Gain control is essential for the proper function of any sensory system. However, the precise mechanisms for achieving effective gain control in the brain are unknown. Based on our understanding of the existence and strength of connections in the insect olfactory system, we analyze the conditions that lead to controlled gain in a randomly connected network of excitatory and inhibitory neurons. We consider two scenarios for the variation of input into the system. In the first case, the intensity of the sensory input controls the input currents to a fixed proportion of neurons of the excitatory and inhibitory populations. In the second case, increasing intensity of the sensory stimulus will both, recruit an increasing number of neurons that receive input and change the input current that they receive. Using a mean field approximation for the network activity we derive relationships between the parameters of the network that ensure that the overall level of activity of the excitatory population remains unchanged for increasing intensity of the external stimulation. We find that, first, the main parameters that regulate network gain are the probabilities of connections from the inhibitory population to the excitatory population and of the connections within the inhibitory population. Second, we show that strict gain control is not achievable in a random network in the second case, when the input recruits an increasing number of neurons. Finally, we confirm that the gain control conditions derived from the mean field approximation are valid in simulations of firing rate models and Hodgkin-Huxley conductance based models.

Asteroids provide fundamental clues to the formation and evolution of planetesimals. Collisional models based on the depletion of the primordial main belt of asteroids predict 10–15 craters >400 km should have formed on Ceres, the largest object between Mars and Jupiter, over the last 4.55 Gyr. Likewise, an extrapolation from the asteroid Vesta would require at least 6–7 such basins. However, Ceres’ surface appears devoid of impact craters >∼280 km. Here, we show a significant depletion of cerean craters down to 100–150 km in diameter. The overall scarcity of recognizable large craters is incompatible with collisional models, even in the case of a late implantation of Ceres in the main belt, a possibility raised by the presence of ammoniated phyllosilicates. Our results indicate that a significant population of large craters has been obliterated, implying that long-wavelength topography viscously relaxed or that Ceres experienced protracted widespread resurfacing.

Risk factors for breast cancer are often confusing and contradictory. Discrepancies are likely due to different subtypes having divergent risk factors. An important distinction between breast cancer subtypes is hormone-receptor status. Compared to women diagnosed with estrogen receptor positive (ER+) breast cancer, those with estrogen receptor negative (ER−) tumors are usually diagnosed at a younger age and have a higher mortality [1]. Few studies have attempted to explain ‘why’ breast cancer subtypes have different risk factors.

It has long been accepted that modern reproductive patterns are likely contributors to breast cancer susceptibility because of their influence on hormones such as estrogen and the importance of these hormones in breast cancer. We conducted a meta-analysis to assess whether this ‘evolutionary mismatch hypothesis’ can explain susceptibility to both estrogen receptor positive (ER-positive) and estrogen receptor negative (ER-negative) cancer. Our meta-analysis includes a total of 33 studies and examines parity, age of first birth and age of menarche broken down by estrogen receptor status. We found that modern reproductive patterns are more closely linked to ER-positive than ER-negative breast cancer. Thus, the evolutionary mismatch hypothesis for breast cancer can account for ER-positive breast cancer susceptibility but not ER-negative breast cancer.

In a meta-analysis published by myself and co-authors, we report differences in the life history risk factors for estrogen receptor negative (ER−) and estrogen receptor positive (ER+) breast cancers. Our meta-analysis did not find the association of ER− breast cancer risk with fast life history characteristics that Hidaka and Boddy suggest in their response to our article. There are a number of possible explanations for the differences between their conclusions and the conclusions we drew from our meta-analysis, including limitations of our meta-analysis and methodological challenges in measuring and categorizing estrogen receptor status. These challenges, along with the association of ER+ breast cancer with slow life history characteristics, may make it challenging to find a clear signal of ER− breast cancer with fast life history characteristics, even if that relationship does exist. The contradictory results regarding breast cancer risk and life history characteristics illustrate a more general challenge in evolutionary medicine: often different sub-theories in evolutionary biology make contradictory predictions about disease risk. In this case, life history models predict that breast cancer risk should increase with faster life history characteristics, while the evolutionary mismatch hypothesis predicts that breast cancer risk should increase with delayed reproduction. Whether life history tradeoffs contribute to ER− breast cancer is still an open question, but current models and several lines of evidence suggest that it is a possibility.

Cancer therapy selects for cancer cells resistant to treatment, a process that is fundamentally evolutionary. To what extent, however, is the evolutionary perspective employed in research on therapeutic resistance and relapse? We analyzed 6,228 papers on therapeutic resistance and/or relapse in cancers and found that the use of evolution terms in abstracts has remained at about 1% since the 1980s. However, detailed coding of 22 recent papers revealed a higher proportion of papers using evolutionary methods or evolutionary theory, although this number is still less than 10%. Despite the fact that relapse and therapeutic resistance is essentially an evolutionary process, it appears that this framework has not permeated research. This represents an unrealized opportunity for advances in research on therapeutic resistance.