The reproduction of the green sea turtles is characterized by the temperature dependent sex determination (TSD). Green sea turtle eggs are laid asexually. Temperature during hatching determines the sex of baby green sea turtles. In order to study the population dynamics of the green sea turtles and understand the dynamics of the sex ratio, in this paper we establish a stage-structured model by incorporating TSD and the ratio dependent Holling III functional response in the reproduction process of the green sea turtle population. The effects of incubation temperature and sex ratio deviation on persistence of the population are captured by the sole basic reproduction number. The persistent mode can be either a stable equilibrium or periodic oscillations. Numerical simulations and sensitive analysis help us to identify vital parameters in our model. Our research in the paper is in favor of elevating sexual encounter rates, reducing the searching time for males and increasing survival odds from baby state into adult in order to maintain sustainability of the green sea turtles.

Olfaction informs animal navigation for foraging, social interaction, and threat evasion. However, turbulent flow on the spatial scales of most animal navigation leads to intermittent odor information and presents a challenge to simple gradient-ascent navigation. Here we present two strategies for iterative gradient estimation and navigation via olfactory cues in 2D space: tropotaxis, spatial concentration comparison (i.e., instantaneous comparison between lateral olfactory sensors on a navigating animal) and klinotaxis, spatiotemporal concentration comparison (i.e., comparison between two subsequent concentration samples as the animal moves through space). We then construct a hybrid model that uses klinotaxis but utilizes tropotactic information to guide its spatial sampling strategy. We find that for certain body geometries in which bilateral sensors are closely-spaced (e.g., mammalian nares), klinotaxis outperforms tropotaxis; for widely-spaced sensors (e.g., arthropod antennae), tropotaxis outperforms klinotaxis. We find that both navigation strategies perform well on smooth odor gradients and are robust against noisy gradients represented by stochastic odor models and real turbulent flow data. In some parameter regimes, the hybrid model outperforms klinotaxis alone, but not tropotaxis.

Time perception is fundamental for decision-making, adaptation, and survival. In the peak-interval (PI) paradigm, one of the critical features of time perception is its scale invariance, i.e., the error in time estimation increases linearly with the to-be-timed interval. Brain lesions can profoundly alter time perception, but do they also change its scalar property? In particular, hippocampus (HPC) lesions affect the memory of the reinforced durations. Experiments found that ventral hippocampus (vHPC) lesions shift the perceived durations to longer values while dorsal hippocampus (dHPC) lesions produce opposite effects. Here we used our implementation of the Striatal Beat Frequency (SBFML) model with biophysically realistic Morris-Lecar (ML) model neurons and a topological map of HPC memory to predict analytically and verify numerically the effect of HPC lesions on scalar property. We found that scalar property still holds after both vHPC and dHPC lesions in our SBFML-HPC network simulation. Our numerical results show that PI durations are shifted in the correct direction and match the experimental results. In our simulations, the relative peak shift of the behavioral response curve is controlled by two factors: (1) the lesion size, and (2) the cellular-level memory variance of the temporal durations stored in the HPC. The coefficient of variance (CV) of the behavioral response curve remained constant over the tested durations of PI procedure, which suggests that scalar property is not affected by HPC lesions.

Comment on Proc Natl Acad Sci U S A. 2020 Nov 17;117(46):28572-28575.

The volatility of an environment significantly impacts cooperative behavior. In environments where viability-threatening events occur on a shorter timescale than reproduction, it is reasonable to measure the costs and benefits of cooperation in terms of their direct effect on survival probability. Then, the number of offspring increases with lifespan. With such a model, is it possible for cooperation to be evolutionarily stable, and how does cooperation depend on the benefit and cost of such interactions, and the volatility of the environment? In this paper, we develop an N-player survivor's dilemma in which prisoner's dilemma payoffs in an iteration are survival rates, and expected lifespan is the measure of reproductive fitness. We investigate cost, benefit, and volatility parameter ranges where various cooperative behaviors may occur. We observe that free-riding results in indirect punishment as the cheated partner's early death leaves the defector vulnerable. For 2- and 3-player versions of the game, we identify parameter regions where the repeated game becomes equivalent to a Harmony, Stag Hunt, or Prisoner's Dilemma static game and discuss evolutionary stability. We find that with two individuals, the initial fraction of cooperators necessary for cooperation to be selected for decreases as the benefit to cost ratio increases and as environmental volatility decreases. With the presence of a third individual, there also exists a parameter region where cooperation can invade an initially all-defecting population.

Can a regulated, legal market for wildlife products protect species threatened by poaching? It is one of the most controversial ideas in biodiversity conservation. Perhaps the most convincing reason for legalizing wildlife trade is that trade revenue could fund the protection and conservation of poached species. In this paper, we examine the possible poacher-population dynamic consequences of legal trade funding conservation. The model consists of a manager scavenging carcasses for wildlife product, who then sells the product, and directs a portion of the revenue towards funding anti-poaching law enforcement. Through a global analysis of the model, we derive the critical proportion of product the manager must scavenge, and the critical proportion of trade revenue the manager must allocate towards increased enforcement, in order for legal trade to lead to abundant long-term wildlife populations. We illustrate how the model could inform management with parameter values derived from the African elephant literature, under a hypothetical scenario where a manager scavenges elephant carcasses to sell ivory. We find that there is a large region of parameter space where populations go extinct under legal trade unless a significant portion of trade revenue is directed towards protecting populations from poaching. The model is general and therefore can be used as a starting point for exploring the consequences of funding many conservation programs using wildlife trade revenue.

A well-functioning placenta is critical for healthy fetal development, as the placenta brings fetal blood in close contact with nutrient rich maternal blood, enabling exchange of nutrients and waste between mother and fetus. The feto-placental circulation forms a complex branching structure, providing blood to fetal capillaries, which must receive sufficient blood flow to ensure effective exchange, but at a low enough pressure to prevent damage to placental circulatory structures. The branching structure of the feto-placental circulation is known to be altered in complications such as fetal growth restriction, and the presence of regions of vascular dysfunction (such as hypovascularity or thrombosis) are proposed to elevate risk of placental pathology. Here we present a methodology to combine micro-computed tomography and computational model-based analysis of the branching structure of the feto-placental circulation in ex vivo placentae from normal term pregnancies. We analyse how vascular structure relates to function in this key organ of pregnancy; demonstrating that there is a 'resilience' to placental vascular structure-function relationships. We find that placentae with variable chorionic vascular structures, both with and without a Hyrtl's anastomosis between the umbilical arteries, and those with multiple regions of poorly vascularised tissue are able to function with a normal vascular resistance. Our models also predict that by progressively introducing local heterogeneity in placental vascular structure, large increases in feto-placental vascular resistances are induced. This suggests that localised heterogeneities in placental structure could potentially provide an indicator of increased risk of placental dysfunction.

Size-spectrum models are a recent class of models describing the dynamics of a whole community based on a description of individual organisms. The models are motivated by marine ecosystems where they cover the size range from multicellular plankton to the largest fish. We propose to extend the size-spectrum model with spatial components. The spatial dynamics is governed by a random motion and a directed movement in the direction of increased fitness, which we call 'fitness-taxis'. We use the model to explore whether spatial irregularities of marine communities can occur due to the internal dynamics of predator-prey interactions and spatial movements. This corresponds to a pattern-formation analysis generalized to an entire ecosystem but is not limited to one prey and one predator population. The analyses take the form of Fourier analysis and numerical experiments. Results show that diffusion always stabilizes the equilibrium but fitness-taxis destabilizes it, leading to non-stationary spatially inhomogeneous population densities, which are travelling in size. However, there is a strong asymmetry between fitness-induced destabilizing effects and diffusion-induced stabilizing effects with the latter dominating over the former. These findings reveal that fitness taxis acts as a possible mechanism behind pattern formations in ecosystems with high diversity of organism sizes, which can drive the emergence of spatial heterogeneity even in a spatially homogeneous environment.

SARS-CoV-2 rapidly spread from a regional outbreak to a global pandemic in just a few months. Global research efforts have focused on developing effective vaccines against COVID-19. However, some of the basic epidemiological parameters, such as the exponential epidemic growth rate and the basic reproductive number, R0, across geographic areas are still not well quantified. Here, we developed and fit a mathematical model to case and death count data collected from the United States and eight European countries during the early epidemic period before broad control measures were implemented. Results show that the early epidemic grew exponentially at rates between 0.18 and 0.29/day (epidemic doubling times between 2.4 and 3.9 days). We found that for such rapid epidemic growth, high levels of intervention efforts are necessary, no matter the goal is mitigation or containment. We discuss the current estimates of the mean serial interval, and argue that existing evidence suggests that the interval is between 6 and 8 days in the absence of active isolation efforts. Using parameters consistent with this range, we estimated the median R0 value to be 5.8 (confidence interval: 4.7-7.3) in the United States and between 3.6 and 6.1 in the eight European countries. We further analyze how vaccination schedules depend on R0, the duration of protective immunity to SARS-CoV-2, and show that individual-level heterogeneity in vaccine induced immunity can significantly affect vaccination schedules.

The development of multicellular organisms relies on correct patterns of cell fates to produce functional tissues in the mature organism. A commonly observed developmental pattern consists of alternating cell fates, where neighboring cells take on distinct cell fates characterized by contrasting gene and protein expression levels, and this cell fate pattern repeats over two or more cells. The patterns produced by these fate decisions are regulated by a small number of highly conserved signaling networks, some of which are mediated by long range diffusible signals and others mediated by local contact-dependent signals. However, it is not completely understood how local and long range signals associated with these networks interact to produce fate patterns that are both robust and flexible. Here we analyze mathematical models to investigate the patterning of cell fates in an array of cells, focusing on a two cell repeating pattern. Bifurcation analysis of a multicellular ODE model, where we consider the cells as discrete compartments, suggests that cells must balance sensitivity to external signals with robustness to perturbations. To focus on the patterning dynamics close to the bifurcation point, we derive a continuum PDE model that integrates local and long range signaling. For those cells with dynamics close to the bifurcation point, sensitivity to long range signals determines how far a pattern extends in space, while the number of local signaling connections determines the type of pattern produced. This investigation provides a general framework for understanding developmental patterning, and how both long range and local signals play a role in generating features observed across biology, such as species differences in nematode vulval development and insect bristle patterning, as well as medically relevant processes such as control of stem cell fate in the intestinal crypt.