Effects of delay, truncations and density dependence in reproduction schedules on stability of nonlinear Leslie matrix models

Nonstationary and Chaotic Dynamics in Age-Structured Population Models

“…A third possibility is = ( ) or = ( ) which means that the elements in (1) depend on the total population . Two of the most frequently used fecundity functions are the compensatory Beverton and Holt relation ( ) = (1 + ) −1 ; see [13,36] and the overcompensatory Ricker relation, ( ) = exp(− ), first proposed by [37] and later applied in [11,14,16]. Note that both fecundity functions referred to above are members of the Deriso Schnute family ( ) = (1 − ) 1/ ( = −1 gives the Beverton and Holt relation while → 0 results in the Ricker case).…”

“…The papers referred to above mainly consider linear models. In the 1970s and later, it has been more and more common to consider nonlinear (density dependent) terms too, as accounted for in the classical papers [11,12], as well as in [13][14][15][16][17][18][19][20]. Some of these papers scrutinize the dynamics of concrete species, and others deal with theoretical aspects exclusively.…”

On Nonlinear Age- and Stage-Structured Population Models

“…References to lots of other examples may be found in Caswell (2001). Guckenheimer et al (1977); Silva and Hallam (1993) and Wikan and Mjolhus (1995;1996) have paid attention to the dynamics of (1) in unstable and chaotic parameter regions. Wikan (1997); Davydova et al (2003); Mjolhus et al (2005) and Cushing (2006) focus is on the dynamics of species who reproduce only once at the end of their lifes.…”

An Analysis of a Semelparous Population Model with Density-Dependent Fecundity and Density-Dependent Survival Probabilities

“…Particularly in fishery models, this has often been motivated by the assumption that most density effects are present only in the first year of life. Examples of theoretical studies which deal with nonstationary and chaotic behaviour as well as behaviour linked to concrete species may be found in [1][2][3][4][5][6][7]. In case of ergodic properties we refer to [8][9][10]; see also [11].…”