Effects of Sample Size on Estimates of Population Growth Rates Calculated with Matrix Models

BACKGROUND: Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (lambda) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of lambda-Jensen's Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of lambda due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of lambda. METHODOLOGY/PRINCIPAL FINDINGS: Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating lambda for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of lambda with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography. CONCLUSIONS/SIGNIFICANCE: We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities

Similar Neural Activity during Fear and Disgust in the Rat Basolateral Amygdala

Much research has focused on how the amygdala processes individual affects, yet little is known about how multiple types of positive and negative affects are encoded relative to one another at the single-cell level. In particular, it is unclear whether different negative affects, such as fear and disgust, are encoded more similarly than negative and positive affects, such as fear and pleasure. Here we test the hypothesis that the basolateral nucleus of the amygdala (BLA), a region known to be important for learned fear and other affects, encodes affective valence by comparing neuronal activity in the BLA during a conditioned fear stimulus (fear CS) with activity during intraoral delivery of an aversive fluid that induces a disgust response and a rewarding fluid that induces a hedonic response. Consistent with the hypothesis, neuronal activity during the fear CS and aversive fluid infusion, but not during the fear CS and rewarding fluid infusion, was more similar than expected by chance. We also found that the greater similarity in activity during the fear- and disgust-eliciting stimuli was specific to a subpopulation of cells and a limited window of time. Our results suggest that a subpopulation of BLA neurons encodes affective valence during learned fear, and furthermore, within this subpopulation, different negative affects are encoded more similarly than negative and positive affects in a time-specific manner

Context-Dependent Encoding of Fear and Extinction Memories in a Large-Scale Network Model of the Basal Amygdala

The basal nucleus of the amygdala (BA) is involved in the formation of context-dependent conditioned fear and extinction memories. To understand the underlying neural mechanisms we developed a large-scale neuron network model of the BA, composed of excitatory and inhibitory leaky-integrate-and-fire neurons. Excitatory BA neurons received conditioned stimulus (CS)-related input from the adjacent lateral nucleus (LA) and contextual input from the hippocampus or medial prefrontal cortex (mPFC). We implemented a plasticity mechanism according to which CS and contextual synapses were potentiated if CS and contextual inputs temporally coincided on the afferents of the excitatory neurons. Our simulations revealed a differential recruitment of two distinct subpopulations of BA neurons during conditioning and extinction, mimicking the activation of experimentally observed cell populations. We propose that these two subgroups encode contextual specificity of fear and extinction memories, respectively. Mutual competition between them, mediated by feedback inhibition and driven by contextual inputs, regulates the activity in the central amygdala (CEA) thereby controlling amygdala output and fear behavior. The model makes multiple testable predictions that may advance our understanding of fear and extinction memories

New technologies for examining neuronal ensembles in drug addiction and fear

Correlational data suggest that learned associations are encoded within neuronal ensembles. However, it has been difficult to prove that neuronal ensembles mediate learned behaviours because traditional pharmacological and lesion methods, and even newer cell type-specific methods, affect both activated and non-activated neurons. Additionally, previous studies on synaptic and molecular alterations induced by learning did not distinguish between behaviourally activated and non-activated neurons. Here, we describe three new approaches—Daun02 inactivation, FACS sorting of activated neurons and c-fos-GFP transgenic rats — that have been used to selectively target and study activated neuronal ensembles in models of conditioned drug effects and relapse. We also describe two new tools — c-fos-tTA mice and inactivation of CREB-overexpressing neurons — that have been used to study the role of neuronal ensembles in conditioned fear