Bifurcations of cycles in nonlinear semelparous Leslie matrix models

2020 ◽  
Vol 80 (4) ◽  
pp. 1187-1207
Author(s):  
Ryusuke Kon
Keyword(s):  
2009 ◽  
Vol 59 (1) ◽  
pp. 127-144 ◽  
Author(s):  
Lia Hemerik ◽  
Chris Klok ◽  
Maja Roodbergen

AbstractMany 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.


1980 ◽  
Vol 18 (1) ◽  
pp. 16-30 ◽  
Author(s):  
C.C. Travis ◽  
W.M. Post ◽  
D.L. DeAngelis ◽  
J. Perkowski

Biometrics ◽  
1974 ◽  
Vol 30 (3) ◽  
pp. 547 ◽  
Author(s):  
A. L. Jensen
Keyword(s):  

1989 ◽  
Vol 2 (1) ◽  
pp. 37-67 ◽  
Author(s):  
Poul Einer Hansen
Keyword(s):  

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