of a threatened species (ensure R is as high as possible) or decrease the abundance of a pest (ensure R is as low as possible) and wish to know, therefore, which phases in the life cycle are the most important, since it is there that should be the focus of our efforts. In fact, there have been two distinct, though related approaches to this decomposition of R.
The term life table response experiment (LTRE) was initially used to describe studies in which the varied effects of a factor, for example a pollutant, on growth, survival and reproduction were combined to generate a meaningful overall response – the effect on R (Caswell, 1989). The key here is that the pollutant exerts its directly measurable effects on the growth, survival and reproduction of individuals, but we may be most interested in the overall, combined effect at the population level, that is, R. Subsequently, and now much more commonly, the term LTRE analysis has been used to describe retrospective analysis of populations subjected to different levels of a factor, with a view to determining the respective contributions of growth, survival and reproduction to overall differences in R. The contrast is between combination in the first case and decomposition in the second.
APPLICATION 4.3 Customised conservation of northern wheatears
Species threatened with extinction often persist as a series of small, fragmented populations. Conservation programmes must then tread a fine line between being focused on the particular needs of specific threatened fragments and retaining a commonality of approach that makes the programme as a whole affordable and practicable. With these ideas in mind, three small populations of the northern wheatear, Oenanthe oenanthe, one of the most rapidly declining breeding birds in Europe, were studied in the Netherlands (Van Oosten et al., 2015), where numbers have dropped by at least 80% since 1990. Of the three populations, numbers in the 1990s (females holding territories) increased from five to 30 at Aekingerzand (A) but decreased from 165 to 34 at Castricum (C) and fluctuated between 45 and 69 at Den Helder (D). Field data were therefore collected between 2007 and 2011 both to estimate the sizes of the breeding populations (Figure 4.18a) and to monitor the demographic processes (vital rates) determining the population sizes: fecundity, juvenile (first year) and adult survival, and in this case immigration.
Figure 4.18 Analyses of life table response experiments (LTREs) can guide customised conservation. (a) Population sizes of northern wheatears, Oenanthe oenanthe (numbers of breeding territorial females) 2007–11 at three study sites in the Netherlands, as observed and as estimated from a matrix model integrating data on survival and fecundity. The variation in the estimates (box‐and‐whisker plots) arises because those estimates are taken regularly from chains generated by Monte Carlo Markov Chain (MCMC) procedures. The IPM does a good job at capturing the dynamics of the populations. (b) Contributions of the four vital rates (fecundity, f, juvenile and adult survival, ϕj and ϕa, and immigration, I) to the population growth rates observed in the Aekingerzand (purple) and Castricum (green) populations compared with that at Den Helder.
Source: After Van Oosten et al. (2015).
A matrix model integrating data on survival and fecundity was fitted to these demographic data and proved successful in recreating the observed population dynamics (Figure 4.18a), which in turn provides us with confidence that the IPM can usefully be used in an LTRE analysis. The results of this are shown in Figure 4.18b, comparing populations A and C to population D, as a benchmark, in terms of the contributions of the differences in vital rates to the overall differences in R. The relatively high rate of increase at site C (albeit from a low base) appears to be driven largely by immigration with some contribution from juvenile survival. The clear decrease at site A (R negative) resulted from low fecundity and adult survival.
The LTRE analysis, therefore, argues, most fundamentally, for customised approaches to be taken to local populations, since the forces driving their dynamics can be so different. Indeed, Van Oosten et al. (2015) conclude their study by explaining how they have responded to the analysis. To counteract the problems at site A, they introduced wire mesh covers to protect the nests and nesting adults, which led to an immediate more‐than‐doubling of fecundity and no predation by foxes, previously the main culprits. To support site C, so reliant on immigration, their strategy has been to protect site D, the main source of those immigrants. Fortunately, site D itself supports the most stable population of the three, and the strategy therefore is simply to protect the habitat there for the sake of that population and of others, like C, that rely on it.
4.8.3 Sensitivity and elasticity analysis
sensitivities and elasticities
In contrast to the retrospective LTRE analysis of the data contained in population projection matrices or IPMs, it is also possible to carry out prospective sensitivity or elasticity analyses (Caswell, 2001). Without going into the algebraic details, the general principle is one of ‘perturbing’ the values of elements, or combinations of elements, in the matrix, and then noting the effects of those perturbations on aggregate properties such as R. The sensitivity of each element (i.e. each transition, birth or survival, in the overall life cycle) is the amount by which R would change for a given absolute change in the value of the matrix element, with the value of all the other elements held constant. Thus, sensitivities are highest for those processes that have the greatest power to influence R. However, whereas survival elements (gs and ps) are constrained to lie between 0 and 1, fecundities are not, and R therefore tends to be more sensitive to absolute changes in survival than to absolute changes of the same magnitude in fecundity. Moreover, R can be sensitive to an element in the matrix even if that element takes the value 0 (because sensitivities measure what would happen if there was an absolute change in its value). These shortcomings are overcome, though, by using the elasticity of each element to determine its contribution to R, since this measures the proportional change in R resulting from a proportional change in that element. Conveniently, too, with the matrix formulation, the elasticities sum to 1, so that the meaning of an elasticity of 0.5, say, is clear: the element concerned accounts for half the variation in R.
APPLICATION 4.4 Elasticity analysis and population management
elasticity analysis and the management of armadillo abundance
Elasticity analysis offers an especially direct route towards focused plans for the management of abundance. For example, an elasticity analysis has been applied to the population dynamics of nine‐banded armadillos, Dasypus novemcinctus, in Mississippi, USA. The armadillo is a reservoir of infection of the causative agent of leprosy, Mycobacterium leprae, and indeed the only known non‐human vertebrate host of the disease in the Americas (see Oli et al. (2017) who also carry out an elasticity
