Memory Systems, the Epistemic Arrow of Time, and the Second Law

The epistemic arrow of time is the fact that our knowledge of the past seems to be both of a different kind and more detailed than our knowledge of the future. Just like with the other arrows of time, it has often been speculated that the epistemic arrow arises due to the second law of thermodynamics. In this paper, we investigate the epistemic arrow of time using a fully formal framework. We begin by defining a memory system as any physical system whose present state can provide information about the state of the external world at some time other than the present. We then identify two types of memory systems in our universe, along with an important special case of the first type, which we distinguish as a third type of memory system. We show that two of these types of memory systems are time-symmetric, able to provide knowledge about both the past and the future. However, the third type of memory systems exploits the second law of thermodynamics, at least in all of its instances in our universe that we are aware of. The result is that in our universe, this type of memory system only ever provides information about the past. We also argue that human memory is of this third type, completing the argument. We end by scrutinizing the basis of the second law itself. This uncovers a previously unappreciated formal problem for common arguments that try to derive the second law from the "Past Hypothesis", i.e., from the claim that the very early universe was in a state of extremely low entropy. Our analysis is indebted to prior work by one of us but expands and improves upon this work in several respects.

A New Class of Weighted CUSUM Statistics

A change point is a location or time at which observations or data obey two different models: before and after. In real problems, we may know some prior information about the location of the change point, say at the right or left tail of the sequence. How does one incorporate the prior information into the current cumulative sum (CUSUM) statistics? We propose a new class of weighted CUSUM statistics with three different types of quadratic weights accounting for different prior positions of the change points. One interpretation of the weights is the mean duration in a random walk. Under the normal model with known variance, the exact distributions of these statistics are explicitly expressed in terms of eigenvalues. Theoretical results about the explicit difference of the distributions are valuable. The expansions of asymptotic distributions are compared with the expansion of the limit distributions of the Cramér-von Mises statistic and the Anderson and Darling statistic. We provide some extensions from independent normal responses to more interesting models, such as graphical models, the mixture of normals, Poisson, and weakly dependent models. Simulations suggest that the proposed test statistics have better power than the graph-based statistics. We illustrate their application to a detection problem with video data.

Caution is warranted when using animal space-use and movement to infer behavioral states

BACKGROUND

Identifying the behavioral state for wild animals that can't be directly observed is of growing interest to the ecological community. Advances in telemetry technology and statistical methodologies allow researchers to use space-use and movement metrics to infer the underlying, latent, behavioral state of an animal without direct observations. For example, researchers studying ungulate ecology have started using these methods to quantify behaviors related to mating strategies. However, little work has been done to determine if assumed behaviors inferred from movement and space-use patterns correspond to actual behaviors of individuals.

METHODS

Using a dataset with male and female white-tailed deer location data, we evaluated the ability of these two methods to correctly identify male-female interaction events (MFIEs). We identified MFIEs using the proximity of their locations in space as indicators of when mating could have occurred. We then tested the ability of utilization distributions (UDs) and hidden Markov models (HMMs) rendered with single sex location data to identify these events.

RESULTS

For white-tailed deer, male and female space-use and movement behavior did not vary consistently when with a potential mate. There was no evidence that a probability contour threshold based on UD volume applied to an individual's UD could be used to identify MFIEs. Additionally, HMMs were unable to identify MFIEs, as single MFIEs were often split across multiple states and the primary state of each MFIE was not consistent across events.

CONCLUSIONS

Caution is warranted when interpreting behavioral insights rendered from statistical models applied to location data, particularly when there is no form of validation data. For these models to detect latent behaviors, the individual needs to exhibit a consistently different type of space-use and movement when engaged in the behavior. Unvalidated assumptions about that relationship may lead to incorrect inference about mating strategies or other behaviors.

Differential post-fledging habitat use of Nearctic-Neotropical migratory birds within an urbanized landscape

BACKGROUND

Persistent declines in migratory songbird populations continue to motivate research exploring contributing factors to inform conservation efforts. Nearctic-Neotropical migratory species' population declines have been linked to habitat loss and reductions in habitat quality due to increasing urbanization in areas used throughout the annual cycle. Despite an increase in the number of studies on post-fledging ecology, generally characterized by the period between fledging and dispersal from natal areas or migration, contextual research linking post-fledging survival and habitat use to anthropogenic factors remains limited.

METHODS

Here, we examined habitat use of post-fledging habitat-generalist gray catbirds (Dumetella caroliniensis), and habitat-specialist wood thrushes (Hylocichla mustelina), up to 88 days after fledging within an urbanized landscape. These Neotropical migratory species share many life-history traits, exhibit differential degrees of habitat specialization, and co-occur in urbanized landscapes. Starting from daily movement data, we used time-integrated Brownian bridges to generate probability density functions of each species' probability of occurrence, and home range among 16 land cover classes including roads from the US Geological Survey National Land Cover Database for each species.

RESULTS

Habitat use differed between pre- and post-independence periods. After controlling for factors that influence habitat use (i.e., pre- or post-independence period, fate (whether individuals survived or not), and land cover class), we found that wood thrushes occupied home ranges containing six times more forest land cover than catbirds. In contrast, catbirds occupied home ranges containing twice the area of roads compared to wood thrushes. Wood thrushes had greater variance for area used (km2) among land cover classes within home ranges compared to catbirds. However, once fledglings achieved independence from parents, wood thrushes had lower variance associated with area used compared to catbirds.

CONCLUSIONS

Our findings support predictions that habitat-generalist gray catbirds spend more time in developed areas, less time in forest habitat, and use areas with more roads than the forest-specialist wood thrush. We found strong effects of pre- and post-independence periods on all of the response variables we tested. Species-specific habitat use patterns will likely be affected by projected increases in urbanization over the next several decades leading to further reductions in available forest habitat and increased road density, and will have important implications for the ecology and conservation of these birds.

NONPARAMETRIC GOODNESS-OF-FIT TESTS FOR UNIFORM STOCHASTIC ORDERING

We propose L^p distance-based goodness-of-fit (GOF) tests for uniform stochastic ordering with two continuous distributions F and G, both of which are unknown. Our tests are motivated by the fact that when F and G are uniformly stochastically ordered, the ordinal dominance curve R = FG^-1 is star-shaped. We derive asymptotic distributions and prove that our testing procedure has a unique least favorable configuration of F and G for p ∈ [1,∞]. We use simulation to assess finite-sample performance and demonstrate that a modified, one-sample version of our procedure (e.g., with G known) is more powerful than the one-sample GOF test suggested by Arcones and Samaniego (2000, Annals of Statistics). We also discuss sample size determination. We illustrate our methods using data from a pharmacology study evaluating the effects of administering caffeine to prematurely born infants.

Evaluating distributional shifts in home range estimates

A variety of methods are commonly used to quantify animal home ranges using location data acquired with telemetry. High-volume location data from global positioning system (GPS) technology provide researchers the opportunity to identify various intensities of use within home ranges, typically quantified through utilization distributions (UDs). However, the wide range of variability evident within UDs constructed with modern home range estimators is often overlooked or ignored during home range comparisons, and challenges may arise when summarizing distributional shifts among multiple UDs. We describe an approach to gain additional insight into home range changes by comparing UDs across isopleths and summarizing comparisons into meaningful results. To demonstrate the efficacy of this approach, we used GPS location data from 16 bighorn sheep (Ovis canadensis) to identify distributional changes before and after habitat alterations, and we discuss advantages in its application when comparing home range size, overlap, and joint-space use. We found a consistent increase in bighorn sheep home range size when measured across home range levels, but that home range overlap and similarity values decreased when examined at increasing core levels. Our results highlight the benefit of conducting multiscale assessments when comparing distributions, and we encourage researchers to expand comparative home range analyses to gain a more comprehensive evaluation of distributional changes and to evaluate comparisons across home range levels.

Wolves adapt territory size, not pack size to local habitat quality

1. Although local variation in territorial predator density is often correlated with habitat quality, the causal mechanism underlying this frequently observed association is poorly understood and could stem from facultative adjustment in either group size or territory size. 2. To test between these alternative hypotheses, we used a novel statistical framework to construct a winter population-level utilization distribution for wolves (Canis lupus) in northern Ontario, which we then linked to a suite of environmental variables to determine factors influencing wolf space use. Next, we compared habitat quality metrics emerging from this analysis as well as an independent measure of prey abundance, with pack size and territory size to investigate which hypothesis was most supported by the data. 3. We show that wolf space use patterns were concentrated near deciduous, mixed deciduous/coniferous and disturbed forest stands favoured by moose (Alces alces), the predominant prey species in the diet of wolves in northern Ontario, and in proximity to linear corridors, including shorelines and road networks remaining from commercial forestry activities. 4. We then demonstrate that landscape metrics of wolf habitat quality - projected wolf use, probability of moose occupancy and proportion of preferred land cover classes - were inversely related to territory size but unrelated to pack size. 5. These results suggest that wolves in boreal ecosystems alter territory size, but not pack size, in response to local variation in habitat quality. This could be an adaptive strategy to balance trade-offs between territorial defence costs and energetic gains due to resource acquisition. That pack size was not responsive to habitat quality suggests that variation in group size is influenced by other factors such as intraspecific competition between wolf packs.