Integral Rein Control in Physiology

Increasing Complexity Can Increase Stability in a Self-Regulating Ecosystem

“…Initially R increases linearly with P . However when the resource enters the range [15,85] it no longer increases with increasing P , but stabilises at ≈ 15. As P increases, R remains at the same value whereas the sum of population effects decreases.…”

“…Regulation is still observed with the following changes (data not shown): population size can be reduced by a quarter (further reductions tend lead to unstable populations due to increased variance produced by the stochastic GA) and increased beyond 100,000 (available computation time considerations led to a population of 2000 individuals being used for data collection); the λ parameter that determines the width of the fitness function can be halved or increased by a magnitude; the α and β parameters can be increased to 0.05 and 1 and reduced to 0.00005 and 0.001 respectively; the death rate can be decreased by one and increased by two magnitudes; the discrete e and E alleles can be replaced with double floating point values over the range [-1,1]; the assumption of a fixed population can be replaced with a variable population with logistic growth dynamics up to a carrying capacity, K, the value of which can vary over the same range for the fixed population. In both simulations R initially increases with P until P drives R into the range [15,85] at which point the population rapidly converges to a single A trait: α = 0,Ā ≈ 15; α = 0.0025,, A ≈ 20. With no population effects as P continues to increase,Ā and R track P until it goes past 85.…”

“…With no population effects as P continues to increase,Ā and R track P until it goes past 85. With population effects when P reaches the range [15,85], R no longer increases but remains fixed at ≈ 15 until P ≈ 65. As P increases, the sum of the population effects decreases in (d).…”

“…core body temperature in mammals) are maintained within a range of values by separate, unidirectional control reins that oppose forces that seek to perturb the variable. The rein control concept has since been developed in a physiological context [15] and latterly applied to analysis of a simplified Daisyworld model [16][17] [18]. In this model the [E, A low ] and the [e, A high ] sub-populations can be regarded as unidirectional control reins.…”

“…The bi-allelic Θ locus is represented with a double floating point number in the range [-1,1]. An individual will have the e allele if −1 > Θ < 0 and the E allele if 0 > Θ < 1 The A locus is represented with a double floating point number in the range [15,85] and specifies the point that the individual is best adapted to within the range of resource values. Equation 1 is used to calculate an individual's fitness which is a parabolic function of the resource.…”