New solutions for Parker sperm competition model

Parker et al. (2013) created a general model for sperm allocation under a trade-off between male investment of resources \(R\) into pre-copulatory effort (e.g. search time) \(T\) versus post-copulatory effort (e.g. ejaculate) \(U\). Their model is interesting because it encompasses a range of different scenarios of female remating and the type of competition between males. For female remating scenarios, the risk model has females mating … Continue reading New solutions for Parker sperm competition model

Playing with a new model for fugitive coexistence

I recently read a paper by Kawecki (2017), which presents a new mechanism for something analogous to fugitive coexistence. The paper has a really great literature overview, which I won’t be able to do justice here. In short, fugitive coexistence is when an inferior species persists on a patchy landscape by being a better coloniser: when a local extinction occurs, they are quicker to arrive … Continue reading Playing with a new model for fugitive coexistence

Fixation probability of birth-death process

The goal is to understand where Eq. 2 of the Supplementary section of Sigmund et al. (2010) came from. We are considering a finite population within which individuals are pursuing different game-theoretic strategies. At each timestep, a pair of individuals is chosen at random, and they engage in a social learning process, where individual \( i\) will adopt the strategy of individual \( j\) according … Continue reading Fixation probability of birth-death process

Understanding the neigbour-modulated inclusive fitness approach

The goal is to understand Equation 4.2 of Rodrigues and Kokko (2016). To understand the technique, I read through Taylor et al. (2007), and Taylor and Frank (1996), specifically examples 4, 4a and 4b. Very briefly, we begin with a matrix \( A = [w_{i,j} ] \) whose elements represent the genetic contribution of class \( j \) to class \( i \). Then for … Continue reading Understanding the neigbour-modulated inclusive fitness approach

Fibonacci numbers and alternating signs in species responses to press perturbation in a food chain

In a paper from 2001, Dambacher and Rossignol made a curious observation: Fibonacci numbers appear in the adjoint and absolute feedback matrices that result from a weighted-predictions matrix type analysis (Dambacher et al. 2003) on food chains. The weighted-predictions matrix analysis is a way of predicting how species in a food web will respond to a the press perturbation of one of the species, so … Continue reading Fibonacci numbers and alternating signs in species responses to press perturbation in a food chain

The change in the distance from the convex hull to the internal equilibrium during assembly

Law & Morton (unpub.) found that the distance between the interior equilibrium and the convex hull, measured as mean , increased as a permanent food web assembly progressed. I did a small set of assembly runs to test the robustness of this result, and to discover what causes to increase. An introduction to permanence and example of how it is calculated can be found in … Continue reading The change in the distance from the convex hull to the internal equilibrium during assembly

Permanence and the distance from the convex hull to the interior equilibrium

Background To use permanence, Lotka-Volterra dynamics have to be assumed, because it is only in this case that a sufficient condition for permanence is known: \[ \dot{x}_{i} = x_i \cdot f_i(x) = x_i \cdot (r_i + (A \cdot x)_i) \quad \forall i = 1, \ldots, n. \] Such a dynamical system is permanent if two conditions hold (Hofbauer and Sigmund 1988, The theory of evolution … Continue reading Permanence and the distance from the convex hull to the interior equilibrium