Historical Lattice Trees.

We prove that the rescaled historical processes associated to critical spread-out lattice trees in dimensions d>8 converge to historical Brownian motion. This is a functional limit theorem for measure-valued processes that encodes the genealogical structure of the underlying random trees. Our results are applied elsewhere to prove that random walks on lattice trees, appropriately rescaled, converge to Brownian motion on super-Brownian motion.

On the range of lattice models in high dimensions.

We investigate the scaling limit of the range (the set of visited vertices) for a general class of critical lattice models, starting from a single initial particle at the origin. Conditions are given on the random sets and an associated "ancestral relation" under which, conditional on longterm survival, the rescaled ranges converge weakly to the range of super-Brownian motion as random sets. These hypotheses also give precise asymptotics for the limiting behaviour of the probability of exiting a large ball, that is for the extrinsic one-arm probability. We show that these conditions are satisfied by the voter model in dimensions d ≥ 2 , sufficiently spread out critical oriented percolation and critical contact processes in dimensions d > 4 , and sufficiently spread out critical lattice trees in dimensions d > 8 . The latter result proves Conjecture 1.6 of van der Hofstad et al. (Ann Probab 45:278-376, 2017) and also has important consequences for the behaviour of random walks on lattice trees in high dimensions.

Liver lesions in demersal fishes near a large ocean outfall on the San Pedro Shelf, California.

The prevalence of toxicopathic liver lesions in demersal fish on the San Pedro Shelf, California was determined for a 15-year period (1988-2003). Fish livers were sampled at fixed locations as part of the Orange County Sanitation Districts (OCSD) ocean monitoring program. Histopathological examination of selected fish liver tissues was studied to determine whether the wastewater discharge had affected fish health. The prevalence of toxicopathic lesion classes neoplasms (NEO), preneoplastic foci of cellular alteration (FCA), and hydropic vacuolation (HYDVAC) varied among species and locations. For all species sampled, severe lesions occurred in 6.2% of the fish examined (n=7,694). HYDVAC (4.1%) was the most common toxicopathic lesion type followed by FCA (1.4%) and NEO (0.7%). HYDVAC occurred only in white croaker (Genyonemus lineatus), accounting for 84.8% of the toxicopathic lesions for this species. Prevalence of HYDVAC, NEO, and FCA in white croaker was 15.2, 2.0, and 0.7%, respectively. The prevalence of HYDVAC and NEO in white croaker increased with age and size but there was no sexual difference. A linear regression model was used for hypothesis testing to account for significant differences in fish size (and age for croakers) at the different sampling locations. This analysis showed that for HYDVAC there was no spatial or location effect for lesion rate or size/age of onset. For NEO, the model predicted that white croaker near the wastewater outfall may acquire these lesions at a smaller size/younger age, and at a higher rate, than at other sites. However, this result may be biased due to the unequal size frequency distributions and the low prevalence of NEO in white croaker at the different sampling sites. Bigmouth sole (Hippoglossina stomata) had a prevalence of FCA and NEO of 1.3 and 0.35%, respectively, but the prevalence and distribution of lesions was too few for statistical testing. There was no sexual difference for lesion prevalence in hornyhead turbot (Pleuronichthys verticalis) and the prevalence of FCA and NEO was 3.4 and 0.37%, respectively. FCA prevalence increased with size in hornyhead turbot and there were no significant spatial differences for lesion rates and fish size at lesion onset. Overall, consistent spatial differences for lesion prevalence were not demonstrated and highlight the analytical difficulties of detecting a possible point source impact when the effect is rare, correlated with the size/age structure of the population, and may be caused by exposure to unknown multiple sources. Thus, the usefulness of liver histopathology as a point-source monitoring tool is best applied to where the spatial scale of impact generally exceeds the home range of the target species.

The relationships of biochemical endpoints to histopathology and population metrics in feral flatfish species collected near the municipal wastewater outfall of Orange County, California, USA.

In July 2000, 330 individuals of three flatfish species were collected from reference locations and nine sites surrounding the outfall of the Orange County (CA, USA) Sanitation District (OCSD) municipal wastewater discharge. Species included hornyhead turbot (Pleuronichthys verticalis), English sole (Pleuronectes vetulus), and bigmouth sole (Hippoglossina stomata). Livers of sampled animals were examined for the expression of vitellogenin (in males), cytochrome P450 1A (CYP1A), and DNA damage (comet assay). Biliary fluorescent aromatic compounds (FACs) were also measured. Comparisons with tissue and sediment contaminant residues, liver histopathology, and population estimates were assessed to determine whether relationships exist between levels of biological organization. The CYP1A results indicated exposure to planar aromatic hydrocarbons at one nearshore site. Regression analysis of all English sole CYP1A to total sediment polychlorinated biphenyls (PCBs) (r2 = 0.97; p < 0.05) indicated a significant correlation. Widespread exposure to estrogens was observed at all sites without correlation to the abundance of the three species examined. Fluorescent aromatic compounds demonstrated no correlation to CYP1A expression. Overall, histopathology and biochemical endpoints did not indicate significant adverse effects in fish at the OCSD outfall.