arXiv subjects

Hiro-Sato Niwa

Publications and source records attributed to Hiro-Sato Niwa.

9 recordsLinked to original sources

arXiv2022

Broken symmetry of recruitment fluctuations in marine fishes: Lévy-stable laws and beyond

Recruitment is calculated by summing random offspring-numbers entering the population, where the number of summands (i.e. spawning population size) is also a random process. A priori, it is not clear that individual reproductive variability would have a significant impact on aggregate measures for monitoring populations. Usually these variations are averaged out in a large population, and the aggregate output is merely influenced by population-wide environmental disturbances such as climate and fisheries. However, such arguments break down if the distribution of the individual offspring numbers is heavy-tailed. In a world with power-law offspring-number distribution with exponent $1<α<2$, the recruitment distribution has a putative power-law regime in the tail with the same $α$. The question is to what extent individual reproductive variability can have a noticeable impact on the recruitment under environmentally driven population fluctuations. This question is answered by considering the Lévy-stable fluctuations as embedded in a randomly varying environment. I report fluctuation scaling and asymmetric fluctuations in recruitment of commercially exploited fish stocks throughout the North Atlantic. The linear scaling of recruitment standard deviation with recruitment level implies that the individual reproductive variability is dominated by population fluctuations. The totally asymmetric (skewed to the right) character is a sign of idiosyncratic variation in reproductive success.

q-bio.PE↗

arXiv2022

Total consensus under high reproductive-variance conditions

Star-shaped branching patterns of genealogies are common in marine species. High-fecundity marine populations are characterized by low ratios of effective to actual population size, which reflect high variance in reproductive success among parents in mass spawns. When extreme reproduction events occur, offspring from very few parents dominate the population (whereby multiple mergers, or subsets of lineages with star-like trees, arise) and thus, the loss of genetic diversity is significant. Under high reproductive-variance conditions (assuming that reproduction occurs by sampling from the Pareto distribution), this paper explores the distribution of heterozygosity across generations. The result shows that zero heterozygosity is not achieved, implying that the populations may decline without evident loss of genetic variation. It is also found that there are singularities in the heterozygosity distributions. However, in the case of high reproductive variance, the locations of the singular points subtly deviate from those of the case where reproduction occurs by Wright-Fisher sampling.

q-bio.PE↗

arXiv2022

Hatchery-induced transition of the effective size in a Pareto population

It seems paradoxical to have observed the absence of reduced effective population sizes $N_{\mathrm{e}}$ under marine hatchery practices. This paper studies the Ryman-Laikre, or two-demographic-component, model of the hatchery impact related to inbreeding in a population with power-law family-size distribution, where hatchery inputs are represented by a Dirac delta function. By examining the asymptotic (i.e. large-population limit) behavior of the normalized sizes (or weights) of families of the mixture population, I derive the distribution properties of the average weight of families (i.e. the sum of the squared weights, $Y$) over the population existing at any given time. The reciprocal of the average weight $Y$ gives the effective number of families (or reproducing lineages) in the population, $N_{\mathrm{e}}=1/Y$. When the specific production in the hatchery (i.e. the number of offspring per broodstock) is low, the most probable value of $N_{\mathrm{e}}$ is close to the lower bound of the $N_{\mathrm{e}}$-distribution. When the specific hatchery-production is increased to a critical value with fixed mixing proportion of hatchery fish, a discontinuous transition takes place, so that the most probable $N_{\mathrm{e}}$ jumps to the upper extreme of the distribution. This hatchery-induced transition is attributed to the breaking of reciprocal symmetry, i.e. the fact that the typical value of $Y$ and its reciprocal (the typical $N_{\mathrm{e}}$) do not vary with the population size in opposite ways. At a high specific hatchery-production, the symmetry breaking disappears.

q-bio.PE↗

arXiv2022

Fluctuation scaling in Lévy-stable recruitment of marine fishes in randomly varying environments

This paper studies the scaling properties of recruitment fluctuations in randomly varying environments, for abundant marine species with extreme reproductive behavior. Fisheries stock-recruitment data from the North Atlantic display fluctuation scaling, a proportionality between the standard deviation and the average recruitment among stocks. The proportionality covers over five orders of magnitude in the range studied. A linear-scaling behavior can be a sign of a universal distribution of the normalized data across stocks. In light of this conjecture, it is demonstrated that the Lévy-stable model offers a better effective description of the recruitment distribution than the log-normal model. Care is devoted to the problem of random sums of random variables. Recruitment is calculated by summing random offspring numbers with infinite variance, where the number of summands (i.e. spawning population size) is also a random process with infinite variance.

q-bio.PE↗

arXiv2022

Reciprocal symmetry breaking in Pareto sampling

Let $W_1,\ldots,W_N$ be a sample of $\mathrm{Pareto}(α)$ random variables normalized by their sum, such that $\sum_i W_i=1$. The $W_i$ may represent the weights of valleys in a spin glass (if $0<α<1$), or the frequency of different lineages (families) in a genealogy. This paper considers a population in which there are $N$ individuals reproducing with $\mathrm{Pareto}(α)$ offspring-number distribution ($1<α<2$). The probability of two randomly-chosen individuals being siblings, $Y_2=\sum_i W_i^2$, gives the sample mean of the normalized size of families, and its reciprocal gives the effective number of families (or reproducing lineages) in the population, $N_{\mathrm{e}}=1/Y_2$. The typical sample mean is very different from the average over all possible samples, i.e. $Y_2$ is not a self-averaging quantity. The typical $Y_2$ and its reciprocal do not vary with $N$ in opposite ways. Non-self-averaging effects are crucial in understanding genetic diversity in mass spawning species such as marine fishes.

math.PR↗

arXiv2006

Exploitation dynamics of fish stocks

I address the question of the fluctuations in fishery landings. Using the fishery statistics time-series collected by the Food and Agriculture Organization of the United Nations since the early 1950s, I here analyze fishing activities and find two scaling features of capture fisheries production: (i) the standard deviation of growth rate of the domestically landed catches decays as a power-law function of country landings with an exponent of value 0.15; (ii) the average number of fishers in a country scales to the 0.7 power of country landings. I show how these socio-ecological patterns may be related, yielding a scaling relation between these exponents. The predicted scaling relation implies that the width of the annual per capita growth-rate distribution scales to the 0.2 power of country landings, i.e. annual fluctuations in per capita landed catches increase with increased per capita catches in highly producing countries. Beside the scaling behavior, I report that fluctuations in the annual domestic landings have increased in the last 30 years, while the mean of the annual growth rate declined significantly after 1972.

q-bio.PE↗

arXiv2005

Power-law scaling in dimension-to-biomass relationship of fish schools

Motivated by the finding that there is some biological universality in the relationship between school geometry and school biomass of various pelagic fishes in various conditions, I here establish a scaling law for school dimensions: the school diameter increases as a power-law function of school biomass. The power-law exponent is extracted through the data collapse, and is close to 3/5. This value of the exponent implies that the mean packing density decreases as the school biomass increases, and the packing structure displays a mass-fractal dimension of 5/3. By exploiting an analogy between school geometry and polymer chain statistics, I examine the behavioral algorithm governing the swollen conformation of large-sized schools of pelagics, and I explain the value of the exponent.

q-bio.PE↗

arXiv2004

Space-irrelevant scaling law for fish school sizes

Universal scaling in the power-law size distribution of pelagic fish schools is established. The power-law exponent of size distributions is extracted through the data collapse. The distribution depends on the school size only through the ratio of the size to the expected size of the schools an arbitrary individual engages in. This expected size is linear in the ratio of the spatial population density of fish to the breakup rate of school. By means of extensive numerical simulations, it is verified that the law is completely independent of the dimension of the space in which the fish move. Besides the scaling analysis on school size distributions, the integrity of schools over extended periods of time is discussed.

q-bio.PE↗

arXiv2003

Power-law versus exponential distributions of animal group sizes

There has been some confusion concerning the animal group-size: an exponential distribution was deduced by maximizing the entropy; lognormal distributions were practically used; a power-law decay with exponent {3/2} was proposed in physical analogy to aerosol condensation. Here I show that the animal group-size distribution follows a power-law decay with exponent 1, and is truncated at a cut-off size which is the expected size of the groups an arbitrary individual engages in. An elementary model of animal aggregation based on binary splitting and coalescing on contingent encounter is presented. The model predicted size distribution holds for various data from pelagic fishes and mammalian herbivores in the wild.

cond-mat.stat-mech↗