Demographic and Component Allee Effects in Southern Lake Superior Gray Wolves

Spatiotemporal dynamics of a diffusive predator-prey model with delay and Allee effect in predator

It has been shown that Allee effect can change predator-prey dynamics and impact species persistence. Allee effect in the prey population has been widely investigated. However, the study on the Allee effect in the predator population is rare. In this paper, we investigate the spatiotemporal dynamics of a diffusive predator-prey model with digestion delay and Allee effect in the predator population. The conditions of stability and instability induced by diffusion for the positive equilibrium are obtained. The effect of delay on the dynamics of system has three different cases: (a) the delay doesn't change the stability of the positive equilibrium, (b) destabilizes and stabilizes the positive equilibrium and induces stability switches, or (c) destabilizes the positive equilibrium and induces Hopf bifurcation, which is revealed (numerically) to be corresponding to high, intermediate or low level of Allee effect, respectively. To figure out the joint effect of delay and diffusion, we carry out Turing-Hopf bifurcation analysis and derive its normal form, from which we can obtain the classification of dynamics near Turing-Hopf bifurcation point. Complex spatiotemporal dynamical behaviors are found, including the coexistence of two stable spatially homogeneous or inhomogeneous periodic solutions and two stable spatially inhomogeneous quasi-periodic solutions. It deepens our understanding of the effects of Allee effect in the predator population and presents new phenomena induced be delay with spatial diffusion.

Impacts of demographic and environmental stochasticity on population dynamics with cooperative effects

Different types of stochasticity play essential roles in shaping complex population dynamics. This paper presents a novel approach to model demographic and environmental stochasticity in a single-species model with cooperative components that are measured by component Allee effects. Our work provides rigorous mathematical proof on stochastic persistence and extinction, ergodicity (i.e., the existence of a unique stationary distribution) and the existence of a nontrivial periodic solution to study the impacts of demographic and environmental stochasticity on population dynamics. The theoretical and numerical results suggest that stochasticity may affect the population system in a variety of ways, specifically: (i) In the weak Allee effects case (e.g., strong cooperative efforts), the demographic stochasticity from the attack rate contributes to the expansion of the population size, while the demographic stochasticity from the handling rate and the environmental stochasticity have the opposite role, and may even lead to population extinction; (ii) In the strong Allee effects case (cooperative efforts not strong enough), both demographic and environmental stochasticity play a similar role in the survival of population, and are related to the initial population level: if the initial population level is large enough, demographic stochasticity and environmental stochasticity may be detrimental to the survival of population, otherwise if the initial population level is small enough, demographic stochasticity and environmental stochasticity may bring survival opportunities for the population that deterministically would extinct indefinitely; (iii) In the extinction case, demographic and environmental stochasticity can not change the trend of population extinction, but they can delay or promote population extinction.

A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves

The first objective of the paper is to implement a two stage Bayesian hierarchical nonlinear model for growth and learning curves, particular cases of longitudinal data with an underlying nonlinear time dependence. The aim is to model simultaneously individual trajectories over time, each with specific and potentially different characteristics, and a time-dependent behavior shared among individuals, including eventual effect of covariates. At the first stage inter-individual differences are taken into account, while, at the second stage, we search for an average model. The second objective is to partition individuals into homogeneous groups, when inter individual parameters present high level of heterogeneity. A new multivariate partitioning approach is proposed to cluster individuals according to the posterior distributions of the parameters describing the individual time-dependent behaviour. To assess the proposed methods, we present simulated data and two applications to real data, one related to growth curve modeling in agriculture and one related to learning curves for motor skills. Furthermore a comparison with finite mixture analysis is shown.

Age at first reproduction in wolves: different patterns of density dependence for females and males

Age at first reproduction constitutes a key life-history trait in animals and is evolutionarily shaped by fitness benefits and costs of delayed versus early reproduction. The understanding of how intrinsic and extrinsic changes affects age at first reproduction is crucial for conservation and management of threatened species because of its demographic effects on population growth and generation time. For a period of 40 years in the Scandinavian wolf (Canis lupus) population, including the recolonization phase, we estimated age at first successful reproduction (pup survival to at least three weeks of age) and examined how the variation among individuals was explained by sex, population size (from 1 to 74 packs), primiparous or multiparous origin, reproductive experience of the partner and inbreeding. Median age at first reproduction was 3 years for females (n = 60) and 2 years for males (n = 74), and ranged between 1 and 8-10 years of age (n = 297). Female age at first reproduction decreased with increasing population size, and increased with higher levels of inbreeding. The probability for males to reproduce later first decreased, reaching its minimum when the number of territories approached 40-60, and then increased with increasing population size. Inbreeding for males and reproductive experience of parents and partners for both sexes had overall weak effects on age at first reproduction. These results allow for more accurate parameter estimates when modelling population dynamics for management and conservation of small and vulnerable wolf populations, and show how humans through legal harvest and illegal hunting influence an important life-history trait like age at first reproduction.

Sperm storage reduces the strength of the mate-finding Allee effect

Mate searching is a key component of sexual reproduction that can have important implications for population viability, especially for the mate-finding Allee effect. Interannual sperm storage by females may be an adaptation that potentially attenuates mate limitation, but the demographic consequences of this functional trait have not been studied. Our goal is to assess the effect of female sperm storage durability on the strength of the mate-finding Allee effect and the viability of populations subject to low population density and habitat alteration. We used an individual-based simulation model that incorporates realistic representations of the demographic and spatial processes of our model species, the spur-thighed tortoise (Testudo graeca). This allowed for a detailed assessment of reproductive rates, population growth rates, and extinction probabilities. We also studied the relationship between the number of reproductive males and the reproductive rates for scenarios combining different levels of sperm storage durability, initial population density, and landscape alteration. Our results showed that simulated populations parameterized with the field-observed demographic rates collapsed for short sperm storage durability, but were viable for a durability of one year or longer. In contrast, the simulated populations with a low initial density were only viable in human-altered landscapes for sperm storage durability of 4 years. We find that sperm storage is an effective mechanism that can reduce the strength of the mate-finding Allee effect and contribute to the persistence of low-density populations. Our study highlights the key role of sperm storage in the dynamics of species with limited movement ability to facilitate reproduction in patchy landscapes or during population expansion. This study represents the first quantification of the effect of sperm storage durability on population dynamics in different landscapes and population scenarios.

Compensatory mortality in a recovering top carnivore: wolves in Wisconsin, USA (1979-2013)

Populations of large terrestrial carnivores are in various stages of recovery worldwide and the question of whether there is compensation in mortality sources is relevant to conservation. Here, we show variation in Wisconsin wolf survival from 1979 to 2013 by jointly estimating the hazard of wolves' radio-telemetry ending (endpoint) and endpoint cause. In previous analyses, wolves lost to radio-telemetry follow-up (collar loss) were censored from analysis, thereby assuming collar loss was unconfounded with mortality. Our approach allowed us to explicitly estimate hazard due to collar loss and did not require censoring these records from analysis. We found mean annual survival was 76% and mean annual causes of mortality were illegal killing (9.4%), natural and unknown causes (9.5%), and other human-caused mortality such as hunting, vehicle collisions and lethal control (5.1%). Illegal killing and natural mortality were highest during winter, causing wolf survival to decrease relative to summer. Mortality was highest during early recovery and lowest during a period of sustained population growth. Wolves again experienced higher risk of human-caused mortality relative to natural mortality as wolves expanded into areas with more human activity. We detected partial compensation in human- and natural-caused mortality since 2004 as the population saturated more available habitat. Prior to 2004, we detected additivity in mortality sources. Assessments of wolf survival and cause of mortality rates and the finding of partial compensation in mortality sources will inform wolf conservation and management efforts by identifying sources and sinks, finding areas of conservation need, and assessing management zone delineation.