Due to human activity, many species have strongly declined in number and are currently threatened with extinction. Management directed at conservation of these species can benefit from the use of simple population models such as matrix models. However, for many species, data on survival and reproduction are scarce. Therefore, we set up a general framework based on a matrix model with three parameters: reproduction, juvenile (=first year survival) and adult survival in which incomplete data can be analysed. This framework is applicable to species that can mature after their first year of life. The point in a calendar year at which the population size is determined, i.e. the census time, is varied. We discuss the differences and the similarities between matrices modelling the same population at different census times. The population growth rate and the elasticity of the survival and reproduction parameters have been determined analytically. From these we made, as a visual diagnostic tool (general framework), plots of the growth rate and the elasticity pattern and their dependence on actual values of the reproduction parameter and the juvenile and adult survival. To illustrate the use of this framework we plot and discuss literature data on survival and/or reproduction of a few bird species with a juvenile stage of one year in the light of our modelling results.
Many populations of wader species have shown a strong decline in number in Western-Europe in recent years. The use of simple population models such as matrix models can contribute to conserve these populations by identifying the most profitable management measures. Parameterization of such models is often hampered by the availability of demographic data (survival and reproduction). In particular, data on survival in the pre-adult (immature) stage of wader species that remain in wintering areas outside Europe are notoriously difficult to obtain, and are therefore virtually absent in the literature. To diagnose population decline in the wader species; Black-tailed Godwit, Curlew, Lapwing, Oystercatcher, and Redshank, we extended an existing modelling framework in which incomplete demographic data can be analysed, developed for species with a pre-adult stage of one year. The framework is based on a Leslie matrix model with three parameters: yearly reproduction (number of fledglings per pair), yearly pre-adult (immature) and yearly adult (mature) survival. The yearly population growth rate of these populations and the relative sensitivity of this rate to changes in survival and reproduction parameters (the elasticity) were calculated numerically and, if possible, analytically. The results showed a decrease in dependence on reproduction and an increase in pre-adult survival of the population growth rate with an increase in the duration of the pre-adult stage. In general, adult survival had the highest elasticity, but elasticity of pre-adult survival increased with time to first reproduction, a result not reported earlier. Model results showed that adult survival and reproduction estimates reported for populations of Redshank and Curlew were too low to maintain viable populations. Based on the elasticity patterns and the scope for increase in actual demographic parameters we inferred that conservation of the Redshank and both Curlew populations should focus on reproduction. For one Oystercatcher and the Black-tailed Godwit populations we suggested a focus on both reproduction and pre-adult survival. For the second Oystercatcher population pre-adult survival seemed the most promising target for conservation. And for the Lapwing populations all demographic parameters should be considered.
The resident Greylag goose population in the Netherlands has strongly increased in number which led to conflict with agricultural interests, public concern on goose hunting and legal debate on the need to regulate geese. Such a debate can be facilitated by insight in population development and the effectiveness of management options. In this paper we analyse the historic population development and apply density independent and density dependent models to investigate possible future population development and the impact of management on this development. We explored the influence of density dependence by applying the amount of gosling rearing habitat as the first limiting factor. The models were parameterised with life-history data of two well studied populations during their exponential growth phase as a proxy for the total Dutch population for which life-history data are unavailable. The effectiveness of two management options aimed to reduce population growth: culling birds and egg reduction are assessed with these models. The developed models can be used as a management tool to evaluate the consequences of different measures in advance of their implementation. The results show significant positive growth rates which approximate the growth rate of the total Dutch population based on census data. With density dependence in the amount of gosling rearing habitat the population will grow for another one or two decades before it stabilizes. Of the two considered management options culling birds is more effective in reducing bird numbers than egg reduction. This conclusion holds both under density independent and density dependent conditions.