting to patches where the local reproductive success was high, individual birds could track spatio-temporal variations in the quality of breeding patches (the quality of breeding patches can be affected by different factors, such as food availability, the presence of predators or ectoparasites, which can vary in space and time at different scales). Such an observational study may nevertheless have confounded the role of conspecific reproductive success with the effect of a correlated factor (e.g. the local activities of a predator). In other words, individuals may have been influenced directly by the factor responsible for the low local reproductive success or indirectly by the low success of their neighbours. Thus, an experimental approach was needed to address this question. Estimates of demographic parameters (other than reproductive success) and studies of the response of marked individuals to changes in their environment usually face problems associated with variability in the probability of detecting individuals and with nonindependence among events occurring on a local scale. Further, very few studies on dispersal have attempted to address the causal nature of relationships by experimentally manipulating factors. Here we present an experiment designed to test for an effect of local reproductive success of conspecifics on behavioural decisions of individuals regarding dispersal and recruitment. The experiment was carried out on Kittiwakes within a large seabird colony in northern Norway. It involved (i) the colour banding of several hundreds of birds; (ii) the manipulation (increase/decrease) of the local reproductive success of breeding groups on cliffpatches; and (iii) the detailed survey of attendance and activities of birds on these patches. It also involved the manipulation of the nest content of marked individuals breeding within these patches (individuals failing at the egg stage were expected to respond in terms of dispersal to the success of their neighbours). This allowed us to test whether a lower local reproductive success would lower (1) the attendance of breeders at the end of the breeding season; (2) the presence of prospecting birds; and (3) the proportion of failed breeders that came back to breed on the same patch the year after. In this paper, we discuss how we dealt with (I) the use of return rates to infer differences in dispersal rates; (II) the trade-off between sample sizes and local treatment levels; and (III) potential differences in detection probabilities among locations. We also present some results to illustrate the design and implementation of the experiment.     

Estimation of Population Mean Under Non Response in Two-Occasion Rotation Patterns

The present article is an attempt to study the effect of non response at both occasions in search of good rotation patterns over two occasions. Ratio-type estimators were proposed for estimating the population mean at current occasion in presence of non response at both the occasions in two-occasion successive (rotation) sampling. Detail behaviors of proposed estimators were studied. Proposed estimators were compared with the estimator using no information from previous (first) occasion. Performances of the proposed estimators were demonstrated via empirical studies.     

Chain-type ratio estimator in successive sampling using multi-auxiliary information

ABSTRACT

The present work is an attempt to make use of several auxiliary variables at both the occasions for improving the precision of estimates at the current occasion on two occasions of successive sampling. Chain-type ratio estimator has been proposed for estimating the population mean at current occasion in two occasions rotation (successive) sampling. Theoretical properties of the proposed estimator have been investigated. The proposed estimator has been compared with simple mean estimator when there is no matching and with the ratio estimator in successive sampling when information is available on one auxiliary variable on both the occasions. Optimum replacement strategy has also been discussed. Theoretical results have been justified through empirical investigation.     

Some Effective Rotation Patterns in Estimation of Population Mean in Two-Occasion Successive Sampling

This article is an attempt to explore some effective rotation patterns in estimation of current population mean in two occasions successive sampling. Utilizing the readily available information on an auxiliary variable on both occasions and the information on study variable from the previous occasion, some efficient estimation procedures have been suggested. Optimum replacement strategies and the efficiencies of the proposed estimators have been discussed. Empirical studies are carried out and suitable recommendations are made.     

Mark-resighting analysis of a California gull population

California gulls ( Larus californicus ) of known age and sex were censused on their breeding colony in 1979, 1980 and 1984 through 1993. Ages of 235 males and 196 females ranged from 4 to 27 years. Age classes used in the analysis were limited to 17, 4 through 19, and 20 or more as a final age category because data on gulls over 20 were sparse. Survival declined with age in a way that was parsimoniously modelled with a quadratic function. Other factors, sex and time, did not explain any variation in survival. Resighting depended on age, sex and time. Younger adults skipped breeding more frequently than did older adults, and females skipped breeding more frequently than did males. There was also good evidence for time dependence in resighting probability, but its inclusion in the model occurred at the expense of interpretability and precision. In a data set such as this, resighting probability may assume more importance than a mere 'nuisance parameter'. In this study, resighting history measured attendance at the breeding ground. In turn, attendance rates may be a manifestation of reproductive strategy, which can also have consequences for survival. In this situation, there may be heterogeneity in both survival and resighting probability that is unexplained by the model. While such complexity may well be a nuisance to deal with, it can also point to important biological questions.     

Mark-resighting analysis of a California gull population

California gulls ( Larus californicus ) of known age and sex were censused on their breeding colony in 1979, 1980 and 1984 through 1993. Ages of 235 males and 196 females ranged from 4 to 27 years. Age classes used in the analysis were limited to 17, 4 through 19, and 20 or more as a final age category because data on gulls over 20 were sparse. Survival declined with age in a way that was parsimoniously modelled with a quadratic function. Other factors, sex and time, did not explain any variation in survival. Resighting depended on age, sex and time. Younger adults skipped breeding more frequently than did older adults, and females skipped breeding more frequently than did males. There was also good evidence for time dependence in resighting probability, but its inclusion in the model occurred at the expense of interpretability and precision. In a data set such as this, resighting probability may assume more importance than a mere 'nuisance parameter'. In this study, resighting history measured attendance at the breeding ground. In turn, attendance rates may be a manifestation of reproductive strategy, which can also have consequences for survival. In this situation, there may be heterogeneity in both survival and resighting probability that is unexplained by the model. While such complexity may well be a nuisance to deal with, it can also point to important biological questions.     

Estimation of population product in presence of non-response in successive sampling

The design of this paper is to examine the problem of estimation of finite population product in mail surveys for the current occasion in the context of sampling on two occasions is attempted when there is non-response on both the occasions. Estimators for the current occasion are derived as a particular case when there is non-response on first and second occasion only. The gain in efficiency of the proposed estimate over the direct estimate using no information gathered on the first occasion is computed. The proposed strategy has been compared with other estimators. An empirical study is carried out to study the performance of the proposed strategy.     

Estimation of population mean in successive sampling under super-population model in presence of random non response situations

The present work is an attempt to estimate the population mean on the current occasion in two-occasion successive (rotation) sampling in presence of random non response situations. The estimation strategy has been constructed under a super-population model design approach with the help of imputation technique. The estimators proposed on the current occasion cover the cases of occurrences random non responses on either of the occasions. Detail behaviors of the proposed class of estimators have been studied and its performance has been examined with the sample mean estimator. The results are demonstrated through empirical studies which establish the effectiveness of the proposed class of estimators. Suitable recommendations have been put forward to the survey statisticians for its practical application.     

The importance of intentions in the mechanism of reproductive behaviour formation

In a situation of low fertility like that operating nowadays, studying the determinants of reproductive behaviour is very important. In a context such as Western industrialized one, in which birth control induces a feature of consciousness into fertility conduct, reproductive intentions have a fundamental role. This paper examines the mechanism which leads to the formation of reproductive behaviour starting from intentions, with reference to a large city in Italy, where fertility is very low, Milan. In addition, the hypothesis that women have innate and unobservable propensities toward family formation is verified through a simultaneous equations model. It allows to control for the potential endogeneity of reproductive intentions in determining subsequent behaviour. Results partially confirm this hypothesis: no significant correlation is found between unobservable components influencing intentions and behaviour. The relevance of reproductive intentions for subsequent fertility behaviour is, however, pointed out.     

Multistate recapture models: modelling incomplete individual histories

Multistate capture-recapture models are a natural generalization of the usual one-site recapture models. Similarly, individuals are sampled on discrete occasions, at which they may be captured or not. However, contrary to the one-site case, the individuals can move within a finite set of states between occasions. The growing interest in spatial aspects of population dynamics presently contributes to making multistate models a very promising tool for population biology. We review first the interest and the potential of multistate models, in particular when they are used with individual states as well as geographical sites. Multistate models indeed constitute canonical capture-recapture models for individual categorical covariates changing over time, and can be linked to longitudinal studies with missing data and models such as hidden Markov chains. Multistate models also provide a promising tool for handling heterogeneity of capture, provided states related to capturability can be defined and used. Such an approach could be relevant for population size estimation in closed populations. Multistate models also constitute a natural framework for mixtures of information in individual history data. Presently, most models can be fit using program MARK. As an example, we present a canonical model for multisite accession to reproduction, which fully generalizes a classical one-site model. In the generalization proposed, one can estimate simultaneously age-dependent rates of accession to reproduction, natal and breeding dispersal. Finally, we discuss further generalizations - such as a multistate generalization of growth rate models and models for data where the state in which an individual is detected is known with uncertainty - and prospects for software development.     

Multistate recapture models: Modelling incomplete individual histories

Multistate capture-recapture models are a natural generalization of the usual one-site recapture models. Similarly, individuals are sampled on discrete occasions, at which they may be captured or not. However, contrary to the one-site case, the individuals can move within a finite set of states between occasions. The growing interest in spatial aspects of population dynamics presently contributes to making multistate models a very promising tool for population biology. We review first the interest and the potential of multistate models, in particular when they are used with individual states as well as geographical sites. Multistate models indeed constitute canonical capture-recapture models for individual categorical covariates changing over time, and can be linked to longitudinal studies with missing data and models such as hidden Markov chains. Multistate models also provide a promising tool for handling heterogeneity of capture, provided states related to capturability can be defined and used. Such an approach could be relevant for population size estimation in closed populations. Multistate models also constitute a natural framework for mixtures of information in individual history data. Presently, most models can be fit using program MARK. As an example, we present a canonical model for multisite accession to reproduction, which fully generalizes a classical one-site model. In the generalization proposed, one can estimate simultaneously age-dependent rates of accession to reproduction, natal and breeding dispersal. Finally, we discuss further generalizations - such as a multistate generalization of growth rate models and models for data where the state in which an individual is detected is known with uncertainty - and prospects for software development.     

Grey Predictive Process Control Charts

The present article intends to develop some imputation methods to reduce the impact of non response at both the occasions in two-occasion successive (rotation) sampling. Utilizing the auxiliary information, which is only available at the current occasion, estimators have been proposed for estimating the population mean at the current occasion. Estimators for the current occasion are also derived as a particular case when there is non response either on the first occasion or second occasion. Behaviors of the proposed estimators are studied and their respective optimum replacement policies are also discussed. To study the effectiveness of the suggested imputation methods, performances of the proposed estimators are compared in two different situations, with and without non response. The results obtained are demonstrated with the help of empirical studies.     

Search of Good Rotation Patterns to Improve the Precision of Estimates at Current Occasion

In rotation (successive) sampling, it is common practice to use the information collected on a previous occasion to improve the precision of the estimates at current occasion. The previous information may be in the form of an auxiliary character, the character under study itself, or both. In the present work, information on an auxiliary character, which is readily available on all the occasions, has been used along with the information on study character from the previous and current occasion. Consequently, chain type difference and regression estimators have been proposed for estimating the population mean at second (current) occasion in the two occasions rotation (successive) sampling. The proposed estimators have been compared with sample mean estimator when there is no matching and the optimum estimator, which is the combination of the means of the matched and unmatched portions of the sample at the second occasion. Optimum replacement policy is also discussed. Theoretical results have been justified through empirical interpretation.     

Costs of reproduction: Assessing responses to brood size manipulation on life-history and behavioural traits using multi-state capture-recapture models

Costs of reproduction are fundamental trade-offs shaping the evolution of life histories. There has been much interest, discussion and controversy about the nature and type of reproductive costs. The manipulation of reproductive effort (e.g. brood size manipulation) may alter not only life-history traits such as future adult survival rate and future reproductive effort, but also behavioural decisions affecting recapture/resighting and dispersal probabilities. We argue that many previous studies of the costs of reproduction may have erroneously concluded the existence or non-existence of such costs because of their use of local return rates to assess survival. In this paper, we take advantage of the modern multistate capture-recapture methods to highlight how the accurate assessment of the costs of reproduction requires incorporating not only recapture probability, but also behavioural 'state' variables, for example dispersal status and current reproductive investment. The inclusion of state-dependent decisions can radically alter the conclusions drawn regarding the costs of reproduction on future survival or reproductive investment. We illustrate this point by re-analysing data collected to address the question of the costs of reproduction in the collared flycatcher and the great tit. We discuss in some detail the methodological issues and implications of the analytical techniques.     

Testing recapture model MT for departure from homogeneity

This paper presents a method of testing for animal heterogeneity when the capture effort is not constant from occasion to occasion. The basic set of statistics used is a lower triangular matrix whose (I,k)th element is the proportion of those animals caught on the next (i+1)the occasion who have been caught k times until now. Both theoretical and simulation evidence is presented that the new procedure is superior to methods previously suggested. The method may breakdown for certain kinds of behavioural response.     

RATIO-TO-SIZE ESTIMATORS OF MEAN PER SUBUNIT IN TWO-STAGE SAMPLING OVER TWO OCCASIONS

We propose here some strategies for estimating the population mean per subunit at the current occasion and change in mean from one occasion to the next based on two-stage sampling on two successive occasions. Estimators of the mean in two-stage sampling over successive occasions have so far been based on the knowledge of the total number of subunits (elements), M⁰ in the population or on assumed equal sizes for the primary units. We have therefore given the ratio-to-size estimators for the population mean per subunit on the current occasion and the change in mean over the two occasions where M⁰ is not known. The results obtained also apply to the situation where M¹ is correlated with the variable of interest y.     

On the use of several auxiliary variables in estimation of current population mean in successive sampling

ABSTRACT

The present work intends to put emphasis on the role of several auxiliary variables on both the occasions to improve the precision of estimates at current occasion in two-occasion successive sampling. Utilizing the readily available information on several auxiliary variables on both occasions and the information on study variable from the previous occasion, an efficient estimation procedure of population mean on current occasion has been suggested. Optimum replacement strategy and the efficiencies of the proposed estimator have been discussed. Empirical studies are carried out, and appropriate recommendations have been put forward for practical applications.     

The use of auxiliary variables in capture-recapture modelling: An overview

I review the use of auxiliary variables in capture-recapture models for estimation of demographic parameters (e.g. capture probability, population size, survival probability, and recruitment, emigration and immigration numbers). I focus on what has been done in current research and what still needs to be done. Typically in the literature, covariate modelling has made capture and survival probabilities functions of covariates, but there are good reasons also to make other parameters functions of covariates as well. The types of covariates considered include environmental covariates that may vary by occasion but are constant over animals, and individual animal covariates that are usually assumed constant over time. I also discuss the difficulties of using time-dependent individual animal covariates and some possible solutions. Covariates are usually assumed to be measured without error, and that may not be realistic. For closed populations, one approach to modelling heterogeneity in capture probabilities uses observable individual covariates and is thus related to the primary purpose of this paper. The now standard Huggins-Alho approach conditions on the captured animals and then uses a generalized Horvitz-Thompson estimator to estimate population size. This approach has the advantage of simplicity in that one does not have to specify a distribution for the covariates, and the disadvantage is that it does not use the full likelihood to estimate population size. Alternately one could specify a distribution for the covariates and implement a full likelihood approach to inference to estimate the capture function, the covariate probability distribution, and the population size. The general Jolly-Seber open model enables one to estimate capture probability, population sizes, survival rates, and birth numbers. Much of the focus on modelling covariates in program MARK has been for survival and capture probability in the Cormack-Jolly-Seber model and its generalizations (including tag-return models). These models condition on the number of animals marked and released. A related, but distinct, topic is radio telemetry survival modelling that typically uses a modified Kaplan-Meier method and Cox proportional hazards model for auxiliary variables. Recently there has been an emphasis on integration of recruitment in the likelihood, and research on how to implement covariate modelling for recruitment and perhaps population size is needed. The combined open and closed 'robust' design model can also benefit from covariate modelling and some important options have already been implemented into MARK. Many models are usually fitted to one data set. This has necessitated development of model selection criteria based on the AIC (Akaike Information Criteria) and the alternative of averaging over reasonable models. The special problems of estimating over-dispersion when covariates are included in the model and then adjusting for over-dispersion in model selection could benefit from further research.     

The use of auxiliary variables in capture-recapture modelling: an overview

I review the use of auxiliary variables in capture-recapture models for estimation of demographic parameters (e.g. capture probability, population size, survival probability, and recruitment, emigration and immigration numbers). I focus on what has been done in current research and what still needs to be done. Typically in the literature, covariate modelling has made capture and survival probabilities functions of covariates, but there are good reasons also to make other parameters functions of covariates as well. The types of covariates considered include environmental covariates that may vary by occasion but are constant over animals, and individual animal covariates that are usually assumed constant over time. I also discuss the difficulties of using time-dependent individual animal covariates and some possible solutions. Covariates are usually assumed to be measured without error, and that may not be realistic. For closed populations, one approach to modelling heterogeneity in capture probabilities uses observable individual covariates and is thus related to the primary purpose of this paper. The now standard Huggins-Alho approach conditions on the captured animals and then uses a generalized Horvitz-Thompson estimator to estimate population size. This approach has the advantage of simplicity in that one does not have to specify a distribution for the covariates, and the disadvantage is that it does not use the full likelihood to estimate population size. Alternately one could specify a distribution for the covariates and implement a full likelihood approach to inference to estimate the capture function, the covariate probability distribution, and the population size. The general Jolly-Seber open model enables one to estimate capture probability, population sizes, survival rates, and birth numbers. Much of the focus on modelling covariates in program MARK has been for survival and capture probability in the Cormack-Jolly-Seber model and its generalizations (including tag-return models). These models condition on the number of animals marked and released. A related, but distinct, topic is radio telemetry survival modelling that typically uses a modified Kaplan-Meier method and Cox proportional hazards model for auxiliary variables. Recently there has been an emphasis on integration of recruitment in the likelihood, and research on how to implement covariate modelling for recruitment and perhaps population size is needed. The combined open and closed 'robust' design model can also benefit from covariate modelling and some important options have already been implemented into MARK. Many models are usually fitted to one data set. This has necessitated development of model selection criteria based on the AIC (Akaike Information Criteria) and the alternative of averaging over reasonable models. The special problems of estimating over-dispersion when covariates are included in the model and then adjusting for over-dispersion in model selection could benefit from further research.