Offspring Distribution Research Articles

Dispersal of optimal foragers in a patchy environment: Simulations with a mathematical model and tests of predictions in field experiments

To predict the effect of density on the dispersal of foraging parasitoids, we developed a spatially explicit individual-based model in which parasitoids move among host patches at random but use an optimal decision-rule about when to leave these patches. We used a simple decision rule where an individual forager exploits a patch as long as the instantaneous attack rate is higher than the average attack rate it has experienced in the environment. Such a rule implies that foragers compute and remember attack rates as they forage. Simulations with different combinations of patch distribution, host density, mutual interference, and parasitoid density predicted that dispersal distance should increase with parasitoid density. To test this prediction, we used data from two field experiments in which we released either few or many adults of the aphid parasitoid Aphelinus asychis in replicated sites, and subsequently assessed dispersal from the spatial distribution of parasitoid offspring. In the first experiment, we did not to detect a relation between the number released and dispersal distance, but in the second experiment, dispersal distance increased with initial density, as predicted by our model. We propose two hypotheses to explain the discrepancy between the experiments. Different levels of environmental variability among experiments, resulting from differences in experimental designs, could cause differences in statistical conclusions. However, there could be a threshold density below which dispersal is not density-dependent, and this threshold may have been exceeded in the second experiment where large releases involved many more individuals than in the first experiment. In any case, our approach linked individual behavior and spatial distribution, and our results show that the insect distributions in the field can be predicted, qualitatively, from theory about individual behavior.

Total-current population-dependent branching processes: analysis via stochastic approximation

We consider continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. We assume finite second-moment conditions and use the stochastic approximation technique for the analysis. In particular, we identify an appropriate ordinary differential equation (ODE) and show that either of the two events occurs with a certain probability: (a) the time-asymptotic proportion of the populations converges to the attractors or saddle points of the ODE, (b) it enters every neighbourhood and exits some neighbourhood of a saddle point infinitely often. We also prove a finite time approximation result for the stochastic trajectory. Further, we analyse a branching process with attack and acquisition, which captures the competition in online viral markets; for this case, the probability of approximation equals one.

Critical Markov branching process with infinite variance allowing Poisson immigration with increasing intensity

The article studies a single-type critical Markov branching process with infinite variance of the offspring distribution. The process admits also an immigration component at the time points of a non-homogeneous Poisson process. If additionally the mean number of immigrants is infinite, then proper limit distributions are obtained, under suitable normalization of the sample paths, depending on the rate of change of the intensity of the Poisson process.

Branching processes with immigration in a random environment—The Grincevičius–Grey setup

We determine the tail asymptotics of the stationary distribution of a branching process with immigration in a random environment, when the immigration distribution dominates the offspring distribution. The assumptions are the same as in the Grincevičius–Grey theorem for the stochastic recurrence equation.

The Effect of Prenatal Docosahexaenoic Acid Supplementation on Offspring Fat Mass and Distribution at 24 Months Old

BackgroundExcessive gestational weight gain (GWG) is related to increased offspring fat accrual, and increased fat mass (FM) is related to obesity development. Prenatal DHA supplementation has been linked to lower levels of offspring FM; however, conflicting data exist. ObjectivesThis study aimed to determine if there is a protective effect of prenatal DHA supplementation on offspring fat accrual and adipose tissue deposition at 24 mo in offspring born to females who gain excessive weight compared with nonexcessive weight during pregnancy. We also explored if the effect of DHA dose on FM differed by offspring sex. MethodsInfants born to females who participated in the Assessment of DHA on Reducing Early Preterm Birth randomized controlled trial (ADORE) were recruited. In ADORE, females were randomly assigned to either a high or low prenatal DHA supplement. Offspring body composition and adipose tissue distribution were measured using dual-energy x-ray absorptiometry (DXA). GWG was categorized as excessive or not excessive based on clinical guidelines. ResultsFor total FM, there was a significant main effect for the DHA dose (P = 0.03); however, the dose by GWG status was nonsignificant (P = 0.44). Therefore, a higher prenatal DHA dose was related to greater offspring FM (622.9 g greater) and unrelated to GWG status. When investigating a DHA dose by sex effect, a significant main effect for DHA dose (P = 0.01) was detected for central FM. However, no interaction was detected (P = 0.98), meaning that both boys and girls had greater central FM if their mother was assigned to the higher DHA dose. ConclusionsGreater prenatal DHA supplementation was associated with greater offspring FM and adipose tissue distribution at 24 mo. It will be important to understand if these effects persist into childhood.This trial was registered at clinicaltrials.gov as NCT03310983.

Estimating the reproduction number and transmission heterogeneity from the size distribution of clusters of identical pathogen sequences

Quantifying transmission intensity and heterogeneity is crucial to ascertain the threat posed by infectious diseases and inform the design of interventions. Methods that jointly estimate the reproduction number R and the dispersion parameter k have however mainly remained limited to the analysis of epidemiological clusters or contact tracing data, whose collection often proves difficult. Here, we show that clusters of identical sequences are imprinted by the pathogen offspring distribution, and we derive an analytical formula for the distribution of the size of these clusters. We develop and evaluate an inference framework to jointly estimate the reproduction number and the dispersion parameter from the size distribution of clusters of identical sequences. We then illustrate its application across a range of epidemiological situations. Finally, we develop a hypothesis testing framework relying on clusters of identical sequences to determine whether a given pathogen genetic subpopulation is associated with increased or reduced transmissibility. Our work provides tools to estimate the reproduction number and transmission heterogeneity from pathogen sequences without building a phylogenetic tree, thus making it easily scalable to large pathogen genome datasets.

Coalescent processes emerging from large deviations

The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman’s coalescent process, which produces a binary tree, emerges universally from many microscopic models in which the variance in the number of offspring is finite. It is understood that power-law offsprings distributions with infinite variance can result in a very different type of coalescent structure with merging of more than two lineages. Here, we investigate the regime where the variance of the offspring distribution is finite but comparable to the population size. This is achieved by studying a model in which the log offspring sizes have stretched exponential tails. Such offspring distributions are motivated by biology, where they emerge from a toy model of growth in a heterogeneous environment, but also from mathematics and statistical physics, where limit theorems and phase transitions for sums over random exponentials have received considerable attention due to their appearance in the partition function of Derrida’s random energy model (REM). We find that the limit coalescent is a β-coalescent—a previously studied model emerging from evolutionary dynamics models with heavy-tailed offspring distributions. We also discuss the connection to previous results on the REM.

Seasonal differences in amounts of oviposition habitat and egg‐laying by caddisflies in rivers with regulated versus unregulated flows

Abstract Few studies consider spatio‐temporal variation in egg‐laying for benthic insects in streams. However, such variation can have lasting effects on the numbers and distribution of offspring and subsquent life‐cycle stages. For species that require specific egg‐laying habitats, such as rocks that protrude from the water surface (emergent rocks, ER), densities of egg‐laying habitat can affect densities of benthic eggs and even larvae for some species. For such species, changes in water levels alter the spatio‐temporal distribution of ER and can affect densities of eggs and, potentially, larvae. Below dams, modified flow regimes may alter the temporal availability of ER. In this study we tested whether river regulation altered the availability of oviposition habitat and changed the phenology of oviposition compared to unregulated rivers. At multiple sites in two regulated (Murrumbidgee, Tumut) and three unregulated (Goobarragandra, Goodradigbee, Micalong) rivers (south‐east Australia), we surveyed densities of ER and egg masses of five species of caddisflies (family Hydrobiosidae) seasonally over 3 years (2019–2021). Samples of adults also were collected during two seasons using light traps. High flows in both regulated rivers submerged all rocks during spring and summer and low‐flow releases stranded rocks above the waterline at all (Murrumbidgee River) or most (Tumut River) sites during autumn and winter. No ER or egg masses were observed on any date in the Murrumbidgee River, despite relatively large catches of adults. On the Tumut River, low densities of ER and egg masses were twice observed at one site, during seasons (winter, autumn) when oviposition was low in the unregulated rivers. In unregulated rivers, ER and egg masses (five species, four genera) were present at all sites but with lower densities in winter than in other seasons. During peak oviposition periods, densities of egg masses per site were not strongly related to densities of ER. In summer 2019, ER in two unregulated rivers were blanketed by sheets of algae and sediment that appeared to prevent oviposition because no egg masses were observed at this time. In regulated rivers, aseasonal flows precluded egg‐laying by submerging (summer, autumn) or stranding (winter, spring) all or most ER. In contrast, ER were available all year in the unregulated rivers and egg‐laying occurred all year, except when ER were blanketed by algae and sediment. Within seasons, local densities of egg masses may be limited by numbers of gravid females, rather than numbers of ER, which differs from previous research. Identifying impediments to reproduction is critical to understanding variability in population numbers in natural and altered systems. Our observations of oviposition failure downstream of dams present a new hypothesis for why some insect species are absent from channels where flows are regulated for irrigation. Blankets of algae may similarly preclude reproduction in rivers with low‐flow conditions, but this remains untested.

A universal right tail upper bound for supercritical Galton–Watson processes with bounded offspring

We consider a supercritical Galton–Watson process Zn whose offspring distribution has mean m>1 and is bounded by some d∈{2,3,…}. As is well-known, the associated martingale Wn=Zn/mn converges a.s. to some nonnegative random variable W∞. We provide a universal upper bound for the right tail of W∞ and Wn, which is uniform in n and in all offspring distributions with given m and d, namely: P(Wn≥x)≤c1exp−c2m−1mxd,∀n∈N∪{+∞},∀x≥0,for some explicit constants c1,c2>0. For a given offspring distribution, our upper bound decays exponentially as x→∞, which is actually suboptimal, but our bound is universal: it provides a single effective expression – which does not require large x – and is valid simultaneously for all supercritical bounded offspring distributions.

Species-wide survey of the expressivity and complexity spectrum of traits in yeast.

Assessing the complexity and expressivity of traits at the species level is an essential first step to better dissect the genotype-phenotype relationship. As trait complexity behaves dynamically, the classic dichotomy between monogenic and complex traits is too simplistic. However, no systematic assessment of this complexity spectrum has been carried out on a population scale to date. In this context, we generated a large diallel hybrid panel composed of 190 unique hybrids coming from 20 natural isolates representative of the S. cerevisiae genetic diversity. For each of these hybrids, a large progeny of 160 individuals was obtained, leading to a total of 30,400 offspring individuals. Their mitotic growth was evaluated on 38 conditions inducing various cellular stresses. We developed a classification algorithm to analyze the phenotypic distributions of offspring and assess the trait complexity. We clearly found that traits are mainly complex at the population level. On average, we found that 91.2% of cross/trait combinations exhibit high complexity, while monogenic and oligogenic cases accounted for only 4.1% and 4.7%, respectively. However, the complexity spectrum is very dynamic, trait specific and tightly related to genetic backgrounds. Overall, our study provided greater insight into trait complexity as well as the underlying genetic basis of its spectrum in a natural population.

Branching model with state dependent offspring distribution for Chlamydia spread

Chlamydiae are bacteria with an interesting unusual developmental cycle. Initially, a single bacterium in its infectious form (elementary body, EB) enters the host cell, where it converts into its dividing form (reticulate body, RB), and divides by binary fission. Since only the EB form is infectious, before the host cell dies, RBs start to convert into EBs. After the host cell dies RBs do not survive. We model the population growth by a 2-type discrete-time branching process, where the probability of duplication depends on the state. Maximizing the EB production leads to a stochastic optimization problem. Simulation study shows that our novel model is able to reproduce the main features of the development of the population.

On the fixation probability of an advantageous allele in a population with skewed offspring distribution

On the fixation probability of an advantageous allele in a population with skewed offspring distribution

Exact calculation of end-of-outbreak probabilities using contact tracing data.

A key challenge for public health policymakers is determining when an infectious disease outbreak has finished. Following a period without cases, an estimate of the probability that no further cases will occur in future (the end-of-outbreak probability) can be used to inform whether or not to declare an outbreak over. An existing quantitative approach (the Nishiura method), based on a branching process transmission model, allows the end-of-outbreak probability to be approximated from disease incidence time series, the offspring distribution and the serial interval distribution. Here, we show how the end-of-outbreak probability under the same transmission model can be calculated exactly if data describing who-infected-whom (the transmission tree) are also available (e.g. from contact tracing studies). In that scenario, our novel approach (the traced transmission method) is straightforward to use. We demonstrate this by applying the method to data from previous outbreaks of Ebola virus disease and Nipah virus infection. For both outbreaks, the traced transmission method would have determined that the outbreak was over earlier than the Nishiura method. This highlights that collection of contact tracing data and application of the traced transmission method may allow stringent control interventions to be relaxed quickly at the end of an outbreak, with only a limited risk of outbreak resurgence.

Estimating the Lambda measure in multiple-merger coalescents

Multiple-merger coalescents, also known as Λ-coalescents, have been used to describe the genealogy of populations that have a skewed offspring distribution or that undergo strong selection. Inferring the characteristic measure Λ, which describes the rates of the multiple-merger events, is key to understand these processes. So far, most inference methods only work for some particular families of Λ-coalescents that are described by only one parameter, but not for more general models. This article is devoted to the construction of a non-parametric estimator of the density of Λ that is based on the observation at a single time of the so-called Site Frequency Spectrum (SFS), which describes the allelic frequencies in a present population sample. First, we produce estimates of the multiple-merger rates by solving a linear system, whose coefficients are obtained by appropriately subsampling the SFS. Then, we use a technique that aggregates the information extracted from the previous step through a kernel type of re-construction to give a non-parametric estimation of the measure Λ. We give a consistency result of this estimator under mild conditions on the behavior of Λ around 0. We also show some numerical examples of how our method performs.

Branching processes in random environments with thresholds

AbstractMotivated by applications to COVID dynamics, we describe a model of a branching process in a random environment $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving periods of increase and decrease leading to supercritical and subcritical regimes. Even though the process is not Markov, we identify subsequences at random time points $\{(\tau_j, \nu_j)\}$ —specifically the values of the process at crossing times, viz. $\{(Z_{\tau_j}, Z_{\nu_j})\}$ —along which the process retains the Markov structure. Under mild moment and regularity conditions, we establish that the subsequences possess a regenerative structure and prove that the limiting normal distributions of the growth rates of the process in supercritical and subcritical regimes decouple. For this reason, we establish limit theorems concerning the length of supercritical and subcritical regimes and the proportion of time the process spends in these regimes. As a byproduct of our analysis, we explicitly identify the limiting variances in terms of the functionals of the offspring distribution, threshold distribution, and environmental sequences.

Intrinsic randomness in epidemic modelling beyond statistical uncertainty

Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever observe a single epidemic, and therefore cannot empirically determine aleatoric uncertainty. Here, we characterise both epistemic and aleatoric uncertainty using a time-varying general branching process. Our framework explicitly decomposes aleatoric variance into mechanistic components, quantifying the contribution to uncertainty produced by each factor in the epidemic process, and how these contributions vary over time. The aleatoric variance of an outbreak is itself a renewal equation where past variance affects future variance. We find that, superspreading is not necessary for substantial uncertainty, and profound variation in outbreak size can occur even without overdispersion in the offspring distribution (i.e. the distribution of the number of secondary infections an infected person produces). Aleatoric forecasting uncertainty grows dynamically and rapidly, and so forecasting using only epistemic uncertainty is a significant underestimate. Therefore, failure to account for aleatoric uncertainty will ensure that policymakers are misled about the substantially higher true extent of potential risk. We demonstrate our method, and the extent to which potential risk is underestimated, using two historical examples.

How contact patterns destabilize and modulate epidemic outbreaks

The spread of a contagious disease clearly depends on when infected individuals come into contact with susceptible ones. Such effects, however, have remained largely unexplored in the study of epidemic outbreaks. In particular, it remains unclear how the timing of contacts interacts with the latent and infectious stages of the disease. Here, we use real-world physical proximity data to study this interaction and find that the temporal statistics of actual human contact patterns (i) destabilize epidemic outbreaks and (ii) modulate the basic reproduction number R 0. We explain both observations by distinct aspects of the observed contact patterns. On the one hand, we find the destabilization of outbreaks to be caused by the temporal clustering of contacts leading to over-dispersed offspring distributions and increased probabilities of otherwise rare events (zero- and super-spreading). Notably, our analysis enables us to disentangle previously elusive sources of over-dispersion in empirical offspring distributions. On the other hand, we find the modulation of R 0 to be caused by a periodically varying contact rate. Both mechanisms are a direct consequence of the memory in contact behavior, and we showcase a generative process that reproduces these non-Markovian statistics. Our results point to the importance of including non-Markovian contact timings into studies of epidemic outbreaks.

Maternal exercise improves markers of metabolic signaling and reduces inflammation in brown adipose tissue of offspring

Maternal obesity impacts approximately one-third of pregnant people and impacts offspring through the transmission of obesogenic and diabetic traits. Pregnant patients often spend considerable time sedentary, which has been associated with harmful cardiometabolic changes. Our recent data show that compared with sedentary conditions, voluntary exercise during pregnancy in mice shifts adipose distribution of offspring away from energy storing white adipose tissue towards energy burning brown adipose tissue (BAT), which could improve energy metabolism over the lifespan. The objective of this study was to test the hypothesis that voluntary exercise in pregnant mice improves metabolic signaling pathways and reduces markers of inflammation in BAT from offspring. To test this, female C57BL/6J mice were placed on control diet and allocated to sedentary versus voluntary running wheel exercise cages. Voluntary wheel running was allowed for two weeks prior to breeding and throughout weaning. When offspring were 16 weeks of age, they were euthanized for collection of BAT. The study groups were male sedentary (n=9), female sedentary (n=11), male exercise (n=12), female exercise (n=8). Quantitative real-time polymerase chain reaction was used to measure mRNA of fibroblast-growth factor receptors (β-klotho, Fgfr1, Fgfr2) and inflammation markers (IL10, IL1β, TNFα) in BAT. Outcomes were analyzed by two-way ANOVA to assess effects of exercise, sex, and their interaction. Offspring from exercised mothers had a significant decrease in mRNA of IL1β (1.4±0.4 male sedentary vs. 0.4±0.1 male exercise vs. 1.1±0.2 female sedentary vs. 0.8 ±0.2 female exercise; PSex=0.668, PEX=0.006, PInt=0.098) and TNFα (0.9±0.1 male sedentary vs. 0.5±0.1 male exercise vs. 1.3±0.3 female sedentary vs. 0.6 ±0.1 female exercise; PSex=0.126, PEX=0.007, PInt=0.562) and an increase in Fgfr2 (1.1±0.2 male sedentary vs. 1.7±0.3 male exercise vs. 1.3±0.3 female sedentary vs. 3.8 ±1.2 female exercise; PSex=0.063, PEX=0.011, PInt=0.096) in BAT, which was largely independent of sex. There was no significant main effect of either sex or exercise on IL10, Fgfr1, or β-klotho mRNA in BAT. These data suggest that maternal exercise is associated with decreased inflammation and increased protective metabolic signaling in BAT. This could impact energy metabolism given increasing evidence for advantageous metabolic adaptations with increased BAT health and signaling. Additional studies are needed to further understand the impact of maternal exercise on adipose health, energy metabolism, and cardiovascular outcomes in offspring over the lifespan. American Heart Association Undergraduate Summer Fellowship, Department of Obstetrics and Gynecology at Penn State Milton S Hershey Medical Center, and Dani Peress MD Memorial Fund from the Society of Maternal Fetal Medicine This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Smoothing distributions for conditional Fleming–Viot and Dawson–Watanabe diffusions

We study the distribution of the unobserved states of two measure-valued diffusions of Fleming–Viot and Dawson–Watanabe type, conditional on observations from the underlying populations collected at past, present and future times. If seen as nonparametric hidden Markov models, this amounts to finding the smoothing distributions of these processes, which we show can be explicitly described in recursive form as finite mixtures of laws of Dirichlet and gamma random measures respectively. We characterize the time-dependent weights of these mixtures, accounting for potentially different time intervals between data collection times, and fully describe the implications of assuming a discrete or a nonatomic distribution for the underlying process that drives mutations. In particular, we show that with a nonatomic mutation offspring distribution, the inference automatically upweights mixture components that carry, as atoms, observed types shared at different collection times. The predictive distributions for further samples from the population conditional on the data are also identified and shown to be mixtures of generalized Pólya urns, conditionally on a latent variable in the Dawson–Watanabe case.

A Kesten–Stigum type theorem for a supercritical multitype branching process in a random environment

Consider a supercritical d-type branching process $Z_n^{i} = $ $ (Z_n^i(1), \cdots, Z_n^i(d)), \,n\geq 0,$ in an i.i.d. environment $\xi =(\xi_0, \xi_1, \ldots)$, starting with one particle of type $i$, whose offspring distributions of generation $n$ depend on the environment $\xi_n$ at time $n$. In the deterministic environment case, the famous Kesten-Stigum (1966) theorem states essentially that, if the mean matrix of the offspring distribution has spectral radius $\rho >1$, then for all $i,j =1, \ldots, d$, almost surely $ \lim_{n\rightarrow \infty} \frac{Z_{n}^{i}(j)}{\rho^n }$ exists and is finite; moreover, the limit variables are non-degenerate if and only if $\mathbb{E} \left(Z_1^{i}(j) \log^{+} Z_1^{i}(j)\right)<+\infty$ for all $i$ and $j$. The extension to the random environment case with $d=1$ has been done by Athreya and Karlin (1971) and Tanny (1988). Extending the Kesten-Stigum theorem to the random environment case with $d>1$ is a long-standing problem. The main objective of this paper is to resolve this delicate problem. In particular, under simple conditions, we prove that for any $1\le i,j\le d$, as $n \rightarrow +\infty$, $Z_n^{i}(j)/\mathbb{E}_\xi Z_n^{i}(j) \rightarrow W^{i}$ in probability, where $W^i$ is a non-negative random variable, $ \mathbb{E}_\xi Z_n^{i}(j)$ is the conditional expectation of $Z_n^{i}(j)$ given the environment $\xi$, which diverges to $\infty$ with geometric rate in the sense that $ \frac{1}{n} \log \mathbb{E}_\xi Z_n^{i}(j) \rightarrow \gamma >0$ almost surely, $\gamma$ being the Lyapunov exponent of the mean matrices of the offspring distributions; moreover $W^i$ are non-degenerate for all $i $ if and only if $\mathbb{E}\left(\frac{Z_1^{i}(j)}{M_0(i,j)}\log^{+}\frac{Z_1^{i}(j)}{M_0(i,j)}\right)<+\infty$ for all $i$ and $j$, where $M_0(i,j)$ is the conditioned mean of the number of children of type $j$ produced by a particle of type $i$ at time $0$, given the environment $\xi$. The key idea of the proof is the introduction of a non-negative martingale $(W_n^{i})$ which converges a.s. to $W^i$, and which reduces to the well-known fundamental martingale in the deterministic environment case. In addition, we prove that the direction $Z_n^{i}/ \| Z_n^{i} \|$ converges in law conditioned on the explosion event $\{\|Z_n^i\| \rightarrow +\infty\}$. The case of stationary and ergodic environment is also considered. Our results open ways to prove important properties such as central limit theorems with convergence rate and large deviation asymptotics.