Density‐ and size‐dependent mortality in fish early life stages

The importance of survival and growth variations early in life for population dynamics depends on the degrees of compensatory density dependence and size dependence in survival at later life stages. Quantifying density‐ and size‐dependent mortality at different juvenile stages is therefore important to understand and potentially predict the recruitment to the population. We applied a statistical state‐space modelling approach to analyse time series of abundance and mean body size of larval and juvenile fish. The focus was to identify the importance of abundance and body size for growth and survival through successive larval and juvenile age intervals, and to quantify how the dynamics propagate through the early life to influence recruitment. We thus identified both relevant ages and mechanisms (i.e. density dependence and size dependence in survival and growth) linking recruitment variability to early life dynamics. The analysis was conducted on six economically and ecologically important fish populations from cold temperate and sub‐arctic marine ecosystems. Our results underscore the importance of size for survival early in life. The comparative analysis suggests that size‐dependent mortality and density‐dependent growth frequently occur at a transition from pelagic to demersal habitats, which may be linked to competition for suitable habitat. The generality of this hypothesis warrants testing in future research.publishedVersio

Long-term change in a behavioural trait: truncated spawning distribution and demography in Northeast Arctic cod

Harvesting may be a potent driver of demographic change and contemporary evolution, which both may have great impacts on animal populations. Research has focused on changes in phenotypic traits that are easily quantifiable and for which time series exist, such as size, age, sex, or gonad size, whereas potential changes in behavioural traits have been under-studied. Here, we analyse potential drivers of long-term changes in a behavioural trait for the Northeast Arctic stock of Atlantic cod Gadus morhua, namely choice of spawning location. For 104 years (1866–1969), commercial catches were recorded annually and reported by county along the Norwegian coast. During this time period, spawning ground distribution has fluctuated with a trend towards more northerly spawning. Spawning location is analysed against a suite of explanatory factors including climate, fishing pressure, density dependence, and demography. We find that demography (age or age at maturation) had the highest explanatory power for variation in spawning location, while climate had a limited effect below statistical significance. As to potential mechanisms, some effects of climate may act through demography, and explanatory variables for demography may also have absorbed direct evolutionary change in migration distance for which proxies were unavailable. Despite these caveats, we argue that fishing mortality, either through demographic or evolutionary change, has served as an effective driver for changing spawning locations in cod, and that additional explanatory factors related to climate add no significant information

Do abiotic mechanisms determine interannual variability in length-at-age of juvenile Arcto-Norwegian cod?

For the large Arcto-Norwegian stock of cod (Gadus morhua L.) in the Barents Sea, year-to-year variability in growth is well documented. Here three hypotheses for the observed inverse relation between abundance and the mean length-at-age of juveniles (ages 1–4) are suggested and evaluated. Based on comprehensive data, we conclude that year-to-year differences in length-at-age are mainly determined by density-independent mechanisms during the pelagic first half year of the fishes’ life. Enhanced inflow from the southwest leads to an abundant cohort at the 0- group stage being distributed farther east into colder water masses, causing lower postsettlement growth rates. We can not reject density-dependent growth effects related to variability in food rations, but our data do not suggest this to be the main mechanism. Another hypothesis suggests that lower growth rates during periods of high abundance are a result of density-dependent mechanisms causing the geographic range of juveniles to extend eastwards into colder water masses. This is rejected mainly because year-to-year differences in mean length are established by age 2, which is too early for movements over large distances

List Distinguishing Number of pth Power of Hypercube and Cartesian Powers of a Graph

A graph G is said to be k-distinguishable if every vertex of the graph can be colored from a set of k colors such that no non-trivial automorphism fixes every color class. The distinguishing number D(G) is the least integer k for which G is k-distinguishable. If for each we have a list L(v) of colors, and we stipulate that the color assigned to vertex v comes from its list L(v) then G is said to be -distinguishable where The list distinguishing number of a graph, denoted is the minimum integer k such that every collection of lists with admits an distinguishing coloring. In this paper, we prove thatwhen a connected graph G is prime with respect to the Cartesian product then for where is the Cartesian product of the graph G taken r times. The power of a graph (Some authors use to denote the pth power of G, to avoid confusion with the notation of Cartesian power of graph G we use for the pth power of G.) G is the graph whose vertex set is V(G) and in which two vertices are adjacent when they have distance less than or equal to p. We determine for all where is the hypercube of dimension n. © 2020, Springer Nature Switzerland AG