Investigating the effects of predator removal and habitat management on nest success and breeding population size of a farmland passerine: a case study

Passerines are especially vulnerable to predation at the pre-independence stage. Although the role of nest success in British farmland passerine declines is contentious, improvement in nest success through sympathetic management could play a role in their reversal. Because habitat is known to interact with predation, management options for mitigation will need to consider effects of nest predation. We present results from an observational study of a population of Common Blackbird Turdus merula on a farm which has experienced a range of agri-environment and game-management options, including a period with nest predator control, as a case study to address some of these issues. We used an information theoretic model comparison procedure to look for evidence of interactions between habitat and nest predation, and then asked whether habitat management and nest predator abundances could explain population trends at the site through their effects on nest success. Interactions were detected between measures of predator abundance and habitat variables, and these varied with nest stage - habitat within the vicinity of the nest appeared to be important at the egg stage, and nest-placement characteristics were important at the nestling stage. Although predator control appeared to have a positive influence on Blackbird breeding population size, the non-experimental set-up meant we could not eliminate other potential explanations. Variation in breeding population size did not appear to be influenced by variation in nest success alone. Our study demonstrates that observational data can only go so far in detection of such effects, and we discuss how it might be taken further. Agri-environment and game-management techniques are likely to influence nest predation pressure on farmland passerines, but the patterns, mechanisms and importance to population processes remain not wholly understood.

Investigating the effects of predator removal and habitat management on nest success and breeding population size of a farmland passerine: a case study

Passerines are especially vulnerable to predation at the pre-independence stage. Although the role of nest success in British farmland passerine declines is contentious, improvement in nest success through sympathetic management could play a role in their reversal. Because habitat is known to interact with predation, management options for mitigation will need to consider effects of nest predation. We present results from an observational study of a population of Common Blackbird Turdus merula on a farm which has experienced a range of agri-environment and game-management options, including a period with nest predator control, as a case study to address some of these issues. We used an information theoretic model comparison procedure to look for evidence of interactions between habitat and nest predation, and then asked whether habitat management and nest predator abundances could explain population trends at the site through their effects on nest success. Interactions were detected between measures of predator abundance and habitat variables, and these varied with nest stage - habitat within the vicinity of the nest appeared to be important at the egg stage, and nest-placement characteristics were important at the nestling stage. Although predator control appeared to have a positive influence on Blackbird breeding population size, the non-experimental set-up meant we could not eliminate other potential explanations. Variation in breeding population size did not appear to be influenced by variation in nest success alone. Our study demonstrates that observational data can only go so far in detection of such effects, and we discuss how it might be taken further. Agri-environment and game-management techniques are likely to influence nest predation pressure on farmland passerines, but the patterns, mechanisms and importance to population processes remain not wholly understood.

Some general comparative points on Chao’s and Zelterman’s estimators of population size

Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

Some general comparative points on Chao's and Zelterman's estimators of the population size

Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

Extending Zelterman’s approach for robust estimation of population size to zero-truncated clustered data

Estimation of population size with missing zero-class is an important problem that is encountered in epidemiological assessment studies. Fitting a Poisson model to the observed data by the method of maximum likelihood and estimation of the population size based on this fit is an approach that has been widely used for this purpose. In practice, however, the Poisson assumption is seldom satisfied. Zelterman (1988) has proposed a robust estimator for unclustered data that works well in a wide class of distributions applicable for count data. In the work presented here, we extend this estimator to clustered data. The estimator requires fitting a zero-truncated homogeneous Poisson model by maximum likelihood and thereby using a Horvitz-Thompson estimator of population size. This was found to work well, when the data follow the hypothesized homogeneous Poisson model. However, when the true distribution deviates from the hypothesized model, the population size was found to be underestimated. In the search of a more robust estimator, we focused on three models that use all clusters with exactly one case, those clusters with exactly two cases and those with exactly three cases to estimate the probability of the zero-class and thereby use data collected on all the clusters in the Horvitz-Thompson estimator of population size. Loss in efficiency associated with gain in robustness was examined based on a simulation study. As a trade-off between gain in robustness and loss in efficiency, the model that uses data collected on clusters with at most three cases to estimate the probability of the zero-class was found to be preferred in general. In applications, we recommend obtaining estimates from all three models and making a choice considering the estimates from the three models, robustness and the loss in efficiency. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

ONeSAMP: a program to estimate effective population size using approximate Bayesian computation

The estimation of effective population size from one sample of genotypes has been problematic because most estimators have been proven imprecise or biased. We developed a web-based program, ONeSAMP that uses approximate Bayesian computation to estimate effective population size from a sample of microsatellite genotypes. ONeSAMP requires an input file of sampled individuals' microsatellite genotypes along with information about several sampling and biological parameters. ONeSAMP provides an estimate of effective population size, along with 95% credible limits. We illustrate the use of ONeSAMP with an example data set from a re-introduced population of ibex Capra ibex.

Comparative evaluation of a new effective population size estimator based on approximate Bayesian computation

We describe and evaluate a new estimator of the effective population size (N-e), a critical parameter in evolutionary and conservation biology. This new "SummStat" N-e. estimator is based upon the use of summary statistics in an approximate Bayesian computation framework to infer N-e. Simulations of a Wright-Fisher population with known N-e show that the SummStat estimator is useful across a realistic range of individuals and loci sampled, generations between samples, and N-e values. We also address the paucity of information about the relative performance of N-e estimators by comparing the SUMMStat estimator to two recently developed likelihood-based estimators and a traditional moment-based estimator. The SummStat estimator is the least biased of the four estimators compared. In 32 of 36 parameter combinations investigated rising initial allele frequencies drawn from a Dirichlet distribution, it has the lowest bias. The relative mean square error (RMSE) of the SummStat estimator was generally intermediate to the others. All of the estimators had RMSE > 1 when small samples (n = 20, five loci) were collected a generation apart. In contrast, when samples were separated by three or more generations and Ne less than or equal to 50, the SummStat and likelihood-based estimators all had greatly reduced RMSE. Under the conditions simulated, SummStat confidence intervals were more conservative than the likelihood-based estimators and more likely to include true N-e. The greatest strength of the SummStat estimator is its flexible structure. This flexibility allows it to incorporate any, potentially informative summary statistic from Population genetic data.

A bagging-based correction for the mixture model estimator of population size

Estimation of a population size by means of capture-recapture techniques is an important problem occurring in many areas of life and social sciences. We consider the frequencies of frequencies situation, where a count variable is used to summarize how often a unit has been identified in the target population of interest. The distribution of this count variable is zero-truncated since zero identifications do not occur in the sample. As an application we consider the surveillance of scrapie in Great Britain. In this case study holdings with scrapie that are not identified (zero counts) do not enter the surveillance database. The count variable of interest is the number of scrapie cases per holding. For count distributions a common model is the Poisson distribution and, to adjust for potential heterogeneity, a discrete mixture of Poisson distributions is used. Mixtures of Poissons usually provide an excellent fit as will be demonstrated in the application of interest. However, as it has been recently demonstrated, mixtures also suffer under the so-called boundary problem, resulting in overestimation of population size. It is suggested here to select the mixture model on the basis of the Bayesian Information Criterion. This strategy is further refined by employing a bagging procedure leading to a series of estimates of population size. Using the median of this series, highly influential size estimates are avoided. In limited simulation studies it is shown that the procedure leads to estimates with remarkable small bias.

Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.

Restricted dispersal reduces the strength of spatial density dependence in a tropical bird population

Spatial processes could play an important role in density-dependent population regulation because the disproportionate use of poor quality habitats as population size increases is widespread in animal populations-the so-called buffer effect. While the buffer effect patterns and their demographic consequences have been described in a number of wild populations, much less is known about how dispersal affects distribution patterns and ultimately density dependence. Here, we investigated the role of dispersal in spatial density dependence using an extraordinarily detailed dataset from a reintroduced Mauritius kestrel (Falco punctatus) population with a territorial (despotic) breeding system. We show that recruitment rates varied significantly between territories, and that territory occupancy was related to its recruitment rate, both of which are consistent with the buffer effect theory. However, we also show that restricted dispersal affects the patterns of territory occupancy with the territories close to release sites being occupied sooner and for longer as the population has grown than the territories further away. As a result of these dispersal patterns, the strength of spatial density dependence is significantly reduced. We conclude that restricted dispersal can modify spatial density dependence in the wild, which has implications for the way population dynamics are likely to be impacted by environmental change.

What limits insect fecundity? Body size- and temperature-dependent egg maturation and oviposition in a butterfly

1. Large female insects usually have high potential fecundity. Therefore selection should favour an increase in body size given that these females get opportunities to realize their potential advantage by maturing and laying more eggs. However, ectotherm physiology is strongly temperature-dependent, and activities are carried out sufficiently only within certain temperature ranges. Thus it remains unclear if the fecundity advantage of a large size is fully realized in natural environments, where thermal conditions are limiting. 2. Insect fecundity might be limited by temperature at two levels; first eggs need to mature, and then the female needs time for strategic ovipositing of the egg. Since a female cannot foresee the number of oviposition opportunities that she will encounter on a given day, the optimal rate of egg maturation will be governed by trade-offs associated with egg- and time-limited oviposition. As females of different sizes will have different amounts of body reserves, size-dependent allocation trade-offs between the mother’s condition and her egg production might be expected. 3. In the temperate butterfly Pararge aegeria , the time and temperature dependence of oviposition and egg maturation, and the interrelatedness of these two processes were investigated in a series of laboratory experiments, allowing a decoupling of the time budgets for the respective processes. 4. The results show that realized fecundity of this species can be limited by both the temperature dependence of egg maturation and oviposition under certain thermal regimes. Furthermore, rates of oviposition and egg maturation seemed to have regulatory effects upon each other. Early reproductive output was correlated with short life span, indicating a cost of reproduction. Finally, large females matured more eggs than small females when deprived of oviposition opportunities. Thus, the optimal allocation of resources to egg production seems dependent on female size. 5. This study highlights the complexity of processes underlying rates of egg maturation and oviposition in ectotherms under natural conditions. We further discuss the importance of temperature variation for egg- vs. time-limited fecundity and the consequences for the evolution of female body size in insects.