Overcoming the impossibility of age-balanced harvest.

In many countries, sustainability targets for managed fisheries are often expressed in terms of a fixed percentage of the carrying capacity. Despite the appeal of such a simple quantitative target, an unintended consequence may be a significant tilting of the proportions of biomass across different ages, from what they would have been under harvest-free conditions. Within the framework of a widely used age-structured model, we propose a novel quantitative definition of "age-balanced harvest" that considers the age-class composition relative to that of the unfished population. We show that achieving a perfectly age-balanced policy is impossible if we harvest any fish whatsoever. However, every non-trivial harvest policy has a special structure that favours the young. To quantify the degree of age-imbalance, we propose a cross-entropy function. We formulate an optimisation problem that aims to attain an "age-balanced steady state", subject to adequate yield. We demonstrate that near balanced harvest policies are achievable by sacrificing a small amount of yield. These findings have important implications for sustainable fisheries management by providing insights into trade-offs and harvest policy recommendations.

Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations.

Allometric settings of population dynamics models are appealing due to their parsimonious nature and broad utility when studying system level effects. Here, we parameterise the size-scaled Rosenzweig-MacArthur differential equations to eliminate prey-mass dependency, facilitating an in depth analytic study of the equations which incorporates scaling parameters' contributions to coexistence. We define the functional response term to match empirical findings, and examine situations where metabolic theory derivations and observation diverge. The dynamical properties of the Rosenzweig-MacArthur system, encompassing the distribution of size-abundance equilibria, the scaling of period and amplitude of population cycling, and relationships between predator and prey abundances, are consistent with empirical observation. Our parameterisation is an accurate minimal model across 15+ orders of mass magnitude.

Shifts in evolutionary balance of phenotypes under environmental changes.

Environments shape communities by driving individual interactions and the evolutionary outcome of competition. In static, homogeneous environments a robust, evolutionary stable, outcome is sometimes reachable. However, inherently stochastic, this evolutionary process need not stabilize, resulting in a dynamic ecological state, often observed in microbial communities. We use evolutionary games to study the evolution of phenotypic competition in dynamic environments. Under the assumption that phenotypic expression depends on the environmental shifts, existing periodic relationships may break or result in formation of new periodicity in phenotypic interactions. The exact outcome depends on the environmental shift itself, indicating the importance of understanding how environments influence affected systems. Under periodic environmental fluctuations, a stable state preserving dominant phenotypes may exist. However, rapid environmental shifts can lead to critical shifts in the phenotypic evolutionary balance. This might lead to environmentally favoured phenotypes dominating making the system vulnerable. We suggest that understanding of the robustness of the system's current state is necessary to anticipate when it will shift to a new equilibrium via understanding what level of perturbations the system can take before its equilibrium changes. Our results provide insights in how microbial communities can be steered to states where they are dominated by desired phenotypes.

Square root identities for harvested Beverton-Holt models.

We introduce the term net-proliferation rate for a class of harvested single species models, where harvest is assumed to reduce the survival probability of individuals. Following the classical maximum sustainable yield calculations, we establish relations between the proliferation and net-proliferation that are economically and sustainably favored. The resulting square root identities are analytically derived for species following the Beverton-Holt recurrence considering three levels of complexity. To discuss the generalization of the results, we compare the square root result to the optimal survival rate of the Pella-Tomlinson model. Furthermore, to test the practical relevance of the square root identities, we fit a stochastic Pella-Tomlinson model to observed Barramundi fishery data from the Southern Gulf of Carpentaria, Australia. The results show that for the estimated model parameters, the equilibrium biomass levels resulting from the MSY harvest and the square root harvest are similar, supporting the claim that the square root harvest can serve as a rule-of-thumb. This application, with its inherited model uncertainty, sparks a risk sensitivity analysis regarding the probability of populations falling below an unsustainable threshold. Characterization of such sensitivity helps in the understanding of both dangers of overfishing and potential remedies.

Mistakes can stabilise the dynamics of rock-paper-scissors games.

A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium.

Evolutionary games under incompetence.

The adaptation process of a species to a new environment is a significant area of study in biology. As part of natural selection, adaptation is a mutation process which improves survival skills and reproductive functions of species. Here, we investigate this process by combining the idea of incompetence with evolutionary game theory. In the sense of evolution, incompetence and training can be interpreted as a special learning process. With focus on the social side of the problem, we analyze the influence of incompetence on behavior of species. We introduce an incompetence parameter into a learning function in a single-population game and analyze its effect on the outcome of the replicator dynamics. Incompetence can change the outcome of the game and its dynamics, indicating its significance within what are inherently imperfect natural systems.

Hospital's instability wedges.

In this study, we define a hospital congestion episode as a situation where the number of new patients needing admission is greater than the number of available beds in the hospital, and investigate the likelihood that the current day's midnight occupancy will exceed any specified threshold level. We demonstrate that this measure of risk exhibits a characteristic sensitivity phenomenon that we have named as hospital's instability wedge. In particular, it is seen that frequently even small changes in the numbers of patients admitted or discharged can dramatically change the risk of exceeding the threshold, thereby changing the risk of subsequent congestion episodes. While this finding captures a salient difficulty of operating a modern public hospital, it also opens up an opportunity for monitoring and alleviating the above defined risk with only small changes in admission, discharge, and cancellation rates. A case study with recent patient journey data from Flinders Medical Centre in South Australia is presented.

Heroin users in Australia: population trends.

The aim of this paper is to identify certain important population trends among heroin users in Australia for the period 1971 - 97, such as: population growth, initiation, i.e. the number who were initiated to heroin in a given year, and quitting, i.e. the number that quit using heroin. For this purpose, we summarize and extract relevant characteristics from data from National Drug Strategy Household Survey (NDSHS 1998) conducted in Australia in 1998. We devise a systematic procedure to estimate historical trends from questions concerning past events. It is observed from our findings that the size of the heroin user population in Australia is in a sharp increase, especially from the early 1980s onwards. The general trend obtained for the period 1971 - 97 is strikingly similar to that obtained by Hall et al. (2000) for the dependent heroin user population in Australia, even though their study was based on different datasets and a different methodology. In our reconstruction of the time history we also detect a levelling-off prior to 1990. Initiation is also observed to be on a sharp increase. The latter trend is accompanied by a similar trend of quitting, perhaps indicating a relatively short heroin use career. A sharp decrease in both initiation and quitting is observed after 1990. In conclusion, in the case of the trend in the population of heroin users a high rate of growth has been identified that is consistent with the existing literature. In the process, we demonstrated that even a static survey such as NDSHS 1998 can, sometimes, be used to extract historical (dynamic) trends of certain important variables.