Linear-In-The-Parameters Oblique Least Squares (LOLS) Provides More Accurate Estimates of Density-Dependent Survival.

Vasco M N C S Vieira,Oscar R Huanel,Marie-Laure Guillemin,Aschwin H Engelen,Erik V Thuesen

doi:10.1371/journal.pone.0167418

Abstract

Survival is a fundamental demographic component and the importance of its accurate estimation goes beyond the traditional estimation of life expectancy. The evolutionary stability of isomorphic biphasic life-cycles and the occurrence of its different ploidy phases at uneven abundances are hypothesized to be driven by differences in survival rates between haploids and diploids. We monitored Gracilaria chilensis, a commercially exploited red alga with an isomorphic biphasic life-cycle, having found density-dependent survival with competition and Allee effects. While estimating the linear-in-the-parameters survival function, all model I regression methods (i.e, vertical least squares) provided biased line-fits rendering them inappropriate for studies about ecology, evolution or population management. Hence, we developed an iterative two-step non-linear model II regression (i.e, oblique least squares), which provided improved line-fits and estimates of survival function parameters, while robust to the data aspects that usually turn the regression methods numerically unstable.

Highlights

Survival is one of the determinants of population viability
Gracilaria chilensis exhibited a clear pattern of maximum survival attained at optimal intermediate densities (Fig 1)
The Linear-in-the-parameters Oblique Least Squares (LOLS) applied to each of the life-cycle stages showed no significant differences between males, females and diploids for any of the survival function parameters (Fig 1B and Table 1)

Summary

Introduction

Survival is one of the determinants of population viability. Its accurate estimation and manipulation is essential for the management of endangered species, invasive species, plagues and commercially exploited species. The integration of both competition and Allee effects inevitably leads to a non-linear density-dependent survival function. This function can be transposed into a 3rd degree polynomial in order to density (x).

Results

Conclusion