Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics

Abstract

We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis.

Autocrine signaling explains the emergence of Allee effects in cancer cell populations

“…Our model was fitted to experimental data, and we found that a weak Allee effect best explained the empirical observations. This is in accordance with the findings of Fadai et al [39] who also observed a weak Allee effect in breast cancer cell populations.…”

“…Another potential cause of the effect was proposed by Konstorum et al [38], who investigated the impact of feedback regulation in cancer stem cell dynamics. An explanation in terms of density-dependent proliferation rates was explored by Johnson et al [18], and similarly by Fadai et al [39], who both connected the per-capita growth rates in an individual-based model with coefficients in an ODE-model that recapitulated the growth rate decline as the cell populations became smaller. Neither of these results were directly linked to production and consumption of secreted factors among the cell populations.…”

Biomechanical modelling of cancer: Agent‐based force‐based models of solid tumours within the context of the tumour microenvironment

“…Type I -Single cell per lattice site MCTS [48][49][50]; Allee-effect in tumour growth [51]; cell-vessel interactions [52]; cell-cell interactions [53]; cell adhesion [54][55][56][57]; monolayers [58]; phenotypic heterogeneity [59][60][61][62] Type II -Compartment model. Multiple cells per lattice site coarse-grained proliferative rim [63,64]; exclusion processes [65] Type III -Single cell covers multiple lattice sites (Cellular-Potts) MCTS [66]; cell adhesion [67,68]; angiogenesis [69]; cell-fibre interaction [70]; monolayers [71] Type IV -Multiple (or single) cell(s) per lattice site, movement though velocity channels (lattice gas cellular automata) MCTS [72]; cell-fibre interaction [73]; cell-ECM interaction [74]; Allee-effect in tumour growth [75] F I G U R E 2 Schematic diagram indicating the basic physical properties of cells in centre-based models, showing on the left a single cell in isolation primed for mitosis, in the middle that seed cell having undergone mitosis creating two daughter cells and on the right two mature cells in contact under a balance of forces focuses on centre-based models (CBM) in which the cell geometry is simplified with each cell considered to be a viscoelastic sphere subject to small deformations, described by the position of its centre, , in the domain (hence centre-based) and its radius, , see leftmost image of Figure 2.…”

Small-scale spatial structure affects predator-prey dynamics and coexistence

“…Another important neighbour-dependent effect in the context of population dynamics in ecology and cell biology is the incorporation of an Allee effect where proliferation and death rates are incorporated into the IBM so that there can be a net negative growth rate at low density and a net positive growth rate at higher densities (Stephens et al 1999;Johnston et al 2017;Fadai et al 2019). Understanding how these kinds of interactions that lead to Allee effects would influence the formation of spatial structure is an open question that could be analysed by extending the modelling framework that we have presented here.…”